# Amortizing intractable inference in large language models

arXiv: https://arxiv.org/abs/2310.04363 · HTML: https://mlsanity.com/paper/2310.04363/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- Builds on 76 of its 99 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 30 of 76)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [It's Not Just Size That Matters: Small Language Models Are Also Few-Shot Learners](https://mlsanity.com/paper/2009.07118/) (2020)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts](https://mlsanity.com/paper/2105.03023/) (2021)
- [A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Stories](https://mlsanity.com/paper/1604.01696/) (2016)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [FUDGE: Controlled Text Generation With Future Discriminators](https://mlsanity.com/paper/2104.05218/) (2021)

## Built on by (most cited first, 30 of 97)

- [Scaling Diffusion Language Models via Adaptation from Autoregressive Models](https://mlsanity.com/paper/2410.17891/) (2024)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [SDAR: A Synergistic Diffusion-AutoRegression Paradigm for Scalable Sequence Generation](https://mlsanity.com/paper/2510.06303/) (2025)
- [Self-Evolving Curriculum for LLM Reasoning](https://mlsanity.com/paper/2505.14970/) (2025)
- [Self-Improvement in Language Models: The Sharpening Mechanism](https://mlsanity.com/paper/2412.01951/) (2024)
- [Probabilistic Inference in Language Models via Twisted Sequential Monte Carlo](https://mlsanity.com/paper/2404.17546/) (2024)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Amortizing intractable inference in diffusion models for vision, language, and control](https://mlsanity.com/paper/2405.20971/) (2024)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [Language Models are Hidden Reasoners: Unlocking Latent Reasoning Capabilities via Self-Rewarding](https://mlsanity.com/paper/2411.04282/) (2024)
- [Learning diverse attacks on large language models for robust red-teaming and safety tuning](https://mlsanity.com/paper/2405.18540/) (2024)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction](https://mlsanity.com/paper/2410.08134/) (2024)
- [KL-Regularized Reinforcement Learning is Designed to Mode Collapse](https://mlsanity.com/paper/2510.20817/) (2025)
- [Flow of Reasoning: Training LLMs for Divergent Reasoning with Minimal Examples](https://mlsanity.com/paper/2406.05673/) (2024)
- [Adaptable Logical Control for Large Language Models](https://mlsanity.com/paper/2406.13892/) (2024)
- [Efficient Reinforcement Learning with Large Language Model Priors](https://mlsanity.com/paper/2410.07927/) (2024)
- [Trajectory Balance with Asynchrony: Decoupling Exploration and Learning for Fast, Scalable LLM Post-Training](https://mlsanity.com/paper/2503.18929/) (2025)
- [Latent Thought Models with Variational Bayes Inference-Time Computation](https://mlsanity.com/paper/2502.01567/) (2025)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [From Few to Many: Self-Improving Many-Shot Reasoners Through Iterative Optimization and Generation](https://mlsanity.com/paper/2502.00330/) (2025)
- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [BIRD: A Trustworthy Bayesian Inference Framework for Large Language Models](https://mlsanity.com/paper/2404.12494/) (2024)
- [Learning to Sample Effective and Diverse Prompts for Text-to-Image Generation](https://mlsanity.com/paper/2502.11477/) (2025)
- [ChemSafetyBench: Benchmarking LLM Safety on Chemistry Domain](https://mlsanity.com/paper/2411.16736/) (2024)
- [GFlowVLM: Enhancing Multi-step Reasoning in Vision-Language Models with Generative Flow Networks](https://mlsanity.com/paper/2503.06514/) (2025)
- [Pessimistic Backward Policy for GFlowNets](https://mlsanity.com/paper/2405.16012/) (2024)
- [Optimizing Backward Policies in GFlowNets via Trajectory Likelihood Maximization](https://mlsanity.com/paper/2410.15474/) (2024)
- [Can a Bayesian Oracle Prevent Harm from an Agent?](https://mlsanity.com/paper/2408.05284/) (2024)

## Abstract (arXiv)

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.