Stabilizing Iterative Self-Training with Verified Reasoning via Symbolic Recursive Self-Alignment

TL;DR

This paper introduces NSRSA, a method that stabilizes recursive self-training by integrating symbolic verification to ensure reasoning quality, thereby reducing errors and improving model performance in iterative self-improvement tasks.

Contribution

NSRSA is the first framework to embed symbolic verification into recursive self-training, effectively filtering flawed reasoning and enhancing model reliability.

Findings

NSRSA rejects 34% of solutions with flawed reasoning.

Constructing DPO preferences from NSRSA improves reward accuracy from 46% to 63%.

NSRSA reduces the impact of lucky guesses in self-training data.

Abstract

Recursive self-improvement--where a model iteratively trains on its own outputs--promises sustained capability growth but faces a fundamental obstacle: recursive drift. As models train on self-generated data across multiple iterations, errors in intermediate reasoning compound, leading to mode collapse and performance degradation. We propose Neuro-Symbolic Recursive Self-Alignment (NSRSA), which stabilizes iterative self-training by embedding a symbolic verification subsystem that gates training data quality at the reasoning step level. Unlike outcome-only filtering (which admits "lucky guesses" with flawed reasoning), NSRSA verifies each arithmetic operation via sympy, checks logical flow consistency across reasoning steps, and enforces domain constraints. We evaluate NSRSA on GSM8K using Qwen3-4B-Thinking across 5 self-training iterations under five conditions: no verification, outcome verification, majority voting, full NSRSA symbolic verification, and NSRSA with DPO. Our filtering analysis shows that NSRSA rejects approximately 34% of correct-answer solutions that pass outcome verification, eliminating "lucky guesses" with flawed reasoning from the training set. We further demonstrate that constructing DPO preference pairs from NSRSA verification teaches the model to distinguish sound from flawed reasoning (reward accuracy 46% to 63%). NSRSA provides an extensible framework that demonstrates how external symbolic verification can make recursive self-improvement measurable and reliable within domains where automated verification is available.