Daily Papers

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-1/2 and spin-1 chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as ν= 0.60 pm 0.02, distinct from the Gaussian value 0.5 but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent z=1.986 pm 0.005. The result z < 2 is incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.

Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.

A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap.

We study the scalar curvature of the Fisher information metric on the microscopic coupling-parameter manifold of lattice spin models at criticality. For a d-dimensional lattice with periodic boundary conditions and n = L^d sites, the Fisher manifold has m = d cdot n dimensions (one per bond), and we find |R(J_c)| sim n^{d_R} with d_R = (dν+ 2η)/(dν+ η), where ν and η are the correlation-length and anomalous-dimension critical exponents. For 2D Ising (ν= 1, η= 1/4), this predicts d_R = 10/9, confirmed by exact transfer-matrix computations (L = 6--9: d_R = 1.1115 pm 0.0002) and multi-seed MCMC through L = 24. For 3D Ising (ν= 0.630, η= 0.0363), the prediction d_R = 1.019 is consistent with MCMC on L^3 tori up to L = 10 (power-law fit: d_R = 1.040). For 2D Potts q = 3 (predicted 33/29 approx 1.138), FFT-MCMC through L = 40 shows d_eff oscillating non-monotonically around sim 1.20, consistent with O(1/(ln L)^2) logarithmic corrections. For q = 4 (predicted 22/19), effective exponents oscillate with strong logarithmic corrections. The Ricci decomposition identity R_3 = -R_1/2, R_4 = -R_2/2 holds to 5--6 digits for all models. This exponent is distinct from Ruppeiner thermodynamic curvature and reflects the collective geometry of the growing Fisher manifold. We provide falsification criteria and predictions for additional universality classes.

Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments. This approach can efficiently solve certain quantum problems that are classically intractable, suggesting potential advantages of harnessing quantum data. However, addressing large-scale problems still requires significant amounts of data beyond the limited computational resources of near-term quantum devices. We propose a scalable ML framework called Geometrically Local Quantum Kernel (GLQK), designed to efficiently learn quantum many-body experimental data by leveraging the exponential decay of correlations, a phenomenon prevalent in noncritical systems. In the task of learning an unknown polynomial of quantum expectation values, we rigorously prove that GLQK substantially improves polynomial sample complexity in the number of qubits n, compared to the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, GLQK achieves constant sample complexity, independent of n. We numerically demonstrate its high scalability in two learning tasks on quantum many-body phenomena. These results establish new avenues for utilizing experimental data to advance the understanding of quantum many-body physics.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

In the age of misinformation, hallucination -- the tendency of Large Language Models (LLMs) to generate non-factual or unfaithful responses -- represents the main risk for their global utility. Despite LLMs becoming increasingly multilingual, the vast majority of research on detecting and quantifying LLM hallucination are (a) English-centric and (b) focus on machine translation (MT) and summarization, tasks that are less common ``in the wild'' than open information seeking. In contrast, we aim to quantify the extent of LLM hallucination across languages in knowledge-intensive long-form question answering. To this end, we train a multilingual hallucination detection model and conduct a large-scale study across 30 languages and 6 open-source LLM families. We start from an English hallucination detection dataset and rely on MT to generate (noisy) training data in other languages. We also manually annotate gold data for five high-resource languages; we then demonstrate, for these languages, that the estimates of hallucination rates are similar between silver (LLM-generated) and gold test sets, validating the use of silver data for estimating hallucination rates for other languages. For the final rates estimation, we build a knowledge-intensive QA dataset for 30 languages with LLM-generated prompts and Wikipedia articles as references. We find that, while LLMs generate longer responses with more hallucinated tokens for higher-resource languages, there is no correlation between length-normalized hallucination rates of languages and their digital representation. Further, we find that smaller LLMs exhibit larger hallucination rates than larger models.

Evaluating the writing capabilities of large language models (LLMs) remains a significant challenge due to the multidimensional nature of writing skills and the limitations of existing metrics. LLM's performance in thousand-words level and open-ended writing is inadequately assessed by traditional reference-based metrics or modern LLM-as-a-judge methods. We propose Tree-of-Writing (ToW), to resolve the implicit inconsistency often found when LLM-as-a-judge aggregates all sub-features in text evaluation. ToW incorporates a tree-structured workflow by explicitly modeling the aggregation weights of sub-features. We also present HowToBench, a large-scale Chinese writing benchmark encompassing 12 genres and 1302 instructions across three task categories: contextual completion, outline-guided writing, and open-ended generation. ToW successfully mitigates the biases, achieving a 0.93 Pearson correlation with human judgments. Furthermore, we detect that both overlap-based text generation metrics and popular LLM-as-a-judge practices are vulnerable to textual disturbances, while ToW is robust to them. We also uncover a negative correlation between input length and content-related scores in the Guide task, showcasing that it cannot be simply improved by input-side information piling.

Direct Preference Optimization (DPO) is widely utilized in the Reinforcement Learning from Human Feedback (RLHF) phase to align Large Language Models (LLMs) with human preferences, thereby enhancing both their harmlessness and efficacy. However, it has been observed that DPO tends to over-optimize for verbosity, which can detrimentally affect both performance and user experience. In this paper, we conduct an in-depth theoretical analysis of DPO's optimization objective and reveal a strong correlation between its implicit reward and data length. This correlation misguides the optimization direction, resulting in length sensitivity during the DPO training and leading to verbosity. To address this issue, we propose a length-desensitization improvement method for DPO, termed LD-DPO. The proposed method aims to desensitize DPO to data length by decoupling explicit length preference, which is relatively insignificant, from the other implicit preferences, thereby enabling more effective learning of the intrinsic preferences. We utilized two settings (Base and Instruct) of Llama2-13B, Llama3-8B, and Qwen2-7B for experimental validation on various benchmarks including MT-Bench and AlpacaEval 2. The experimental results indicate that LD-DPO consistently outperforms DPO and other baseline methods, achieving more concise responses with a 10-40% reduction in length compared to DPO. We conducted in-depth experimental analyses to demonstrate that LD-DPO can indeed achieve length desensitization and align the model more closely with human-like preferences.

Speculative decoding accelerates language-model inference by drafting future tokens the target model verifies in parallel. A diffusion-style drafter such as DFlash drafts an entire block in one forward pass. It is trained on the per-position marginals rather than on the joint distribution over the block, so the tokens it emits are individually plausible yet jointly incoherent. We introduce LiLiCorr, a Lightweight Likelihood-based model that Correlates the per-position marginals such a drafter produces. It keeps the top-K tokens at each position and processes them jointly, emitting an in and an out vector for each. Two candidates at consecutive positions match when the earlier out vector aligns, in cosine similarity, with the later in vector. Training scores the correct pairings highest and pushes competing ones down, so coherent blocks outscore incoherent ones. The joint distribution over the block, exponential in its length, is never materialized. One lightweight network pass produces all the vectors, the pairwise scores follow as batched matrix operations, leaving only a cheap greedy walk sequential. We co-train the DFlash drafter with LiLiCorr, so it proposes candidates that correlate into longer accepted sequences. Over the vanilla DFlash drafter it builds on, LiLiCorr accepts more and serves faster at all 72 settings we test: nine benchmarks at two target sizes under greedy and temperature-one decoding, plus a throughput sweep over six concurrencies, two input lengths and three output-entropy tiers. It raises acceptance length by 7 to 19%, while its single-pass scoring head costs only about 3% of the per-block latency. Against three concurrently developed methods that also restore coherence at draft time, all equally optimized on a common stack, LiLiCorr holds the highest throughput in 63 of those settings, ties within a measured noise floor in 6, and trails in only 3.

In recent years, medical information technology has made it possible for electronic health record (EHR) to store fairly complete clinical data. This has brought health care into the era of "big data". However, medical data are often sparse and strongly correlated, which means that medical problems cannot be solved effectively. With the rapid development of deep learning in recent years, it has provided opportunities for the use of big data in healthcare. In this paper, we propose a temporal-saptial correlation attention network (TSCAN) to handle some clinical characteristic prediction problems, such as predicting death, predicting length of stay, detecting physiologic decline, and classifying phenotypes. Based on the design of the attention mechanism model, our approach can effectively remove irrelevant items in clinical data and irrelevant nodes in time according to different tasks, so as to obtain more accurate prediction results. Our method can also find key clinical indicators of important outcomes that can be used to improve treatment options. Our experiments use information from the Medical Information Mart for Intensive Care (MIMIC-IV) database, which is open to the public. Finally, we have achieved significant performance benefits of 2.0\% (metric) compared to other SOTA prediction methods. We achieved a staggering 90.7\% on mortality rate, 45.1\% on length of stay. The source code can be find: https://github.com/yuyuheintju/TSCAN.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Recent works have demonstrated great success in pre-training large-scale autoregressive language models on massive GPUs. To reduce the wall-clock training time, a common practice is to increase the batch size and learning rate. However, such practice is often brittle and leads to a so-called stability-efficiency dilemma: increasing the batch sizes and learning rates leads to better training efficiency but can also result in training instability, leading to poor generalization accuracy or failed runs. To better understand this phenomenon, we conduct an in-depth analysis on large-scale pre-training experiments replicating the GPT-2 model. We find that there is a strong correlation between training instability and extreme values of gradient variance, and that samples with long sequence lengths contribute to these extreme gradient variance values, especially at the beginning of the training, indicating that long sequence length can be a main source of training instability. Based on the analysis, we present a Sequence Length Warmup method that aims to solve the training stability-efficiency dilemma. Experiments replicating GPT-2 models show that our approach enables stable training with 8x larger batch size and 4x larger learning rate, whereas the baseline approach struggles with training instability. To achieve the same or better zero-shot evaluation results, our method reduces the required number of training tokens and wall clock time by up to 2.2x and 3.7x, respectively. Experiments replicating GPT-3 model (125M) show that our approach enables stable training with 8x larger batch size and 40x larger learning rate, and retains 99% of the zero-shot accuracy on 11 tasks using 10x less data and 17x less time compared to the original GPT-3 training recipe, while the baseline diverges under the same settings and only retain 95% of accuracy under lower learning rate.

LLM-based auto-annotators have become a key component of the LLM development process due to their cost-effectiveness and scalability compared to human-based evaluation. However, these auto-annotators can introduce complex biases that are hard to remove. Even simple, known confounders such as preference for longer outputs remain in existing automated evaluation metrics. We propose a simple regression analysis approach for controlling biases in auto-evaluations. As a real case study, we focus on reducing the length bias of AlpacaEval, a fast and affordable benchmark for chat LLMs that uses LLMs to estimate response quality. Despite being highly correlated with human preferences, AlpacaEval is known to favor models that generate longer outputs. We introduce a length-controlled AlpacaEval that aims to answer the counterfactual question: "What would the preference be if the model's and baseline's output had the same length?". To achieve this, we first fit a generalized linear model to predict the biased output of interest (auto-annotator preferences) based on the mediators we want to control for (length difference) and other relevant features. We then obtain length-controlled preferences by predicting preferences while conditioning the GLM with a zero difference in lengths. Length-controlling not only improves the robustness of the metric to manipulations in model verbosity, we also find that it increases the Spearman correlation with LMSYS' Chatbot Arena from 0.94 to 0.98. We release the code and leaderboard at https://tatsu-lab.github.io/alpaca_eval/ .

