# Provably Learning from Modern Language Models via Low Logit Rank

arXiv: https://arxiv.org/abs/2512.09892 · HTML: https://mlsanity.com/paper/2512.09892/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 30 of 32)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [Mechanistic Interpretability for AI Safety -- A Review](https://mlsanity.com/paper/2404.14082/) (2024)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Stealing Part of a Production Language Model](https://mlsanity.com/paper/2403.06634/) (2024)
- [The emergence of clusters in self-attention dynamics](https://mlsanity.com/paper/2305.05465/) (2023)
- [Saturated Transformers are Constant-Depth Threshold Circuits](https://mlsanity.com/paper/2106.16213/) (2021)
- [The Role of Coverage in Online Reinforcement Learning](https://mlsanity.com/paper/2210.04157/) (2022)
- [Dynamic metastability in the self-attention model](https://mlsanity.com/paper/2410.06833/) (2024)
- [Language Generation in the Limit](https://mlsanity.com/paper/2404.06757/) (2024)
- [Learning Compositional Functions with Transformers from Easy-to-Hard Data](https://mlsanity.com/paper/2505.23683/) (2025)
- [Transformers Learn to Implement Multi-step Gradient Descent with Chain of Thought](https://mlsanity.com/paper/2502.21212/) (2025)
- [Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges](https://mlsanity.com/paper/2502.01612/) (2025)
- [Learning in Observable POMDPs, without Computationally Intractable Oracles](https://mlsanity.com/paper/2206.03446/) (2022)
- [Clustering Mixtures with Almost Optimal Separation in Polynomial Time](https://mlsanity.com/paper/2112.00706/) (2021)
- [Planning in Observable POMDPs in Quasipolynomial Time](https://mlsanity.com/paper/2201.04735/) (2022)
- [Provably learning a multi-head attention layer](https://mlsanity.com/paper/2402.04084/) (2024)
- [Six Lectures on Linearized Neural Networks](https://mlsanity.com/paper/2308.13431/) (2023)
- [(Im)possibility of Automated Hallucination Detection in Large Language Models](https://mlsanity.com/paper/2504.17004/) (2025)
- [On the Performance of Empirical Risk Minimization with Smoothed Data](https://mlsanity.com/paper/2402.14987/) (2024)
- [Learning Hidden Markov Models Using Conditional Samples](https://mlsanity.com/paper/2302.14753/) (2023)
- [Model Stealing for Any Low-Rank Language Model](https://mlsanity.com/paper/2411.07536/) (2024)

## Built on by (most cited first, 3 of 3)

- [Subliminal Effects in Your Data: A General Mechanism via Log-Linearity](https://mlsanity.com/paper/2602.04863/) (2026)
- [Provably Extracting the Features from a General Superposition](https://mlsanity.com/paper/2512.15987/) (2025)
- [Identified-Set Geometry of Distributional Model Extraction under Top-K Censored API Access](https://mlsanity.com/paper/2605.10407/) (2026)

## Abstract (arXiv)

While modern language models and their inner workings are incredibly complex, recent work (Golowich, Liu & Shetty; 2025) has proposed a simple and potentially tractable abstraction for them through the observation that empirically, these language models all seem to have approximately low logit rank. Roughly, this means that a matrix formed by the model's log probabilities of various tokens conditioned on certain sequences of tokens is well approximated by a low rank matrix. In this paper, our focus is on understanding how this structure can be exploited algorithmically for obtaining provable learning guarantees. Since low logit rank models can encode hard-to-learn distributions such as noisy parities, we study a query learning model with logit queries that reflects the access model for common APIs. Our main result is an efficient algorithm for learning any approximately low logit rank model from queries. We emphasize that our structural assumption closely reflects the behavior that is empirically observed in modern language models. Thus, our result gives what we believe is the first end-to-end learning guarantee for a generative model that plausibly captures modern language models.