Second-Order Problem Solving for Recursive Self-Improvement in Formal Verification

2026-10-05

AI Summary

This study addresses the trial-and-error oscillations and residual latent defects caused by blind parameter patching in recursive self-improvement (RSI) by proposing the SO-RSI framework. This method employs passive execution trajectory monitoring to detect structural anomalies and trigger lightweight diagnostic probes, while accumulating causal evidence through cross-round persistent inquiry memory. Consequently, optimization is elevated to second-order diagnostic investigation that guides systematic workflow editing, achieving a paradigm shift from symptom response to mechanistic understanding. Formal verification using Lean 4 and Verus demonstrates that, under equivalent search budgets, pass rates for proof and code generation improve by 21.8 and 25.8 percentage points, respectively. These results confirm that SO-RSI effectively suppresses failure recurrence and eliminates futile optimization loops.

Abstract

Recursive self-improvement (RSI) enables agents to iteratively optimize their workflows via execution feedback. However, standard RSI typically operates as a first-order optimizer: it repeatedly patches surface-level parameters in response to immediate failure symptoms, often leading to trial-and-error thrashing without resolving underlying mechanisms. To address this limitation, we introduce SO-RSI, a framework that elevates workflow optimization to a second-order diagnostic inquiry, investigating why failures occur before committing to structural interventions. SO-RSI passively monitors execution traces for three structural anomalies (recurrence, opposing edits, and expectation mismatch) to trigger targeted mechanism investigations. By executing lightweight diagnostic probes and maintaining persistent inquiry memory across RSI rounds, SO-RSI accumulates causal evidence to guide systematic workflow edits rather than parameter patches. Across Lean 4 proof generation and Verus-based verifiable code generation, SO-RSI improves final held-out pass rates over Naive RSI by 21.8 and 25.8 percentage points under matched 24-hour search budgets. Behavioral analyses further confirm that SO-RSI substantially suppresses failure recurrence and eliminates unproductive zero-progress optimization loops.

Problem

• Recursive Self-Improvement
• Formal Verification
• First-order Optimization
• Trial-and-error Thrashing

Innovation

• Recursive Self-Improvement
• Second-Order Optimization
• Formal Verification
• Causal Diagnosis
• Workflow Optimization