Relativistic jets from active galactic nuclei are expected to exhibit strong redshift evolution in their radiative output due to the increasing energy density of the cosmic microwave background (CMB). We investigate the role of inverse Compton (IC) scattering of CMB photons in regulating the radio and X-ray emission from large-scale jets using three-dimensional relativistic magnetohydrodynamic simulations coupled with a hybrid Eulerian-Lagrangian particle framework. By keeping the jet dynamics and ambient medium properties fixed across redshifts, we are able to isolate the impact of the cosmological evolution of the CMB on the jet radiation. From our simulations, we construct synthetic spectral energy distributions and intensity maps considering synchrotron and IC/CMB losses along with particle acceleration from shocks. We are able to reproduce the weak redshift dependence of radio luminosity and the strong enhancement of X-ray emission toward high redshift that is observed in radio-loud quasars. At high redshift, the X-ray luminosity follows the expected (1+z)^4 scaling, confirming IC/CMB as the dominant mechanism driving the X-ray enhancement. The resulting X-ray-to-radio flux ratio increases systematically with redshift and is consistent with observational constraints. Finally, we show that slower jets exhibit a stronger redshift evolution of the X-ray enhancement than faster jets, highlighting the critical role of jet propagation length scales and particle energy evolution. The simulations also naturally reproduce the steepening of the radio spectral index with redshift - the α-z relation - thus providing a unified framework that allows to interpret the multiwavelength properties of high-redshift radio sources.

Counting repetitive actions are widely seen in human activities such as physical exercise. Existing methods focus on performing repetitive action counting in short videos, which is tough for dealing with longer videos in more realistic scenarios. In the data-driven era, the degradation of such generalization capability is mainly attributed to the lack of long video datasets. To complement this margin, we introduce a new large-scale repetitive action counting dataset covering a wide variety of video lengths, along with more realistic situations where action interruption or action inconsistencies occur in the video. Besides, we also provide a fine-grained annotation of the action cycles instead of just counting annotation along with a numerical value. Such a dataset contains 1,451 videos with about 20,000 annotations, which is more challenging. For repetitive action counting towards more realistic scenarios, we further propose encoding multi-scale temporal correlation with transformers that can take into account both performance and efficiency. Furthermore, with the help of fine-grained annotation of action cycles, we propose a density map regression-based method to predict the action period, which yields better performance with sufficient interpretability. Our proposed method outperforms state-of-the-art methods on all datasets and also achieves better performance on the unseen dataset without fine-tuning. The dataset and code are available.

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales, however spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work we have developed an unsupervised deep learning (DL) framework for automated classification and interpretation of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system behavior. We demonstrate how this method can be used to rapidly explore large datasets to identify samples of interest, and we apply this approach to directly correlate bulk properties of a model system to microscopic dynamics. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

The global topology of the Universe is a longstanding open question. In this work, we examine the statistical signatures of a positively curved universe with a Friedmann--Lemaitre--Robertson--Walker metric and the topology of a lens space L(p,q). Since these manifolds are generally statistically anisotropic and inhomogeneous, their cosmic microwave background (CMB) covariance matrices contain non-zero off-diagonal entries that depend on observer location. We compute these full harmonic-space covariance matrices for scalar perturbations for arbitrary lens spaces and observer position. Using the Kullback--Leibler divergence, we assess the distinguishability of these spaces from a simply connected three-sphere with the same curvature. The results show that topological signatures can still be significant in a cosmic-variance-limited regime even when the length, d_{rm NC}, of the shortest loop around the Universe through the observer exceeds the diameter, d_{rm LSS}, of the last-scattering surface by up to 10%. This distinguishability depends on the curvature, the lens space and the observer position mainly through the ratio d_{rm NC}/d_{rm LSS}, which is set not only by the curvature radius but also by p, q and the observer location. Therefore, for any value of the spatial curvature, however small, there are lens spaces and observer positions for which 0.985,d_{rm LSS}<d_{rm NC}<1.1,d_{rm LSS}. Such observers would find no matched circles in the CMB large enough to have been detected to date, yet the topology would remain potentially discoverable through its statistical signatures.

Length extrapolation algorithms based on Rotary position embedding (RoPE) have shown promising results in extending the context length of language models. However, understanding how position embedding can capture longer-range contextual information remains elusive. Based on the intuition that different dimensions correspond to different frequency of changes in RoPE encoding, we conducted a dimension-level analysis to investigate the correlation between a hidden dimension of an attention head and its contribution to capturing long-distance dependencies. Using our correlation metric, we identified a particular type of attention heads, which we named Positional Heads, from various length-extrapolated models. These heads exhibit a strong focus on long-range information interaction and play a pivotal role in long input processing, as evidence by our ablation. We further demonstrate the correlation between the efficiency of length extrapolation and the extension of the high-dimensional attention allocation of these heads. The identification of Positional Heads provides insights for future research in long-text comprehension.

Large Reasoning Models (LRMs) achieve remarkable inference-time improvements through parallel thinking. However, existing methods rely on redundant sampling of reasoning trajectories, failing to effectively explore the reasoning space to uncover high-quality solutions. To address these limitations, we propose Decoding Tree Sketching (DTS), a plug-and-play decoding framework for structural multi-trajectory exploration and reasoning selection. For reasoning exploration, DTS sketches a backbone tree of the reasoning space by selectively branching at decision tokens. For reasoning selection, guided by length-accuracy anti-correlation, DTS designs an early termination to prioritize short and reliable trajectories during decoding. Experimental results across four LRMs and datasets demonstrate that DTS significantly enhances accuracy by 14% and reduces repetitive generation by 8% on average. Notably, DTS enables smaller models to outperform larger models with 10times the size, highlighting its potential to strengthen reasoning capabilities.

As large language models (LLMs) are increasingly deployed for systems programming, their ability to generate secure C++ code, where a single memory-safety failure creates an exploitable vulnerability, remains a critical concern. Yet most security evaluations of AI-generated code rely on static analysis alone, which flags warnings without confirming run- time violations or reasoning about untested paths. This study investigates whether AI-generated C++ is measurably less safe than human-written code, and whether common verification tools agree on the risk. We introduce VULBENCH-CPP, a benchmark of 8,918 C++ programs from three open-weight LLMs (Gemma 3 27B IT, LLaMA 3.3 70B Instruct, Qwen 2.5 Coder 32B Instruct) and human authors across 851 competitive-programming tasks. Each program is annotated by four verification tiers: functional testing, static analysis (cppcheck, clang-tidy), dynamic analysis (ASan/UBSan), and bounded model checking (ESBMC). Account- ing for the correlation among solutions to a shared task, we find that AI-generated code is roughly twice as likely as human code to trigger a confirmed runtime violation, even after controlling for code length and test pass-rate. Under static analysis the two look equally safe, but this is misleading: the apparent similarity reflects code length rather than real safety, and the tiers detect largely different classes of violation, demonstrating that no single tier is sufficient. These vulnerability patterns remain consistent across independent generations. We release the benchmark, harness, and annotated results.

Large Audio-Language Models (LALMs) have demonstrated remarkable performance in tasks involving audio perception and understanding, such as speech recognition and audio captioning. However, their reasoning capabilities - critical for solving complex real-world problems - remain underexplored. In this work, we conduct the first exploration into integrating Chain-of-Thought (CoT) reasoning into LALMs to enhance their reasoning ability across auditory modalities. We evaluate representative CoT methods, analyzing their performance in both information extraction and reasoning tasks across sound, music, and speech domains. Our findings reveal that CoT methods significantly improve performance on easy and medium tasks but encounter challenges with hard tasks, where reasoning chains can confuse the model rather than improve accuracy. Additionally, we identify a positive correlation between reasoning path length and accuracy, demonstrating the potential of scaling inference for advanced instruction-following and reasoning. This study not only highlights the promise of CoT in enhancing LALM reasoning capabilities but also identifies key limitations and provides actionable directions for future research.

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

Large Reasoning Models (LRMs) have achieved impressive performance on complex reasoning tasks by generating detailed chain-of-thought (CoT) explanations. However, these responses are often excessively long, containing redundant reasoning steps that inflate inference cost and reduce usability. Controlling the length of generated reasoning without sacrificing accuracy remains an open challenge. Through a systematic empirical analysis, we reveal a consistent positive correlation between model entropy and response length at different reasoning stages across diverse LRMs: the thinking phase exhibits higher entropy, reflecting exploratory behavior of longer responses, while the final answer phase shows lower entropy, indicating a more deterministic solution. This observation suggests that entropy at different reasoning stages can serve as a control knob for balancing conciseness and performance. Based on this insight, this paper introduces Phase Entropy Aware Reward (PEAR), a reward mechanism that incorporating phase-dependent entropy into the reward design. Instead of treating all tokens uniformly, PEAR penalize excessive entropy during the thinking phase and allowing moderate exploration at the final answer phase, which encourages models to generate concise reasoning traces that retain sufficient flexibility to solve the task correctly. This enables adaptive control of response length without relying on explicit length targets or rigid truncation rules. Extensive experiments across four benchmarks demonstrate that PEAR consistently reduces response length while sustaining competitive accuracy across model scales. In addition, PEAR demonstrates strong out-of-distribution (OOD) robustness beyond the training distribution. Our code is available at: https://github.com/iNLP-Lab/PEAR.

Context. Extreme-ultraviolet (EUV) observations have revealed small-scale transient brightenings that may share common physical mechanisms with larger-scale solar flares. A notable feature of solar and stellar flares is the presence of quasi-periodic pulsations (QPPs), which are considered a common and potentially intrinsic characteristic. Aims. We investigate the properties of QPPs detected in EUV brightenings, which are considered small-scale flares, and compare their statistical properties with those observed in solar and stellar flares. Methods. We extracted integrated light curves of 22,623 EUV brightenings in two quiet Sun regions observed by the Solar Orbiter/Extreme Ultraviolet Imager and identified QPPs in their light curves using Fourier analysis. Results. Approximately 2.7 % of the EUV brightenings exhibited stationary QPPs. The QPP occurrence rate increased with the surface area, lifetime, and peak brightness of the EUV brightenings. The detected QPP periods ranged from approximately 15 to 260 seconds, which is comparable to the periods observed in solar and stellar flares. Consistent with observations of QPPs in solar and stellar flares, no correlation was found between the QPP period and peak brightness. However, unlike the trend observed in solar flares, no correlation was found between the QPP period and lifetime/length scale. Conclusions. The presence of QPPs in EUV brightenings supports the interpretation that these events may be small-scale manifestations of flares, and the absence of period scaling with loop length further suggests that standing waves may not be the primary driver of QPPs in these events.

Modern large language models are pretrained on massive datasets, making it difficult to prevent benchmark data from entering their training sets and undermining the reliability of evaluation results. Reliable evaluation is particularly challenging for base models, whose limited instruction-following ability complicates task-based assessment. We introduce Uncheatable Eval, a dynamic benchmark that regularly collects newly published text to evaluate base language models and reduce the risk of data contamination. Drawing on the relationship between a model's predictive ability and its ability to compress data losslessly, we use compression rate to evaluate how well models predict new text. We evaluate 80 models across 14 text categories, study how compression changes with context length, and examine the correlation between compression rate and zero-shot MMLU accuracy. Our results yield three main findings: (1) compression performance follows a consistent scaling trend with model size; (2) attention-based, hybrid, and recurrent models differ in how their compression performance changes as more context becomes available; and (3) lower compression rates are strongly associated with higher zero-shot MMLU accuracy. Code is available at https://github.com/Jellyfish042/uncheatable_eval.

