SPECTRA-RSI: Counterfactual Spectral Sketching and Anytime-Valid Gating for Modular Recursive Self-Improvement

Abstract

Recursive self-improvement, or RSI, requires more than generating better model updates: each iteration must determine what capabilities changed, which modules caused those changes, and whether the update introduces regressions. Spectra-RSI addresses this through counterfactual spectral sketching, a framework for measuring and controlling modular model updates. The method learns causal capability fingerprints by applying small interventions to model experts. It then compares base and candidate models using paired evaluations and structured recovery to identify capability changes and the experts responsible. The framework also detects changes in the capability basis over successive iterations and refreshes its internal representation when necessary. A key contribution is separating diagnosis from acceptance. Statistical intervals support attribution, while protected evaluation streams use anytime-valid tests so updates can be monitored continuously without increasing the risk of accepting harmful regressions. Spectra-RSI combines causal expert attribution, compressed behavioral measurements, drift-aware recovery, and statistically controlled acceptance into a unified framework for repeated model improvement. Implementation: https://github.com/andrew-jeremy/compressed-sense-spectal-recursive-self-improvement

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