arXiv subjects

Luan Vejsiu

Publications and source records attributed to Luan Vejsiu.

3 recordsLinked to original sources

arXiv2026

Spectral Origins of the Self-Correction Blind Spot in Autoregressive Generation

Large 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, error-depth 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 reinforcement-learning-based self-correction. We close these gaps with SPARC, a spectral-algebraic 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.

cs.LG↗

arXiv2026

Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling

Test-time scaling (TTS) has emerged as a powerful paradigm for improving the reasoning performance of large language models (LLMs) by investing additional compute at inference time. A central component of TTS is the \emph{verifier}, which selects or scores candidate solutions to guide the search process. While prior work has explored the benefit of verification, a fundamental question remains underexplored: \emph{what is the optimal granularity of verification under a given compute budget?} Coarse-grained outcome reward models (ORMs) and fine-grained process reward models (PRMs) represent two extremes, yet neither alone achieves compute-optimality across all regimes. In this paper, we establish a unified theoretical framework, called \textbf{GRACE} (\underline{G}ranularity-\underline{R}egulated \underline{A}daptive \underline{C}omputational \underline{E}fficiency), that characterizes the optimal verification granularity as an explicit function of problem difficulty, verifier accuracy, and compute budget. We prove that there exists a phase transition: fine-grained verification dominates when either the compute budget is large or the problem is hard, whereas coarse-grained verification is preferred in the low-budget, easy-problem regime. Our theory unifies Best-of-$N$, beam search, and step-level MCTS within a single Pareto-optimality framework, and motivates an adaptive granularity strategy that provably achieves the compute-performance Pareto frontier. Empirical results on MATH-500, GSM8K, and AIME benchmarks corroborate all four theoretical claims, with our adaptive strategy outperforming fixed-granularity baselines by up to 3.1\% accuracy at matched compute.

cs.CL↗

arXiv2025

Context-Enhanced Granular Edit Representation for Efficient and Accurate ASR Post-editing

Despite ASR technology being full-scale adopted by industry and for large portions of the population, ASR systems often have errors that require editors to post-edit text quality. While LLMs are powerful post-editing tools, baseline full rewrite models have inference inefficiencies because they often generate the same redundant text over and over again. Compact edit representations have existed but often lack the efficacy and context required for optimal accuracy. This paper introduces CEGER (Context-Enhanced Granular Edit Representation), a compact edit representation that was generated for highly accurate, efficient ASR post-editing. CEGER allows LLMs to generate a sequence of structured, fine-grained, contextually rich commands to modify the original ASR output. A separate expansion module deterministically reconstructs the corrected text based on the commands. Extensive experiments on the LibriSpeech dataset that were conducted, CEGER achieves state-of-the-art accuracy, achieving the lowest word error rate (WER) versus full rewrite and prior compact representations.

cs.CL↗