Large Language Models (LLMs) are increasingly relied upon for solving complex reasoning tasks in domains such as mathematics, logic, and multi-step question answering. A growing line of work seeks to improve reasoning quality by scaling inference time compute particularly through Process Reward Models (PRMs), used to reward the reasoning at intermediate steps. While effective, these methods introduce substantial computational overhead, especially when generating large numbers of solutions in parallel. In this paper, we investigate whether PRMs can be used mid-generation to provide early signals that enable the rejection of suboptimal candidates before full generation of step is complete. We introduce the hypothesis that PRMs are also Partial Reward Models, meaning that the scores they assign to partially completed reasoning step are predictive of final output quality. This allows for principled early rejection based on intermediate token-level signals. We support this hypothesis both theoretically, by proving that the risk of discarding optimal beams decreases exponentially with generation length and empirically, by demonstrating a strong correlation between partial and final rewards across multiple reward models. On math reasoning benchmarks, our method achieves up to 1.4times-9times reduction in inference FLOPs without degrading final performance. These results suggest that early rejection is a powerful mechanism for improving the compute-efficiency of reasoning in LLMs.

In this work we update the L-Galaxies semi-analytic model (SAM) to better follow the physical processes responsible for the growth of bulges via disc instabilities (leading to pseudo-bulges) and mergers (leading to classical bulges). We address the former by considering the contribution of both stellar and gaseous discs in the stability of the galaxy, and we update the latter by including dissipation of energy in gas-rich mergers. Furthermore, we introduce angular momentum losses during cooling and find that an accurate match to the observed correlation between stellar disc scale length and mass at z ~ 0.0 requires that the gas loses 20% of its initial specific angular momentum to the corresponding dark matter halo during the formation of the cold gas disc. We reproduce the observed trends between the stellar mass and specific angular momentum for both disc- and bulge-dominated galaxies, with the former rotating faster than the latter of the same mass. We conclude that a two-component instability recipe provides a morphologically diverse galaxy sample which matches the observed fractional breakdown of galaxies into different morphological types. This recipe also enables us to obtain an excellent fit to the morphology-mass relation and stellar mass function of different galactic types. Finally, we find that energy dissipation during mergers reduces the merger remnant sizes and allows us to match the observed mass-size relation for bulge-dominated systems.

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent β; communication is captured by a message-length fidelity curve γ(m); dependence is captured by an effective shared-error correlation ρ; and a context window W imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep b-ary trees with correlated inputs and lossy communication: a single scalar α_ρ (combining γ(m), ρ, and fan-in b) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent s and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when s>β, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

WALL-WM is a World Action Model that shifts video-action learning from chunk-centric optimization to event-grounded Vision-Language-Action pretraining, using semantically coherent action events as the atomic unit of learning. Existing WAMs commonly initialize from multimodal or video foundation models and then optimize fixed-length action chunks conditioned directly on the current observation and instruction. Although convenient, this chunk-centric formulation creates a fundamental granularity mismatch. Language describes semantic goals and events, vision evolves through continuous scene dynamics, and actions operate at control-level timescales; forcing all three into the same fixed-length prediction window turns VLA training into short-horizon correlation fitting. WALL-WM addresses this mismatch by organizing both supervision and data around semantic events. Specifically, it pairs event-grounded VLA pretraining with a data ecosystem built from event-level captions and cluster-balanced sampling, enabling scalable learning over diverse behaviors, scenes, and task structures. From the same event-pretrained backbone, WALL-WM supports two complementary inference modes. The event mode consumes next-event descriptions and enables variable-length execution chunks, while the unified mode uses a VLM with Staircase Decoding to condition conventional fixed-length chunk inference while preserving a gradient-continuous VLA path. Together with Muon-optimizer-based large-scale pretraining infrastructure, WALL-WM provides a practical scale-up recipe for general-purpose WAMs. Experiments show that WALL-WM generalizes broadly across language, scenes, and tasks, achieving state-of-the-art performance in large-scale real-world generalization evaluation.

Best-of-N inference scaling (drawing N candidate answers from a language model and returning the one a reward model ranks highest) improves accuracy by an amount that varies across models, but predicting that amount in advance currently requires running the procedure end-to-end. Prior work links cheap statistics of a model's sampled outputs and validation-set correctness (how often samples agree, how diverse they are, how confident the model is, and where correct samples appear) to model behavior, but does not isolate which of these form a stable, compact predictor of best-of-N gain. We fit ridge predictors on features computed from a single labeled validation-set sampling pass, use bootstrap-Lasso as a stability analysis of the candidate feature set, and give a concentration analysis with an explicit linear-approximation residual. Across three base-model families, six post-training methods, and math and reasoning task domains, the stability analysis identifies a strict three-feature core spanning prompt-level agreement spread, label-assisted first-correct-sample position, and completion-length variance; a compact ridge predictor built from this core plus an entropy add-on reaches Spearman ρ= 0.90 with actual best-of-N gain under a reward-model verifier. The intended use is labeled validation-set screening of candidate configurations before paying the full reward-model scoring cost.

Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation (R^2 approx 0.95) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.

There have been many benchmarks for evaluating long-context language models (LCLMs), but developers often rely on synthetic tasks like needle-in-a-haystack (NIAH) or arbitrary subsets of tasks. It remains unclear whether they translate to the diverse downstream applications of LCLMs, and the inconsistency further complicates model comparison. We investigate the underlying reasons behind current practices and find that existing benchmarks often provide noisy signals due to low coverage of applications, insufficient lengths, unreliable metrics, and incompatibility with base models. In this work, we present HELMET (How to Evaluate Long-context Models Effectively and Thoroughly), a comprehensive benchmark encompassing seven diverse, application-centric categories. We also address many issues in previous benchmarks by adding controllable lengths up to 128k tokens, model-based evaluation for reliable metrics, and few-shot prompting for robustly evaluating base models. Consequently, we demonstrate that HELMET offers more reliable and consistent rankings of frontier LCLMs. Through a comprehensive study of 51 LCLMs, we find that (1) synthetic tasks like NIAH are not good predictors of downstream performance; (2) the diverse categories in HELMET exhibit distinct trends and low correlation with each other; and (3) while most LCLMs achieve perfect NIAH scores, open-source models significantly lag behind closed ones when the task requires full-context reasoning or following complex instructions -- the gap widens with increased lengths. Finally, we recommend using our RAG tasks for fast model development, as they are easy to run and more predictive of other downstream performance; ultimately, we advocate for a holistic evaluation across diverse tasks.

The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using Euclidean distances "d" as in Szekely et al, we use "similarity", which can be defined as "exp(-d/s)", where the scaling parameter s>0 controls how rapidly the similarity falls off with distance. Scale parameters are chosen by maximizing the similarity correlation. The motivation for using "similarity" originates in spectral clustering theory (see e.g. Ng et al 2001, Advances in Neural Information Processing Systems 14: 849-856). We show that a particular form of similarity correlation is asymptotically equivalent to distance correlation for large values of the scale parameter. Furthermore, we extend similarity correlation to coherence between complex valued vectors, including its partitioning into real and imaginary contributions. Several toy examples are used for comparing distance and similarity correlations. For instance, points on a noiseless straight line give distance and similarity correlation values equal to 1; but points on a noiseless circle produces near zero distance correlation (dCorr=0.02) while the similarity correlation is distinctly non zero (sCorr=0.36). In distinction to the distance approach, similarity gives more importance to small distances, which emphasizes the local properties of functional relations. This paper represents a preliminary empirical study, showing that the novel similarity association has some distinct practical advantages over distance based association.For the sake of reproducible research, the software code implementing all methods here (using lazarus free-pascal "www.lazarus.freepascal.org"), including all test data, are freely available at: "sites.google.com/site/pascualmarqui/home/similaritycovariance".

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient, the most important is that distance correlation equals zero if and only if the random vectors are independent. There are two different estimators of the distance correlation available in the literature. The first one, proposed by Székely et al. (2007), is based on an asymptotically unbiased estimator of the distance covariance which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance proposed in Székely et al. (2014), proved to be an U-statistic by Székely and Huo (2016). This study evaluates their efficiency (mean squared error) and compares computational times for both methods under different dependence structures. Under conditions of independence or near-independence, the V-estimates are biased, while the U-estimator frequently cannot be computed due to negative values. To address this challenge, a convex linear combination of the former estimators is proposed and studied, yielding good results regardless of the level of dependence.

Great successes have been reported using Reinforcement Learning from Human Feedback (RLHF) to align large language models. Open-source preference datasets and reward models have enabled wider experimentation beyond generic chat settings, particularly to make systems more "helpful" for tasks like web question answering, summarization, and multi-turn dialogue. When optimizing for helpfulness, RLHF has been consistently observed to drive models to produce longer outputs. This paper demonstrates that optimizing for response length is a significant factor behind RLHF's reported improvements in these settings. First, we study the relationship between reward and length for reward models trained on three open-source preference datasets for helpfulness. Here, length correlates strongly with reward, and improvements in reward score are driven in large part by shifting the distribution over output lengths. We then explore interventions during both RL and reward model learning to see if we can achieve the same downstream improvements as RLHF without increasing length. While our interventions mitigate length increases, they aren't uniformly effective across settings. Furthermore, we find that even running RLHF with a reward based solely on length can reproduce most of the downstream improvements over the initial policy model, showing that reward models in these settings have a long way to go.

We present explicit formulas - that are also computer code - for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The returns are strongly correlated with volatility, but have no significant dependence on turnover, directly confirming an earlier result based on a more indirect empirical analysis. We further find empirically that turnover has poor explanatory power for alpha correlations.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

The growth rate of Av(1324) is the last unknown Stanley-Wilf limit of a length-four pattern. Since 2020 the best rigorous lower bound has been the 10.271012 of Bevan, Brignall, Elvey Price and Pantone; we raise it to 10.412263. Their construction lays 1324-avoiders along an infinite staircase of two-cell blocks alternating with single connecting cells, and forbids a 1324 by a local condition on how the points of a block interleave with the components of the cell beside it. Certain points of a block, its leaves, may be exempted from that condition. They exempt them on one axis only, and report that they could not count the possibilities when both are exempted. This paper exempts them on both axes and counts the result. The second relaxation is their own argument read in the other axis, and the Harris correlation inequality bounds the joint count below by the product of the two counts taken separately, at the cost of one factor of the component generating function.

The rapid advancement of artificial intelligence in legal natural language processing demands scalable methods for evaluating text extraction from judicial decisions. This study evaluates 16 unsupervised metrics, including novel formulations, to assess the quality of extracting seven semantic blocks from 1,000 anonymized Russian judicial decisions, validated against 7,168 expert reviews on a 1--5 Likert scale. These metrics, spanning document-based, semantic, structural, pseudo-ground truth, and legal-specific categories, operate without pre-annotated ground truth. Bootstrapped correlations, Lin's concordance correlation coefficient (CCC), and mean absolute error (MAE) reveal that Term Frequency Coherence (Pearson r = 0.540, Lin CCC = 0.512, MAE = 0.127) and Coverage Ratio/Block Completeness (Pearson r = 0.513, Lin CCC = 0.443, MAE = 0.139) best align with expert ratings, while Legal Term Density (Pearson r = -0.479, Lin CCC = -0.079, MAE = 0.394) show strong negative correlations. The LLM Evaluation Score (mean = 0.849, Pearson r = 0.382, Lin CCC = 0.325, MAE = 0.197) showed moderate alignment, but its performance, using gpt-4.1-mini via g4f, suggests limited specialization for legal textse. These findings highlight that unsupervised metrics, including LLM-based approaches, enable scalable screening but, with moderate correlations and low CCC values, cannot fully replace human judgment in high-stakes legal contexts. This work advances legal NLP by providing annotation-free evaluation tools, with implications for judicial analytics and ethical AI deployment.

