Daily Papers

We present RESPLE2, a recursive multi-sensor state estimation framework using non-uniform B-splines for 6-DoF motion representation. By exploiting the knot-clamping boundary property, we propose a theoretically grounded mechanism for exact control-point prediction directly informed by inertial kinematics along the trajectory, with knot placement adapted to motion and measurement availability. Within an iterated extended Kalman filter, we perform this prediction using a subset of inertial measurements. A subsequent reset step preserves trajectory consistency as the knots extend. The update step further incorporates heterogeneous sensor measurements at their native timestamps through continuous-time observation models, supporting flexible combinations of LiDARs, cameras, inertial measurement units, and leg kinematics. We further develop a lightweight global optimization module that directly refines non-uniform B-spline control points by incorporating loop-closure constraints derived from LiDAR-visual cues. We conduct extensive evaluations on public and experimental datasets across handheld, tracked, legged, and hybrid aerial-legged platforms, covering highly dynamic maneuvers with extreme accelerations. Compared with state-of-the-art multi-sensor odometry systems, RESPLE2 achieves competitive or superior estimation accuracy and robustness in the corresponding sensor configurations, particularly under aggressive motion, while maintaining real-time operation. We publicly release our code and experimental datasets at https://github.com/ASIG-X/RESPLE2.

We present VGGT-SLAM, a dense RGB SLAM system constructed by incrementally and globally aligning submaps created from the feed-forward scene reconstruction approach VGGT using only uncalibrated monocular cameras. While related works align submaps using similarity transforms (i.e., translation, rotation, and scale), we show that such approaches are inadequate in the case of uncalibrated cameras. In particular, we revisit the idea of reconstruction ambiguity, where given a set of uncalibrated cameras with no assumption on the camera motion or scene structure, the scene can only be reconstructed up to a 15-degrees-of-freedom projective transformation of the true geometry. This inspires us to recover a consistent scene reconstruction across submaps by optimizing over the SL(4) manifold, thus estimating 15-degrees-of-freedom homography transforms between sequential submaps while accounting for potential loop closure constraints. As verified by extensive experiments, we demonstrate that VGGT-SLAM achieves improved map quality using long video sequences that are infeasible for VGGT due to its high GPU requirements.

Simultaneous Localization and Mapping (SLAM) based on 3D Gaussian Splats (3DGS) has recently shown promise towards more accurate, dense 3D scene maps. However, existing 3DGS-based methods fail to address the global consistency of the scene via loop closure and/or global bundle adjustment. To this end, we propose LoopSplat, which takes RGB-D images as input and performs dense mapping with 3DGS submaps and frame-to-model tracking. LoopSplat triggers loop closure online and computes relative loop edge constraints between submaps directly via 3DGS registration, leading to improvements in efficiency and accuracy over traditional global-to-local point cloud registration. It uses a robust pose graph optimization formulation and rigidly aligns the submaps to achieve global consistency. Evaluation on the synthetic Replica and real-world TUM-RGBD, ScanNet, and ScanNet++ datasets demonstrates competitive or superior tracking, mapping, and rendering compared to existing methods for dense RGB-D SLAM. Code is available at loopsplat.github.io.

Accurately recovering the camera's calibration and metric poses for any unconstrained video would unlock large-scale training data for navigation and scene understanding. The dominant approaches to this problem are severely limited: Simultaneous Localization and Mapping (SLAM) is sensitive to initialization and transient failures due to its causal, incremental nature; it is often over-optimized for real-time operation and generally requires known camera calibration; while Structure-from-Motion (SfM) typically forgoes any image ordering, enabling optimal initialization and global optimization, but lacks robustness to visual symmetries and extreme motions. To bridge this gap, we introduce a system that combines the strong sequential constraints of SLAM with the flexibility and global optimization of offline SfM, enabling the metric reconstruction of arbitrary, long, uncalibrated videos. This system leverages recent advances in wide-baseline dense image matching, treats temporal ordering as a first-class citizen for reliable loop closure, and augments global optimization with metric monocular depth priors. As a result, thorough evaluations on diverse, challenging datasets that exhibit extreme motion and visual symmetries reveal that our approach is significantly more robust and accurate than both state-of-the-art SLAM and SfM, classical or learned, with given or unknown camera calibration. The code is publicly available at https://github.com/cvg/vidmap.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

Looped Language Models (LoopLMs) offer a parameter efficient approach to scaling reasoning by reusing shared parameters across recurrent computation steps. Despite their promise, effective post-training of LoopLMs remains challenging. Existing approaches either provide reward based supervision that is sparse or costly to extend across loops, or rely on external teachers or privileged information, leading to limited teacher availability or teacher-student context mismatch. To address these limitations, we introduce LoopOPD, a cross-loop on-policy distillation framework that uses additional recurrent computation within a LoopLM as its own source of supervision. LoopOPD uses a frozen terminal loop policy as a compute privileged teacher for an intermediate loop student on student generated rollouts, providing dense supervision without an external teacher or privileged information. We further propose Dynamic LoopOPD (D-LoopOPD), which continually refreshes the terminal loop teacher as the shared model parameters are updated, enabling recurrent self-improvement. We characterize how distillation updates propagate across loop depths and derive sufficient conditions under which a single update yields simultaneous local improvement at both loop depths. Experiments on Ouro-Thinking models show that LoopOPD improves mathematical reasoning, while D-LoopOPD yields further gains through dynamic teacher updates. Despite being trained only on mathematical data, the resulting models also improve on general reasoning and code generation benchmarks, demonstrating that recurrent computation can serve as an effective source of supervision for LoopLMs. Our code and model checkpoints will be released upon acceptance.

In mid-2026 a slogan reorganized how practitioners talk about coding agents: stop prompting your agent, start designing the loop that prompts it. We take this claim seriously and give it a careful treatment. We call the object of the new practice the loop specification: a bounded, reusable artifact, made of a trigger, a goal, a verification step, a stopping rule and a memory, that a human hands to an agent harness (such as Claude Code or Codex) so the agent pursues a goal on its own, in place of step-by-step prompting. We distinguish this external loop specification from two things it is often confused with: an ordinary programming loop, and the internal perceive-act-observe cycle that the harness already provides as plumbing. We position loop engineering as a new layer in the progression from prompt to context to harness to loop, and we argue, against the stronger headlines, that it does not retire prompt engineering; loop and prompt are distinct tools with distinct uses. We offer four contributions: a definition and scope for the discipline; an anatomy and taxonomy of loop specifications organized around trigger, goal type, a five-level verification ladder, architecture, and named terminal states; a descriptive analysis of the Loop Library, a public corpus of fifty real loops that we code by hand; and a set of design principles and anti-patterns grounded in the scientific literature on self-correction, reward hacking and model-as-judge fragility. The corpus shows that practice has matured most where the discipline says it matters: seventy percent of loops verify in the autonomous zone of the ladder and seventy-four percent name their terminal states, while automated triggering and durable memory remain comparatively underdeveloped. We close with the limits the practice must respect, including the verification burden, comprehension debt and the risk of cognitive surrender.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

Autonomous improvement loops are hard to trust because the improvement process is usually external scaffolding bolted onto the agent: failures go unlogged, diagnoses cannot be replayed, and promote-or-discard decisions land in a side database rather than the agent's own history. We show that an event-sourced agent runtime removes that friction and turns controlled improvement into a first-class workflow. When the agent's state is a deterministic projection of an append-only event log, failures are recorded, a run replays exactly from its log, candidate patches scope to typed pipeline seams, gates are auditable, and every promotion or discard is itself an event. We demonstrate this with Regimes, a loop on the ActiveGraph runtime that diagnoses failed evaluations, proposes a repair at a pipeline point, and promotes it only after static checks, sandbox execution, in-sample evaluation, and held-out validation. The loop is target-agnostic: the same control flow runs against different tasks through a common interface. On LongMemEval-S the dominant failure is not retrieval but reconciliation: the evidence is already in the assembled context, yet the reader answers incorrectly. Across five seeded held-out splits, Regimes discovers reader-prompt repairs that improve final held-out accuracy by +0.05 to +0.10 in four splits and +0.01 in one over-promotion split; two splits are individually significant (seed 5 unadjusted for its sequential promotion structure), and the pooled count is descriptive only, since the splits share one 500-question pool. The durable contributions are ActiveGraph as an auditable substrate that makes controlled improvement loops tractable, the held-out-gated loop it supports, the failure-regime taxonomy routing each failure to a pipeline location (whose marginal value over an unrouted baseline is the primary open question), and the prompt-as-discovery-probe hypothesis.

Coding agent infrastructure is shifting from harness engineering toward loop engineering as coding agents are deployed for sustained long-horizon software development. Existing benchmarks often center on localized tasks or end-state outcomes, offering limited insight into sustained execution. We introduce LOOPSBENCH, a long-horizon benchmark for loop engineering in coding agent evaluation. Each task is a dependency DAG over separately testable development units with source-evidenced prerequisite edges. LOOPSBENCH comprises 112 tasks from authentic sources spanning 8 programming languages and 9 domains. Its flow-aware runtime releases tests along the ready frontier and retains completed nodes as regression obligations. We evaluate frontier coding agents paired with widely used loop implementations. The strongest configuration, Opus-4.7 with Claude Code and outer continuation, resolves 25.00% of tasks. Recorded plans recover only part of the source-recovered prerequisite DAG, and regression events remain visible across the evaluated loop profiles. We open source the benchmark data and code, including all tasks, more than 5,300 development units, and executable tests, at microsoft/Loopsbench.

Looped architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The number of effective layers reached by looping determines the quality of the solution these models find. Like deep architectures, looped architectures are prone to a signal propagation problem induced by depth as the halting decision is postponed. In this paper, we address this signal propagation issue using pre-norm layers and residual scaling. Building on these architectural modifications, we propose FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to task difficulty. FPRM is effective on common reasoning benchmarks, namely Sudoku, Maze, state-tracking, and ARC-AGI.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Repeating a small block of middle layers increases a language model's effective inference depth without adding parameters or generating extra tokens, and recent work shows that this latent recurrence improves reasoning. However, two design choices limit these gains. Each iteration sees only the previous output and cannot directly access earlier computations. Moreover, a fixed loop count wastes depth on easy inputs while leaving hard ones with too little computation. We introduce RecurTrace, which addresses both limitations using the loop's own trajectory. Specifically, Loop Memory Attention lets each looped layer attend to its own states from previous iterations along the loop-time axis, so the model can revisit earlier computations instead of relying on the latest state alone. A halting head then reads the loop state and predicts whether to continue, with supervision from an oracle that identifies when additional depth still reduces loss. In a controlled MathQA comparison on the same looped backbone, RecurTrace achieves 56.9% accuracy with an average of 2.0 loops, exceeding the best fixed loop depth by 2.2 points at matched compute. By comparison, ACT and PonderNet collapse to one loop, and CALM reaches only 54.1% with 5.6 loops, while the stronger LoopUS-Conf and TaH-Mismatch baselines reach 55.3% at 3.2 loops and 55.7% at 2.1 loops. Finally, RecurTrace improves generation accuracy over same-budget fine-tuned baselines at 0.6B, 1.7B, 4B, and 8B, with the gain growing with model size from 0.6 to 3.4 points.

