Stabilizing Iterative Self-Training with Verified Reasoning via Symbolic Recursive Self-Alignment
This addresses the issue of performance degradation in recursive self-improvement for AI models, particularly in domains like math reasoning, though it is incremental as it builds on existing self-training methods with a novel verification component.
The paper tackles the problem of recursive drift in iterative self-training by proposing Neuro-Symbolic Recursive Self-Alignment (NSRSA), which uses symbolic verification to filter training data at the reasoning step level, resulting in the rejection of 34% of correct-answer solutions with flawed reasoning and improved reward accuracy from 46% to 63%.
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.