LawZero's Scientist AI trains a Predictor toward the Bayesian posterior, with an objective that penalizes inconsistent probabilities among latent explanations. We ask whether current frontier language models, with no such training, are already consistent in this sense zero-shot: do their probability judgments satisfy the law of total probability, P(X)=sum_z P(z)P(X|z), when the latent z must be inferred from records in the context? In separate single-turn calls, models are asked for P(X), for P(z) over the latent's states, and for P(X|z); a causal family applies the same test to P(y|do(x)) and the back-door adjustment. Every query has an exact ground-truth probability, and a subset of items is asked in three wordings to separate persistent incoherence from rewording noise. Across seven models, GPT-6.1 Sol and Claude Opus 5.5 are the most coherent (mean absolute residual 0.08 and 0.12 log-odds, about 2 percentage points). Claude Haiku 5.5, Gemini 3.8 Flash and DeepSeek V4-Pro show persistent incoherence (0.27-0.35 log-odds) that is mostly item-specific rather than a shared offset. Within every model, larger residuals go with larger errors against the truth (Spearman 0.40-0.62), so the residual, which needs no ground truth, flags unreliable answers. Reasoning length does not predict coherence, across models or within a model across rewordings of the same question. Simple consistency checks pass almost everywhere; the failures are specific to reasoning through a latent variable. Code and data: https://github.com/ppotash/latent-coherence

We study the relationship between vocabulary size and text length in a corpus of 75 literary works in English, authored by six writers, distinguishing between the contributions of three grammatical classes (or ``tags,'' namely, {\it nouns}, {\it verbs}, and {\it others}), and analyze the progressive appearance of new words of each tag along each individual text. While the power-law relation prescribed by Heaps' law is satisfactorily fulfilled by total vocabulary sizes and text lengths, the appearance of new words in each text is on the whole well described by the average of random shufflings of the text, which does not obey a power law. Deviations from this average, however, are statistically significant and show a systematic trend across the corpus. Specifically, they reveal that the appearance of new words along each text is predominantly retarded with respect to the average of random shufflings. Moreover, different tags are shown to add systematically distinct contributions to this tendency, with {\it verbs} and {\it others} being respectively more and less retarded than the mean trend, and {\it nouns} following instead this overall mean. These statistical systematicities are likely to point to the existence of linguistically relevant information stored in the different variants of Heaps' law, a feature that is still in need of extensive assessment.

Large language models (LLMs) have achieved remarkable progress in natural language generation, yet they continue to display puzzling behaviors -- such as repetition and incoherence -- even when exhibiting low perplexity. This highlights a key limitation of conventional evaluation metrics, which emphasize local prediction accuracy while overlooking long-range structural complexity. We introduce correlation dimension, a fractal-geometric measure of self-similarity, to quantify the epistemological complexity of text as perceived by a language model. This measure captures the hierarchical recurrence structure of language, bridging local and global properties in a unified framework. Through extensive experiments, we show that correlation dimension (1) reveals three distinct phases during pretraining, (2) reflects context-dependent complexity, (3) indicates a model's tendency toward hallucination, and (4) reliably detects multiple forms of degeneration in generated text. The method is computationally efficient, robust to model quantization (down to 4-bit precision), broadly applicable across autoregressive architectures (e.g., Transformer and Mamba), and provides fresh insight into the generative dynamics of LLMs.

A new approach to solving random matrix models directly in the large N limit is developed. First, a set of numerical values for some low-pt correlation functions is guessed. The large N loop equations are then used to generate values of higher-pt correlation functions based on this guess. Then one tests whether these higher-pt functions are consistent with positivity requirements, e.g., langle tr M^{2k} rangle ge 0. If not, the guessed values are systematically ruled out. In this way, one can constrain the correlation functions of random matrices to a tiny subregion which contains (and perhaps converges to) the true solution. This approach is tested on single and multi-matrix models and handily reproduces known solutions. It also produces strong results for multi-matrix models which are not believed to be solvable. A tantalizing possibility is that this method could be used to search for new critical points, or string worldsheet theories.

Pre-trained models have revolutionized natural language understanding. However, researchers have found they can encode artifacts undesired in many applications, such as professions correlating with one gender more than another. We explore such gendered correlations as a case study for how to address unintended correlations in pre-trained models. We define metrics and reveal that it is possible for models with similar accuracy to encode correlations at very different rates. We show how measured correlations can be reduced with general-purpose techniques, and highlight the trade offs different strategies have. With these results, we make recommendations for training robust models: (1) carefully evaluate unintended correlations, (2) be mindful of seemingly innocuous configuration differences, and (3) focus on general mitigations.

We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation.

Probing neural models for the ability to perform downstream tasks using their activation patterns is often used to localize what parts of the network specialize in performing what tasks. However, little work addressed potential mediating factors in such comparisons. As a test-case mediating factor, we consider the prediction's context length, namely the length of the span whose processing is minimally required to perform the prediction. We show that not controlling for context length may lead to contradictory conclusions as to the localization patterns of the network, depending on the distribution of the probing dataset. Indeed, when probing BERT with seven tasks, we find that it is possible to get 196 different rankings between them when manipulating the distribution of context lengths in the probing dataset. We conclude by presenting best practices for conducting such comparisons in the future.

The increasingly widespread adoption of large language models has highlighted the need for improving their explainability. We present context length probing, a novel explanation technique for causal language models, based on tracking the predictions of a model as a function of the length of available context, and allowing to assign differential importance scores to different contexts. The technique is model-agnostic and does not rely on access to model internals beyond computing token-level probabilities. We apply context length probing to large pre-trained language models and offer some initial analyses and insights, including the potential for studying long-range dependencies. The source code and an interactive demo of the method are available.

Why do language models fail on long inputs? The common answer is length. We show that, for retrieval, length is cheap and competition is not. On five open models (0.5B to 3B parameters, four families), neutral filler costs nothing: accuracy stays at 0.97 to 1.00, up to 32K tokens on Qwen2.5-1.5B. Statements in the format of the evidence, placed at the same positions, drop it to 0.16 to 0.33. A single statement that gives the queried key a rival value multiplies the loss by 9 to 110, and every additional rival adds to it. Inside the model, one quantity tracks the failure: the attention mass left on the evidence. Across 126,473 trials it explains up to 58% of the variance in loss; log length explains at most 8%. The masked-filler protocol behind the claim that length alone hurts reproduces on MMLU (11 to 18 points lost at 30K tokens), but fails a visible control in retrieval: masking costs 45 accuracy points at 32K tokens, while the same filler left visible costs none. In retrieval, context rot is a competition for attention. We release the probe and all 126K trial-level measurements.

Single-cell CRISPR screens summarize each perturbation by how far cells move from their unperturbed state, averaging over cell-to-cell variation. Whether the cells moved together is not captured: two perturbations with identical effect magnitude can differ qualitatively, one driving cells along a shared trajectory, the other scattering them around the same mean. We define SheshaP coherence (S_p), the mean cosine similarity between individual cell displacement vectors and their mean, and ask what it adds across six Perturb-seq datasets (2,285 perturbations; CRISPRa, CRISPRi, Cas9 knockout). Coherence and effect magnitude are closely coupled (Spearman ρ=0.84--0.98), and the coupling persists in a foundation-model embedding, under alternative effect-size definitions, and when analysis is restricted to responding cells. Associations reported without conditioning on effect size largely recover it, shown here for two comparisons that vanish under conditioning. Effect size accounts for 89--96\% of coherence variance; within the remainder, coherence is negatively associated with apoptosis and p53 signalling in the two largest screens. Two standard responder classifiers agree on only 68\% of cells. Directional coherence is largely a restatement of effect magnitude, and heterogeneity measures should report their redundancy with effect size as a matter of course. S_p is implemented in the open-source shesha-geometry Python package.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

Aligned instruction following models can better fulfill user requests than their unaligned counterparts. However, it has been shown that there is a length bias in evaluation of such models, and that training algorithms tend to exploit this bias by learning longer responses. In this work we show how to train models that can be controlled at inference time with instructions containing desired length constraints. Such models are superior in length instructed evaluations, outperforming standard instruction following models such as GPT4, Llama 3 and Mixtral.

Differentially private learning algorithms inject noise into the learning process. While the most common private learning algorithm, DP-SGD, adds independent Gaussian noise in each iteration, recent work on matrix factorization mechanisms has shown empirically that introducing correlations in the noise can greatly improve their utility. We characterize the asymptotic learning utility for any choice of the correlation function, giving precise analytical bounds for linear regression and as the solution to a convex program for general convex functions. We show, using these bounds, how correlated noise provably improves upon vanilla DP-SGD as a function of problem parameters such as the effective dimension and condition number. Moreover, our analytical expression for the near-optimal correlation function circumvents the cubic complexity of the semi-definite program used to optimize the noise correlation matrix in previous work. We validate our theory with experiments on private deep learning. Our work matches or outperforms prior work while being efficient both in terms of compute and memory.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

In the context of C^* dynamical systems, we consider a locally compact group G acting by ^*-automorphisms on a C^* algebra U of observables, and assume a state of U that satisfies the clustering property with respect to a net of group elements of G. That is, the two-point connected correlation function vanishes in the limit on the net, when one observable is translated under the group action. Then we show that all higher order connected correlation functions (Ursell functions, or classical cumulants) and all free correlation functions (free cumulants, from free probability) vanish at the same rate in that limit. Additionally, we show that mean clustering, also called ergodicity, extends to higher order correlations. We then apply those results to equilibrium states of quantum spin lattice models. Under certain assumptions on the range of the interaction, high temperature Gibbs states are known to be exponentially clustering w.r.t. space translations. Combined with the Lieb-Robinson bound, one obtains exponential clustering for space-time translations outside the Lieb-Robinson light-cone. Therefore, by our present results, all the higher order connected and free correlation functions will vanish exponentially under space-time translations outside the Lieb-Robinson light cone, in high temperature Gibbs states. Another consequence is that their long-time averaging over a space-time ray vanishes for almost every ray velocity.

Length-penalized reinforcement learning can shorten chain-of-thought reasoning while hiding an influence that drives the model's answer. In our experiments, training with length penalties does not stop misleading hints from steering models, even though the models' chains of thought mention the hint much less often. A token-accuracy evaluation would count these runs as successful because they use fewer reasoning tokens with little accuracy loss; it would miss whether the remaining trace still shows what drove the answer. We train Qwen3-4B and Qwen3-14B variants with different target chain lengths, then evaluate them with biasing-hint interventions on held-out MMLU-Pro-R and four transfer benchmarks. Compression sharply cuts reasoning tokens, preserves most multiple-choice accuracy, and leaves hint influence near baseline. At the strongest target, lower-bound faithfulness falls to 63.1% of baseline for Qwen3-14B and 69.4% for Qwen3-4B; the raw rate at which a monitor catches hint use falls from 69% to 49% and from 60% to 48%. To separate length from content, we randomly delete sentences from uncompressed baseline chains until the remaining text matches the compressed length. Even after this length matching, compressed chains disclose the hint 7-35 percentage points less often than baseline chains that we shorten at random, for both Qwen3 sizes and all five evaluation distributions. Compression therefore does more than shorten reasoning, preferentially removing the cues a monitor needs to see what influenced the answer. Together, these results reveal a compression-monitorability frontier in which cheaper reasoning can preserve answers while making the influences behind them harder to detect.

An industrial process includes many devices, variables, and sub-processes that are physically or electronically interconnected. These interconnections imply some level of correlation between different process variables. Since most of the alarms in a process plant are defined on process variables, alarms are also correlated. However, this can be a nuisance to operators, for one fault might trigger a, sometimes large, number of alarms. So, it is essential to find and correct correlated alarms. In this paper, we study different methods and techniques proposed to measure correlation or similarity between alarms. The similarity indices are first analytically calculated and then studied and compared. The results are also validated using Monte-Carlo simulation.