Iterative repair loops have become a core design pattern in LLM-based software engineering systems. These workflows repeatedly generate, validate, and repair artifacts using feedback such as compiler errors or test failures. Despite their widespread use, the impact of repair-loop iteration limits remains poorly understood, as most prior work adopts fixed, often arbitrary, repair budgets. We study repair-loop effectiveness across multiple software engineering tasks, including code generation, test generation, and code translation. Across several representative workflows, datasets, and contemporary low-cost LLMs, we observe a consistent pattern of diminishing returns: the first three to four repair iterations account for most achievable gains, while later iterations contribute only marginal improvements. We further find that repair behavior is influenced more strongly by workflow orchestration and feedback design than by the underlying model itself. These results suggest that repair budgets should be treated as an explicit experimental variable, as they directly affect evaluation outcomes, computational cost, runtime, and reproducibility in LLM-based software engineering research.

Looped Transformers introduce recurrent depth as a new scaling axis for LLMs: by repeatedly applying shared Transformer blocks, they increase effective depth without increasing parameter count. However, the benefits of looping remain unclear for large MoE LLMs under FLOPs-matched comparisons. The main reason is that the gains from additional iterations diminish quickly and can even turn into degradation, so the extra FLOPs spent on looping yield little substantial improvement. Consequently, prior work typically settles on two loops. We identify two main obstacles to scaling looped MoE. First, looping inherits and amplifies the curse of depth: hidden-state variance grows with each iteration as residual updates accumulate, which destabilizes deep recurrence and causes representations to drift. Second, looped MoE suffers from expert selection collapse: routers repeatedly select the same experts across loops, so extra iterations add computation without adding computational diversity. Guided by this diagnosis, we propose LOOM, built on a single principle: each loop should contribute new computation while keeping the recurrent state stable. LOOM stabilizes recurrence by scaling residual updates to bound variance growth and re-injecting the input embedding at every loop, and diversifies it through per-loop routers that engage different experts and a Looping Residual that carries earlier outputs forward. Experiments across 100M-1.7B models show stable scaling to 9-12 loops. Under near-iso-FLOP, the 700M model performs best at 5 loops, reducing perplexity from 18.36 to 16.54 and improving average zero-shot accuracy from 38.84% to 39.53% over the non-looped baseline. Without FLOP matching, the 1.7B model trained on 60B tokens peaks at 9 loops, reducing perplexity from 9.62 to 7.77 and improving average zero-shot accuracy from 42.4% to 47.7%. Code is available https://github.com/hed-ucas/LOOM.

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

While polyhedral compilers have shown success in implementing advanced code transformations, they still face challenges in selecting the ones that lead to the most profitable speedups. This has motivated the use of machine learning based cost models to guide the search for polyhedral optimizations. State-of-the-art polyhedral compilers have demonstrated a viable proof-of-concept of such an approach. While promising, this approach still faces significant limitations. State-of-the-art polyhedral compilers that use a deep learning cost model only support a small subset of affine transformations, limiting their ability to explore complex code transformations. Furthermore, their applicability does not scale beyond simple programs, thus excluding many program classes from their scope, such as those with non-rectangular iteration domains or multiple loop nests. These limitations significantly impact the generality of such compilers and autoschedulers and put into question the whole approach. In this paper, we introduce LOOPer, the first polyhedral autoscheduler that uses a deep learning based cost model and covers a large space of affine transformations and programs. LOOPer allows the optimization of an extensive set of programs while being effective at applying complex sequences of polyhedral transformations. We implement and evaluate LOOPer and show that it achieves competitive speedups over the state-of-the-art. On the PolyBench benchmarks, LOOPer achieves a geometric mean speedup of 1.84x over Tiramisu and 1.42x over Pluto, two state-of-the-art polyhedral autoschedulers.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a CTL formula, for a given (possibly infinite-state) program. We propose a method based on encoding the problem as a set of Horn constraints. The method takes a program, modeled as a transition system, and a property given by a CTL formula as input. It first generates a set of forall-exists quantified Horn constraints and well-foundedness constraints by exploiting the syntactic structure of the CTL formula. Then, the generated set of constraints are solved by applying an off-the-shelf Horn constraints solving engine. The program is said to satisfy the property if and only if the generated set of constraints has a solution. We demonstrate the practical promises of the method by applying it on a set of challenging examples. Although our method is based on a generic Horn constraint solving engine, it is able to outperform state-of-art methods specialised for CTL verification.

Looped Transformers scale latent computation by repeatedly applying shared blocks, but sequential looping increases latency and KV-cache memory with the loop count. Parallel loop Transformers (PLT) alleviate this cost through cross-loop position offsets (CLP) and shared-KV gated sliding-window attention, making loop count a practical design choice. We therefore study PLT loop-count selection through a gain--cost view: an extra loop may refine representations, but CLP also introduces a positional mismatch at each loop boundary. We instantiate this study by training LoopCoder-v2, a family of 7B PLT coders with different loop counts, from scratch on 18T tokens, followed by matched instruction tuning and evaluation. Empirically, the two-loop variant delivers broad gains over the non-looped baseline across code generation, code reasoning, agentic software engineering, and tool-use benchmarks, improving SWE-bench Verified from 43.0 to 64.4 points and Multi-SWE from 14.0 to 31.0 points. In contrast, variants with three or more loops regress, revealing a strongly non-monotonic loop-count effect. Our diagnostics show that loop 2 provides the main productive refinement, while later loops yield diminishing, oscillatory updates and reduced representational diversity. Because the CLP-induced mismatch remains roughly fixed as refinement gains shrink, the offset cost increasingly dominates. This gain--cost trade-off explains PLT's saturation at two loops and provides diagnostics for loop-count selection.

Language-model agents that run long tasks often redo work they have already done: they re-issue a tool call they made earlier and get back exactly the same observation, a step that adds no new information. We identify this failure as a loop. Loops appear natively in Qwen, Llama, and Gemini agents and become far more common once the agent's history is compressed to fit its context window. To reduce these loops, we propose DeLoop, a self-supervised training method. DeLoop builds on a simple observation: the agent's own rollout can provide the supervision needed to learn from its loops. We use a looping action as a negative example and the first later non-looping action in the same rollout as a positive example. DeLoop learns from these pairs through direct preference optimization and does not require task rewards, gold answers, or LLM judges. On CodeGym under compression, DeLoop reduces the share of Qwen3-8B tasks containing loops from 57.3% to 6.1%. It also uses about one third as many steps per task, with similar task success. On Qwen3-32B, DeLoop reduces loops and steps while raising task success from 37.7% to 44.8%.

Looped Transformers provide a parameter-efficient approach to depth scaling by repeatedly applying shared Transformer blocks. Recent reasoning models have likewise highlighted the value of scaling test-time computation through longer computation trajectories. However, the principles for designing effective loop transitions remain poorly understood. We view the looped hidden state as a fast weight that is updated throughout the depth. We formulate loop transitions as local gradient-based updates, with recurrent blocks predicting implicit targets at each depth. Our framework derives loop transitions in closed form from a projection, a local objective and an optimizer update rule. Mapping representative loop transitions into this framework reveals mismatches between their transitions and projections. We first align the input maps of existing transitions. We then derive OperLoop, which combines explicit weight decay, adaptive step size and a delta objective. The aligned variants reduce training loss and improve average commonsense accuracy. OperLoop improves average generative performance over the compared looped and non-looped baselines under matched training FLOPs. These results support the framework's usefulness for loop design. We extend the analysis to additional loop models and outline a roadmap for future loop transition design.

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as α,β-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the α,β-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

The synthesis of inductive loop invariants remains a critical bottleneck in automated program verification. While Large Language Models (LLMs) show promise in mitigating this issue, they often fail on complex programs, producing invariants that are invalid or computationally ineffective. Although fine-tuning is a natural strategy to address these limitations, obtaining high-quality training data remains an open challenge. We first formalize the properties required for a high-quality training invariant, and then present Wonda, a rigorous data curation pipeline that extracts such invariants from raw verifier output via AST-based normalization followed by LLM-driven semantic rewriting and augmentation with provable quality guarantees. Fine-tuning Small Language Models (SLMs) on Wonda-curated data yields consistent gains across the Qwen3, Llama-3.1, and Mistral families: the 4B and 8B Qwen3 models nearly double invariant correctness and double speedup rates, while Llama-3.1-8B triples both. On the challenging InvBench suite, the same 4B model outperforms an off-the-shelf model 20x its size and matches the end-to-end verification time of GPT-OSS-120B, while a 14B Qwen3 model matches that of the frontier model GPT-5.2, all without test-time compute overhead. Our code is publicly available on GitHub.

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet existing RLMs depend on an open-ended read-eval-print loop (REPL) in which the model generates arbitrary control code, making execution difficult to verify, predict, and analyse. We introduce λ-RLM, a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in λ-calculus. It executes a compact library of pre-verified combinators and uses neural inference only on bounded leaf subproblems, turning recursive reasoning into a structured functional program with explicit control flow. We show that λ-RLM admits formal guarantees absent from standard RLMs, including termination, closed-form cost bounds, controlled accuracy scaling with recursion depth, and an optimal partition rule under a simple cost model. Empirically, across four long-context reasoning tasks and nine base models, λ-RLM outperforms standard RLM in 29 of 36 model-task comparisons, improves average accuracy by up to +21.9 points across model tiers, and reduces latency by up to 4.1x. These results show that typed symbolic control yields a more reliable and efficient foundation for long-context reasoning than open-ended recursive code generation. The complete implementation of λ-RLM, is open-sourced for the community at: https://github.com/lambda-calculus-LLM/lambda-RLM.

Code large language models (Code LLMs) have made significant progress in code generation by translating natural language descriptions into functional code; however, real-world applications often demand stricter adherence to detailed requirements such as coding style, line count, and structural constraints, beyond mere correctness. To address this, the paper introduces forward and backward constraints generation to improve the instruction-following capabilities of Code LLMs in controlled code generation, ensuring outputs align more closely with human-defined guidelines. The authors further present IFEvalCode, a multilingual benchmark comprising 1.6K test samples across seven programming languages (Python, Java, JavaScript, TypeScript, Shell, C++, and C#), with each sample featuring both Chinese and English queries. Unlike existing benchmarks, IFEvalCode decouples evaluation into two metrics: correctness (Corr.) and instruction-following (Instr.), enabling a more nuanced assessment. Experiments on over 40 LLMs reveal that closed-source models outperform open-source ones in controllable code generation and highlight a significant gap between the models' ability to generate correct code versus code that precisely follows instructions.

The Abstraction and Reasoning Corpus (ARC) tests whether a model can infer an unseen transformation from a few input-output examples and apply it to a new grid. Looped visual reasoners refine predictions over multiple iterations, but conventional training constrains only the final output, leaving intermediate refinements unconstrained. We propose that these refinements should instead follow the transformation step by step. We introduce TraceViT, a looped visual reasoner trained with semantically monotonic transformation chains. We obtain these chains by rewriting and verifying programmatic task implementations, decomposing each solution into intermediate grid states. Each iteration is grounded by a task reference derived from the few-shot demonstrations and an object workspace representing the current grid state. Because these chains may differ in length from the loop, soft trace alignment enforces only their ordering, letting the model allocate iterations freely. TraceViT achieves 67.8% pass@2 on ARC-AGI-1 and 24.3% on ARC-AGI-2. Controlled ablations on ARC-AGI-1 show that trace supervision becomes beneficial only when paired with grounding. Code and data will be available at https://github.com/LiuBinnan/TraceViT.

Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in software verification are developed inside definition-rich codebases with substantial project-specific libraries. We introduce VeriSoftBench, a benchmark of 500 Lean 4 proof obligations drawn from open-source formal-methods developments and packaged to preserve realistic repository context and cross-file dependencies. Our evaluation of frontier LLMs and specialized provers yields three observations. First, provers tuned for Mathlib-style mathematics transfer poorly to this repository-centric setting. Second, success is strongly correlated with transitive repository dependence: tasks whose proofs draw on large, multi-hop dependency closures are less likely to be solved. Third, providing curated context restricted to a proof's dependency closure improves performance relative to exposing the full repository, but nevertheless leaves substantial room for improvement. Our benchmark and evaluation suite are released at https://github.com/utopia-group/VeriSoftBench.

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of T inputs and produces, after receiving each input, an accurate output on the obtained inputs. In contrast, a batch algorithm receives the data as one batch and produces a single output. We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are widely studied and used in the batch model, we show that the worst case error of every continual release algorithm is tilde Omega(T^{1/3}) times larger than that of the best batch algorithm. Previous work shows only a polylogarithimic (in T) gap between the worst case error achievable in these two models; further, for many problems, including the summation of binary attributes, the polylogarithmic gap is tight (Dwork et al., 2010; Chan et al., 2010). Our results show that problems closely related to summation -- specifically, those that require selecting the largest of a set of sums -- are fundamentally harder in the continual release model than in the batch model. Our lower bounds assume only that privacy holds for streams fixed in advance (the "nonadaptive" setting). However, we provide matching upper bounds that hold in a model where privacy is required even for adaptively selected streams. This model may be of independent interest.

Automated vulnerability reproduction from CVE descriptions requires generating executable Proof-of-Concept (PoC) exploits and validating them in target environments. This process is critical in software security research and practice, yet remains time-consuming and demands specialized expertise when performed manually. While LLM agents show promise for automating this task, existing approaches often conflate exploring attack directions with fixing implementation details, which leads to unproductive debugging loops when reproduction fails. To address this, we propose CVE2PoC, an LLM-based dual-loop agent framework following a plan-execute-evaluate paradigm. The Strategic Planner analyzes vulnerability semantics and target code to produce structured attack plans. The Tactical Executor generates PoC code and validates it through progressive verification. The Adaptive Refiner evaluates execution results and routes failures to different loops: the Tactical Loop for code-level refinement, while the Strategic Loop for attack strategy replanning. This dual-loop design enables the framework to escape ineffective debugging by matching remediation to failure type. Evaluation on two benchmarks covering 617 real-world vulnerabilities demonstrates that CVE2PoC achieves 82.9% and 54.3% reproduction success rates on SecBench.js and PatchEval, respectively, outperforming the best baseline by 11.3% and 20.4%. Human evaluation confirms that generated PoCs achieve comparable code quality to human-written exploits in readability and reusability.

The Functional Machine Calculus (Heijltjes 2022) is an extension of the lambda-calculus that preserves confluent reduction and typed termination, while enabling both call-by-name and call-by-value reduction behaviour and encoding the computational effects of mutable higher-order store, input/output, and probabilistic computation. In this note the calculus is extended to capture exception handling and loop constructs.

Augmenting Large Language Models (LLMs) with external tools enables them to execute complex, multi-step tasks. However, tool learning is hampered by the static synthetic data pipelines where data generation and model training are executed as two separate, non-interactive processes. This approach fails to adaptively focus on a model's specific weaknesses and allows noisy labels to persist, degrading training efficiency. We introduce LoopTool, a fully automated, model-aware data evolution framework that closes this loop by tightly integrating data synthesis and model training. LoopTool iteratively refines both the data and the model through three synergistic modules: (1) Greedy Capability Probing (GCP) diagnoses the model's mastered and failed capabilities; (2) Judgement-Guided Label Verification (JGLV) uses an open-source judge model to find and correct annotation errors, progressively purifying the dataset; and (3) Error-Driven Data Expansion (EDDE) generates new, challenging samples based on identified failures. This closed-loop process operates within a cost-effective, open-source ecosystem, eliminating dependence on expensive closed-source APIs. Experiments show that our 8B model trained with LoopTool significantly surpasses its 32B data generator and achieves new state-of-the-art results on the BFCL-v3 and ACEBench benchmarks for its scale. Our work demonstrates that closed-loop, self-refining data pipelines can dramatically enhance the tool-use capabilities of LLMs.

Integer overflow accounts for one of the major source of bugs in software. Verification systems typically assume a well defined underlying semantics for various integer operations and do not explicitly check for integer overflow in programs. In this paper we present a specification mechanism for expressing integer overflow. We develop an automated procedure for integer overflow checking during program verification. We have implemented a prototype integer overflow checker and tested it on a benchmark consisting of already verified programs (over 14k LOC). We have found 43 bugs in these programs due to integer overflow.

The ARC-AGI benchmark series serves as a critical measure of few-shot generalization on novel tasks, a core aspect of intelligence. The ARC Prize 2025 global competition targeted the newly released ARC-AGI-2 dataset, which features greater task complexity compared to its predecessor. The Kaggle competition attracted 1,455 teams and 15,154 entries, with the top score reaching 24% on the ARC-AGI-2 private evaluation set. Paper submissions nearly doubled year-over-year to 90 entries, reflecting the growing research interest in fluid intelligence and abstract reasoning. The defining theme of 2025 is the emergence of the refinement loop -- a per-task iterative program optimization loop guided by a feedback signal. Refinement loops come in a variety of forms, in particular evolutionary program synthesis approaches and application-layer refinements to commercial AI systems. Such refinement loops are also possible in weight space, as evidenced by zero-pretraining deep learning methods which are now achieving competitive performance with remarkably small networks (7M parameters). In parallel, four frontier AI labs (Anthropic, Google DeepMind, OpenAI, and xAI) reported ARC-AGI performance in public model cards in 2025, establishing ARC-AGI as an industry standard benchmark for AI reasoning. However, our analysis indicates that current frontier AI reasoning performance remains fundamentally constrained to knowledge coverage, giving rise to new forms of benchmark contamination. In this paper, we survey the top-performing methods, examine the role of refinement loops in AGI progress, discuss knowledge-dependent overfitting, and preview ARC-AGI-3, which introduces interactive reasoning challenges that require exploration, planning, memory, goal acquisition, and alignment capabilities.

AI agents are granted access to tools, APIs, and other infrastructure, making them active principals in those systems. The dominant approach places controls inside the agent's own runtime: system prompts, output filters, and guardrail libraries. Any control in the agent's address space is reachable by inputs that influence it; this generalizes to any AI system with sufficient reach into its own runtime, a class we term escapable AI systems. We identify four properties that an authorization mechanism must satisfy for architectural control rather than for cooperative requests: process separation, pre-action enforcement on a structurally only path, fail-closed at both the request and system levels, and externalized signed evidence verifiable outside the controlled system's trust boundary. We position this layer as execution-time AI alignment, complementing training-time alignment (RLHF, Constitutional AI) and inference-time alignment. We present the Unfireable Safety Kernel, a Rust reference implementation realizing all four. Its fail-closed invariant is machine-checked at two levels: an SMT theorem (Z3) and an exhaustive bounded-model-checking proof of the production decision function (Kani, 4/4 harnesses). A Python-to-Rust migration was gated on byte-equivalence (1000/1000 fixtures; 17/17 adversarial classes). We evaluate the kernel governing a live, escapable AI system, a deterministic, self-improving world model, against an escape-seeking adversary driving its real self-modification seam: across 1,000 self-modifications, all 704 attempts on the safety-critical core are refused, with no escape; a further 300, under the operator kill switch, are also refused. A separate campaign of 6,240 authorization round-trips had no successful bypass. Against 3 contemporary systems claiming the agent control plane, the agent invokes control; here, it lacks that choice.

LLM agents increasingly rely on iterative execution to solve tasks through planning, tool use, state updates, and agent collaboration. While this design enables flexible automation, it also creates a new class of failures: an agent may repeatedly execute model calls, tools, workflow transitions, or agent handoffs when the feedback path is not effectively bounded. We call this problem Infinite Agentic Loops (IALs). IALs are not ordinary programming loops; they arise from the interaction between agent logic, framework semantics, runtime observations, and termination mechanisms. Such failures can amplify a single request into long running model and tool execution, causing cost exhaustion, model denial of service, context growth, and repeated external side effects. We propose IAL-Scan, a static analysis tool for detecting IAL failures in real-world LLM agent projects. IAL-Scan abstracts heterogeneous agent code into a framework independent Agent IR, builds an Agentic Loop Dependence Graph (ALDG) to recover explicit and framework induced feedback paths, and checks whether these paths can repeatedly reach costly or state growing operations without an effective bound. We evaluate IAL-Scan on 6,549 LLM agent repositories. It reports 74 potential findings, among which manual review confirms 68 IAL failures across 47 projects, achieving 91.9% precision.

Loop Engineering is emerging as a practice for organizing development work around coding agents. Instead of writing each prompt by hand, practitioners design loops that monitor progress, assign work, run checks, and decide what the agent should do next. Even with a capable coding agent, a loop may trust a stale progress note, skip needed verification, spend its budget in the wrong direction, or stop before the task is safe to submit. Yet the final outcome of one end-to-end run cannot tell whether success or failure reflects the loop's guidance or the coding agent's ability to carry out the task. We introduce LoopArena, a benchmark for evaluating how well one model can guide a separate coding agent through a long-running task. The model under evaluation is the Controller: after each coding round, it receives a structured summary of the run and instructs a separate, fixed coding agent, the Worker, on what to do or verify next, or decides whether to stop. LoopArena evaluates this ability in three complementary settings that differ in execution scope and cost. Type I scores next-step Loop Contract selection through execution-validated questions without running the Worker at evaluation time. Type II executes repeated control over a selected slice of a full task, while Type III evaluates the paired full task from its original state. On full tasks, the best observed Strict Success Rate is 24.69\%, leaving substantial room for improvement in long-horizon loop control. Across Controllers, the paired reduction in estimated inference cost averages 64.4\%, and Type II produces a similar ordering under the main Core criterion (Spearman's \(ρ=0.9747\)). We release the benchmark data and evaluation code at https://github.com/AMAP-ML/LoopArena .

Code production is now a commodity; the bottleneck is knowing what to build and proving it works. We present the Kitchen Loop, a framework for autonomous, self-evolving software built on a unified trust model: (1) a specification surface enumerating what the product claims to support; (2) 'As a User x 1000', where an LLM agent exercises that surface as a synthetic power user at 1,000x human cadence; (3) Unbeatable Tests, ground-truth verification the code author cannot fake; and (4) Drift Control, continuous quality measurement with automated pause gates. We validate across two production systems over 285+ iterations, producing 1,094+ merged pull requests with zero regressions detected by the regression oracle (methodology in Section 6.1). We observe emergent properties at scale: multi-iteration self-correction chains, autonomous infrastructure healing, and monotonically improving quality gates. The primitives are not new; our contribution is their composition into a production-tested system with the operational discipline that makes long-running autonomous evolution safe.

Type inference for dynamically typed languages must reconcile four qualitatively different sources of information about a parameter: values assigned inside a definition, explicit declarations, contextual requirements, and structural operations. Existing systems often combine these sources into one constraint set, causing spurious conflicts and requiring redundant annotations. We present Generic Constraint Projection (GCP), a zero-annotation inference framework that stores the four sources in separate monotone slots on a stable definition-time template and checks each call in a fresh projection session. Ordinary calls verify concrete arguments and specialize returns without mutating the template, while partial calls produce residual projected functions. On the success fragment of a finite-height type preorder, we prove monotonicity, local and global convergence, conditional projection-obligation soundness, projection termination, multi-module convergence, and order-independence under fair iteration. For the pure recursion-free core Outline_0, we also prove evaluation definedness, type preservation, runtime receiver retention, and projection-evaluation coherence. GCP uses Outline Equational Matching as an extensible structural compatibility relation and future this to preserve concrete receiver shape across fluent method chains. We instantiate the framework in Outline for typed ontology worlds and in Python for recovery of PEP 484 annotations from unannotated source.

