# Building LLM architecture

**URL:** <https://discuss.huggingface.co/t/building-llm-architecture/168704>\
**Category:** Research\
**Created:** [September 26, 2025, 10:52am UTC](https://discuss.huggingface.co/t/building-llm-architecture/168704 "2025-09-26T10:52:15Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![dannyyeung](https://sea2.discourse-cdn.com/hellohellohello/user_avatar/discuss.huggingface.co/dannyyeung/32/52757_2.png) [@dannyyeung](https://discuss.huggingface.co/u/dannyyeung)\
**Post date:** [September 26, 2025, 11:13pm UTC](https://discuss.huggingface.co/t/building-llm-architecture/168704/3 "2025-09-26T23:13:27Z")

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I asked my AI who know something about semantic attractor dynamics and prime number gaps.  
[https://discuss.huggingface.co/t/164607/5](https://discuss.huggingface.co/t/164607/5)

## And this is its reply, hope it help.

[https://chatgpt.com/share/68d7c80f-7608-8010-be48-bc72196ad178](https://chatgpt.com/share/68d7c80f-7608-8010-be48-bc72196ad178) \<= this link can see those formula better.

Yes: your **square ↔ pronic** alternation can be turned into a useful **anchor–edge memory scaffold** for LLMs.

- **Squares** act as _anchors_ (stable “1” with scale/magnitude).
- **Pronics** act as _edges/transitions_ (contextual “0” defined by its two neighboring anchors).  
This yields a multi-scale positional/memory scheme with ~O(N)O(\sqrt{N}) anchor slots for a length-NN sequence—handy for long-context retrieval and compression.

* * *

## Why this is promising

Your recurrence

an+1=an+⌈an⌉,a1=1a\_{n+1}=a\_n+\lceil\sqrt{a\_n}\rceil,\quad a\_1=1

produces diffs Δa=1,2,2,3,3,4,4,…\Delta a = 1,2,2,3,3,4,4,\ldots (each integer repeats twice). That induces a very clean **two-phase geometry** :

- **Odd indices** (perfect squares m2m^2) → _anchors_ with intrinsic scale mm.
- **Even indices** (pronics m(m+1)m(m+1)) → _edges_ that bind consecutive anchors m2↔(m+1)2m^2 \leftrightarrow (m{+}1)^2.

Intuition: anchors are “stable lattice states”, pronics are “allowed transitions”. This is exactly the structure many long-context systems want: a sparse set of global reference points (anchors) plus local bridges (edges).

* * *

## A concrete design: Nitya-PE (Positional Encoding) + Anchor-Edge Attention

**Encoding for token position tt:**

- m=⌊t⌋m=\lfloor \sqrt{t}\rfloor (segment index / scale)
- ϵ=t−m2\epsilon = t-m^2 (offset within the [m2,(m+1)2][m^2,(m+1)^2] segment)
- Phase bit b=1[t is a square]b = \mathbb{1}[t \text{ is a square}]

Form a feature vector, then project to model dim:

- u1=tu\_1=\sqrt{t} (magnitude/scale)
- u2=ϵ/(2m+1)u\_2=\epsilon / (2m+1) (normalized in-segment offset)
- u3=bu\_3=b (anchor/edge phase)

Use PE(t)=W [u1,u2,u3]\text{PE}(t)=W,[u\_1,u\_2,u\_3] (learned linear WW), optionally concatenated with your usual RoPE/ALiBi/relative biases.

**Attention bias (Anchor-Edge mask):**

- Give a small learned _bonus_ for queries to attend to:
  1. their nearest anchor m2m^2,
  2. the bridging edge m(m+1)m(m{+}1), and
  3. the next anchor (m+1)2(m{+}1)^2.

- Within a segment (between m2m^2 and (m+1)2(m+1)^2), allow more _order-insensitive_ aggregation; across segments, keep _order-sensitive_ weighting.  
(Rationale: your diffs are flat inside segments and “jump” only at boundaries—those jumps are natural event markers.)

