ThinkBit: Search Codewords, Recalibrate Scales, Select by Reasoning

Reasoning language models generate thousands of tokens per answer, and generation speed is limited by memory bandwidth, so storing weights in two bits instead of bfloat16 can potentially make inference 8times cheaper. Two-bit methods are usually judged by perplexity and multiple-choice question-answering accuracy, both of which say little about whether a model can still reason through more difficult problems. We present ThinkBit, a strictly scalar two-bit framework built to preserve reasoning, in which every weight is an integer codeword times a bfloat16 scale shared by a group of weights. We first use a sensitivity metric to assign each layer a ternary, 2-bit, or 3-bit tier to allocate bitwidths optimally among layers. This is followed by a layerwise Gumbel-softmax-based scalar quantization algorithm that searches for optimal codewords block by block. Since a layerwise scheme does not capture how quantized layers interact with each other, we recalibrate scales, with the codewords frozen, using a knowledge-distillation-based loss against the teacher model. We then perform a short quantization-aware training (QAT) stage that lets the model mimic the base model's distribution by reassigning codewords. Finally, a paired reasoning test on training problems selects the final checkpoint between the recalibration stage and the QAT stage. On Qwen3-1.7B at matched size, our recalibrated checkpoint scores 46.7 on MATH-500 against 30.0 for EfficientQAT trained on the same data, and 73.0 after QAT on reasoning traces; at 0.52 GB it is smaller than every published 2-bit GGUF of the model yet more accurate on MATH-500. We show that this framework scales and up to 14B, a 3.74 GB model scores 94.8 on MATH-500, against 97.5 for the 29.5 GB bfloat16 model.