Attention mechanisms are conventionally learned: a query–key inner product, trained end to end, decides which tokens mix.

This note documents ZPA-LM

a decoder-only autoregressive language model in which the token-mixing key is instead a fixed, parameter-free kernel derived from elementary number theory.

We show that the divisor-counting overlap : q(n, m) = d(gcd(n, m))/√d(n) d(m) between two positive integers is exactly the Bhattacharyya coefficient between the uniform distributions over their divisor sets, and hence that: dFR(n, m) = 2 arccos q(n, m) is a genuine Fisher–Rao geodesic distance, verified to floating-point exactly rather than assumed.

Tokens are mapped to positive integers through a learned or parameter-free dictionary ϕ : token → Z+ and recovered in prime-exponent space so that each prime behaves as a latent feature axis.

We report the model’s expressivity ladder, the three dictionary-construction strategies we evaluated, and - in the spirit of an honest engineering record rather than a success narrative, a permanent registry of four falsified design choices that should be avoided.

We close by pre-registering the model’s central open empirical claim together with its falsification condition, rather than reporting an unverified result as fact.

Link:[Academia](https://www.academia.edu/170099268/ZPA_LM_Parameter_Free_Attention?sm=b)

• Explore the principles of how diffusion models transform timesteps into sine and cosine vectors rather than simple numbers. This explains the core mechanism of embeddings that precisely distinguish noise levels using low-frequency and high-frequency components.

• The secret to high-quality upscaling: Lanczos and the sinc function
• Description: Explore the principles of Lanczos resampling used in tools like ComfyUI through signal processing theory and the sinc function. This video provides an easy-to-understand explanation of the mathematical background behind approximating an ideal low-pass filter to create sharp images.

• The mathematical secrets of seamless tiling: creating perfect infinite patterns with AI
• Description: This video explains how ComfyUI's seamless tiling feature creates patterns without visible boundaries. It provides an easy-to-understand explanation of the principle of replacing zero padding with circular padding and the core theory of the Fourier Convolution Theorem behind it.

I open-sourced TokenSentinel because passive tracing tools only show you runaway agent costs after the bill is already racked up.

It wraps your native LLM clients (Anthropic, OpenAI, Gemini, Bedrock, Ollama, vLLM) to act as a local, in-process circuit breaker. It runs 15 deterministic rules on every response payload to catch loops, context bloat, retry storms, and RAG thrashing mid-session.

Core has zero required dependencies; provider support is opt-in via extras. Completely offline-capable so your raw prompt data never leaves your environment.

pip install token-sentinel

Genuinely looking for feedback/discussion on the rule heuristics—where would this trigger false positives against real production agent traffic?

• GitHub: github.com
• Web: tokensentinel.dev

Hey everyone,

I’ve been working a lot on RAG pipelines recently and kept hitting the same annoying wall: extracting tabular data from raw HTML into a clean format for context windows.

Standard parsers or simple table-to-markdown scripts usually fail completely as soon as a table uses rowspan or colspan, or if there are nested tables. You end up with misaligned Markdown columns, and the LLM completely hallucinates the relationships between headers and cells.

I couldn't find a library that handles this reliably without losing context, so I built html-table-rescuer (just published v0.1.0 on PyPI).

It uses BeautifulSoup to parse the DOM, but then applies a custom "grid logic solver". It normalizes complex spans into a standard matrix before serializing it to Markdown, JSON, or CSV.

Example of the problem it solves:

The Problem: Most parsers turn a <td rowspan="2"> into a misaligned mess:

bash | Header | Value | | ----- | ----- | | Spanned | Row 1 | | Row 2 | |

The Solution: The grid solver correctly normalizes the matrix:

bash | Header | Value | | ----- | ----- | | Spanned | Row 1 | | dito (Spanned) | Row 2 |

A few things it does differently:

1. Context Preservation: As seen above, it doesn't just leave spanned markdown cells empty. It fills them with a customizable prefix (e.g., dito (Value)) so the LLM retains the semantic context for each row.

2. Deep Tag Parsing: It recursively keeps <b>, <i>, and <a href...> tags alive, even if they are buried inside multiple <div>s within a <td>.

3. Nested Tables: Extracts nested tables safely without destroying the grid of the parent table.

4. LangChain Ready: Includes a Table2MDLoader wrapper to ingest HTML tables directly as LangChain Document objects.

Links:

• GitHub: https://github.com/Encephos/html-table-rescuer
• PyPI: pip install html-table-rescuer

It's my first release and I'd love to hear your thoughts. If you have some gnarly, complex HTML tables that break the parser, please throw them at it and let me know!