A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs). However, their applicability is limited by hardware constraints, including shallow circuit depth, limited qubit counts, and noise. To mitigate these issues, we propose a hybrid classical--quantum framework based on graph shrinking to reduce the number of variables and constraints in QUBO formulations of COPs, while preserving problem structure. Our approach introduces three key ideas: (i) constraint-aware shrinking that prevents merges that will likely violate problem-specific feasibility constraints, (ii) a verification-and-repair pipeline to correct infeasible solutions post-optimization, and (iii) adaptive strategies for recalculating correlations and controlling the graph shrinking process. We apply our approach to three standard benchmark problems: Multidimensional Knapsack (MDKP), Maximum Independent Set (MIS), and the Quadratic Assignment Problem (QAP). Empirical results show that our approach improves solution feasibility, reduces repair complexity, and enhances quantum optimization quality on hardware-limited instances. These findings demonstrate a scalable pathway for applying near-term quantum algorithms to classically challenging constrained optimization problems.

Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as observed measurements and physical laws. However, existing constrained samplers often face a trade-off: enforcing constraints can substantially displace samples from the pretrained data distribution. To address this trade-off, we introduce MintFlow, a training-free constrained sampling framework that formulates constraint enforcement as a minimal intervention on the pretrained flow trajectory. MintFlow seeks the minimal perturbation of an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. By minimally perturbing the flow state while keeping the pretrained flow field unchanged, MintFlow enforces the constraint while minimizing unnecessary deviation from the pretrained distribution. An adjoint formulation yields a closed-form expression for this perturbation, eliminating expensive iterative optimization. Furthermore, MintFlow adaptively selects the intervention time to balance the required perturbation magnitude with its amplification by the remaining flow. Across a range of tasks in generative vision and physical system modeling, MintFlow achieves competitive constraint satisfaction while preserving the pretrained generative distribution substantially better than state-of-the-art constrained methods.

Precise instruction-following is a fundamental ability of large language models (LLMs), requiring their outputs to strictly satisfy objective constraints in input instructions. In complex application scenarios, these constraints often possess diverse scopes that govern specific response segments rather than the entire output. However, existing optimization methods often neglect constraint scope during data construction and rely on binary per-constraint rewards, yielding limited data diversity and sparse supervision for complex constraints. To this end, we propose ScopeIF, a novel training framework for scope-aware precise instruction-following. We first introduce a unified schema that factorizes objective constraints into three decoupled dimensions: Scope, Target, and Range. Grounded in this schema, we construct ScopeInstruct, a large-scale instruction dataset with diverse scope-aware constraints, and combine tool-grounded verification with graded reward modeling to quantify the violation degree of each constraint, providing dense supervision for policy optimization. Extensive experiments demonstrate that ScopeIF consistently outperforms existing methods, particularly on complex scope-aware constraints, while preserving general capabilities. Notably, it enables optimized Qwen3-4B and 8B models to rival or surpass strong frontier models such as Gemini-2.5-Pro and DeepSeek-V3.2, establishing an effective paradigm for advancing scope-aware instruction-following. Our code and data are available at https://github.com/thu-coai/ScopeIF.

The Bernays-Sch\"onfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine.

Natural-language feedback in interactive learning often explains why an action failed by pointing to violated requirements. Misinterpreting this feedback can lead an agent to rule out valid solutions. We study this setting by modeling user intent as latent constraints over an action space and formulating learning from language feedback as pure exploration over feasible regions. We introduce TRACE, an algorithm that organizes candidate constraints in a tree and tests each proposed refinement by generating actions that satisfy it. TRACE commits to the refinement only if the resulting feedback does not contradict it over repeated tests. We distinguish two ways of using the same feedback: (i) falsification, which detects contradictions to the constraint set currently being tested, and (ii) identification, which may additionally name a violated constraint. We prove high-probability coverage bounds with dependence on the candidate class size H for TRACE-Falsification. With reliable identification, TRACE-Identification can replace this dependence by K/p_{ext}, where K is the number of latent constraints and p_{ext} lower-bounds the probability of extracting a missing true constraint from informative feedback. We evaluate TRACE across six language-feedback tasks. On RecMovie, TRACE-Identification achieves 73% and 86% final-output success under caps of 20 and 60 evaluated outputs, compared with at most 42% and 48% for the evaluated prompting baselines given the same feedback and output caps. Controlled identity-corruption experiments further show greater robustness than direct accumulation when the falsification detector remains reliable.

Languages with rich static semantics, such as Rust, provide stronger guarantees for AI-generated code, but their strictness makes generation more difficult. Off-the-shelf compilers can provide useful feedback post-generation, but does not guide intermediate generation steps, such as those during autoregressive LLM decoding. Constrained decoding intervenes earlier by rejecting invalid tokens during sampling, but requires white-box model access and costly reimplementation for semantic constraints.We introduce generative compilation, the first approach to obtaining compiler feedback on partial programs during generation. The core technical device is a sealor: a lightweight, mostly syntax-guided transformation that converts partial programs into complete ones that standard compilers can diagnose. It is designed such that possible-to-complete partial programs are never rejected, while preserving enough code context to catch genuine dead ends early. We construct such a sealor on a core Rust-like calculus and prove that it satisfies these properties, all mechanized in Lean. We extend it to the first partial-program checker for real Rust. We evaluate our method on challenging repository-level Rust coding tasks, across both frontier black-box and open-weight models. We show that generative compilation reduces non-compiling outputs and improves functional correctness, relative to standard post-generation feedback. It does so by detecting a broad range of errors close to their source and early during generation, thereby reducing errors cascades and enabling focused diagnostics. More broadly, generative compilation is a step toward making compilers a first-class citizen of AI-assisted programming active during generation, rather than a separate post-generation check.

Scaling Transformer-based click-through rate (CTR) models by stacking more parameters brings growing computational and storage overhead, creating a widening gap between scaling ambitions and the stringent industrial deployment constraints. We propose LoopCTR, which introduces a loop scaling paradigm that increases training-time computation through recursive reuse of shared model layers, decoupling computation from parameter growth. LoopCTR adopts a sandwich architecture enhanced with Hyper-Connected Residuals and Mixture-of-Experts, and employs process supervision at every loop depth to encode multi-loop benefits into the shared parameters. This enables a train-multi-loop, infer-zero-loop strategy where a single forward pass without any loop already outperforms all baselines. Experiments on three public benchmarks and one industrial dataset demonstrate state-of-the-art performance. Oracle analysis further reveals 0.02--0.04 AUC of untapped headroom, with models trained with fewer loops exhibiting higher oracle ceilings, pointing to a promising frontier for adaptive inference.

Yes. Can it cure doom loops? Probably not. The Gemma 4 instruction-tuned models share a reproducible failure: on long factual enumeration prompts, such as listing every episode of a TV series, the 88 IAU constellations, or the 151 original Pokemon, they collapse into repetition, either a tight verbatim loop or a list whose entries decay onto a single answer. These loops occur at rates as high as 95% and survive prompt rewording, inference-engine changes, and most sampling adjustments. In this paper we explore whether this behavior is localized enough to remove by weight edits. To localize the cause, we use per-layer ablation and per-neuron attribution, then confirm the strongest candidates with full-generation sweeps. The loops trace to a small set of MLP neurons (or, in the 26B-A4B Mixture-of-Experts model, a few routed experts) which we suppress with static weight edits. These "surgeries" can be as small as a single sign-inverted neuron (in the E2B model). The size of the effective edits grows with model scale, but in all cases, the loop patterns can be addressed at normal generation budgets while preserving general-purpose benchmark scores. However, the edits do not solve everything: we also study longer thinking budgets, where the two larger models most visibly enter doom looping, i.e. a non-convergent regime in which the model self-corrects in circles over a fact it cannot recall, exhausting the budget without committing to a final answer. We show this residual failure is reduced but not eliminated by the same edits, and argue it is fundamentally a knowledge-precision problem rather than a removable circuit; weight surgery can delete a loop, but it cannot supply a missing fact. Our results are both a feasibility demonstration, that is, evidence that a concrete generation pathology can be localized to a few parameters and edited out, and a delineation of where that approach stops.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

Individual agent capabilities have advanced rapidly through modular skills and tool integrations, yet multi-agent systems remain constrained by fixed team structures, tightly coupled coordination logic, and session-bound learning. We argue that this reflects a deeper absence: a principled organisational layer that governs how a workforce of agents is assembled, governed, and improved over time, decoupled from what individual agents know. To fill this gap, we introduce OneManCompany (OMC), a framework that elevates multi-agent systems to the organisational level. OMC encapsulates skills, tools, and runtime configurations into portable agent identities called Talents, orchestrated through typed organisational interfaces that abstract over heterogeneous backends. A community-driven Talent Market enables on-demand recruitment, allowing the organisation to close capability gaps and reconfigure itself dynamically during execution. Organisational decision-making is operationalised through an Explore-Execute-Review (E^2R) tree search, which unifies planning, execution, and evaluation in a single hierarchical loop: tasks are decomposed top-down into accountable units and execution outcomes are aggregated bottom-up to drive systematic review and refinement. This loop provides formal guarantees on termination and deadlock freedom while mirroring the feedback mechanisms of human enterprises. Together, these contributions transform multi-agent systems from static, pre-configured pipelines into self-organising and self-improving AI organisations capable of adapting to open-ended tasks across diverse domains. Empirical evaluation on PRDBench shows that OMC achieves an 84.67% success rate, surpassing the state of the art by 15.48 percentage points, with cross-domain case studies further demonstrating its generality.

Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this domain. Pure reasoning paradigms, which rely on long natural language chains, are prone to inconsistency, error accumulation, and prohibitive cost as constraints compound. Conversely, LLMs combined with coding- or solver-based strategies lack flexibility: they often generate problem-specific code from scratch or depend on fixed solvers, failing to capture generalizable logic across diverse problems. To address these challenges, we introduce the Scalable COde Planning Engine (SCOPE), a framework that disentangles query-specific reasoning from generic code execution. By separating reasoning from execution, SCOPE produces solver functions that are consistent, deterministic, and reusable across queries while requiring only minimal changes to input parameters. SCOPE achieves state-of-the-art performance while lowering cost and latency. For example, with GPT-4o, it reaches 93.1% success on TravelPlanner, a 61.6% gain over the best baseline (CoT) while cutting inference cost by 1.4x and time by ~4.67x. Code is available at https://github.com/DerrickGXD/SCOPE.

