# Rethinking the Understanding Ability across LLMs through Mutual Information

arXiv: https://arxiv.org/abs/2505.23790 · HTML: https://mlsanity.com/paper/2505.23790/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 25 May 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 33)

- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [Fact or Fiction: Verifying Scientific Claims](https://mlsanity.com/paper/2004.14974/) (2020)
- [LLM2Vec: Large Language Models Are Secretly Powerful Text Encoders](https://mlsanity.com/paper/2404.05961/) (2024)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [Using an LLM to Help With Code Understanding](https://mlsanity.com/paper/2307.08177/) (2023)
- [When Scaling Meets LLM Finetuning: The Effect of Data, Model and Finetuning Method](https://mlsanity.com/paper/2402.17193/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Table Meets LLM: Can Large Language Models Understand Structured Table Data? A Benchmark and Empirical Study](https://mlsanity.com/paper/2305.13062/) (2023)
- [Are ChatGPT and GPT-4 General-Purpose Solvers for Financial Text Analytics? A Study on Several Typical Tasks](https://mlsanity.com/paper/2305.05862/) (2023)
- [Entropy and mutual information in models of deep neural networks](https://mlsanity.com/paper/1805.09785/) (2018)
- [Testing AI on language comprehension tasks reveals insensitivity to underlying meaning](https://mlsanity.com/paper/2302.12313/) (2023)
- [Open, Closed, or Small Language Models for Text Classification?](https://mlsanity.com/paper/2308.10092/) (2023)
- [Encoder vs Decoder: Comparative Analysis of Encoder and Decoder Language Models on Multilingual NLU Tasks](https://mlsanity.com/paper/2406.13469/) (2024)
- [Your Transformer is Secretly Linear](https://mlsanity.com/paper/2405.12250/) (2024)
- [The Vulnerability of Language Model Benchmarks: Do They Accurately Reflect True LLM Performance?](https://mlsanity.com/paper/2412.03597/) (2024)
- [Interpreting and Steering LLMs with Mutual Information-based Explanations on Sparse Autoencoders](https://mlsanity.com/paper/2502.15576/) (2025)
- [Line Goes Up? Inherent Limitations of Benchmarks for Evaluating Large Language Models](https://mlsanity.com/paper/2502.14318/) (2025)
- [LLMs' Reading Comprehension Is Affected by Parametric Knowledge and Struggles with Hypothetical Statements](https://mlsanity.com/paper/2404.06283/) (2024)
- [Are Decoder-Only Large Language Models the Silver Bullet for Code Search?](https://mlsanity.com/paper/2410.22240/) (2024)

## Built on by (most cited first, 1 of 1)

- [FlowNIB: An Information Bottleneck Analysis of Bidirectional vs. Unidirectional Language Models](https://mlsanity.com/paper/2506.00859/) (2025)

## Abstract (arXiv)

Recent advances in large language models (LLMs) have revolutionized natural language processing, yet evaluating their intrinsic linguistic understanding remains challenging. Moving beyond specialized evaluation tasks, we propose an information-theoretic framework grounded in mutual information (MI) to achieve this. We formalize the understanding as MI between an input sentence and its latent representation (sentence-level MI), measuring how effectively input information is preserved in latent representation. Given that LLMs learn embeddings for individual tokens, we decompose sentence-level MI into token-level MI between tokens and sentence embeddings, establishing theoretical bounds connecting these measures. Based on this foundation, we theoretically derive a computable lower bound for token-level MI using Fano's inequality, which directly relates to token-level recoverability-the ability to predict original tokens from sentence embedding. We implement this recoverability task to comparatively measure MI across different LLMs, revealing that encoder-only models consistently maintain higher information fidelity than their decoder-only counterparts, with the latter exhibiting a distinctive late-layer "forgetting" pattern where mutual information is first enhanced and then discarded. Moreover, fine-tuning to maximize token-level recoverability consistently improves understanding ability of LLMs on tasks without task-specific supervision, demonstrating that mutual information can serve as a foundation for understanding and improving language model capabilities.