[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86442-en":3,"doc-seo-86442-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86442,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Spectral Origins of the Self-Correction Blind Spot in Autoregressive Generation","Large autoregressive language models exhibit a self-correction blind spot: identical errors are reliably fixed when externally attributed, yet remain uncorrected when produced in the model’s own output. Prior work documents the effect empirically but lacks a formal decoding-based explanation, quantitative activation conditions for correction markers, and convergence guarantees for reinforcement-learning self-correction. SPARC introduces a spectral-algebraic theory defining an error-propagation operator, proving the blind spot occurs iff its spectral radius is ≥1. It yields a sharp activation threshold and RL convergence conditions validated across multiple backbones with tight spectral predictions.","arXiv :2607 .09803v 1 [ cs .LG] 9 Jul 2026  \nSpectral Origins of the Self-Correction Blind Spot in Autoregressive Generation  \nIngrid Petrova, Luan Vejsiu  \nEuropean University of Tirana [ingrid.petrova@uet.edu.al](ingrid.petrova@uet.edu.al)  \nAbstract  \nLarge autoregressive language models exhibit a self-correction blind spot: they reliably fix identical errors when attributed to an external source yet fail to fix the same errors in their own outputs. Prior work has documented this phenomenon empirically, through controlled error injection, errordepth decompositions, RL-based verifier–corrector training, and intrinsic self-verification, but offers no formal model of why generating a token suppresses the ability to detect its error, no quantitative activation condition for correction markers, and no convergence guarantee for reinforcementlearning-based self-correction. We close these gaps with SPARC, a spectralalgebraic theory of self-correction in autoregressive generation. We define the error-propagation operator as the product of per-step attention Jacobians on the residual stream and prove that the blind spot arises if and only if the spectral radius of this operator is at least one. We derive a sharp activation threshold, given as a function of the spectral radius, that a correction marker must exceed, recovering the 89.3% blind-spot reduction observed with a simple “Wait” marker. We further prove that RL-based verifier–corrector training converges at a rate proportional to the squared coupling strength over the square root of the number of samples if and only if the verifier–corrector coupling matrix has spectral norm below one, and that this criterion is invariant across residual-stream autoregressive modalities, unifying text LLMs and autoregressive image and video generation. Experiments across four backbones and a visual autoregressive probe validate every theorem, with spectral predictions matching measured blind-spot rates within 3.2% RMSE.  \n1 Introduction  \nLarge language models (LLMs) have become transformative across natural language processing, yet they remain unreliable: they make mistakes, follow unproductive reasoning paths, and fail to revise errors in their own outputs (Tsui, 2025; Kumar et al., 2025) . Selfcorrection—the ability of a model to detect and revise errors in its own generation—is a prerequisite for trustworthy deployment. A striking empirical finding, however, is the Self-Correction Blind Spot: LLMs can identify and correct an error when it is attributed to an external source (a user, a tool) but systematically fail to correct the identical error when it appears in their own output (Tsui, 2025) . Across fourteen open-source models the blind-spot rate averages 64.5%, and even a simple prompt-level intervention—appending the token“Wait” —reduces it by 89.3%, suggesting the capability is latent but suppressed during standard decoding.  \nA wave of recent work has refined this picture. Li (2025) decompose self-correction into detectability and correctability and propose the Error Depth Hypothesis, observing that correction success is non-monotonic in how deeply an error is embedded in the reasoning trace. Ma et al. (2025) show that reinforcement learning (RL)—not supervised fine-tuning (SFT)—is what installs usable self-correction, via a two-stage verifier–corrector pipeline (S2R). Lee et al. (2025) train an intrinsic verifier (ReVISE) and expose a refinement-instability regime in which self-refinement degrades output quality. Iterative self-feedback (Madaan  \net al., 2023; Shinn et al., 2023), RL-based self-correction training (Kumar et al., 2024), and confidence-aware verification (Li et al., 2024; Liu et al., 2024) all improve self-correction empirically but rest on the same foundational question that none of them answers formally: why does generating a token suppress the ability to detect its error?  \nLimitations of prior work. All existing accounts are empirical or phenomenological. Thereis (","cbCain1KhO8Om8tJ","https://ap.wps.com/l/cbCain1KhO8Om8tJ","pdf",416433,4,1,17,"English","en",105,"# Introduction\n## Limitations of prior work\n## Our approach\n## Contributions\n# Spectral Results","[{\"question\":\"What is the self-correction blind spot in autoregressive generation?\",\"answer\":\"Models can correct an identical error when it is attributed to an external source, but fail to correct the same error when it appears in their own generated output.\"},{\"question\":\"How does SPARC formally explain why token generation suppresses error detection?\",\"answer\":\"SPARC defines an error-propagation operator as a product of per-step attention Jacobians on the residual stream, showing the blind spot arises if and only if the operator’s spectral radius is at least one.\"},{\"question\":\"What determines whether a correction marker will activate self-correction?\",\"answer\":\"A correction marker with sensitivity κ activates self-correction only when κ exceeds a sharp threshold κ⋆(ρ) determined by the spectral radius of the error-propagation 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is the self-correction blind spot in autoregressive generation?","Question",{"text":75,"@type":76},"Models can correct an identical error when it is attributed to an external source, but fail to correct the same error when it appears in their own generated output.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does SPARC formally explain why token generation suppresses error detection?",{"text":80,"@type":76},"SPARC defines an error-propagation operator as a product of per-step attention Jacobians on the residual stream, showing the blind spot arises if and only if the operator’s spectral radius is at least one.",{"name":82,"@type":73,"acceptedAnswer":83},"What determines whether a correction marker will activate self-correction?",{"text":84,"@type":76},"A correction marker with sensitivity κ activates self-correction only when κ exceeds a sharp threshold κ⋆(ρ) determined by the spectral radius of the error-propagation 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