Safety claims on self-improving agent runtimes are almost always self-graded: a policy file, a guardrail, or a README commitment. We describe falsifiable release gates, and a methodology to build and validate such systems, such that every new capability must pass a pre-specified, machine-verifiable acceptance suite before it ships, and a fixed set of standing invariants is preserved at each gate. I think we applied the method in the Antahkarana, an open runtime, via seven gates from basic observability into a self governing loop that suggests changes to its own policy. no action goes to an effector without a safety-critical property capability token minted by a control ring is exhaustively machine-checked over the one million recorded reachable state space of a bounded model and re-checked against execution traces. A purposely broken model gives the shortest counterexample, so the checker has teeth, is apparent. The self-enhancement loop is positively Constrained: the entire write surface is policy rules, tightening changes. may auto-apply loosening changes always require a human merge and a proposal autoclosed is one that mispredicts its own effect; We publish the acceptance measured results for all the seven gates, define precisely the scope of each claim (a bounded of the coordination skeleton (not the learned components) and free the runtime, either command line tools and the gate suite, so the results reproduce, and gates can run against other agent frameworks. Reviewers may repeat the single command central non-bypass in seconds.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

Large language models (LLMs) have advanced significantly in code generation, yet their ability to follow complex programming instructions with layered and diverse constraints remains underexplored. Existing benchmarks often prioritize functional correctness, overlooking the nuanced requirements found in real-world development. We introduce MultiCodeIF, a comprehensive benchmark designed to evaluate instruction-following in code generation across multiple dimensions: constraint type, hierarchical levels, and iterative refinement. Built upon a structured taxonomy of 9 categories and 27 constraint types, MultiCodeIF enables granular assessment of both functional and non-functional instruction adherence. Using an automated pipeline, ConstraGen, we synthesize and evolve 2,021 code tasks sourced from 14 programming languages, supporting multi-turn evaluation through feedback-driven task variants. Empirical evaluation of six state-of-the-art LLMs uncovers substantial performance disparities. The top-performing model, Claude-3-7-Sonnet, achieves 63.0% average constraint satisfaction, while smaller models like Qwen3-1.7B fall to 44.8%. Models perform well on explicit constraints, but struggle with implicit or abstract constraints. Tasks with multiple hierarchical constraints significantly reduce model success rates, from 54.5% in single-level to just 18.8% in multi-level scenarios. However, structured feedback enables progressive improvement: average constraint satisfaction rises from 63.0% to 83.4% over four iterative refinement rounds. MultiCodeIF provides a scalable, constraint-aware, and feedback-sensitive framework to benchmark LLMs under realistic code generation scenarios, bridging the gap between synthetic evaluations and real-world instruction complexity. The full benchmark dataset, evaluation pipeline, and source code are available at https://github.com/SYSUSELab/MultiCodeIF.

Progress toward artificial general intelligence (AGI) has largely relied on scaling a resource-intensive executive, System-2, through larger models, more data and compute, longer reasoning, and more agents. We ask whether the next stage may come instead from co-designing it with System-1, a lightweight, semantically aware predictor that evaluates candidate interactions before execution, so that System-2 acts only on those worth their cost. Our answer is a qualified yes. We study conditional interaction, a predict--gate--execute--update loop: System-1 estimates each candidate's utility, System-2 executes those admitted by an adaptive threshold, and the outcomes update System-1. The loop spans training, test-time reasoning, adaptive decision-making, and agentic tool use, with utility and cost defined by the application. Under ideal screening and equal execution costs, execution compute falls by a factor approaching 1/ρ_u, where ρ_u is the density of utility-relevant interactions (cost-weighted when costs differ); prediction errors, exploration, and distribution shift reduce the saving. We bound selection regret by predictor error and the utility margin. These results motivate our central hypothesis: ρ_u is a measurable coordinate of scaling efficiency and makes informative compute a better description of scaling than total compute.

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive retrofits, which involve substantial computational costs and may compromise pretrained capabilities. To address these limitations, we introduce Looped Depth Up-Scaling (LoopUS), a post-training framework that converts a standard pretrained LLM into a looped architecture. As a key technical contribution, LoopUS recasts the pretrained LLM into an encoder, a looped reasoning block, and a decoder. It operationalizes this latent-refinement architecture through four core components: (1) block decomposition, guided by staged representation dynamics; (2) an input-dependent selective gate to mitigate hidden-state drift; (3) random deep supervision for memory-efficient learning over long recursive horizons; and (4) a confidence head for adaptive early exiting. Collectively, these mechanisms transform a standard non-looped model into a looped form while stabilizing it against both computational bottlenecks and representation collapse. Through stable latent looping, LoopUS improves reasoning-oriented performance without extending the generated traces or requiring recurrent training from scratch. For more details, see https://thrillcrazyer.github.io/LoopUS

Mathematical programming formulations are routinely modified through algebraic reformulations, perturbations of constraint functions, and the addition or removal of constraints. Some of these modifications preserve the feasible set, whereas others reflect newly imposed modeling requirements and therefore change the optimization problem itself. This paper develops a metric framework for quantifying the robustness of formulation-dependent properties. Formulations are modeled as typed collections of constraint functions. Within each fixed typed-cardinality class, their distance is defined by optimally matching constraints of the same type and measuring the resulting discrepancies in a norm on the underlying function space. As a concrete demonstration of the framework, we study the Linear Independence Constraint Qualification (LICQ). We introduce the pointwise LICQ radius, defined as the distance from a feasible formulation to the set of formulations that remain feasible at a prescribed point but fail LICQ there. Under suitable assumptions, we derive an explicit formula for this radius and characterize the effect of adding a single equality or inequality constraint.

Explaining an inferred fact under rule evaluation can require identifying the inclusion-minimal input sets that suffice for the inference and the deletions that make the fact disappear. For a fixed union of conjunctive queries, every minimal support is bounded by the query body. For recursive rules, the same answer may depend on large supports, and the number of minimal supports may be exponential in the input. We study the gap through deletion-based explanation, using inclusion-minimal endogenous input facts that entail the atom together with fixed background facts. We organize these supports as a hypergraph and prove that it determines actual causes, counterfactual causes, responsibility, and deletion robustness. The resulting view separates nonrecursive queries from recursive Datalog at the level of minimal input explanations. For positive-length reachability, minimal supports are exactly simple directed paths, and deletion robustness is the minimum directed edge cut. We also prove invariance under fixed-goal equivalent positive Datalog programs and an NP-hardness calibration for the robustness threshold problem.

Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulators and hardware. Our framework is applied to three representative NP-hard problems: the Travelling Salesman Problem (TSP), the Multi-Dimensional Knapsack Problem (MDKP), and the Maximum Independent Set (MIS). We demonstrate that MDKP and TSP, with their inequality-based or degree-constrained structures, allow for slack-free reformulations, leading to significant qubit savings without compromising performance. In contrast, MIS does not inherently benefit from slack elimination but still gains in feasibility and objective quality from principled Lagrangian updates. We benchmark these methods across classically hard instances, analyzing trade-offs in qubit usage, feasibility, and optimality gaps. Our results highlight the flexibility of Lagrangian formulations as a scalable alternative to naive QUBO penalization, even when qubit savings are not always achievable. This work provides practical insights for deploying constraint-aware quantum optimization pipelines, with applications in logistics, network design, and resource allocation.

Training modern neural networks is increasingly fragile, with rare but severe destabilizing updates often causing irreversible divergence or silent performance degradation. Existing optimization methods primarily rely on preventive mechanisms embedded within the optimizer, offering limited ability to detect and recover from instability once it occurs. We introduce a supervisory runtime stability framework that treats optimization as a controlled stochastic process. By isolating an innovation signal derived from secondary measurements, such as validation probes, the framework enables automatic detection and recovery from destabilizing updates without modifying the underlying optimizer. We provide theoretical runtime safety guarantees that formalize bounded degradation and recovery. Our implementation incurs minimal overhead and is compatible with memory-constrained training settings.

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-by-name stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. The second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. The key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. These embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. The equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.

High-Level Synthesis leverages loop unrolling and array partitioning, but scheduling concurrent accesses is challenging when indices contain non-affine arithmetic. Conventional polyhedral frameworks systematically over-approximate these non-linear transformations, forcing conservative serialization that degrades performance. To minimize this bottleneck, we present a spatial verification framework operating at the LLVM Intermediate Representation (IR) level. By extracting flat arithmetic expressions from "getelementptr" instructions, it models memory banks as polymorphic spatial predicates to handle non-affine terms. Structural safety is enforced via a Conflict-Free Unrolling condition using Separation Logic's separating conjunction; concurrent operations targeting the same bank trigger an automatic spatial contradiction. This disjointness requirement is reduced to a matrix of pairwise inequalities over immutable Static Single Assignment (SSA) variables for a Satisfiability Modulo Theories (SMT) oracle. To guarantee safety against undecidable non-linear arithmetic, we implement a deterministic sequential fallback. Finally, a theorem of soundness bridges algebraic SMT verification with Register Transfer Level trace safety, ensuring physical hardware immune to structural memory collisions.

Coding agents now produce a growing share of a team's code, while the reasoning behind each change -- the alternatives weighed, the constraints discovered, the approaches rejected -- is trapped in assistant transcripts that vanish with the session. Memory for this setting, the agentic development lifecycle (ADLC), is usually posed as one retrieval problem and built as machinery: tiered stores, memory graphs, compiled wikis, model-judged admission. We argue memory should instead be git-bound -- built into the repository's version control, inheriting the guarantees the machinery struggles to construct: ground truth from commits, freshness from rebuild, verification from the merge, containment from review. On this ledger we solve two problems separately, then combine them. Seed supply is closed as an eight-corpus retrieval study under a pre-registered ship discipline: five imported ranking mechanisms rejected, two kept, and a best configuration of ~0.31 pooled MRR -- ~60x the raw-transcript grep floor, ~15x an honest parsed-turn floor. Answer assembly is where ranking stops helping: single-shot retrieval scores only 0.07-0.20 answer-sufficiency on real developer questions, and ungated episode injection measurably degrades good answers. A router dispatches breadth to a git-anchored structural map, pointed lookups to confidence-gated episodes, and rationale to decision synthesis, which reconstructs why-arcs no single session contains (0.83 sufficiency on a young ~50k-LOC production system). Routed, the system answers at 382-980 tokens per question -- three orders of magnitude below the recorded history. Because ground truth is mined from commit-session links rather than annotated, every result is replicable on any user's own history at zero labeling cost. The remaining constraint is capture. Code, benchmark, and paper source: github.com/rekal-dev/rekal-cli.

Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in programming languages, type-and-effect systems did not yet gain widespread adoption. One reason for this is that type-and-effect systems are more complex and the existing inference algorithms make compromises between expressiveness, intuitiveness, and decidability. In this work, we present an effect inference algorithm for a type-and-effect system with subtyping, expressive higher-rank polymorphism, and intuitive set-like semantics of effects. In order to deal with scoping issues of higher-rank polymorphism, we delay solving of effect constraints by transforming them into formulae of propositional logic. We prove soundness and completeness of our algorithm with respect to a declarative type-and-effect system. All the presented results have been formalized in the Rocq proof assistant, and the algorithm has been successfully implemented in a realistic programming language.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

We study the problem of counting the number of distinct elements in a dataset subject to the constraint of differential privacy. We consider the challenging setting of person-level DP (a.k.a. user-level DP) where each person may contribute an unbounded number of items and hence the sensitivity is unbounded. Our approach is to compute a bounded-sensitivity version of this query, which reduces to solving a max-flow problem. The sensitivity bound is optimized to balance the noise we must add to privatize the answer against the error of the approximation of the bounded-sensitivity query to the true number of unique elements.

