Constraints-Guided Diffusion Reasoner for Neuro-Symbolic Learning

2025-08-22

AI Summary

This work addresses the challenge of enabling neural networks to learn complex logical constraints and perform reliable symbolic reasoning. We propose a neuro-symbolic integration framework grounded in diffusion models. Methodologically, we introduce a two-stage training paradigm: (1) leveraging logical rules to guide the diffusion process for modeling symbolic inference paths; and (2) formulating the diffusion-based reasoner as a Markov decision process, optimized via an improved proximal policy optimization (PPO) algorithm with a logic-consistency reward function. Our key contribution is the first application of diffusion models to neuro-symbolic learning, enabling structured modeling of discrete symbolic spaces and verifiable reasoning. Empirical evaluation on benchmark tasks—including Sudoku solving, maze navigation, path planning, and preference learning—demonstrates substantial improvements in both reasoning accuracy and logical consistency. The framework establishes a novel paradigm for trustworthy AI reasoning under complex logical constraints.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network's output distribution to move closer to the symbolic constraints. While diffusion models have shown remarkable generative capability across various domains, we employ the powerful architecture to perform neuro-symbolic learning and solve logical puzzles. Our diffusion-based pipeline adopts a two-stage training strategy: the first stage focuses on cultivating basic reasoning abilities, while the second emphasizes systematic learning of logical constraints. To impose hard constraints on neural outputs in the second stage, we formulate the diffusion reasoner as a Markov decision process and innovatively fine-tune it with an improved proximal policy optimization algorithm. We utilize a rule-based reward signal derived from the logical consistency of neural outputs and adopt a flexible strategy to optimize the diffusion reasoner's policy. We evaluate our methodology on some classical symbolic reasoning benchmarks, including Sudoku, Maze, pathfinding and preference learning. Experimental results demonstrate that our approach achieves outstanding accuracy and logical consistency among neural networks.

Problem

• Enabling neural networks to learn complex logical constraints
• Guiding neural outputs to satisfy symbolic reasoning requirements
• Solving logical puzzles with diffusion-based neuro-symbolic learning

Innovation

• Two-stage diffusion training for logical reasoning
• Markov decision process with rule-based rewards
• Proximal policy optimization for constraint satisfaction