Scaling Post-Training Ternarisation to Qwen3-8B Capability Retention, Reproduction, Lossless Packing, and Packed Execution

Ultra-low-bit language models can reduce storage and memory bandwidth, but a nominal "1.58-bit" label does not fully describe the stored representation, retained capability, or runtime behavior. We study an end-to-end post-training conversion of Qwen, an instruction-tuned 4B-parameter model, using KOTMS rotation, E2M-ATQ ternarization, and GPTQ-style error compensation from TWLA. The experiment is weight-only: activations remain at 16-bit precision, so ILA-AMP is omitted. We evaluate effective bit accounting, task capability retention, perplexity, calibration sensitivity, checkpoint composition, and deployment behavior. The final conversion uses 1.641 effective bits per weight for quantized linear weights, with 81.62% of model parameters targeted. Across ten scored capability comparisons, accuracy falls from 64.5% to 54.7%. Degradation is uneven: BoolQ retains 84.6% chance-corrected teacher performance, while ARC-Challenge retains 43.8%. Perplexity rises from 13.639 to 18.748 on WikiText-2, 24.700 to 31.992 on PTB, and 19.831 to 28.966 on C4. A subsequent packing run preserves the ternary planes and scales, reducing reported model size from 8.29 GiB to 3.96 GiB with essentially unchanged perplexity. A separate third-party packing attempt was lossy and is excluded from the primary artifact claim. The packed artifact has not been benchmarked end-to-end for task accuracy or generation throughput. A preliminary Triton GEMV microbenchmark is 4.6x slower than FP16 cuBLAS on one tested shape. We therefore do not claim that compression alone yields faster inference.

Serving large language models (LLMs) under diverse deployment constraints requires flexible trade-offs between accuracy, memory footprint, and throughput. However, conventional quantization methods typically require a separate checkpoint for each target bit-width. We introduce Recurrent Residual Quantization (RRQ), a post-training quantization (PTQ) framework that represents weights as a low-bit quantized base together with a sequence of quantized residual corrections, enabling multiple effective precisions from a single checkpoint. Starting from a 2-bit model obtained via post-training quantization (PTQ) or round-to-nearest (RTN), RRQ progressively adds lightweight 2-bit residuals generated via RTN to construct 4-, 6-, and 8-bit representations. The method is calibration-free and avoids joint multi-bit optimization. In our Qwen3-8B setup, the full all-RTN 2-/4-/6-/8-bit package is constructed in 1,293 seconds, 3.3 times faster than the measured MatGPTQ construction. Experiments on six recent LLMs show competitive accuracy at 6 and 8 bits, with model-dependent behavior at 4 bits. The code will be made publicly available upon publication.

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.