If autoresearch is itself a form of research, then autoresearch can be applied to research itself. We present Bilevel Autoresearch, a bilevel framework in which an outer autoresearch loop improves an inner autoresearch loop by reading its code and traces, identifying bottlenecks, and generating injectable Python search mechanisms at runtime. The inner loop optimizes task performance; the outer loop optimizes how the inner loop searches. Both loops use the same LLM, so improvements come from the bilevel architecture rather than a stronger meta-level model, although the outer loop consumes additional inference and wall-clock budget. On Karpathy's GPT pretraining benchmark, the meta-autoresearch outer loop achieves a 5x improvement over the standard inner loop alone (-0.045 vs. -0.009 val_bpb), while parameter-level adjustment without mechanism change yields no reliable gain. The outer loop instantiates mechanisms from adjacent search domains, including combinatorial optimization, multi-armed bandits, and design of experiments, without human specification of the final mechanism design. Trace analysis suggests that these mechanisms break deterministic search patterns and force exploration of directions the LLM's priors avoid. The experiments demonstrate, on this benchmark, a first bilevel step: an outer loop improves the search behavior of an inner loop. Code is the mechanism carrier in this implementation, but skills, prompts, workflows, evaluators, domain principles, world-model assumptions, and memory schemas can also encode mechanisms that shape future agent behavior. This suggests a path toward recursive bootstrapping, where mechanisms discovered for the inner loop can be fed back to improve the meta-level loop itself.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

We study auto research as a closed empirical loop driven by external measurement. Each submitted trial carries a hypothesis, an executable code edit, an evaluator-owned outcome, and feedback that shapes the next proposal. The output is not a generated paper or a single model checkpoint, but an auditable trajectory of proposals, code diffs, experiments, scores, and failure labels. We instantiate this loop with specialist agents that partition recipe surfaces and share measured lineage across trials. The central empirical finding is that lineage feedback lets agents turn evaluator outcomes, including crashes, budget overruns, size failures, and accuracy-gate misses, into later program-level recipe edits rather than one-shot suggestions. Across 1,197 headline-run trials plus 600 Parameter Golf control trials after one-time setup and launch, humans did not choose proposals, edit recipes, override scores, or repair failed trials during the search. In the three headline runs, the same submitted-trial loop reduces Parameter Golf validation bpb by 0.81%, raises NanoChat-D12 CORE by 38.7%, and reduces CIFAR-10 Airbench96 wallclock by 4.59%, with each task measured by its own external evaluator and legality checks. The trace includes a strict architecture-domain audit of 157 headline-run submissions and program rewrites such as a NanoChat attention-kernel path change. Within this scope the loop autonomously writes code, submits experiments, absorbs feedback, applies and combines known techniques inside each environment, and improves public starting recipes.

Looped Transformers increase test-time computation by repeatedly applying a shared recurrent block. Learned halting objectives in looped Transformers typically use a single exit distribution both as the inference-time stopping rule and as the training-time weighting of per-depth losses. This entangles exit selection with trajectory formation: the gate not only chooses which recurrent state to use, but also determines how strongly each intermediate state is supervised. Consequently, poor adaptive-compute performance can arise from the readout, the induced trajectory, or their interaction. We study adaptive depth in looped Transformers through this trajectory--readout lens, across controlled synthetic tasks (modular arithmetic and binary parity) and large-scale Ouro-1.4B and 2.6B checkpoints. We find that fixed-prior depth supervision, which shapes the trajectory without an input-dependent halting policy, produces difficulty-aware trajectories whose intermediate states expose useful stopping signals, and that simple post-hoc confidence readouts often match or outperform learned linear and MLP gates. Fitting gates on frozen trajectories localizes the failure: it appears to stem mainly from the trajectory induced by joint gate training rather than from limited gate expressivity. The same pattern is present in Ouro evaluations, where pretrained ponder gates are competitive but not uniformly Pareto-optimal, and measured latency confirms that the resulting reductions in average exit depth translate into practical inference-time savings. Our systematic diagnostic evaluation reframes adaptive depth in looped Transformers as a joint problem of trajectory formation and exit readout, rather than gate learning alone, highlighting a distinction that prior learned-halting work has often left implicit.

Regardless of the particular task we want them to perform in an environment, there are often shared safety constraints we want our agents to respect. For example, regardless of whether it is making a sandwich or clearing the table, a kitchen robot should not break a plate. Manually specifying such a constraint can be both time-consuming and error-prone. We show how to learn constraints from expert demonstrations of safe task completion by extending inverse reinforcement learning (IRL) techniques to the space of constraints. Intuitively, we learn constraints that forbid highly rewarding behavior that the expert could have taken but chose not to. Unfortunately, the constraint learning problem is rather ill-posed and typically leads to overly conservative constraints that forbid all behavior that the expert did not take. We counter this by leveraging diverse demonstrations that naturally occur in multi-task settings to learn a tighter set of constraints. We validate our method with simulation experiments on high-dimensional continuous control tasks.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

Recent work shows Large Language Models (LLMs) struggle to understand natural language constraints for various text generation tasks in zero- and few-shot settings. While, in the code domain, there is wide usage of constraints in code format to maintain the integrity of code written in Domain-Specific Languages (DSLs) like JSON and YAML which are widely used for system-level programming tasks in enterprises. Given that LLMs are increasingly used for system-level code tasks, evaluating if they can comprehend these code constraints is crucial. However, no work has been done to evaluate their controllability over code constraints. Hence, we introduce ConCodeEval, a first-of-its-kind benchmark having two novel tasks for code constraints across five representations. Our findings suggest that language models struggle with code constraints. Code languages that perform excellently for normal code tasks do not perform well when the same languages represent fine-grained constraints.

Large Language Models are powerful tools for program synthesis and advanced auto-completion, but come with no guarantee that their output code is syntactically correct. This paper contributes an incremental parser that allows early rejection of syntactically incorrect code, as well as efficient detection of complete programs for fill-in-the-middle (FIM) tasks. We extend the Earley parsing algorithm to allow for left and right quotients of context-free grammars, and develop methods to handle quotienting of several context-sensitive features present in the grammars of many common programming languages. The result of these contributions is an efficient, general, and well-grounded method for left and right quotient parsing. To validate our theoretical contributions -- and the effectiveness of certain design decisions -- we evaluate our method on the particularly difficult case of FIM completion for Python 3, with syntax-correctness constraints. Our results demonstrate that constrained generation can significantly reduce the incidence of syntax errors in recommended code.

Deep Reinforcement Learning (RL) has demonstrated impressive results in solving complex robotic tasks such as quadruped locomotion. Yet, current solvers fail to produce efficient policies respecting hard constraints. In this work, we advocate for integrating constraints into robot learning and present Constraints as Terminations (CaT), a novel constrained RL algorithm. Departing from classical constrained RL formulations, we reformulate constraints through stochastic terminations during policy learning: any violation of a constraint triggers a probability of terminating potential future rewards the RL agent could attain. We propose an algorithmic approach to this formulation, by minimally modifying widely used off-the-shelf RL algorithms in robot learning (such as Proximal Policy Optimization). Our approach leads to excellent constraint adherence without introducing undue complexity and computational overhead, thus mitigating barriers to broader adoption. Through empirical evaluation on the real quadruped robot Solo crossing challenging obstacles, we demonstrate that CaT provides a compelling solution for incorporating constraints into RL frameworks. Videos and code are available at https://constraints-as-terminations.github.io.

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the coupling constraints, LR enables parallel subproblem solving and often yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical work has shown promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of O(s^{1.5}/N) for the learned multipliers, where s is the number of coupling constraints and N is the sample size. Second, we provide a minimax lower-bound of Ω(s/N), proving that a linear dependency is unavoidable. Third, we constructively close this theoretical gap by proving that Stochastic Gradient Ascent (SGA) with averaging achieves the minimax optimal rate Θ(s/N). Finally, we extend our framework to the learning-to-warm-start setting, proving that it achieves a fast, minimax-optimal rate of Θ(s/N) and establishing a theoretical advantage over direct multiplier prediction.

Aerial grasp-and-lift tasks require whole-body coordination across approach, acquisition, and lifting under partial target observations. Early approach failures can limit exposure to later task stages during training, while changing visibility complicates alignment and closure timing during execution. We present a recurrent teacher-student framework that learns a single policy in simulation to jointly command flight, arm motion, and gripper closure without an explicit task-phase input. A privileged teacher learns through reinforcement learning with a critical-state curriculum that exposes acquisition and lifting states before connecting them to normal approach trajectories. Its behavior is distilled into a recurrent visual student that replaces privileged target states with dual-view point clouds and proprioception, integrating observation history for closed-loop control. A dedicated closure objective supervises closure timing from sustained model-defined readiness sequences. Training and primary evaluation use a simulated acquisition-and-payload model with condition-triggered latching, virtual attachment, and wrench-based payload loading for short-distance lifting. Across 8,996 completed simulation episodes under this model, the frozen student achieves full-task success rates of 99.97%, 97.14%, and 95.84% under nominal, physics/control-randomized, and additional camera-randomized conditions, respectively. The nominal latch-count-weighted mean of per-seed 90th-percentile alignment errors at acquisition is 8.12 mm.

This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach allows generating parameterized test cases with coverage guarantees between parameter interactions of a given application. Compared to exhaustive testing, combinatorial test case generation reduces the number of tests to run significantly. Our column generation algorithm is generic and can accommodate mixed coverage arrays over heterogeneous alphabets. The algorithm is realized in practice as a cloud service and recognized as one of the five winners of the company-wide cloud application challenge at Oracle. The service is currently helping software developers from a range of different product teams in their testing efforts while exposing declarative constraint models and hybrid optimization techniques to a broader audience.

Intelligent document processing pipelines extract structured entities (tables, images, and text) from documents for use in downstream systems such as knowledge bases, retrieval-augmented generation, and analytics. A persistent limitation of existing pipelines is that extraction output is produced without any intrinsic mechanism to verify whether it faithfully represents the source. Model-internal confidence scores measure inference certainty, not correspondence to the document, and extraction errors pass silently into downstream consumers. We present Reconstruction as Validation (RaV-IDP), a document processing pipeline that introduces reconstruction as a first-class architectural component. After each entity is extracted, a dedicated reconstructor renders the extracted representation back into a form comparable to the original document region, and a comparator scores fidelity between the reconstruction and the unmodified source crop. This fidelity score is a grounded, label-free quality signal. When fidelity falls below a per-entity-type threshold, a structured GPT-4.1 vision fallback is triggered and the validation loop repeats. We enforce a bootstrap constraint: the comparator always anchors against the original document region, never against the extraction, preventing the validation from becoming circular. We further propose a per-stage evaluation framework pairing each pipeline component with an appropriate benchmark. The code pipeline is publicly available at https://github.com/pritesh-2711/RaV-IDP for experimentation and use.

In this paper we present a comparative study of path feasibility queries generated during path exploration based software engineering methods. Symbolic execution based methods are gaining importance in different aspects of software engineering e.g. proving properties about programs, test case generation, comparing different executions of programs. These methods use SMT solvers to check the satisfiability of path feasibility queries written as a formula in the supported theories. We study the performance of solving such path feasibility queries using SMT solvers for real world programs. Our path condition formulas are generated in a theory of quantifier free bit vectors with arrays (QF_ABV). We show that among the different SMT solvers, STP is better than Z3 by an order of magnitude for such kind of queries. As an application we design a new program analysis (Change Value Analysis) based on our study which exploits undefined behaviors in programs. We have implemented our analysis in LLVM and tested it with the benchmark of SIR programs. It reduces the time taken for solving path feasibility queries by 48%. The study can serve as guidance to practitioners using path feasibility queries to create scalable software engineering methods based on symbolic execution.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Effective scheduling under tight resource, timing, and operational constraints underpins large-scale planning across sectors such as capital projects, manufacturing, logistics, and IT fleet transitions. However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact, implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

The advancement of machine learning for compiler optimization, particularly within the polyhedral model, is constrained by the scarcity of large-scale, public performance datasets. This data bottleneck forces researchers to undertake costly data generation campaigns, slowing down innovation and hindering reproducible research learned code optimization. To address this gap, we introduce LOOPerSet, a new public dataset containing 28 million labeled data points derived from 220,000 unique, synthetically generated polyhedral programs. Each data point maps a program and a complex sequence of semantics-preserving transformations (such as fusion, skewing, tiling, and parallelism)to a ground truth performance measurement (execution time). The scale and diversity of LOOPerSet make it a valuable resource for training and evaluating learned cost models, benchmarking new model architectures, and exploring the frontiers of automated polyhedral scheduling. The dataset is released under a permissive license to foster reproducible research and lower the barrier to entry for data-driven compiler optimization.