Machine translation tests masked diffusion language models (dLLMs) because every source token must be rendered faithfully, while fixed canvas decoding must choose target length before denoising. Existing masked diffusion decoding work mainly studies token unmasking order, leaving this length decision under-explored despite its direct effect on coverage and redundancy. We introduce Entropy-Valley (EV), a training-free length selector that scores candidate target canvases by mean predictive entropy from all-mask forward passes and selects the canvas the backbone is most prepared to fill. Relative to a baseline using training corpus length statistics, EV recovers 64.9%, 65.3%, and 33.0% of the COMET-22 gain from reference target lengths on EntoZh, ZhtoEn, and EntoDe. Our diagnostics show that denoising-friendly lengths need not match reference lengths. Evaluation by three translation experts supports the EnleftrightarrowZh adequacy gains, with stronger evidence on ZhtoEn. Compared with a LLaMA-3-8B autoregressive (AR) model trained on the same fine-tuning data, the EV system ties on EntoZh and leads on ZhtoEn; an oracle-length diagnostic further shows that, in this masked diffusion MT setting, deciding which tokens to reveal first matters less than how the target length is supplied.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

The diversity in length constitutes a significant characteristic of text. Due to the long-tail distribution of text lengths, most existing methods for scene text recognition (STR) only work well on short or seen-length text, lacking the capability of recognizing longer text or performing length extrapolation. This is a crucial issue, since the lengths of the text to be recognized are usually not given in advance in real-world applications, but it has not been adequately investigated in previous works. Therefore, we propose in this paper a method called Length-Insensitive Scene TExt Recognizer (LISTER), which remedies the limitation regarding the robustness to various text lengths. Specifically, a Neighbor Decoder is proposed to obtain accurate character attention maps with the assistance of a novel neighbor matrix regardless of the text lengths. Besides, a Feature Enhancement Module is devised to model the long-range dependency with low computation cost, which is able to perform iterations with the neighbor decoder to enhance the feature map progressively. To the best of our knowledge, we are the first to achieve effective length-insensitive scene text recognition. Extensive experiments demonstrate that the proposed LISTER algorithm exhibits obvious superiority on long text recognition and the ability for length extrapolation, while comparing favourably with the previous state-of-the-art methods on standard benchmarks for STR (mainly short text).

We explore different ways to utilize position-based cross-attention in seq2seq networks to enable length generalization in algorithmic tasks. We show that a simple approach of interpolating the original and reversed encoded representations combined with relative attention allows near-perfect length generalization for both forward and reverse lookup tasks or copy tasks that had been generally hard to tackle. We also devise harder diagnostic tasks where the relative distance of the ideal attention position varies with timestep. In such settings, the simple interpolation trick with relative attention is not sufficient. We introduce novel variants of location attention building on top of Dubois et al. (2020) to address the new diagnostic tasks. We also show the benefits of our approaches for length generalization in SCAN (Lake & Baroni, 2018) and CFQ (Keysers et al., 2020). Our code is available on GitHub.

In the past two years, several points of view have been proposed to address the question of the generalization of the theory of free probability to random tensors with different invariances, and it is unclear at this point whether they lead to the same notions of tensorial free cumulants and freeness. One way to approach this problem, developed by Collins, Gurau and the second named author for local unitary invariant random tensors, relies on finite size quantities involving averages over the invariance group, and whose asymptotics naturally possess the properties expected for tensorial generalizations of free cumulants of arbitrary orders. At this point, this approach has only been carried out for certain distributions, and for a subset of the moments that define such theories, and a more systematic and exhaustive study is lacking. This is the program initiated in this paper: we link this approach to the one proposed by Nechita and Park; extend a number of their results as well as those of the aforementioned paper to arbitrary orders of fluctuations, thereby generalizing higher order free cumulants; push further the study of distributions with larger invariance groups; detail the link with the asymptotics of the free-energies of the tensor HCIZ and BGW integrals; and provide formulae for tensorial free cumulants of products of tensors. Another important question is that of the definition of concrete distributions whose tensorial free-cumulants take non-trivial values. We compute the tensorial free cumulants for Gaussian random tensors with non-trivial covariances, and show that they provide such examples.

This study investigates retrieval-augmented summarization by specifically examining the impact of exemplar summary lengths under length constraints, not covered by previous work. We propose a Diverse Length-aware Maximal Marginal Relevance (DL-MMR) algorithm to better control summary lengths. This algorithm combines the query relevance with diverse target lengths in retrieval-augmented summarization. Unlike previous methods that necessitate exhaustive exemplar exemplar relevance comparisons using MMR, DL-MMR considers the exemplar target length as well and avoids comparing exemplars to each other, thereby reducing computational cost and conserving memory during the construction of an exemplar pool. Experimental results showed the effectiveness of DL-MMR, which considers length diversity, compared to the original MMR algorithm. DL-MMR additionally showed the effectiveness in memory saving of 781,513 times and computational cost reduction of 500,092 times, while maintaining the same level of informativeness.

We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our beta-TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art beta-VAE objective for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the latent variables model is trained using our framework.

Token serves as the fundamental unit of computation in modern autoregressive models, and generation length directly influences both inference cost and reasoning performance. Despite its importance, existing approaches lack fine-grained length modeling, operating primarily at the coarse-grained sequence level. We introduce the Length Value Model (LenVM), a token-level framework that models the remaining generation length. By formulating length modeling as a value estimation problem and assigning a constant negative reward to each generated token, LenVM predicts a bounded, discounted return that serves as a monotone proxy for the remaining generation horizon. This formulation yields supervision that is annotation-free, dense, unbiased, and scalable. Experiments on LLMs and VLMs demonstrate LenVM provides a highly effective signal at inference time. On the LIFEBench exact length matching task, applying LenVM to a 7B model improves the length score from 30.9 to 64.8, significantly outperforming frontier closed-source models. Furthermore, LenVM enables continuous control over the trade off between performance and efficiency. On GSM8K at a budget of 200 tokens, LenVM maintains 63% accuracy compared to 6 percent for token budget baseline. It also accurately predicts total generation length from the prompt boundary. Finally, LenVM's token-level values offer an interpretable view of generation dynamics, revealing how specific tokens shift reasoning toward shorter or longer regimes. Results demonstrate that LenVM supports a broad range of applications and token length can be effectively modeled as a token-level value signal, highlighting the potential of LenVM as a general framework for length modeling and as a length-specific value signal that could support future RL training. Code is available at https://github.com/eric-ai-lab/Length-Value-Model.

Contrastive Language-Image Pre-training (CLIP) has been the cornerstone for zero-shot classification, text-image retrieval, and text-image generation by aligning image and text modalities. Despite its widespread adoption, a significant limitation of CLIP lies in the inadequate length of text input. The length of the text token is restricted to 77, and an empirical study shows the actual effective length is even less than 20. This prevents CLIP from handling detailed descriptions, limiting its applications for image retrieval and text-to-image generation with extensive prerequisites. To this end, we propose Long-CLIP as a plug-and-play alternative to CLIP that supports long-text input, retains or even surpasses its zero-shot generalizability, and aligns the CLIP latent space, making it readily replace CLIP without any further adaptation in downstream frameworks. Nevertheless, achieving this goal is far from straightforward, as simplistic fine-tuning can result in a significant degradation of CLIP's performance. Moreover, substituting the text encoder with a language model supporting longer contexts necessitates pretraining with vast amounts of data, incurring significant expenses. Accordingly, Long-CLIP introduces an efficient fine-tuning solution on CLIP with two novel strategies designed to maintain the original capabilities, including (1) a knowledge-preserved stretching of positional embedding and (2) a primary component matching of CLIP features. With leveraging just one million extra long text-image pairs, Long-CLIP has shown the superiority to CLIP for about 20% in long caption text-image retrieval and 6% in traditional text-image retrieval tasks, e.g., COCO and Flickr30k. Furthermore, Long-CLIP offers enhanced capabilities for generating images from detailed text descriptions by replacing CLIP in a plug-and-play manner.

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

The correlation between black hole mass, M_{rm bh}, and stellar velocity dispersion, σ_0, is revisited using 137 galaxies with quantitative bar strengths and enhanced morphological awareness. Interpreted within the `Triangal' evolutionary framework, gas-rich and gas-poor assembly pathways emerge in the M_{rm bh}-σ_0 diagram. To quantify these scaling relations, a symmetric Bayesian hierarchical regression code, dubbed the Symmetric COvariance Population Estimator (SCOPE), is introduced. Unlike conditional estimators (e.g., LINMIX), SCOPE derives the intrinsic population covariance, natively accommodating asymmetric measurement errors while guaranteeing directional invariance between axes. Primeval, dust-poor S0 galaxies (including dwarf early-type galaxies with R_{rm e,gal} ~ 1 kpc) follow a shallow relation (M_{rm bh}proptoσ_0^{2.5--3.1}). Explained via the virial theorem, this flattening reframes expectations for intermediate-mass black holes. In contrast, tracing the `Disc Down-sizing' sequence - where dry mergers erase discs - yields a steep relation for massive elliptical and ellicular galaxies (M_{rm bh}proptoσ_0^{7.8pm1.4}). Applying a single, monolithic scaling relation across all morphologies inadvertently averages over different formation histories, potentially skewing AGN virial f-factor calibrations and systematically under-predicting the ultra-massive black holes needed to generate the nanohertz gravitational wave background. Furthermore, strongly barred, dust-poor S0 galaxies appear offset to higher σ_0, while this dynamical signature is lost in the complexities of spiral galaxies. Ultimately, these morphology-dependent relations provide physically-motivated benchmarks for cosmological simulations and a framework for disentangling regimes driven by AGN feedback from those driven by mergers.

Speculative decoding typically characterizes speedup by draft tokens accepted per verification round. Lossless verification preserves the target model's output distribution and thus expected completion length, making this metric a meaningful efficiency proxy. Relaxed (lossy) verification accepts tokens that lossless verification would reject, potentially altering that distribution. We identify a length inflation phenomenon: relaxed verification lengthens completions, primarily by extending reasoning traces, largely offsetting apparent gains in accepted tokens per round. We evaluate existing training-free relaxed verification rules on twelve target-drafter pairs against lossless verification on identical prompts, measuring completion length, verifier rounds, wall-clock time, and task accuracy. At each rule's most relaxed evaluated setting, relaxed verification on average accepts 1.34times as many tokens per round but produces 1.54times longer completions. For rules with higher acceptance lengths, tokens accepted only under relaxed verification tend to have low target-model probability, contributing to length inflation. For rules that reduce verifier rounds, accuracy typically drops substantially. Further analysis traces some failures to continued reasoning that exhausts the budget needed to deliver a final answer. Overall, accepted tokens per round alone is an unreliable measure of decoding speed under relaxed verification. Completion length and verifier rounds must also be reported to assess actual efficiency.

Trajectories in complex systems often contain structure that is not captured by the population-averaged, scalar statistics traditionally used to describe them. Here we reconstruct, through independent numerical re-simulation rather than literature review, a systematic search across representational forms - from single scalar statistics, through two independent discrete multi-feature classification attempts, to a trajectory-level structural representation and a diagnostic surrogate test, to a continuous low-dimensional compression - applied to the same underlying trajectory ensemble in a critical complex system. Predictive failure is not explained by insufficient correlation: one discrete representation's own strongest individual feature correlates with the target more strongly (r=0.588) than the eventual successful representation's own headline statistic (r=0.540), yet fails to separate the ensemble's two most consequential cases - while the continuous representation succeeds, robustly, across eight independent scale-removal folds (r=0.677-0.717, all p<0.001). The determining factor was not correlation strength but whether the representation preserved the structure relevant to prediction. These results indicate that the choice of representation determines whether predictive structure in complex systems becomes accessible - a scientific variable in its own right, not a downstream analysis choice.

