Liquid Reasoning Transformers: A Sudoku-Based Prototype for Chess-Scale Algorithmic Tasks

TL;DR

The paper introduces the Liquid Reasoning Transformer (LRT), a novel adaptive-depth transformer architecture that iteratively refines reasoning, demonstrated on Sudoku with high accuracy and potential for complex tasks like chess.

Contribution

It presents a new transformer model with adaptive reasoning depth, incorporating discard and stop mechanisms, and evaluates its effectiveness on Sudoku as a structured reasoning benchmark.

Findings

Achieved 98.68% digit accuracy on Sudoku

Demonstrated stable inference with discard and stop gates

Outlined extensions for complex reasoning tasks like chess

Abstract

The Liquid Reasoning Transformer (LRT) is a transformer architecture designed for inference with adaptive depths using iterative changes, discard-based correction, and a learned stopping mechanism. Instead of relying on a single feedforward pass, the model updates a recurrent reasoning token across multiple internal steps, allowing it to correct early errors and allocate computation based on input difficulty. We evaluate the LRT on Sudoku as a controlled testbed for structured reasoning and show that it achieves strong performance, reaching 98.68% digit accuracy and 36.30% full-puzzle accuracy without using symbolic rules or search. Analyzing internal patterns shows that the discard and stop gates play different, important roles in stabilizing inferences and adjusting computational depth. We discuss how these mechanisms extend naturally to chess-scale reasoning tasks and outline extensions for multi-token reasoning and larger domains.