# SequenceMatch: Imitation Learning for Autoregressive Sequence Modelling with Backtracking

arXiv: https://arxiv.org/abs/2306.05426 · HTML: https://mlsanity.com/paper/2306.05426/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 28 of its 43 references that are in the map.
- First posted on arXiv 8 Jun 2023.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [IQ-Learn: Inverse soft-Q Learning for Imitation](https://mlsanity.com/paper/2106.12142/) (2021)
- [Scaling Autoregressive Video Models](https://mlsanity.com/paper/1906.02634/) (2019)
- [Imitation Learning via Off-Policy Distribution Matching](https://mlsanity.com/paper/1912.05032/) (2019)
- [Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation](https://mlsanity.com/paper/2204.01171/) (2022)
- [A Survey on Generative Adversarial Networks: Variants, Applications, and Training](https://mlsanity.com/paper/2006.05132/) (2020)
- [A Theoretical Analysis of the Repetition Problem in Text Generation](https://mlsanity.com/paper/2012.14660/) (2020)
- [Toward Diverse Text Generation with Inverse Reinforcement Learning](https://mlsanity.com/paper/1804.11258/) (2018)
- [MAUVE Scores for Generative Models: Theory and Practice](https://mlsanity.com/paper/2212.14578/) (2022)
- [LS-IQ: Implicit Reward Regularization for Inverse Reinforcement Learning](https://mlsanity.com/paper/2303.00599/) (2023)
- [Adversarial Soft Advantage Fitting: Imitation Learning without Policy Optimization](https://mlsanity.com/paper/2006.13258/) (2020)
- [A Simple Contrastive Learning Objective for Alleviating Neural Text Degeneration](https://mlsanity.com/paper/2205.02517/) (2022)
- [Lessons Learned from the Training of GANs on Artificial Datasets](https://mlsanity.com/paper/2007.06418/) (2020)
- [Training Wasserstein GANs without gradient penalties](https://mlsanity.com/paper/2110.14150/) (2021)

## Built on by (most cited first, 13 of 13)

- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning](https://mlsanity.com/paper/2503.01067/) (2025)
- [LLMs are Greedy Agents: Effects of RL Fine-tuning on Decision-Making Abilities](https://mlsanity.com/paper/2504.16078/) (2025)
- [Hybrid Inverse Reinforcement Learning](https://mlsanity.com/paper/2402.08848/) (2024)
- [Backtracking Improves Generation Safety](https://mlsanity.com/paper/2409.14586/) (2024)
- [Imitating Language via Scalable Inverse Reinforcement Learning](https://mlsanity.com/paper/2409.01369/) (2024)
- [Implicit Reward as the Bridge: A Unified View of SFT and DPO Connections](https://mlsanity.com/paper/2507.00018/) (2025)
- [Structured Agent Distillation for Large Language Model](https://mlsanity.com/paper/2505.13820/) (2025)
- [Learning Safety Constraints for Large Language Models](https://mlsanity.com/paper/2505.24445/) (2025)
- [SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2605.07711/) (2026)
- [ERGO: Entropy-guided Resetting for Generation Optimization in Multi-turn Language Models](https://mlsanity.com/paper/2510.14077/) (2025)
- [From Demonstrations to Rewards: Alignment Without Explicit Human Preferences](https://mlsanity.com/paper/2503.13538/) (2025)
- [The Bridge-Garden Dilemma in LLM Distillation: Why Mixing Hard and Soft Labels Works](https://mlsanity.com/paper/2605.26246/) (2026)

## Abstract (arXiv)

In many domains, autoregressive models can attain high likelihood on the task of predicting the next observation. However, this maximum-likelihood (MLE) objective does not necessarily match a downstream use-case of autoregressively generating high-quality sequences. The MLE objective weights sequences proportionally to their frequency under the data distribution, with no guidance for the model's behaviour out of distribution (OOD): leading to compounding error during autoregressive generation. In order to address this compounding error problem, we formulate sequence generation as an imitation learning (IL) problem. This allows us to minimize a variety of divergences between the distribution of sequences generated by an autoregressive model and sequences from a dataset, including divergences with weight on OOD generated sequences. The IL framework also allows us to incorporate backtracking by introducing a backspace action into the generation process. This further mitigates the compounding error problem by allowing the model to revert a sampled token if it takes the sequence OOD. Our resulting method, SequenceMatch, can be implemented without adversarial training or architectural changes. We identify the SequenceMatch-chi2 divergence as a more suitable training objective for autoregressive models which are used for generation. We show that empirically, SequenceMatch training leads to improvements over MLE on text generation with language models and arithmetic.