Self-Aware Markov Models for Discrete Reasoning

TL;DR

This paper introduces a self-aware Markov model for discrete reasoning that can correct its mistakes and adapt its computation steps, significantly improving performance on reasoning tasks like Sudoku and Countdown.

Contribution

It proposes a novel learning method for Markov transition kernels that enables self-correction and adaptive computation in discrete reasoning models.

Findings

Achieves 95% validity on Sudoku-Extreme dataset.

Solves 96% of Countdown-4 problems with an average of 10 steps.

Many Countdown problems are solved in just 2 steps.

Abstract

Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their computation to the complexity of a given problem. To address these limitations, we introduce a method based on learning a Markov transition kernel that is trained on its own outputs. This design enables tokens to be remasked, allowing the model to correct its previous mistakes. Furthermore, we do not need a fixed time schedule but use a trained stopping criterion. This allows for adaptation of the number of function evaluations to the difficulty of the reasoning problem. Our adaptation adds two lightweight prediction heads, enabling reuse and fine-tuning of existing pretrained models. On the Sudoku-Extreme dataset we clearly outperform other flow based methods with a validity of 95%. For the Countdown-4 we only need in average of 10 steps to solve almost 96% of them correctly, while many problems can be solved already in 2 steps.