We present ORCA (Omni Research on Calculation in AI) Benchmark - a novel benchmark that evaluates large language models (LLMs) on multi-domain, real-life quantitative reasoning using verified outputs from Omni's calculator engine. In 500 natural-language tasks across domains such as finance, physics, health, and statistics, the five state-of-the-art systems (ChatGPT-5, Gemini~2.5~Flash, Claude~Sonnet~4.5, Grok~4, and DeepSeek~V3.2) achieved only 45--63,% accuracy, with errors mainly related to rounding (35,%) and calculation mistakes (33,%). Results in specific domains indicate strengths in mathematics and engineering, but weaknesses in physics and natural sciences. Correlation analysis (r approx 0.40--0.65) shows that the models often fail together but differ in the types of errors they make, highlighting their partial complementarity rather than redundancy. Unlike standard math datasets, ORCA evaluates step-by-step reasoning, numerical precision, and domain generalization across real problems from finance, physics, health, and statistics.

Formula alpha mining, which generates predictive signals from financial data, is critical for quantitative investment. Although various algorithmic approaches-such as genetic programming, reinforcement learning, and large language models-have significantly expanded the capacity for alpha discovery, systematic evaluation remains a key challenge. Existing evaluation metrics predominantly include backtesting and correlation-based measures. Backtesting is computationally intensive, inherently sequential, and sensitive to specific strategy parameters. Correlation-based metrics, though efficient, assess only predictive ability and overlook other crucial properties such as temporal stability, robustness, diversity, and interpretability. Additionally, the closed-source nature of most existing alpha mining models hinders reproducibility and slows progress in this field. To address these issues, we propose AlphaEval, a unified, parallelizable, and backtest-free evaluation framework for automated alpha mining models. AlphaEval assesses the overall quality of generated alphas along five complementary dimensions: predictive power, stability, robustness to market perturbations, financial logic, and diversity. Extensive experiments across representative alpha mining algorithms demonstrate that AlphaEval achieves evaluation consistency comparable to comprehensive backtesting, while providing more comprehensive insights and higher efficiency. Furthermore, AlphaEval effectively identifies superior alphas compared to traditional single-metric screening approaches. All implementations and evaluation tools are open-sourced to promote reproducibility and community engagement.

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

When rows of an n times d matrix A are given in a stream, we study algorithms for approximating the top eigenvector of the matrix {A}^TA (equivalently, the top right singular vector of A). We consider worst case inputs A but assume that the rows are presented to the streaming algorithm in a uniformly random order. We show that when the gap parameter R = σ_1(A)^2/σ_2(A)^2 = Ω(1), then there is a randomized algorithm that uses O(h cdot d cdot polylog(d)) bits of space and outputs a unit vector v that has a correlation 1 - O(1/R) with the top eigenvector v_1. Here h denotes the number of heavy rows in the matrix, defined as the rows with Euclidean norm at least |{A}|_F/d cdot operatorname{polylog(d)}. We also provide a lower bound showing that any algorithm using O(hd/R) bits of space can obtain at most 1 - Ω(1/R^2) correlation with the top eigenvector. Thus, parameterizing the space complexity in terms of the number of heavy rows is necessary for high accuracy solutions. Our results improve upon the R = Ω(log n cdot log d) requirement in a recent work of Price and Xun (FOCS 2024). We note that the algorithm of Price and Xun works for arbitrary order streams whereas our algorithm requires a stronger assumption that the rows are presented in a uniformly random order. We additionally show that the gap requirements in their analysis can be brought down to R = Ω(log^2 d) for arbitrary order streams and R = Ω(log d) for random order streams. The requirement of R = Ω(log d) for random order streams is nearly tight for their analysis as we obtain a simple instance with R = Ω(log d/loglog d) for which their algorithm, with any fixed learning rate, cannot output a vector approximating the top eigenvector v_1.

This paper reports a methodological pivot from the Open Khipu Repository to the Khipu Field Guide (KFG) database, prompted by stalled progress on the OKR, and a full re-analysis of the resulting 650-khipu sample. Three findings recur across every analysis attempted. First, khipu size confounds nearly every derived structural count, explaining 42-70% of its variance; all subsequent models control for it. Second, the two-letter name prefix (AS, UR, HP, QU, JC, MM, KH) identifies the original cataloger, not a site or period, which turns documentation completeness into a second confound that must be modeled explicitly. Controlling for both, khipus cataloged by Hugo Pereyra's Proyecto Quipu (HP) show significantly fewer Ascher sum-relation types than Gary Urton's (UR) khipus (p = 0.044), while the Ascher-cataloged (AS) khipus are too collinear with their own near-total lack of side/direction documentation to assess (VIF = 5.0). Third, generic structural clustering (UMAP+HDBSCAN) does not separate the pooled 650-khipu sample from two independent null models (permutation and Gaussian), corroborating an independent conclusion already reached by the KFG itself; the same test restricted to a single cataloger (UR) proved not reproducible across runtime environments and is reported here as a methodological caveat rather than evidence of structure. A targeted replication of the KFG's own S/Z-knot spatial-block heuristic for calendar/astronomical khipus recovers 8 of 10 published candidates and proposes 34 additional ones under the same criterion.

Controlling the length of generated text can be crucial in various text-generation tasks, including summarization. Existing methods often require complex model alterations, limiting compatibility with pre-trained models. We address these limitations by developing a simple approach for controlling the length of automatic text summaries by increasing the importance of correctly predicting the EOS token in the cross-entropy loss computation. The proposed methodology is agnostic to architecture and decoding algorithms and orthogonal to other inference-time techniques to control the generation length. We tested it with encoder-decoder and modern GPT-style LLMs, and show that this method can control generation length, often without affecting the quality of the summary.

Firm characteristics are commonly represented as fixed vectors, even though evidence about firms' operations arrives as heterogeneous collections of articles reports. We study how distances between distributions of firm characteristics restrict systematic covariance. For given latent exposure laws, quadratic Wasserstein geometry yields sharp covariance endpoints over admissible couplings. Under a common randomized bi-Lipschitz characteristic-to-exposure map, bounded risk-coordinate slack, and a maintained return-covariance bridge, characteristic-side distance yields a conditional interval for the covariance ceiling. Greater separation then leaves less scope for aligned systematic exposures when these assumptions are tight, while a non-negative transport excess term records the gap between realized and maximum-covariance arrangements. The resulting envelope is scenario analysis rather than an expected-return, no-arbitrage, or identified structural model. Empirically, we proxy characteristic distributions with encoder-only language-model embeddings of financial news articles, disclosures, and analyst reports for Nasdaq firms over 2018-2022. In a dyadic regression with symmetric firm effects, greater pairwise article-embedding W2 distance is associated with weaker return co-movement: the coefficient is 1.920, with 95% interval [1.412, 2.468]. The estimate retains the same sign when returns are measured in a later window, although the feature construction is not point-in-time and the evidence remains reduced form.

Related works used indexes like CKA and variants of CCA to measure the similarity of cross-lingual representations in multilingual language models. In this paper, we argue that assumptions of CKA/CCA align poorly with one of the motivating goals of cross-lingual learning analysis, i.e., explaining zero-shot cross-lingual transfer. We highlight what valuable aspects of cross-lingual similarity these indexes fail to capture and provide a motivating case study demonstrating the problem empirically. Then, we introduce Average Neuron-Wise Correlation (ANC) as a straightforward alternative that is exempt from the difficulties of CKA/CCA and is good specifically in a cross-lingual context. Finally, we use ANC to construct evidence that the previously introduced ``first align, then predict'' pattern takes place not only in masked language models (MLMs) but also in multilingual models with causal language modeling objectives (CLMs). Moreover, we show that the pattern extends to the scaled versions of the MLMs and CLMs (up to 85x original mBERT).Our code is publicly available at \url{https://github.com/TartuNLP/xsim}

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Evaluating free-text explanations is a multifaceted, subjective, and labor-intensive task. Large language models (LLMs) present an appealing alternative due to their potential for consistency, scalability, and cost-efficiency. In this work, we present ACORN, a new dataset of 3,500 free-text explanations and aspect-wise quality ratings, and use it to gain insights into how LLMs evaluate explanations. We observed that replacing one of the human ratings sometimes maintained, but more often lowered the inter-annotator agreement across different settings and quality aspects, suggesting that their judgments are not always consistent with human raters. We further quantified this difference by comparing the correlation between LLM-generated ratings with majority-voted human ratings across different quality aspects. With the best system, Spearman's rank correlation ranged between 0.53 to 0.95, averaging 0.72 across aspects, indicating moderately high but imperfect alignment. Finally, we considered the alternative of using an LLM as an additional rater when human raters are scarce, and measured the correlation between majority-voted labels with a limited human pool and LLMs as an additional rater, compared to the original gold labels. While GPT-4 improved the outcome when there were only two human raters, in all other observed cases, LLMs were neutral to detrimental when there were three or more human raters. We publicly release the dataset to support future improvements in LLM-in-the-loop evaluation here: https://github.com/a-brassard/ACORN.

Compression is fundamental to intelligence. A model that can represent its training data as a short code has discovered regularities that enable generalization. Large neural networks may learn functions far simpler than their parameter counts suggest, but it is challenging to construct codes that realize this simplicity. Parameter-based methods such as quantization produce code lengths that scale with model size, insensitive to how much information the parameters store. Prequential coding bypasses this issue by compressing the training trajectory, but codes the exact data sequence regardless of how much the model learns, yielding large codes when the data has high entropy. We introduce requential coding, where a teacher model selects training samples drawn from the student's own distribution. The student's code records only these selections, which cost bits only where teacher and student disagree. The resulting code length is independent of parameter count and data entropy, and often orders of magnitude shorter than the prequential counterpart, with an advantage that grows with scale. This compression sheds light on phenomena inaccessible to prior compressors. Holding loss fixed, larger models and ensembles compress to much smaller sizes despite more parameters. Plugged into a PAC-Bayes bound, the requential code yields state-of-the-art generalization guarantees for billion-parameter LLMs, outperforming bounds built on aggressive post-training quantization even granted zero error. The bound tightens with scale in the compute-optimal regime, as models become increasingly compressible relative to dataset size. The same code predicts that models gradually overfit when trained for multiple epochs. It also isolates the learnable information in a dataset from its unpredictable, random content, revealing that lower-entropy text holds far more learnable structure than higher-entropy image data.

We extend the context length of Llama-3-8B-Instruct from 8K to 80K via QLoRA fine-tuning. The entire training cycle is super efficient, which takes 8 hours on one 8xA800 (80G) GPU machine. The resulted model exhibits superior performances across a broad range of evaluation tasks, such as NIHS, topic retrieval, and long-context language understanding; meanwhile, it also well preserves the original capability over short contexts. The dramatic context extension is mainly attributed to merely 3.5K synthetic training samples generated by GPT-4 , which indicates the LLMs' inherent (yet largely underestimated) potential to extend its original context length. In fact, the context length could be extended far beyond 80K with more computation resources. Therefore, the team will publicly release the entire resources (including data, model, data generation pipeline, training code) so as to facilitate the future research from the community: https://github.com/FlagOpen/FlagEmbedding.

