Counterexamples to Local Reconstruction Gain as a Proxy for Final Fidelity in Residual Completion

Language models sometimes produce correct outputs even when their inputs are corrupted by deletion, replacement, or misspelling. We study the internal processes accompanying this behavior, which we call context restoration, in controlled attention-only transformers and five pretrained LLMs (1B-32B parameters) across arithmetic, reading comprehension, and multiple-choice reasoning tasks. In the attention-only transformers, restoration emerges spontaneously despite training exclusively on clean sequences, without corruption training or an explicit denoising objective. We find that context restoration follows a two-phase process: early layers localize effects associated with repair at corrupted positions, while later layers accumulate these effects at uncorrupted positions through the residual stream and ultimately concentrate them at the output position. Repair outcome is predictable from hidden states: cosine alignment with the clean state is highly predictive in attention-only models, while linear probes recover additional information in pretrained LLMs. A linear probe using only the corrupted prompt's first-block hidden state predicts failure with mean ROC-AUC 0.78. This enables failure triage under matched or even partially shifted deployment conditions and may reduce unnecessary verification or computation. Failed examples also show substantially greater nonlinearity along corruption directions. Moderate-corruption finetuning increases corruption tolerance while simultaneously reducing displacement-normalized linearization error, associating improved robustness with a more nearly linear response to corruption.

Information locality, the tendency for syntactically related words to appear close together, shapes both human language processing and language model learning. While prior work has examined whether language models can acquire impossible languages, it remains unclear whether they can recover natural language from such input and what this reveals about their inductive biases. We address this by complementing learnability-based approaches with a reconstruction framework: fine-tuning GPT-2 models pre-trained on impossible languages to reconstruct natural English from three perturbation types. Our findings show that the recovered structures exhibit shorter dependency lengths than the original text, mirroring the locality preference observed in unconstrained language model generation and providing a quantitative signature of an architectural bias that learnability experiments alone do not reveal. Recovery difficulty increases with the degree of locality disruption. Structural recovery (dependency Triple F1) dissociates from surface recovery (Exact Match), while fluency dissociates from faithful reconstruction under global shuffling. Sentence length further modulates performance: longer sentences facilitate recovery when local structure is preserved but lead to complete collapse under global shuffling. Finally, recovery difficulty tracks learnability difficulty across perturbation types, suggesting that information locality is the shared constraint governing both.

Post-hoc sparse attention accelerates long-context prefill by routing each query to a small set of token-level interactions. Hard selection, however, assigns zero probability to every omitted chunk: a routing miss cannot be recovered, and a fixed expansion budget spends the same work on easy and ambiguous queries. We introduce Coarse-to-fine Error-aware Dynamic Attention Routing (CEDAR), a coarse-to-fine method that keeps the language model frozen while preserving global coverage. Each semantic chunk contributes a cheap key--value summary to a residual attention path; chunks with high estimated approximation error are then expanded to exact token attention. Exact and summarized contributions are combined in a single softmax normalization, so refinement replaces, rather than duplicates, coarse evidence. We derive an output-error bound governed by within-chunk key/value dispersion and use it to allocate a variable refinement budget. A controlled clustered-attention study shows that residual summaries reduce reconstruction error by more than 98% relative to hard dropping at equal exact-chunk budgets. Experiments on long-context benchmarks demonstrate that CEDAR recovers most of the quality lost by hard sparse routing while maintaining approximately $3\times$ kernel speedup at 128K context.