Can Metadata Fix the Gauge? Calibration Turns Sparse Multi-Source Learning from Sparse PCA into Sparse Mean Recovery

Post-training LLM pruning relies on a small calibration set, usually chosen heuristically and judged by WikiText perplexity or by mean accuracy on general-domain commonsense benchmarks. This single-axis view hides capability-specific effects: at 60% sparsity, strategies separated by $2.85$ points in averaged commonsense accuracy diverge by $51.9$ points in code retention, and across 15 sources no single one preserves all capabilities. We treat calibration as a capability-coverage problem. Balanced, a uniform four-way mixture under a fixed budget, tests the principle on real corpora: it outperforms every evaluated single source, and its margin over C4 grows from $+4.6$ points at 30% sparsity to $+18.8$ at 60%. The advantage holds across model scale and a second model family, and transfers to held-out benchmarks disjoint from calibration construction. When aligned corpora are unavailable, IGSP approximates that mixture from the base model and the evaluation taxonomy alone, outperforming prior self-generation methods by $7.23$--$12.79$ points on the LLaMA main suite. On Qwen2.5-7B, IGSP exceeds Balanced on both the main suite and held-out benchmarks. Capability coverage is a first-order design variable for high-sparsity pruning.

Fixed-budget adaptation from heterogeneous data sources requires deciding not only how much data to use, but how much exposure each source receives. Size-proportional rules can crowd out small sources, whereas difficulty-only rules can chase noisy estimates or allocate residual budget to nearly saturated pools. We introduce CALIBUDGET, a floor-protected, reliability-aware integer allocator that treats source exposure as an explicit adaptation variable. From small train-internal calibration splits, it combines model need, post-floor availability, and bootstrap stability, then produces exact capacity-respecting quotas without changing the model, objective, or total budget. In a controlled setting combining mathematical and commonsense data, CALIBUDGET improves CommonAvg, FragileAvg, and MacroAvg over validation-error-with-floor, the strongest matched comparator, in all three paired LLaMA-2-7B LoRA+ runs. The respective mean gains are 0.56, 0.46, and 0.41 percentage points (pp). Overall increases by 0.18 pp, whereas MathAvg decreases by 0.20 pp, exposing a coverage-retention boundary rather than a uniform gain. CALIBUDGET changes only 1.14-1.42% of the source budget but improves performance in 15 of 24 comparisons across commonsense tasks and seeds. These results suggest that small changes in source quotas can matter; example-level selection can then determine which examples fill each quota.

Frozen EEG representations retain acquisition signatures as well as neural activity. Source predictability alone does not identify what should be removed: it can reflect measurement effects or genuine biological and population differences, which should not be erased. We propose Measurement-Gated Provenance Attenuation (MGPA), built on one principle: measurement evidence determines where correction may act, and preserved information determines what it should aim for. Paired measurement contrasts define a gate outside which nothing changes; inside it, the source score is moved to the value the preserved coordinates already predict: for a fixed affine score, this keeps the same information as any target set by those coordinates and needs the least expected squared movement. Closed-form and critic-guided iterative constructions apply it without source identity or encoder retraining. Three studies test the principle at increasing distance from its assumptions. Under controlled reference changes, where the source-task association is known, MGPA brings source to near chance with task performance unchanged, whereas erasing what predicts source (LEACE) lowers frozen-task AUROC from .753 to .656 while barely touching source; ablations attribute the attenuation to the gate's directions and 2.7x less movement to the conditional target. Across recordings from different devices and electrodes, iterative correction lowers source accessibility while preserving or improving task performance. Finally, one iterative map selected on one task and reused unchanged on existing heads for two others raises their worst-association AUROC (lowest over device-label shifts) by .057 and .019 over LEACE, at a cost to those heads while the training association holds. A reusable correction shows its value in how an existing predictor behaves once acquisition cues stop being reliable, not only in what a probe can read.