Using data from the Galaxy and Mass Assembly (GAMA) survey, we investigate how galaxy properties correlate with the local environment, focusing on the two southern regions of the survey (G02 and G23) that have not previously been examined in this context. We employ two-point and marked correlation functions to quantify the environmental dependence of galaxy color, stellar mass, luminosity across the u, g, r, J, and K bands, as well as star formation rate (SFR) and specific star formation rate (sSFR). We also assess the impact of redshift incompleteness and cosmic variance on these clustering measurements. Our results show that u-r and g-r colors are most strongly correlated with local overdensity, followed by stellar mass. The sSFR exhibits a clear inverse relationship with density of the environment, consistent with the trend observed for u-band luminosity, which traces young stellar populations. In contrast, galaxies brighter in the g, J, and K bands preferentially inhabit denser regions. By comparing our measurements from the southern regions with those from the equatorial regions of GAMA, we find that cosmic variance does not significantly influence our conclusions. However, redshift incompleteness affects the clustering measurements, as revealed through comparisons of subsets within the G02 region. The measured correlations provide key constraints for models of galaxy assembly across mass and environment, while the environmental trends in color and near-infrared luminosity offer a means to trace stellar mass growth and quenching with redshift.

We present a framework for evaluating data-science agents on live, continuously updated data using executable ground truth and format-agnostic factoid scoring. Consider this example query: "what were last week's audience sizes"---the reference answer changes as the underlying data changes, so static references become outdated and standard LLM-as-a-judge pipelines cannot verify responses against a fixed ground truth. Our central contribution, ground-truth-as-code, encodes each expected answer as an executable reference function that recomputes the answer directly from live data at evaluation time, ensuring the reference remains consistent with the system it describes. We combine this with a factoid-level, format-agnostic judge that decomposes both the agent's response and the computed ground truth into atomic claims and scores precision, recall, and accuracy over them, irrespective of the response format (prose, list, table, HTML, etc.). The approach is applicable to agents whose expected outputs can be expressed as executable data computations. We validate the framework through a human--LLM agreement study on an internally developed machine learning skill deployed in production, using a synthetic database constructed to reproduce production schemas and entity relationships. Relative to a natural-language ground-truth baseline, our method achieves a 29% improvement in the Matthews Correlation Coefficient (MCC)---a class-balanced measure of agreement between expert annotators and LLM-as-a-judge predictions---and a 16% reduction in token consumption per test case, while a self-directed baseline lacking explicit ground truth is anti-correlated with human judgment. Agents that perform multi-source data integration and computation over non-stationary data are routinely deployed in industry; we propose ground-truth-as-code as a practical methodology for their evaluation.

While Late Interaction models exhibit strong retrieval performance, many of their underlying dynamics remain understudied, potentially hiding performance bottlenecks. In this work, we focus on two topics in Late Interaction retrieval: a length bias that arises when using multi-vector scoring, and the similarity distribution beyond the best scores pooled by the MaxSim operator. We analyze these behaviors for state-of-the-art models on the NanoBEIR benchmark. Results show that while the theoretical length bias of causal Late Interaction models holds in practice, bi-directional models can also suffer from it in extreme cases. We also note that no significant similarity trend lies beyond the top-1 document token, validating that the MaxSim operator efficiently exploits the token-level similarity scores.

Chain-of-Thought (CoT) has substantially empowered Large Language Models (LLMs) to tackle complex reasoning tasks, yet the verbose nature of explicit reasoning steps incurs prohibitive inference latency and computational costs, limiting real-world deployment. While existing compression methods - ranging from self-training to Reinforcement Learning (RL) with length constraints - attempt to mitigate this, they often sacrifice reasoning capability for brevity. We identify a critical failure mode in these approaches: explicitly optimizing for shorter trajectories triggers rapid entropy collapse, which prematurely shrinks the exploration space and stifles the discovery of valid reasoning paths, particularly for challenging questions requiring extensive deduction. To address this issue, we propose Compress responses for Easy questions and Explore Hard ones (CEEH), a difficulty-aware approach to RL-based efficient reasoning. CEEH dynamically assesses instance difficulty to apply selective entropy regularization: it preserves a diverse search space for currently hard questions to ensure robustness, while permitting aggressive compression on easier instances where the reasoning path is well-established. In addition, we introduce a dynamic optimal-length penalty anchored to the historically shortest correct response, which effectively counteracts entropy-induced length inflation and stabilizes the reward signal. Across six reasoning benchmarks, CEEH consistently reduces response length while maintaining accuracy comparable to the base model, and improves Pass@k relative to length-only optimization.

We propose a fully data-driven approach to designing mutual information (MI) estimators. Since any MI estimator is a function of the observed sample from two random variables, we parameterize this function with a neural network (MIST) and train it end-to-end to predict MI values. Training is performed on a large meta-dataset of 625,000 synthetic joint distributions with known ground-truth MI. To handle variable sample sizes and dimensions, we employ a two-dimensional attention scheme ensuring permutation invariance across input samples. To quantify uncertainty, we optimize a quantile regression loss, enabling the estimator to approximate the sampling distribution of MI rather than return a single point estimate. This research program departs from prior work by taking a fully empirical route, trading universal theoretical guarantees for flexibility and efficiency. Empirically, the learned estimators largely outperform classical baselines across sample sizes and dimensions, including on joint distributions unseen during training. The resulting quantile-based intervals are well-calibrated and more reliable than bootstrap-based confidence intervals, while inference is orders of magnitude faster than existing neural baselines. Beyond immediate empirical gains, this framework yields trainable, fully differentiable estimators that can be embedded into larger learning pipelines. Moreover, exploiting MI's invariance to invertible transformations, meta-datasets can be adapted to arbitrary data modalities via normalizing flows, enabling flexible training for diverse target meta-distributions.

Large Language Models (LLMs) vary in their abilities on a range of tasks. Initiatives such as the Open LLM Leaderboard aim to quantify these differences with several large benchmarks (sets of test items to which an LLM can respond either correctly or incorrectly). However, high correlations within and between benchmark scores suggest that (1) there exists a small set of common underlying abilities that these benchmarks measure, and (2) items tap into redundant information and the benchmarks may thus be considerably compressed. We use data from n > 5000 LLMs to identify the most informative items of six benchmarks, ARC, GSM8K, HellaSwag, MMLU, TruthfulQA and WinoGrande (with d=28,632 items in total). From them we distill a sparse benchmark, metabench, that has less than 3% of the original size of all six benchmarks combined. This new sparse benchmark goes beyond point scores by yielding estimators of the underlying benchmark-specific abilities. We show that these estimators (1) can be used to reconstruct each original individual benchmark score with, on average, 1.5% root mean square error (RMSE), (2) reconstruct the original total score with 0.8% RMSE, and (3) have a single underlying common factor whose Spearman correlation with the total score is r = 0.93.

Ask a language model the same question about the same document twenty times, and it sometimes returns two different answers. We built Probity, a benchmark of 60 tasks and 470 items from real venture-financing filings, to measure how often this happens. Then we audited our own corpus and found a defect any excerpt-built benchmark can carry: items whose evidence is missing from the window of text the model is shown. The audit flags 36 items and separates two failures a single flag would conflate: evidence genuinely absent from the window and answers that must be computed from numbers the window does supply. Flagged items change their answers far more often, wobbling at 0.255 against 0.087 on the 427 clean items, and excluding them cuts apparent cross-model agreement by about a fifth. Before testing whether the missing evidence explains the instability, we registered a prediction: re-cut each window to hold its evidence, and instability should fall below a set threshold. It failed: the repair moved wobble by 0.058, with an interval containing zero. We report the association as correlational. Almost all measurements sit where instability cannot show, which bounds what a corpus built for accuracy can say about stability. We release the corpus, all 112,800 raw responses, and the audit as a runnable check for any document benchmark.

Large reasoning models (LRMs) spend substantial test-time compute on long chain-of-thought (CoT) traces, but what *characterizes* an effective CoT remains unclear. While prior work reports gains from lengthening CoTs and increasing review (revisiting earlier steps) via appended *wait* tokens, recent studies suggest that shorter thinking can outperform longer traces. We therefore conduct a systematic evaluation across ten LRMs on math and scientific reasoning. Contrary to the "longer-is-better" narrative, we find that both naive CoT lengthening and increased review are associated with *lower* accuracy. As CoT unfolds step by step, token-level metrics can conflate verbosity with process quality. We introduce a graph view of CoT to extract structure and identify a single statistic-the *Failed-Step Fraction (FSF)*, the fraction of steps in abandoned branches-that consistently outpredicts length and review ratio for correctness across models. To probe causality, we design two interventions. First, we rank candidate CoTs by each metric at test time, where FSF yields the largest pass@1 gains; second, we edit CoTs to remove failed branches, which significantly improves accuracy, indicating that failed branches bias subsequent reasoning. Taken together, these results characterize effective CoTs as those that *fail less* and support *structure-aware* test-time scaling over indiscriminately generating long CoT.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

We develop a transfer learning framework for high-dimensional sparse canonical correlation analysis (CCA) with multiple heterogeneous source datasets. Our goal is to improve estimation of the target canonical coefficient matrices by borrowing information from related sources. We characterize source-target similarity through discrepancies in the joint covariance structure and establish minimax optimal rates under both joint and separate prediction losses, explicitly quantifying the gain from enlarged effective sample size and the cost of heterogeneity. To attain these rates, we first construct an oracle transfer estimator based on debiasing and truncated normalization. We then develop a computationally efficient procedure that adaptively achieves the minimax rate without prior knowledge of the sparsity levels, using aggregation to control transfer bias and a truncated normalization scheme to preserve transfer gains under the scale-sensitive prediction loss. A data-driven source detection procedure is further proposed to identify potentially informative auxiliary datasets. Our analysis also yields a generalized sin-theta perturbation theorem that removes a commonly imposed comparability condition on leading canonical correlations in the sparse CCA problem.

In this research, we compare four different evaluation methods in coevolution on the Majority Function problem. The size of the problem is selected such that evaluation against all possible test cases is feasible. Two measures are used for the comparisons, i.e., the objective fitness derived from evaluating solutions against all test cases, and the objective fitness correlation (OFC), which is defined as the correlation coefficient between subjective and objective fitness. The results of our experiments suggest that a combination of average score and weighted informativeness may provide a more accurate evaluation in coevolution. In order to confirm this difference, a series of t-tests on the preference between each pair of the evaluation methods is performed. The resulting significance is affirmative, and the tests for two quality measures show similar preference on four evaluation methods. %This study is the first time OFC is actually computed on a real problem. Experiments on Majority Function problems with larger sizes and Parity problems are in progress, and their results will be added in the final version.

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.

Previous work has shown correlations between the hidden states of large language models and fMRI brain responses, on language tasks. These correlations have been taken as evidence of the representational similarity of these models and brain states. This study tests whether these previous results are robust to several possible concerns. Specifically this study shows: (i) that the previous results are still found after dimensionality reduction, and thus are not attributable to the curse of dimensionality; (ii) that previous results are confirmed when using new measures of similarity; (iii) that correlations between brain representations and those from models are specific to models trained on human language; and (iv) that the results are dependent on the presence of positional encoding in the models. These results confirm and strengthen the results of previous research and contribute to the debate on the biological plausibility and interpretability of state-of-the-art large language models.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length.

We show that feedforward neural networks with ReLU activation generalize on low complexity data, suitably defined. Given i.i.d. data generated from a simple programming language, the minimum description length (MDL) feedforward neural network which interpolates the data generalizes with high probability. We define this simple programming language, along with a notion of description length of such networks. We provide several examples on basic computational tasks, such as checking primality of a natural number, and more. For primality testing, our theorem shows the following. Suppose that we draw an i.i.d. sample of Theta(N^{delta}ln N) numbers uniformly at random from 1 to N, where deltain (0,1). For each number x_i, let y_i = 1 if x_i is a prime and 0 if it is not. Then with high probability, the MDL network fitted to this data accurately answers whether a newly drawn number between 1 and N is a prime or not, with test error leq O(N^{-delta}). Note that the network is not designed to detect primes; minimum description learning discovers a network which does so.

