# RLSF: Fine-tuning LLMs via Symbolic Feedback

arXiv: https://arxiv.org/abs/2405.16661 · HTML: https://mlsanity.com/paper/2405.16661/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 26 May 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [Recent Advances in Natural Language Processing via Large Pre-Trained Language Models: A Survey](https://mlsanity.com/paper/2111.01243/) (2021)
- [Harnessing the Power of LLMs in Practice: A Survey on ChatGPT and Beyond](https://mlsanity.com/paper/2304.13712/) (2023)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [Translation between Molecules and Natural Language](https://mlsanity.com/paper/2204.11817/) (2022)
- [SPoC: Search-based Pseudocode to Code](https://mlsanity.com/paper/1906.04908/) (2019)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Mol-Instructions: A Large-Scale Biomolecular Instruction Dataset for Large Language Models](https://mlsanity.com/paper/2306.08018/) (2023)
- [LlaSMol: Advancing Large Language Models for Chemistry with a Large-Scale, Comprehensive, High-Quality Instruction Tuning Dataset](https://mlsanity.com/paper/2402.09391/) (2024)
- [Execution-based Code Generation using Deep Reinforcement Learning](https://mlsanity.com/paper/2301.13816/) (2023)
- [StepCoder: Improve Code Generation with Reinforcement Learning from Compiler Feedback](https://mlsanity.com/paper/2402.01391/) (2024)
- [A Large-Scale Survey on the Usability of AI Programming Assistants: Successes and Challenges](https://mlsanity.com/paper/2303.17125/) (2023)
- [Multilingual Large Language Model: A Survey of Resources, Taxonomy and Frontiers](https://mlsanity.com/paper/2404.04925/) (2024)
- [Compilable Neural Code Generation with Compiler Feedback](https://mlsanity.com/paper/2203.05132/) (2022)
- [CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities](https://mlsanity.com/paper/2401.06961/) (2024)
- [Neurosymbolic Reinforcement Learning and Planning: A Survey](https://mlsanity.com/paper/2309.01038/) (2023)
- [CoTran: An LLM-based Code Translator using Reinforcement Learning with Feedback from Compiler and Symbolic Execution](https://mlsanity.com/paper/2306.06755/) (2023)

## Built on by (most cited first, 14 of 14)

- [100 Days After DeepSeek-R1: A Survey on Replication Studies and More Directions for Reasoning Language Models](https://mlsanity.com/paper/2505.00551/) (2025)
- [Neuro-Symbolic Artificial Intelligence: Towards Improving the Reasoning Abilities of Large Language Models](https://mlsanity.com/paper/2508.13678/) (2025)
- [ProofBridge: Auto-Formalization of Natural Language Proofs in Lean via Joint Embeddings](https://mlsanity.com/paper/2510.15681/) (2025)
- [Towards Formal Verification of LLM-Generated Code from Natural Language Prompts](https://mlsanity.com/paper/2507.13290/) (2025)
- [LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision](https://mlsanity.com/paper/2512.18196/) (2025)
- [DualSchool: How Reliable are LLMs for Optimization Education?](https://mlsanity.com/paper/2505.21775/) (2025)
- [Scaling Reinforcement Learning for Content Moderation with Large Language Models](https://mlsanity.com/paper/2512.20061/) (2025)
- [e-SimFT: Alignment of Generative Models with Simulation Feedback for Pareto-Front Design Exploration](https://mlsanity.com/paper/2502.02628/) (2025)
- [CDRL: Certification-Driven Reinforcement Learning for Neutrino Flavor Model Discovery](https://mlsanity.com/paper/2608.20686/) (2026)
- [R1-Fuzz: Specializing Language Models for Textual Fuzzing via Reinforcement Learning](https://mlsanity.com/paper/2509.20384/) (2025)
- [Report for NSF Workshop on AI for Electronic Design Automation](https://mlsanity.com/paper/2601.14541/) (2026)
- [Neuro-symbolic AI for Industrial Configuration](https://mlsanity.com/paper/2609.29947/) (2026)
- [Towards Certificate-Driven Software Porting: A Self-Improving Agentic Harness for Scientific Program Optimization](https://mlsanity.com/paper/2609.34069/) (2026)
- [AIProver: Agentic Auto-Formalization of Mathematical Research via Certificate-Driven Evolving Harness](https://mlsanity.com/paper/2610.05367/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have transformed AI but often struggle with tasks that require domain-specific reasoning and logical alignment. Traditional fine-tuning methods do not leverage the vast amount of symbolic domain-knowledge available to us via symbolic reasoning tools (e.g., provers), and are further limited by sparse rewards and unreliable reward models. We introduce Reinforcement Learning via Symbolic Feedback (RLSF), a novel fine-tuning paradigm where symbolic reasoning tools (e.g., solvers, provers, and algebra systems) provide fine-grained feedback to LLMs. RLSF uses poly-sized certificates (e.g., proofs) generated by symbolic tools to identify and correct errors in model outputs, offering token-level guidance without requiring differentiable reasoning systems. This paradigm bridges the gap between symbolic reasoning and LLM fine-tuning, enabling precise alignment with domain-specific constraints while addressing key limitations of traditional reward signals. Via extensive evaluations, we show that our RLSF-based fine-tuning of LLMs outperforms traditional approaches on five different applications (that have some associated logical or domain constraints), namely, program synthesis from natural language pseudo-code to programming language, three chemistry tasks, and solving the Game of 24. A key takeaway is that fine-tuning via RLSF enables relatively smaller LLMs to significantly outperform closed-source models that are orders of magnitude larger.