# Learning the Error Patterns of Language Models

arXiv: https://arxiv.org/abs/2605.28328 · HTML: https://mlsanity.com/paper/2605.28328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 38 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 22 of 22)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [Flexible and Efficient Grammar-Constrained Decoding](https://mlsanity.com/paper/2502.05111/) (2025)
- [Type-Constrained Code Generation with Language Models](https://mlsanity.com/paper/2504.09246/) (2025)
- [ChopChop: a Programmable Framework for Semantically Constraining the Output of Language Models](https://mlsanity.com/paper/2509.00360/) (2025)
- [HR-MultiWOZ: A Task Oriented Dialogue (TOD) Dataset for HR LLM Agent](https://mlsanity.com/paper/2402.01018/) (2024)
- [SuperCoder: Assembly Program Superoptimization with Large Language Models](https://mlsanity.com/paper/2505.11480/) (2025)
- [Semantics-Guided Synthesis](https://mlsanity.com/paper/2008.09836/) (2020)
- [LOUD: Synthesizing Strongest and Weakest Specifications](https://mlsanity.com/paper/2408.12539/) (2024)
- [Bootstrapping Fuzzers for Compilers of Low-Resource Language Dialects Using Language Models](https://mlsanity.com/paper/2512.05887/) (2025)

## Abstract (arXiv)

When generating outputs for domains with specific validity constraints (e.g., a program should compile), LLMs often fail in a small number of focused ways: for example, by using Python function names when generating TypeScript. We observe that these error patterns can be represented using a small number of constraints that can be learned in practice. We propose prefix filters, which are per-domain-and-LLM symbolic functions, as objects to capture the error patterns, Palla as an algorithm to learn prefix filters efficiently in practice, and implement Palla. Prefix filters learned by Palla i) help us quantitatively analyze the error patterns of LLMs, and ii) can be used to constrain the outputs of a model via constrained sampling algorithms. For example, Palla boosts compile rates for Qwen2.5-1.5B on TypeScript generation, by over 60%, allowing Qwen2.5-1.5B to achieve similar performance to Llama3.1-8B unconstrained.