**Memory compression:**

- Keep external memory only at anchors (and optionally edges).
- Number of anchors up to position NN is ⌊N⌋\lfloor\sqrt{N}\rfloor → ~O(N)O(\sqrt{N}) memory footprints, while still indexing the full length NN.

* * *

## How it’s different from plain binary

Your “1/0” isn’t free-floating; it’s **binary with magnitude and context** :

- “1” = square carries the scale mm explicitly (via t\sqrt{t}).
- “0” = pronic is defined _by_ its neighbors; it encodes _relational_ info (a transition), not a standalone state.

This makes it a natural fit for hierarchical or multi-scale reasoning, with built-in boundary detection (the moments when the diff increases).

* * *

## Relation to known ideas (at a glance)

- **Positional encodings:** complements RoPE/ALiBi/T5-relative by adding an explicit _segment scale_ and _phase_.
- **Hierarchical/long-context attention:** akin to global tokens or skip-lists, but with a **deterministic arithmetic schedule** for where the globals live (the squares) and how to bridge them (the pronics).
- **State-space / memory models:** you can treat anchors as persistent states and pronics as update edges.

* * *

## Minimal experiment you can run

1. **Tasks:** long-range retrieval (needle-in-a-haystack), cross-chapter QA, code with far references, or any long-document summarization.
2. **Models:** a small Transformer baseline (e.g., 100–300M).
3. **Variants:**

- Baseline PE (RoPE or ALiBi)
- Baseline + _Anchor-Edge attention bias_
- Baseline + _Nitya-PE_
- Baseline + both (bias + Nitya-PE)

1. **Metrics:** retrieval hit-rate @k, cross-segment F1 (can it follow references across square boundaries?), perplexity on long contexts, and memory/read latency if you add external memory at anchors.
2. **Ablations:** remove the phase bit; replace u1u\_1 with log⁡t\log t; jitter anchor locations slightly to check robustness.

* * *

## Descending variant (reversible pass)

Your decreasing rule (e.g., 100→90→81→72→⋯→0100\to90\to81\to72\to\cdots\to0) is essentially a **reverse traversal of the same anchor-edge graph**. Two uses:

- **Reversible compression / replay:** write forward (ascending), read back (descending) to reconstruct long chains with low drift.
- **Curriculum & stabilization:** a “cool-down” pass that progressively collapses transitions back into anchors—useful for denoising or for iterative summarization that preserves anchor fidelity.

* * *

## Pseudocode sketch (toy)

```auto
def nitya_features(t):
    import math
    m = int(math.sqrt(t))
    eps = t - m*m
    u1 = math.sqrt(t)
    u2 = eps / (2*m + 1) if (2*m + 1) > 0 else 0.0
    u3 = 1.0 if m*m == t else 0.0 # square = anchor
    return [u1, u2, u3] # project with a learned linear layer

# Attention bias: for a query at t, bonus to nearest anchors/edge
def nitya_bias(t, s):
    import math
    m = int(math.sqrt(t))
    anchors = {m*m, (m+1)*(m+1)}
    edges = {m*(m+1)}
    return 1.0 if s in anchors else (0.5 if s in edges else 0.0)

```

* * *

## Open questions (would love community input)

- Does anchor-edge bias improve fidelity on truly long contexts (\>128k) without extra compute?
- What’s the best way to combine Nitya-PE with RoPE (concat vs. gating vs. mixture-of-positional-experts)?
- Can we push the idea into **external memory** : anchors as keys, pronics as linkers, for O(N)O(\sqrt{N}) retrieval hops?

* * *

**Bottom line:** your “recursive binary-with-magnitude” looks like a clean, testable **multi-scale memory/indexing prior**. If you’re up for it, I can help draft a small training script to benchmark Nitya-PE + anchor-edge attention on a public long-context task and share results.

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_[View the full topic](https://discuss.huggingface.co/t/building-llm-architecture/168704)._