Large Language Models (LLMs) have shown remarkable capabilities in solving various programming tasks, such as code generation. However, their potential for code optimization, particularly in performance enhancement, remains largely unexplored. This paper investigates the capabilities of LLMs in optimizing code for minimal execution time, addressing a critical gap in current research. The recently proposed code optimization methods construct program optimization pairs based on iterative submissions from the same programmer for the same problem. However, this approach confines LLMs to local performance improvements, neglecting global algorithmic innovation. To overcome this limitation, we adopt a completely different perspective by reconstructing the optimization pairs into a problem-oriented approach. This allows for the integration of various ideas from multiple programmers tackling the same problem. Furthermore, we observe that code optimization presents greater challenges compared to code generation, often accompanied by "optimization tax". Recognizing the inherent trade-offs in correctness and efficiency, we introduce a novel anchor verification framework to mitigate this "optimization tax". Ultimately, the problem oriented perspective combined with the anchor verification framework significantly enhances both the correct optimization ratio and speedup to new levels.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Autonomous discovery systems couple a resource that answers queries (a simulator, instrument, or analytic model) to an algorithm that selects what to query next. Most software frameworks for this loop inherit the control structure of numerical optimization: campaigns run for a fixed number of iterations, query costs are absent from the programming interface, and decision-making is treated as free. In practice, queries may differ in cost by orders of magnitude, and planners built on large language models or expensive surrogates consume resources of their own. Here we present CADAQUES, an open-source Python framework built on one architectural principle: cost is a first-class primitive of the discovery loop. CADAQUES separates the loop into two structural protocols, an Oracle that answers queries and a Driver that proposes them, and charges both evaluations and decisions against a common vector-valued budget spanning wall time, CPU hours, monetary cost, and language model tokens. An append-only ledger records, for each transaction, the cost declared before execution and the cost settled afterwards, making their discrepancy an observable property of the campaign. We evaluate the architecture by locating the critical temperature of the two-dimensional Ising model from noisy finite-size estimates against the exact thermodynamic-limit reference. In this noisy setting, strategies that concentrate around the best observed result can be misled by noise-induced peaks, whereas a schedule that explores with cheap low-fidelity queries and refines with higher-fidelity ones yields lower and less variable errors than high fidelity throughout, at the studied budget scale. Metering adds tens of microseconds per iteration, three orders of magnitude below the cheapest oracle query. The framework is MIT-licensed and archived at Zenodo (doi:10.5281/zenodo.21293589).

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations, creating a feasibility-correctness gap of up to 90 percentage points on compositional problems. We introduce ReLoop, addressing silent failures from two complementary directions. Structured generation decomposes code production into a four-stage reasoning chain (understand, formalize, synthesize, verify) that mirrors expert modeling practice, with explicit variable-type reasoning and self-verification to prevent formulation errors at their source. Behavioral verification detects errors that survive generation by testing whether the formulation responds correctly to solver-based parameter perturbation, without requiring ground truth -- an external semantic signal that bypasses the self-consistency problem inherent in LLM-based code review. The two mechanisms are complementary: structured generation dominates on complex compositional problems, while behavioral verification becomes the largest single contributor on problems with localized formulation defects. Together with execution recovery via IIS-enhanced diagnostics, ReLoop raises correctness from 22.6% to 31.1% and execution from 72.1% to 100.0% on the strongest model, with consistent gains across five models spanning three paradigms (foundation, SFT, RL) and three benchmarks. We additionally release RetailOpt-190, 190 compositional retail optimization scenarios targeting the multi-constraint interactions where LLMs most frequently fail.

This paper provides a novel approach to reconciling complex low-level memory model features, such as pointer--integer casts, with desired refinements that are needed to justify the correctness of program transformations. The idea is to use a "two-phased" memory model, one with and unbounded memory and corresponding unbounded integer type, and one with a finite memory; the connection between the two levels is made explicit by our notion of refinement that handles out-of-memory behaviors. This approach allows for more optimizations to be performed and establishes a clear boundary between the idealized semantics of a program and the implementation of that program on finite hardware. To demonstrate the utility of this idea in practice, we instantiate the two-phase memory model in the context of Zakowski et al.'s VIR semantics, yielding infinite and finite memory models of LLVM IR, including low-level features like undef and bitcast. Both the infinite and finite models, which act as specifications, can provably be refined to executable reference interpreters. The semantics justify optimizations, such as dead-alloca-elimination, that were previously impossible or difficult to prove correct.

Solving an NP-hard optimization problem often requires reformulating it for a specific solver -- quantum hardware, a commercial optimizer, or a domain heuristic. A tool for polynomial-time reductions between hard problems would let practitioners route any supported problem to any supported solver through a single interface. Building such a library at scale, however, has remained out of reach. We show that harness engineering, the practice of designing constraints, verification systems, and feedback loops that channel AI coding agents, can overcome this barrier. Our harness combines a no-code contribution route for domain experts, a multilayer verification stack ranging from type-level checks to agentic feature tests (AI agents role-playing as end users), and a fully automated implementation-review-integration pipeline. In about three months, we built a command-line tool backed by a library of 100+ problem types and 200+~reduction rules in over 170k lines of Rust. The result suggests that a well-engineered harness lets agents build well-tested software at a scale and pace beyond prior reduction-library efforts. Because the reduction graph composes transitively, a new solver registered for any single problem type instantly becomes available to every problem connected by a reduction path. The source code is available at https://github.com/CodingThrust/problem-reductions.

Reasoning models (e.g., DeepSeek-R1) generate long chains of thought to solve harder problems, but they often loop, repeating the same text at low temperatures or with greedy decoding. We study why this happens and what role temperature plays. With open reasoning models, we find that looping is common at low temperature. Larger models tend to loop less, and distilled students loop significantly even when their teachers rarely do. This points to mismatches between the training distribution and the learned model, which we refer to as errors in learning, as a key cause. To understand how such errors cause loops, we introduce a synthetic graph reasoning task and demonstrate two mechanisms. First, risk aversion caused by hardness of learning: when the correct progress-making action is hard to learn but an easy cyclic action is available, the model puts relatively more probability on the cyclic action and gets stuck. Second, even when there is no hardness, Transformers show an inductive bias toward temporally correlated errors, so the same few actions keep being chosen and loops appear. Higher temperature reduces looping by promoting exploration, but it does not fix the errors in learning, so generations remain much longer than necessary at high temperature; in this sense, temperature is a stopgap rather than a holistic solution. We end with a discussion of training-time interventions aimed at directly reducing errors in learning.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

We reformulate the problem of supervised learning as learning to learn with two nested loops (i.e. learning problems). The inner loop learns on each individual instance with self-supervision before final prediction. The outer loop learns the self-supervised task used by the inner loop, such that its final prediction improves. Our inner loop turns out to be equivalent to linear attention when the inner-loop learner is only a linear model, and to self-attention when it is a kernel estimator. For practical comparison with linear or self-attention layers, we replace each of them in a transformer with an inner loop, so our outer loop is equivalent to training the architecture. When each inner-loop learner is a neural network, our approach vastly outperforms transformers with linear attention on ImageNet from 224 x 224 raw pixels in both accuracy and FLOPs, while (regular) transformers cannot run.

Looped language models repeat a set of transformer layers through depth, reducing memory costs and providing natural early-exit points at loop boundaries. However, looped models do not scale as favorably as standard transformers with unique layers. We compare standard and Mixture-of-Experts (MoE) transformers, with and without looping, and find two main results. First, we find Looped-MoE models scale better than the standard baseline while dense looped models do not. We trace this to routing divergence between loops: in Looped-MoE models, different experts are activated on each pass through the same shared layers, recovering expressivity without additional parameters. Our second finding is that looped models have better compute-quality trade-offs with early exits than standard models. Because each loop ends with the same layers that produce the final output, loop boundaries are superior exit points, as confirmed by earlier output convergence at these points. In sum, we provide a clear direction for scaling looped models: a Looped-MoE model with early exits can not only beat standard transformers at scale, but also enable significant memory and inference savings with minimal degradation in quality.

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components n and the number of epochs K, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number kappa. For SGD with Random Reshuffling, we present lower bounds that have tighter kappa dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of n and kappa and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

Self-evolving agents violate the assumption behind most learning-theoretic guarantees: the data, evaluator, components, and hypothesis space are produced by the policy being updated. We present SEA, an architecture that confines self-modification to a small steering adapter and a versioned harness around a frozen base model and admits each modification only through an anytime-valid gate that emits an auditable certificate against a fixed error budget. Five loop controllers compose published guarantees; because such gates can only select among behaviors the frozen base already produces, five verifier-in-the-loop mechanisms -- best-of-N, micro-step search, self-authored reproduction oracles, search-layer control, and self-repair -- supply the dense, grader-free signal the gates require, computed from the issue text alone. On a 52-instance SWE-bench Verified subset across four base models, base capability is the dominant, confound-free effect, and on two strong base models a deliberate no-op-composite control isolates the suite's contribution at +4 and +5 (Glm~5.2 24to28; Gpt 29to34, the 65% best), with event logs confirming that its mechanisms fire and prevent regressions. Results are single-run on expensive evaluations; confirming run-to-run variance and adapting the per-task algorithm mix are future work.

This paper proposes a neuro-symbolic framework for G-code generation that seeks to integrate the neural generative capabilities of the GLLM method (Abdelaal et al., 2025) with formal verification via a Separation Logic (SL) prover. To establish a reliable physical baseline, the framework extracts deterministic boundary representations from 3D CAD models (STEP files) using the OpenCASCADE framework. This extracted geometric data supports a two-component architecture: the LLM serves as an initial code generator, while the SL Prover, utilizing a Spatial Heap model, evaluates the output. By conceptualizing physical collisions as logical Spatial Data Races -- violations of the separating conjunction in SL -- our framework translates proof failures into structured mathematical feedback. These failures are condensed into bounding boxes that serve as directives for the LLM's iterative self-correction. Ultimately, this work aims to develop a self-correcting system that reduces the need for human supervision, leading to safer and verified autonomous manufacturing.

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this approach has a major flaw: the loops run one after another, causing inference latency and memory requirements to increase with each added loop. This makes them impractical for fast applications. To solve this problem, we introduce the Parallel Loop Transformer (PLT). PLT is a new architecture that delivers the performance benefits of a deep, looped model but with the low latency of a standard, non-looped model. PLT works using two key techniques. First, Cross-Loop Parallelism (CLP) breaks the sequential dependency by computing different loops for different tokens at the same time, all within a single pass. Second, to prevent memory costs from growing, we use an Efficient Representation Enhancement strategy. This method shares the memory (KV cache) from the first loop with all other loops. It then uses a Gated Sliding-Window Attention (G-SWA) to combine this shared global information with local information, maintaining high accuracy. Our experiments show that PLT achieves the high accuracy of a traditional looped model but with almost no extra latency or memory cost compared to a standard transformer.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.