This article presents a Monte Carlo study on bond percolation in distorted square and triangular lattices. The distorted lattices are generated by dislocating the sites from their regular positions. The amount and direction of the dislocations are random, but can be tuned by the distortion parameter α. Once the sites are dislocated, the bond lengths δ between the nearest neighbors change. A bond can only be occupied if its bond length is less than a threshold value called the connection threshold d. It is observed that when the connection threshold is greater than the lattice constant (assumed to be 1), the bond percolation threshold p_b always increases with distortion. For dle 1, no spanning configuration is found for the square lattice when the lattice is distorted, even very slightly. On the other hand, the triangular lattice not only spans for dle 1, it also shows a decreasing trend for p_b in the low-α range. These variation patterns have been linked with the average coordination numbers of the distorted lattices. A critical value d_c for the connection threshold has been defined as the value of d below which no spanning configuration can be found even after occupying all the bonds satisfying the connection criterion δle d. The behavior of d_c(α) is markedly different for the two lattices.

Reinforcement Learning from Human Feedback relies on reward models to align large language models with human preferences. However, RLHF often suffers from reward hacking, wherein policy learning exploits flaws in the trained reward model to maximize reward scores without genuinely aligning with human preferences. A significant example of such reward hacking is length bias, where reward models usually favor longer responses irrespective of actual response quality. Previous works on length bias have notable limitations, these approaches either mitigate bias without characterizing the bias form, or simply assume a linear length-reward relation. To accurately model the intricate nature of length bias and facilitate more effective bias mitigation, we propose FiMi-RM (Bias Fitting to Mitigate Length Bias of Reward Model in RLHF), a framework that autonomously learns and corrects underlying bias patterns. Our approach consists of three stages: First, we train a standard reward model which inherently contains length bias. Next, we deploy a lightweight fitting model to explicitly capture the non-linear relation between length and reward. Finally, we incorporate this learned relation into the reward model to debias. Experimental results demonstrate that FiMi-RM achieves a more balanced length-reward distribution. Furthermore, when applied to alignment algorithms, our debiased reward model improves length-controlled win rate and reduces verbosity without compromising its performance.

Large language models (LLMs) are increasingly optimized for long reasoning, under the assumption that more reasoning leads to better performance. However, emerging evidence suggests that longer responses can sometimes degrade accuracy rather than improve it. In this paper, we conduct a systematic empirical study of the relationship between reasoning length and answer correctness. We find that LLMs tend to overthink simple problems, generating unnecessarily long outputs, and underthink harder ones, failing to extend their reasoning when it is most needed. This indicates that models might misjudge problem difficulty and fail to calibrate their response length appropriately. Furthermore, we investigate the effects of length reduction with a preference optimization algorithm when simply preferring the shorter responses regardless of answer correctness. Experiments show that the generation length can be significantly reduced while maintaining acceptable accuracy. Our findings highlight generation length as a meaningful signal for reasoning behavior and motivate further exploration into LLMs' self-awareness in reasoning length adaptation.

Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on combined evidence from real-world observations, controlled experiments, and theoretical analysis, we demonstrate that task accuracy typically follows an inverted U-shaped curve with CoT length, where performance initially improves but eventually decreases as the number of CoT steps increases. With controlled experiments, we further uncover the scaling behaviors of the optimal CoT length: it increases with task difficulty but decreases with model capability, exposing an inherent simplicity bias where more capable models favor shorter, more efficient CoT reasoning. This bias is also evident in Reinforcement Learning (RL) training, where models gravitate towards shorter CoTs as their accuracy improves. To have a deep understanding of these dynamics, we establish a simple theoretical model that formally proves these phenomena, including the optimal length's scaling laws and the emergence of simplicity bias during RL. Guided by this framework, we demonstrate significant practical benefits from training with optimally-lengthed CoTs and employing length-aware filtering at inference. These findings offer both a principled understanding of the "overthinking" phenomenon and multiple practical guidelines for CoT calibration, enabling LLMs to achieve optimal reasoning performance with adaptive CoTs tailored to task complexity and model capability.

Block drafters propose several tokens in one forward pass, before earlier target tokens are realised. Their rejection mixes two losses: missing within-block path information and imperfect modelling of observable information. Accepted length cannot distinguish them. We separate the two with an information floor, the minimum expected rejection at a specified conditioning order; rejection above this floor is the model gap. Estimating both from target rollouts across four domains, four open-weight targets, and a frontier API target yields three findings. First, the all-parallel floor reaches 0.286 at the final slot on Qwen3-4B, limiting even the best proposal to 71% per-slot acceptance. Second, one realised token removes 86--100% of this floor, a locality also recovered by an independent mutual-information analysis. Third, current drafters remain far above their floors: the final-slot model gap accounts for 43--64% of DFlash rejection and 85--92% of DSpark's oracle-conditioned rejection. These findings separate the value of short-range conditioning from proposal quality. Guided by this distinction, we replace a context-independent predecessor correction with a prefix-attention head that reads committed context conditional on the predecessor. With supporting backbone components, the resulting Qwen3-4B drafter improves mean serving accepted length by 3.83% over the released DSpark checkpoint across nine tasks, without increasing the conditioning order.

We study quantum state tomography when the unknown state lies in a trace-distance ball of radius R around a known reference state ρ. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write Γ=d(Trsqrtρ)^2+d^2R. For dge2, 0<Rle1, and nge1 copies, the expected risk is Θ(min{R,Γ/n}). At failure probability 0<δle1/3, the minimax confidence radius is \[ Θ\!\left(\min\left\{R,\frac{Γ+\log(1/δ){n}}\right\}\right). \] For varepsilonle c_0R with a universal c_0>0, the copy complexity is Θ((Γ+log(1/δ))/varepsilon^2). For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes during chain-of-thought (CoT) generation, leading to severe overthinking phenomena. In response, recent studies have designed reward functions to reinforce models' behaviors in producing shorter yet correct completions. Nevertheless, we observe that these length-penalty reward functions exacerbate RL training instability: as the completion length decreases, model accuracy abruptly collapses, often occurring early in training. To address this issue, we propose a simple yet effective solution GRPO-lambda, an efficient and stabilized variant of GRPO, which dynamically adjusts the reward strategy by monitoring the correctness ratio among completions within each query-sampled group. A low correctness ratio indicates the need to avoid length penalty that compromises CoT quality, triggering a switch to length-agnostic 0/1 rewards that prioritize reasoning capability. A high ratio maintains length penalties to boost efficiency. Experimental results show that our approach avoids training instability caused by length penalty while maintaining the optimal accuracy-efficiency trade-off. On the GSM8K, GPQA, MATH-500, AMC 2023, and AIME 2024 benchmarks, it improves average accuracy by 1.48% while reducing CoT sequence length by 47.3%.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

Ensembles of neural network weight matrices are studied through the training process for the MNIST classification problem, testing the efficacy of matrix models for representing their distributions, under assumptions of Gaussianity and permutation-symmetry. The general 13-parameter permutation invariant Gaussian matrix models are found to be effective models for the correlated Gaussianity in the weight matrices, beyond the range of applicability of the simple Gaussian with independent identically distributed matrix variables, and notably well beyond the initialisation step. The representation theoretic model parameters, and the graph-theoretic characterisation of the permutation invariant matrix observables give an interpretable framework for the best-fit model and for small departures from Gaussianity. Additionally, the Wasserstein distance is calculated for this class of models and used to quantify the movement of the distributions over training. Throughout the work, the effects of varied initialisation regimes, regularisation, layer depth, and layer width are tested for this formalism, identifying limits where particular departures from Gaussianity are enhanced and how more general, yet still highly-interpretable, models can be developed.

We develop a perturbative framework for systems coupled quadratically to bosonic environments with quadratic Hamiltonians and linear Lindblad operators. The method applies to both single-mode and multimode environments whose initial states may be non-Gaussian and nonstationary. By combining linear evolution in a doubled operator space with a characteristic-function representation, we express ordered multitime environmental correlation functions in terms of derivatives of the initial characteristic function. These correlation functions enter a recursive construction of the time-convolutionless generator at arbitrary finite order. We illustrate the method with a qubit coupled to a damped mode via a two-photon interaction. Initial Fock and thermal states with identical first and second field moments produce different second-order generators through their fourth moments.

Of the various attempts to generalize information theory to multiple variables, the most widely utilized, interaction information, suffers from the problem that it is sometimes negative. Here we reconsider from first principles the general structure of the information that a set of sources provides about a given variable. We begin with a new definition of redundancy as the minimum information that any source provides about each possible outcome of the variable, averaged over all possible outcomes. We then show how this measure of redundancy induces a lattice over sets of sources that clarifies the general structure of multivariate information. Finally, we use this redundancy lattice to propose a definition of partial information atoms that exhaustively decompose the Shannon information in a multivariate system in terms of the redundancy between synergies of subsets of the sources. Unlike interaction information, the atoms of our partial information decomposition are never negative and always support a clear interpretation as informational quantities. Our analysis also demonstrates how the negativity of interaction information can be explained by its confounding of redundancy and synergy.

Today's large language models (LLMs) can solve challenging question-answering tasks, and prompt engineering techniques, such as chain-of-thought (CoT), have gained attention for enhancing the explanation and correctness of outputs. Nevertheless, models require significant time to generate answers augmented with lengthy reasoning details. To address this issue, this paper analyzes the impact of output lengths on LLM inference pipelines and proposes novel metrics to evaluate them in terms of correct conciseness. It also examines the impact of controlling output length through a refined prompt engineering strategy, Constrained-CoT (CCoT), which encourages the model to limit output length. Experiments on pre-trained LLMs demonstrated the benefit of the proposed metrics and the effectiveness of CCoT across different models. For instance, constraining the reasoning of LLaMA2-70b to 100 words improves the accuracy from 36.01\% (CoT) to 41.07\% (CCoT) on the GSM8K dataset, while reducing the average output length by 28 words.

Intrinsic dimension (ID) is an important tool in modern LLM analysis, informing studies of training dynamics, scaling behavior, and dataset structure, yet its textual determinants remain underexplored. We provide the first comprehensive study grounding ID in interpretable text properties through cross-encoder analysis, linguistic features, and sparse autoencoders (SAEs). In this work, we establish three key findings. First, ID is complementary to entropy-based metrics: after controlling for length, the two are uncorrelated, with ID capturing geometric complexity orthogonal to prediction quality. Second, ID exhibits robust genre stratification: scientific prose shows low ID (~8), encyclopedic content medium ID (~9), and creative/opinion writing high ID (~10.5) across all models tested. This reveals that contemporary LLMs find scientific text "representationally simple" while fiction requires additional degrees of freedom. Third, using SAEs, we identify causal features: scientific signals (formal tone, report templates, statistics) reduce ID; humanized signals (personalization, emotion, narrative) increase it. Steering experiments confirm these effects are causal. Thus, for contemporary models, scientific writing appears comparatively "easy", whereas fiction, opinion, and affect add representational degrees of freedom. Our multi-faceted analysis provides practical guidance for the proper use of ID and the sound interpretation of ID-based results.

Commonly used evaluation measures including Recall, Precision, F-Measure and Rand Accuracy are biased and should not be used without clear understanding of the biases, and corresponding identification of chance or base case levels of the statistic. Using these measures a system that performs worse in the objective sense of Informedness, can appear to perform better under any of these commonly used measures. We discuss several concepts and measures that reflect the probability that prediction is informed versus chance. Informedness and introduce Markedness as a dual measure for the probability that prediction is marked versus chance. Finally we demonstrate elegant connections between the concepts of Informedness, Markedness, Correlation and Significance as well as their intuitive relationships with Recall and Precision, and outline the extension from the dichotomous case to the general multi-class case.