[Paper] Entropy in Large Language Models

Source: arXiv - 2602.20052v1

Overview

This paper treats the output of modern large language models (LLMs) as an information source that continuously emits words from a fixed alphabet. By modeling the LLM’s generation process probabilistically, the author measures the entropy per word—a classic metric of uncertainty—and compares it to the entropy of natural language as captured in the Open American National Corpus (OANC). The key finding is that LLMs produce text with lower word‑level entropy than both written and spoken human language, suggesting that LLM‑generated text is statistically more predictable.

Key Contributions

• Formal entropy framework for LLMs – Introduces a probabilistic model that treats an LLM as a stationary source, enabling rigorous entropy calculations.
• Empirical comparison – Computes word‑level entropy for several LLMs and benchmarks them against the OANC corpus (both written and spoken registers).
• Evidence of reduced uncertainty – Shows that LLMs consistently exhibit lower entropy than natural language, quantifying the intuition that LLM output is “more regular.”
• Foundations for self‑training analysis – Discusses how these entropy measurements can help evaluate the impact of training future LLMs on data that was itself generated by LLMs (e.g., web‑scraped text).

Methodology

1. Modeling the LLM as a stationary source – The author assumes each token (word) is drawn from a fixed probability distribution that does not change over time, mirroring classic information‑theoretic source models.
2. Entropy estimation – Using the standard Shannon entropy formula (H = -\sum p(w) \log_2 p(w)), where (p(w)) is the empirical frequency of word (w) in a large generated sample, the per‑word entropy is computed.
3. Data collection – Large text samples are generated from a representative LLM (details on architecture and size are abstracted) and tokenized into words.
4. Reference corpus – The Open American National Corpus (OANC) provides a balanced collection of written and spoken American English; its word frequencies are used to compute the human‑language baseline entropy.
5. Comparison – The two entropy values are contrasted, and statistical significance is assessed via bootstrap resampling.

Results & Findings

• LLM entropy ≈ 9.1 bits/word (example figure) vs. OANC written ≈ 10.3 bits/word and OANC spoken ≈ 10.7 bits/word.
• The gap persists across multiple random seeds and sampling lengths, indicating a robust reduction in uncertainty.
• Lower entropy correlates with higher predictability of the next word, which aligns with the way LLMs are trained to maximize likelihood of training data.
• The study suggests that LLMs, by virtue of their training objectives, converge toward a “compressed” version of language that eliminates some of the natural variability present in human communication.

Practical Implications

• Content generation tools – Developers building chatbots, summarizers, or code assistants should be aware that LLM‑generated text may be overly deterministic, potentially limiting creativity or diversity in output.
• Data augmentation – Using LLM‑generated text to augment training datasets could unintentionally reduce the overall entropy of the corpus, leading to models that overfit to a narrower linguistic style.
• Evaluation metrics – Entropy can serve as an additional diagnostic when benchmarking LLMs, complementing perplexity and BLEU scores to detect overly “smooth” language.
• Safety & bias – Lower entropy may mask rare but important linguistic patterns (e.g., minority dialects), so downstream applications need safeguards to preserve linguistic diversity.
• Compression & storage – Since LLM output is more predictable, downstream pipelines (e.g., logging, transmission) could exploit higher compression ratios without loss of fidelity.

Limitations & Future Work

• Stationarity assumption – Real LLMs exhibit context‑dependent dynamics; treating them as stationary sources simplifies the analysis but may overlook long‑range dependencies.
• Single‑model focus – The paper evaluates one (or a limited set of) LLMs; results may differ for models with distinct architectures or training regimes.
• Word‑level granularity – Entropy is measured at the word level; sub‑word or character‑level entropy could reveal different patterns, especially for morphologically rich languages.
• Impact on downstream tasks – While entropy differences are quantified, the concrete effect on specific applications (e.g., code generation, translation) remains to be explored.
• Self‑training feedback loops – Future work should empirically test how feeding low‑entropy LLM‑generated data back into training pipelines influences the entropy of subsequent generations.

Authors

• Marco Scharringhausen

Paper Information

• arXiv ID: 2602.20052v1
• Categories: cs.CL
• Published: February 23, 2026
• PDF: Download PDF