BitCal-TTS: Bit-Calibrated Test-Time Scaling for Quantized Reasoning Models

Abstract: 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.