RDQ (Residual Distribution Quantization), a PTQ framework whose central contribution is Cascaded Error Compensation, a sequential calibration procedure that captures the actual drifted activations each layer receives and fits per-channel AWQ-style scales against those drifted inputs, with scales folded into preceding RMSNorm weights for exact mathematical equivalence at zero inference overhead.
Abstract
Post-training quantization (PTQ) of large language models degrades sharply below 4-bit precision. We identify the root cause as residual stream distributional drift: quantization noise injected at each transformer layer accumulates in the shared residual representation, causing KL divergence from the FP16 baseline to grow super-linearly with depth (Pearson r=0.999 with log-perplexity, p<0.001, confirmed across all tested methods and bit-widths). We discover that 84% of LLaMA-3-8B layers exhibit non-Gaussian residual distributions (KS test, p<=0.05), and that per-layer residual stream variance grows 6,548x across depth. We propose RDQ (Residual Distribution Quantization), a PTQ framework whose central contribution is Cascaded Error Compensation (CEC): a sequential calibration procedure that captures the actual drifted activations each layer receives (computed by running calibration data through already-quantized upstream layers) and fits per-channel AWQ-style scales against those drifted inputs, with scales folded into preceding RMSNorm weights for exact mathematical equivalence at zero inference overhead. RDQ achieves state-of-the-art results on all three tested architectures: LLaMA-3-8B: 7.55 / 5.62 PPL (W3/W4); Qwen-2.5-7B: 7.46 / 6.38 PPL; Mistral-7B: 6.88 / 5.73 PPL. RDQ beats the best published baseline (LeanQuant/SpinQuant) at every model and bit-width combination, with gains up to -46.4% vs. RTN at W3A16 on LLaMA-3-8B. All output is standard group-128 asymmetric quantization, deployable on Qualcomm AIMET, GGUF, and any standard inference stack at zero runtime overhead.
ACBQ is presented, a simple yet effective framework that simultaneously addresses weight–activation joint quantization and extreme low-bit weight quantization and an adaptive cross-block quantization strategy that explicitly accounts for cross-layer dependencies by encouraging consistency across blocks.
Hailing Wang, Jianglin Lu, Yitian Zhang et al.· Annual Meeting of the Associ...· 0 citations
This work systematically study weight-only post-training quantization across bit-widths, quantization methods, model scales and downstream tasks and establishes that quantization degradation is governed by how errors are introduced at the source and how they accumulate across the network.
Chenxi Zhou, Pengfei Cao, Jin Ye et al.· 0 citations
KronQ, a PTQ framework that challenges the assumption that all output channels contribute equally to the layer-wise reconstruction objective by introducing the gradient covariance into the quantization pipeline, and introduces bidirectional incoherence processing.
Donghyun Lee, Yuhang Li, Ruokai Yin et al.· 0 citations
Layer-wise post-training quantization of large language models minimizes each layer's reconstruction error in isolation, allowing quantization errors to accumulate across depth and causing severe degradation in extreme low-bit regimes. We formulate quantization as a joint optimization over the discrete codes and scales of all layers, driven by two mechanisms: (i) cross-layer error compensation, which maintains the network-level accumulated error through the recursion e_{l+1} = A_l e_l + q_l, with a propagation operator A_l derived from the layer's input differential and a local quantization residual q_l evaluated at teacher features; and (ii) finite-sample feature-statistics matching, which aligns means, projected covariances, and centered empirical kernels between the full-precision and quantized networks under relative normalization. We prove that instantiating the propagation operator as a finite difference of the quantized network makes the recursion exact for arbitrary nonlinear layers, enabling an efficient forward-difference implementation. Binary weights are optimized via a mirror-descent parameterization u = tanh(beta*z) with annealed inverse temperature and group-wise log-scales. On Qwen2.5-1.5B with 1.125-bit group-binary weights, error compensation alone reaches a perplexity ratio of 9.56 +/- 0.15 over the FP16 teacher, outperforming logit distillation (14.09 +/- 0.53; 32 percent relative, more than 8 sigma over 3 seeds) and layer-local reconstruction by two orders of magnitude. The same objective transfers unchanged to 4-bit quantization (1.060 vs. 1.088 for layer-local). Out-of-domain evaluations (C4, CNN/DailyMail) show the advantage of error compensation grows off-domain, while statistics matching keeps feature-statistics discrepancy low off-domain (0.42-0.88 vs. 1.41-2.99 without it), revealing a complementary division of labor between the two mechanisms.
Post-training quantization pipelines routinely leave the softmax output layer in high precision. Yet in small LLMs with modern vocabularies, the head holds 15--30\% of all parameters, so a nominal ``2-bit''model with an fp16 head can store several times as many bits per weight. We pose softmax-layer quantization as a rate-distortion problem under the KL divergence between the original and quantized output distributions. A second-order analysis reveals a class-aware geometry: quantization error is weighted jointly by feature covariance and class-specific softmax curvature. A separability approximation replaces the $Kn\times Kn$ Cholesky with one $n\times n$ factorization rescaled per class, making the lattice encodable by successive interference cancellation, with both statistics from a single forward pass. The resulting method, SoftWater, gives fine grids to frequent, low-variance classes and coarse grids to rare ones, a large gap under Zipfian token distributions. Across five models from 1B to 32B, SoftWater outperforms the released WaterSIC quantizer (near-optimal under linear-layer WMSE but not output KL) at matched head rates on 59 of 60 test points, using none of that pipeline's refinements and cutting head-induced KL by $6.5\times$--$8.3\times$ at 2 bits. On Llama-3.2-1B-Instruct with quantized bodies, a 2-bit head removes 45--60\% of stored bytes for a $2.9$--$3.7\%$ perplexity increase. Because the class-side statistic comes from calibration data, matching calibration to the deployment domain gives the lowest KL on that domain throughout. On a tied model, a 4-bit head is near-lossless and a 2-bit head costs under 4\% perplexity, making head quantization of such models practical.
Weight-only quantization substantially reduces the storage of large language model (LLM) transformer blocks, but practical backends often retain the final language-modeling head (LM-head) in BF16 or FP16. Quantizing this projection naively can strongly perturb the vocabulary-logit distribution. We present ARCHead, a packed LM-head compressor that combines a quantized low-rank core, group-wise INT4 residuals, and a low-rank correction fitted in an activation-derived metric. ARCHead stores no dense BF16 head and reduces persistent LM-head storage by 3.7-3.9x. On Qwen3-8B-Base, it uses 25.6% of BF16 head storage while attaining 1.007 relative perplexity; storage-matched naive INT4 yields 1.14-1.16. Replacing the BF16 head left by AWQ or bitsandbytes adds only 0.006-0.007 cross-entropy, with less than 2% throughput change in our measurements. ARCHead therefore complements block quantizers by compressing the large output projection they can leave untouched. Code is available at https://github.com/suayptalha/archead.
Suayp Talha Kocabay, Talha Rüzgar Akkus, K. Yuksel· 0 citations