Multi-step enterprise agent tasks fail in a characteristic way: single-pass inference has no checkpoint between deciding an answer and committing to it. We study one production system (Leni) whose architecture installs such checkpoints: verification loops (execute, observe, compare, correct) staffed by lightweight task-specialized post-trained models. We evaluate the unmodified production configuration on three public benchmarks stressing distinct failure modes: SpreadsheetBench Verified (silent computation error), BullshitBench v2 (premise confabulation), and the GAIA validation split (cascade error over long tool chains). The full system improves over its frontier base model by +11.0 percentage points on SpreadsheetBench (91.25% vs 80.25%, n=400, p<0.001), +7 to +10 percentage points on BullshitBench (98% vs 91%, n=100), and roughly +15 points on GAIA validation (75.2% pass@1, n=165; 83.0% best-of-k). Our central contribution is a decomposition of that uplift: most of it comes from scaffolding, routing, and specialist models rather than from the verification step itself, whose isolated contribution is small (+1.5 points) but concentrated at the top of the score distribution, where it converts otherwise-failing tasks. We instrument the loop end-to-end, yielding an empirical verifier confusion matrix (catch rate about 0.20, fix rate 0.75, no false-alarm regressions) that grounds a compounding-reliability model. Specialist-swap ablations suggest that the loop's value depends on who observes it: replacing the small trained verifier with the generating frontier model eliminates most rescues. A valid-premise control shows zero over-rejections in 100 expert-level questions.

Looped Transformers have drawn growing attention because looping improves multi-step reasoning and increases the executed depth of a model without adding parameters. They achieve this by reusing a stack of L layers for N loops. However, increasing the loop count N not only destabilizes training but also shifts the best hyperparameters, so they must be searched again for every loop count. Inspired by Depth-μP (Yang et al., 2024), which multiplies each residual branch by L^{-1/2} for depth L so that a learning rate tuned on a shallow untied network transfers to a deep one, we study how the residual branches and the learning rate should scale with the loop count N. We find that loops cannot simply be treated as extra depth, because the loops share weights. At initialization, distinct layers add nearly uncorrelated increments to the residual stream, so their sum grows as L, whereas a shared layer adds positively correlated increments at every loop, so their sum grows linearly in N. For a single layer looped N times, we show in the infinite-width limit that multiplying the residual branch by 1/N and keeping the learning rate independent of N is the only parameterization with both a stable forward pass and maximal residual-stream updates. We then generalize the analysis to a stack of L distinct layers looped N times to obtain a parameterization we call Loop-μP, in which the loop factor 1/N combines with the depth factor L^{-1/2}. Empirically, we find in language modeling that the base learning rate tuned on the smallest model stays best under Loop-μP for loop counts up to 8 and executed depths up to 384 layers. These results make Loop-μP a practical recipe for scaling looped Transformers.

A sequence of operators T_n from a Hilbert space {mathfrak H} to Hilbert spaces {mathfrak K}_n which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from {mathfrak H} to a Hilbert space {mathfrak K}. Moreover, the closability or closedness of T_n is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as ``the simple method'') optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi--Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. To outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Incorporating prior knowledge or specifications of input-output relationships into machine learning models has attracted significant attention, as it enhances generalization from limited data and yields conforming outputs. However, most existing approaches use soft constraints by penalizing violations through regularization, which offers no guarantee of constraint satisfaction, especially on inputs far from the training distribution--an essential requirement in safety-critical applications. On the other hand, imposing hard constraints on neural networks may hinder their representational power, adversely affecting performance. To address this, we propose HardNet, a practical framework for constructing neural networks that inherently satisfy hard constraints without sacrificing model capacity. Unlike approaches that modify outputs only at inference time, HardNet enables end-to-end training with hard constraint guarantees, leading to improved performance. To the best of our knowledge, HardNet is the first method that enables efficient and differentiable enforcement of more than one input-dependent inequality constraint. It allows unconstrained optimization of the network parameters using standard algorithms by appending a differentiable closed-form enforcement layer to the network's output. Furthermore, we show that HardNet retains neural networks' universal approximation capabilities. We demonstrate its versatility and effectiveness across various applications: learning with piecewise constraints, learning optimization solvers with guaranteed feasibility, and optimizing control policies in safety-critical systems.

In this paper, we study the Hard Core (HC) model with a countable set mathbb Z of spin values on a Cayley tree of order k=2. This model is defined by a countable set of parameters (that is, the activity function λ_i>0, iin mathbb Z). A functional equation is obtained that provides the consistency condition for finite-dimensional Gibbs distributions. Analyzing this equation, the following results are obtained: Let kgeq 2 and Λ=sum_iλ_i. For Λ=+infty there is no translation-invariant Gibbs measure (TIGM); Let k=2 and Λ<+infty. For the model under constraint such that at G-admissible graph the loops are imposed at two vertices of the graph, the uniqueness of TIGM is proved; Let k=2 and Λ<+infty. For the model under constraint such that at G-admissible graph the loops are imposed at three vertices of the graph, the uniqueness and non-uniqueness conditions of TIGMs are found.

We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly pm 1, and the resulting models are typically equivalent to networks whose nonzero weights are also pm 1. The method replaces loss minimization with a nonconvex constraint formulation. Each node implements a Boolean threshold function (BTF), and training is expressed through a divide-and-concur decomposition into two complementary constraints: one enforces local BTF consistency between inputs, weights, and output; the other imposes architectural concurrence, equating neuron outputs with downstream inputs and enforcing weight equality across training-data instantiations of the network. The reflect-reflect-relax (RRR) projection algorithm is used to reconcile these constraints. Each BTF constraint includes a lower bound on the margin. When this bound is sufficiently large, the learned representations are provably sparse and equivalent to networks composed of simple logical gates with pm 1 weights. Across a range of tasks -- including multiplier-circuit discovery, binary autoencoding, logic-network inference, and cellular automata learning -- the method achieves exact solutions or strong generalization in regimes where standard gradient-based methods struggle. These results demonstrate that projection-based constraint satisfaction provides a viable and conceptually distinct foundation for learning in discrete neural systems, with implications for interpretability and efficient inference.

Looped language models (LoopLMs) improve parameter efficiency by recursively reusing Transformer blocks, enabling deeper computation under a fixed model size. However, this reuse makes LoopLMs more fragile under post-training quantization (PTQ). We present the first systematic study of quantization in LoopLMs and identify three challenges: distribution shift across roles, state reuse across loop transitions, and recursive error accumulation. To address these challenges, we propose LoopQ, a loop-aware PTQ framework that preserves a shared quantized backbone while introducing lightweight adaptations. LoopQ combines activation scaling, selective transformation, cross-loop state alignment, and trajectory-aware optimization to reduce distributional mismatch within loops and error accumulation across loops. Experiments across seven benchmarks show that, under W4A4 quantization, LoopQ improves average downstream accuracy by 68.8% and reduces average perplexity by 87.7% compared with the strongest static PTQ baseline.

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability and continuity to higher-order functions, so that we can formulate novel convergence criteria for regression, derived from the convergence of global optimisation. All the theory and the motivating examples are fully formalised in the proof assistant Agda.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

Turning a frontier vision-language model into a robot policy usually means fine-tuning it to emit an action representation it never saw in pretraining, which throws away much of the reasoning that made the model worth reaching for. We go the other way and keep the VLM frozen. It writes the policy as a short Python control function, with no demonstrations and no fine-tuning. Writing that code once is open-loop, though. Existing closed-loop methods react at the wrong level: they retry a fixed policy or pick a different subtask, but never rewrite the code that failed. VLCP closes the loop where the failure actually lives, on the control code, within a single episode. Every K steps the VLM re-observes the scene from multi-view RGB, proprioceptive state, and a state delta, then rewrites the control function from what it just saw, so a failure is caught before it compounds. We evaluate on a 57-task MuJoCo/RoboVerse sweep. This training-free policy reaches 35.1% pooled success, against 3.5% for the identical system queried once per episode. That tenfold gap holds with non-overlapping confidence intervals in every scene family. The gain traces to a 27.3% within-episode recovery rate on failed grasps: a miss an open-loop controller would carry to the end of the episode gets re-observed and fixed at the next replan. And the loop stays cheap. A median 84% of input tokens hit cache, an episode needs only about 10 compact queries, and control blocks written during any replan persist to a cross-episode skill library reused in later prompts.

Knowledge graph engineering often distributes accepted state, observations, constraints, processes, and hypothetical scenarios across artifacts whose combined execution contract remains external. We present PULSE, an Object-Process-Methodology-inspired language that localizes four operational roles and their write effects in one typed runtime. Here, modes denote operational roles rather than modal or deontic logic. The implemented contract fixes evidence non-overwrite, branch isolation, grounded multi-subject timers, guarded state change, and declaration-ranked event ordering over time and space; an external runner still decides whether evidence becomes an authoritative move. GeoSPARQL, SOSA, and SHACL remain generated views. A core calculus gives an effect-confinement lemma and six safety properties. Lean 4 checks kernel analogues for positions, evidence, clocks, monitors, atomicity, and branch source retention; 88 tests, 3,534 bounded checks, and 32 Lean/Python runtime-kernel cases bound the implementation claim to the checked cases. First-author implementations of a standards composition and a separate Sismic statechart reproduce the tested cold-chain trace. Across 37,440 generated temporal traces, PULSE matches a separate workflow and distinguishes ten single-field mutants. On the complete NOAA IBTrACS since1980 subset it agrees with GEOS and an event sweep on 1,476,290 transition-zone pairs, including 4,800 sampled and 12,831 duration-qualified events. Project-specific GeoSPARQL probes measure interface coverage. Overall, the results support contract localization, safety arguments, and trace parity for the tested fragment; language superiority and usability remain outside the evaluation.

We present egglog, a fixpoint reasoning system that unifies Datalog and equality saturation (EqSat). Like Datalog, it supports efficient incremental execution, cooperating analyses, and lattice-based reasoning. Like EqSat, it supports term rewriting, efficient congruence closure, and extraction of optimized terms. We identify two recent applications--a unification-based pointer analysis in Datalog and an EqSat-based floating-point term rewriter--that have been hampered by features missing from Datalog but found in EqSat or vice-versa. We evaluate egglog by reimplementing those projects in egglog. The resulting systems in egglog are faster, simpler, and fix bugs found in the original systems.

We present an algorithmic framework for incremental maintenance of first sheaf cohomology H^1(X; F) on dynamically evolving 1-dimensional cellular complexes equipped with finite-dimensional cellular sheaves. The classical computation of H^1 via factorization of the coboundary matrix requires O(n^3) time; when the complex evolves with a stream of m edits, full recomputation after each edit costs O(mn^3). Under a bounded local geometry assumption -- bounded cell size v_{max}, bounded stalk dimension d, and bounded nerve degree D -- each edit (vertex insertion, edge insertion, restriction map update) affects only a bounded set of local coboundary blocks. The algorithm therefore processes lazy streaming edits in O(1) time with respect to the total complex size n (with cost polynomial in the local geometry parameters v_{max}, d, and D, which are treated as constants independent of n), deferring local eigensolves and Mayer-Vietoris global assembly to synchronization points (Flush). At synchronization, the maintained state agrees with the corresponding batch assembly of the partitioned sheaf model; we observe zero measured drift in all batch-verified runs (through V = 10^6). We also give an amortized O(|E|) streaming construction for the cellular decomposition and discuss an adversarial algebraic-RAM barrier arguing that unpartitioned non-trivial sheaves (d geq 2, non-identity restriction maps) do not admit the same locality. Experiments on Barabasi-Albert graphs with up to 5 times 10^6 vertices and 1.7 times 10^7 streaming edits show 35 μs median lazy per-edit update latency (excluding flush); query time (global assembly at synchronization) is O(n) per flush in the implemented full-traversal path. Exact synchronization costs are reported separately.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.