Post-Training Ternarization of Qwen3-4B Capability, Effective Bit Budget, Storage Compression, and Deployment

Ultra-low-bit language models promise reductions in storage and memory traffic, but a nominal "1.58-bit" label does not specify the deployed representation or its execution cost. We study a scale-up of an aggressive post-training conversion pipeline from Qwen3-4B to Qwen3-8B. The conversion uses KOTMS rotation, E2M-ATQ adaptive ternarisation, and GPTQ-style error compensation in a weight-only A16 configuration. We do not claim these algorithms as new. Our contribution is the end-to-end scale-up characterisation: an external reproduction gate, matched 4B/8B capability analysis, cross-corpus perplexity, effective-bit accounting, lossless lattice-aware packing, and direct packed execution. The 8B model reaches a three-corpus perplexity ratio of 1.361x, with WikiText-2, C4, and PTB ratios of 1.318x, 1.393x, and 1.371x. On eight zero-shot tasks at n = 500, mean accuracy is 64.6% versus 72.4% for FP16, corresponding to 78.5% chance-corrected retention and a 7.8-point absolute cost. The matched 4B run retains 69.6%, yielding an 8.9-point 8B advantage. The packed checkpoint is 8.24 GiB and preserves the recorded perplexity to measurement precision. Direct packed execution reaches 15.52 tokens/s in 7.35 GiB, while a preliminary packed GEMV remains slower than FP16 cuBLAS. The result is a validated scale-up baseline: model size improves robustness to aggressive post-training discretisation, actual serialisation is solved for the measured artefact, and direct execution is feasible, while broader seeds, calibration distributions, and kernel optimisation remain open.

In this paper, we present CAT-Q, Cost-efficient and Accurate Ternary Quantization, for compressing and accelerating LLMs. Unlike existing state-of-the-art ternary quantization methods that rely on data-intensive and costly quantization-aware training to mitigate severe performance degradation, CAT-Q is a simple yet effective post-training quantization scheme that is readily applicable to LLMs with diverse architectures and model sizes. It has two key components, learnable modulation (LM) and softened ternarization (ST), which are coupled from an optimization perspective. LM leverages a composition of learnable factors to modulate the distribution of pre-trained high-precision weights and the ternary threshold, making them less sensitive to ternarization. ST further introduces a differentiable transition function to guide the ternarization process toward stable convergence. We show that, for pre-trained LLMs with 1.7B to 8B parameters, CAT-Q can efficiently quantize them into ternary models using only 512 calibration samples, while achieving superior performance than the seminal BitNet 1.58-bit v1 and v2 families (with 1.3B to 7B parameters) trained with 100B tokens, yielding about a 100,000X reduction in training tokens. Moreover, we show for the first time that CAT-Q can quantize much larger pre-trained LLMs having 14B to 235B parameters into leading ternary models within just 8 to 60 hours on 8 A100-80GB GPUs. Code is available at https://github.com/IntelChina-AI/BitTern.

Low-bit quantization shrinks language models but treats precision as a single global hyper-parameter: every weight uses the same bit-width. We introduce Variable Bit-width Quantization (VBQ), a training-time method in which each contiguous group of 64 weights learns its own resolution from {1,2,4,8} bits via a Gumbel-Softmax relaxation, trained jointly by an alternating optimization that gives the precision logits a clean, task-aligned signal. VBQ discovers a consistent, strongly heterogeneous allocation within individual projection types, not merely across layers, impossible to express with per-layer methods: 69% of groups collapse to 1 bit, the LM head averages 1.09 bits, while the first MLP block keeps ~2.5 bits. This pattern is stable enough to freeze into a fixed recipe and reuse without further search. The recipe yields a "bigger-but-smaller" regime: a 131M model at 1.82 mean bits reaches perplexity 4.2 on TinyStories, beating a 55M FP16 model (PPL 4.4) at 3.8x less storage, and lets a 1.46B model on FineWeb-Edu match a 593M FP16 control at ~3.7x less storage with 2.5x more parameters. As quality-per-byte, VBQ is 3.9-8.4x more efficient than FP16. The recipe maps directly to packed low-bit storage, so it also accelerates inference: with custom fused dequantize-and-multiply kernels, memory-bandwidth-bound autoregressive decode is faster at equal output, and the speedup grows with scale (parity at 131M, 1.9x at 1.0B, 4.7x at 9B on Apple silicon). A distributional analysis (KL divergence and argmax-flip rate) reveals a striking mechanism: deeper layers progressively self-heal the quantization error injected by early layers. The win is a from-scratch, train-time phenomenon; scaling the search economically beyond 1.5B parameters remains open. VBQ reframes precision as a learnable, non-uniform resource and shows that spending a fixed bit budget unevenly beats spending it uniformly.