Few Bits, One Law: Toward W2A4KV2

Extreme low-bit LLM compression is most challenging when weights, activations, and KV caches are quantized together: their distributions differ, and quantization errors interact throughout the network. We introduce CanonQ, a unified quantization-aware training framework that addresses these challenges by separating source canonicalization from task-aware adaptation. Fixed rotations and energy normalization map heterogeneous tensor sources to canonical coordinates, enabling frozen Gaussian-reference codebooks to be reused across layers and models. Joint training then adapts the network to the coupled errors of weight, activation, and cache quantization within a common scalar/vector interface. We bound frozen-codebook transfer error and local task loss, and derive an exact normalization-aware straight-through Jacobian that links quantization distortion to gradient bias. The strongest gains arise under joint W2A4KV2 compression: across LLaMA3-1B/3B/8B, CanonQ-Omni achieves up to 14.28× lower WikiText-2 perplexity and up to 57.9% higher mean zero-shot accuracy than prior state-of-the-art and representative quantization baselines. The benefits extend to Qwen3-1.7B, code generation, and mathematical reasoning: on instruction-tuned MobileLLM-Pro-1B at W2A16KV16, CanonQ achieves relative improvements of 41.7% in HumanEval pass@1 and 39.1% in GSM8K exact match over the strongest evaluated quantization baseline.