Frequency Matters: Fast Model-Agnostic Data Curation for Pruning and Quantization

Post-training quantization and pruning rely on a small calibration corpus. Whether specialized domains such as finance require domain-matched calibration data remains unsettled. We argue that the answer depends on the task-level damage caused by compression rather than on domain mismatch. If compression preserves the target capability, changing the calibration corpus has little effect. If compression causes large losses, task-formatted calibration can recover part of the loss. We test this hypothesis across two model families, six compression configurations, three token-matched calibration corpora, and ten financial classification and numerical question-answering tasks. The results support this hypothesis. Quantization largely preserves task performance, and calibration choice has little effect in this case. Pruning reduces numerical QA accuracy by over 40 points. In these damaged settings, another generic corpus does not help, while FinMix, a mixture of financial task examples, recovers a large part of the loss. The link between damage and recovery holds across model families and scales. These findings support a practical rule. Measure task-specific compression damage first, and construct specialized calibration data only when the damage is large.

Structured pruning of large language models (LLMs) offers hardware-efficient compression, yet existing methods require calibration data, gradient computation, or large auxiliary policy networks at pruning time. LILA (Latent-Informed Layer Analysis) scores neuron importance via the Kolmogorov--Smirnov (KS) distance between empirical singular value distributions of the full and neuron-ablated feed-forward network (FFN) weight matrix, providing a closed-form spectral rule requiring no training, calibration data, or auxiliary network. Without any fine-tuning, LILA surpasses PruneNet (45M-parameter RL policy) by 1.57pp in zero-shot accuracy on LLaMA-2-7B at 25% sparsity, and outperforms WikiText-2-calibrated SliceGPT by up to 6.0pp across all sparsity levels, while preserving the original architecture. After one epoch of LoRA recovery fine-tuning, LILA achieves highly competitive performance, matching the heavily calibrated SliceGPT baseline to within a 0.48~pp margin across LLaMA-2-7B and Phi-2, despite using zero calibration data. A Neural Tangent Kernel analysis confirms a 22$\times$ reduction in functional distortion versus random pruning, providing theoretical grounding for the spectral importance criterion. Finally, extending LILA to dynamically allocate sparsity budgets via KS-scores yields state-of-the-art generative preservation at moderate compression, while uncovering fundamental single-layer architectural bottlenecks at higher compression regimes.

LLM compression reduces inference costs and memory requirements, but selecting a method and configuration remains largely empirical because comparable resource reductions can produce different capability losses. We systematically investigate capability scaling-down laws for LLM compression across pruning, quantization, and distillation. Our framework measures capability loss in mathematics, code generation, and question answering, and relates these measurements to model size, training stage, compression settings, data availability, and training exposure. We develop simple predictive relations and evaluate their accuracy, measurement efficiency, and generalization to unseen configurations and model states. Sharing the density response across pruning levels halves the configuration measurements needed to fit a pruning predictor: on new Pythia states, on pre-registered OLMo-2 test states and under Wanda pruning, the compact relation matches a regression fitted with all measurements on math and code to within 0.020 nats per token, with coefficients refitted for each setting. Controlled distillation experiments show that the cost of heavy data reuse recurs across question-answering distributions, while the net benefit depends on the evaluation distribution. We further evaluate the decision value of these predictions by comparing numerical selection with configuration medians and fixed method priorities. Independent evaluations across two model families show that selection captures most of the available cross-method benefit for question answering within the tested candidate sets, where a fixed method priority attains the same regret, with smaller opportunities for mathematics and code. These results clarify the predictive scope of capability scaling-down laws and their use in compression method selection. Our code is publicly available at: https://github.com/LabRAI/scaling_down_law.