What question did this study set out to answer?

This research examines the entropy dynamics of large language models (LLMs) in various settings, particularly focusing on the signal-to-noise characteristics across different conditions.

April 10, 2026Open Access

LLM entropy Grammar+Fisher study

Puntos clave

This research examines the entropy dynamics of large language models (LLMs) in various settings, particularly focusing on the signal-to-noise characteristics across different conditions.
Conducted 10k runs across four regimes (factual, creative, mathematical, philosophical) with three LLM seeds and two control types.
Completed a full factorial matrix of regimes, LLM seeds, and controls to explore output variations.
Utilized scripts for entropy collection and Fisher analysis to aggregate results consistently.
Identified a signal-to-noise separation ranging from 2.2× to 263× across tested conditions.
Both control types converge to a common Fisher tail noise floor around 52–53.
Mathematical and philosophical regimes exhibited the strongest and most consistent elevation above the noise floor.

Resumen

This release updates the preprint and supporting outputs for the LLM entropy Grammar+Fisher study. What is included Updated manuscript PDF: LLMGrammarFisherPreprint. pdf Fisher summaries and aggregation outputs for: all 4 regimes (factual, creative, mathematical, philosophical) LLM seeds 42, 99, 7 controls shuffled, randomᵤniform grammar-seed sweep 0, 1, 2 at fixed LLM seed 42 Key update in this version Completed the full 36/36 regime × LLM-seed × control matrix. Added/standardized creative multi-seed 10k runs (seeds 99 and 7) to match the existing 10k protocol. Regenerated Fisher outputs and merged multi-seed summaries. Updated manuscript text for numerical consistency: signal-to-noise range reported as 2. 2× to 263× controls collapse to a common noise floor of approximately 52–53. Main empirical result Across all tested combinations, both control conditions (shuffled, randomᵤniform) converge to a common Fisher tail noise floor, while real-signal (none) conditions remain consistently above this baseline. The weakest observed separation is 2. 2×, and the strongest is 263× (philosophical, seed 7), with strongest and most consistent elevation in mathematical/philosophical regimes. Reproducibility notes The repository contains the scripts used for: entropy collection (collectₗlmₑntropyₛeries. py) Fisher pipeline (runₗlmₑntropygrammarfisher. py) grammar-seed and multi-seed aggregation (aggregateₗlmfishergrammarₛeedₛweep. py, mergeₗlmfisherₘultiseedₛummaries. py) All outputs in this release were generated with the same SAX→LSTM→Fisher workflow used in the related Sycamore studies.

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