New Theory Explains LLM Self-Correction Blind Spot

Large autoregressive language models (LLMs) exhibit a peculiar "self-correction blind spot": they can reliably correct errors attributed to an external source, yet often fail to fix identical errors present in their own generated outputs. Previous research has empirically documented this phenomenon through various methods, but lacked a formal theoretical explanation for its underlying mechanism. This new work introduces SPARC (Spectral-Algebraic Theory of Self-Correction), which provides a formal model to explain this blind spot. SPARC defines an "error-propagation operator" based on the product of per-step attention Jacobians on the residual stream. The theory proves that the self-correction blind spot emerges precisely when the spectral radius of this operator is one or greater. Furthermore, SPARC derives a precise activation threshold that a correction marker, such as a simple "Wait" prompt, must exceed to enable self-correction, quantitatively matching observed blind-spot reductions. The theory also offers convergence guarantees for reinforcement learning-based self-correction, linking it to the spectral norm of the verifier-corrector coupling matrix. These findings are validated across multiple LLM architectures and visual autoregressive probes, unifying the understanding of self-correction across different generative modalities.