Calibration Bets on the Past: Post-Training Quantization for Financial Time-Series Forecasting

Post-Training Quantization (PTQ) compresses large language models to low bit-widths using a small calibration set, and its quality depends strongly on which samples are chosen. We identify a failure mode in which calibration samples fail to activate outlier channels, hidden dimensions with unusually large activations, causing the quantizer to underestimate their dynamic range and producing per-channel reconstruction errors that dominate layer-wise loss. Motivated by this observation, we argue that PTQ calibration quality is governed more by weighted outlier-channel coverage than by generic sample representativeness, and formulate calibration selection as a weighted set cover problem over outlier channels. The objective is monotone submodular, and the greedy algorithm, COVERCAL, operates on pre-computed activation statistics and requires no GPU time at selection. We further show that the weight choice is internally consistent: under a stylized clipping model, missed weighted coverage upper-bounds surrogate loss, justifying the weighted coverage objective as principled rather than purely empirical. Across LLaMA-2, LLaMA-3, and Mistral, under AWQ and GPTQ backends and five downstream evaluations, COVERCAL improves over random, max-perplexity, max-activation-variance, and stratified baselines, with the largest gains at small calibration budgets. At INT4 with 128 samples, COVERCAL improves MMLU by 1.2 to 1.5 points over random calibration and reduces perplexity degradation by 15 to 30%; with 64 samples, it matches or exceeds random calibration at 256. The contribution is not a new PTQ backend but a formulation of calibration selection as weighted outlier coverage, with a simple, efficient algorithm and a surrogate-based justification.

We introduce the Trajectory-based Quantization Sensitivity Score (TQS), a metric that reframes post-training quantization (PTQ) through the lens of dynamical-systems stability. By modeling the network's rollout as a discrete-time dynamical system, TQS characterizes how quantization-induced errors propagate and amplify over the rollout horizon. Unlike conventional PTQ methods, where sensitivity analysis is often coupled to the quantization procedure, TQS enables a priori sensitivity estimation decoupled from quantizer selection and bit-width assignment. This separation allows for quantization budget planning even for black-box or compiled networks with fused operators. Building on this, we present TQS-PTQ, a flexible mixed-precision framework that requires no calibration data or costly second-order approximations. Our experiments show that a dynamical-systems perspective provides a robust, high-performing pathway for low-precision deployment in resource-constrained settings.

Post-training quantization makes large reasoning models practical under tight memory and latency budgets, but it can distort the online signals that drive adaptive test-time compute allocation. Under a fixed cap on the number of newly generated tokens, miscalibrated confidence can lead to harmful early halting: the model may surface a plausible final line while the underlying reasoning is still wrong, or the controller may stop before the trace has stabilized. We study this interaction for greedy 4-bit inference and propose BitCal-TTS, a lightweight runtime controller that combines (i) inexpensive online proxies for token-level uncertainty and reasoning-trace stability, (ii) a bit-conditioned confidence rescaling that is conservative at low nominal precision, and (iii) a bit-aware post-marker confirmation horizon designed for GSM8K-style structured outputs. The method requires no fine-tuning of the base model and integrates with standard Hugging Face 4-bit inference using forward hooks for logits and last-layer hidden states. On small evaluation shards of GSM8K with Qwen2.5 Instruct models, BitCal-TTS improves exact-match accuracy over a non-bit-aware adaptive baseline at the 7B and 14B scales while preserving substantial token savings relative to fixed-budget decoding. At a token cap of B=512, on the evaluation shards we report (N=54 for 7B and N=35 for 14B; not the full GSM8K test set), accuracy gains are +3.7 points (7B) and +2.8 points (14B), with the premature-stop rate falling from 14.8% to 11.1% on 7B and from 17.1% to 11.4% on 14B. We report Wilson 95% confidence intervals throughout and explicitly discuss the limited statistical power of the partial-shard comparisons. We release code and figure-generation scripts to support full reproduction.