4-Bit Quantization

Post-training quantization (PTQ) assumes that a well-converged model is a quantization-ready model. We show this assumption fails in a structured, measurable, and previously uncharacterized way. Using a calibration-free per-group INT4 probe applied to all 154 publicly available Pythia-160m training checkpoints, we identify a three-phase divergence structure: a rapid-learning phase where both FP32 perplexity and quantization robustness improve together, a meta-stable plateau lasting roughly 70,000 steps where FP32 perplexity stagnates but INT4 gap remains bounded, and an explosive divergence phase where the INT4 gap compounds from 11% to 517% while FP32 perplexity barely moves. Critically, this divergence begins not when the learning rate starts decaying, but precisely when FP32 perplexity converges a finer-grained onset predictor that implies post-convergence weight updates, rather than decay magnitude alone, are the proximate cause. We further show that INT8 quantization is entirely immune throughout all three phases, constraining the mechanism to the coarseness of the 16-level INT4 grid specifically, and rule out weight outlier accumulation as the mechanism via direct kurtosis measurement. Finally, we conduct a controlled fork experiment from the pre-divergence checkpoint comparing three learning rate schedules (cosine continuation, SGDR warm restarts, and our proposed Oscillatory Lock-In) across nine independent runs. SGDR uniformly accelerates divergence (0/9 pairwise wins against cosine), while OLI's settled cool phases reduce the INT4 gap by 2.2 percentage points on average (t = -5.46, p < 0.0001), demonstrating that schedule amplitude calibration, not oscillation alone, determines whether perturbation helps or hurts. Our code, probe implementation, and all 154-checkpoint audit results are released publicly.

Quantization can drastically increase the efficiency of large language and vision models, but typically incurs an accuracy drop. Recently, function-preserving transforms (e.g. rotations, Hadamard transform, channel-wise scaling) have been successfully applied to reduce post-training quantization error, yet a principled explanation remains elusive. We analyze linear-layer quantization via the signal-to-quantization-noise ratio (SQNR), showing that for uniform integer quantization at a fixed bit width, SQNR decomposes into (i) the concentration of weights and activations (capturing spread and outliers), and (ii) the alignment of their dominant variation directions. This reveals an actionable insight: beyond concentration - the focus of most prior transforms (e.g. rotations or Hadamard) - improving alignment between weight and activation can further reduce quantization error. Motivated by this, we introduce block Concentration-Alignment Transforms (CAT), a lightweight linear transformation that uses a covariance estimate from a small calibration set to jointly improve concentration and alignment, approximately maximizing SQNR. Experiments across several LLMs show that CAT consistently matches or outperforms prior transform-based quantization methods at 4-bit precision, confirming the insights gained in our framework.

The emergence of fine-grained numerical formats like NVFP4 presents new opportunities for efficient Large Language Model (LLM) inference. However, it is difficult to adapt existing Post-Training Quantization (PTQ) strategies to these formats: rotation-based methods compromise fine-grained block isolation; smoothing techniques struggle with significant 4-bit quantization errors; and mixed-precision approaches often conflict with hardware constraints on unified-precision computation. To address these challenges, we propose ARCQuant, a framework that boosts NVFP4 performance via Augmented Residual Channels. Distinct from methods that compromise block isolation or hardware uniformity, ARCQuant maintains a strictly unified NVFP4 format by augmenting the activation matrix with quantized residual channels. This design integrates the error compensation process directly into the matrix reduction dimension, enabling the use of standard, highly optimized GEMM kernels with minimal overhead. Theoretical analysis confirms that the worst-case error bound of our dual-stage NVFP4 quantization is comparable to that of standard 8-bit formats such as MXFP8. Extensive experiments on LLaMA and Qwen models demonstrate that ARCQuant achieves state-of-the-art accuracy, comparable to full-precision baselines in perplexity and downstream tasks. Furthermore, deployment on RTX 5090 and RTX PRO 6000 GPUs confirms practical benefits, achieving up to 3x speedup over FP16. Our code is available at https://github.com/actypedef/ARCQuant.

Vision Transformers (ViTs) are essential in computer vision but are computationally intensive, too. Model quantization, particularly to low bit-widths like 4-bit, aims to alleviate this difficulty, yet existing Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT) methods exhibit significant limitations. PTQ often incurs substantial accuracy drop, while QAT achieves high accuracy but suffers from prohibitive computational costs, limited generalization to downstream tasks, training instability, and lacking of open-source codebase. To address these challenges, this paper introduces General, Practical, and Lightning Quantization (GPLQ), a novel framework designed for efficient and effective ViT quantization. GPLQ is founded on two key empirical insights: the paramount importance of activation quantization and the necessity of preserving the model's original optimization basin'' to maintain generalization. Consequently, GPLQ employs a sequential activation-first, weights-later'' strategy. Stage 1 keeps weights in FP32 while quantizing activations with a feature mimicking loss in only 1 epoch to keep it stay in the same ``basin'', thereby preserving generalization. Stage 2 quantizes weights using a PTQ method. As a result, GPLQ is 100x faster than existing QAT methods, lowers memory footprint to levels even below FP32 training, and achieves 4-bit model performance that is highly competitive with FP32 models in terms of both accuracy on ImageNet and generalization to diverse downstream tasks, including fine-grained visual classification and object detection. We will release an easy-to-use open-source toolkit supporting multiple vision tasks.

Post-training quantization (PTQ) is a practical way to reduce the memory footprint of large language models, but low-bit quantization is sensitive to mismatches between the quantization codebook and the empirical weight/activation distributions. We revisit Benford-like leading-digit statistics as a lightweight diagnostic of scale-broad behavior in transformer tensors. Across several model families, we observe a consistent functional dichotomy: transformational nn.Linear weights tend to be Benford-like, whereas LayerNorm parameters systematically deviate. Motivated by this observation, we propose BenQ, a data-free PTQ codebook that uses a simple log-spaced grid as a proxy for scale-broad distributions and applies it selectively to transformational layers while keeping stability-critical parameters in higher precision. In 4-bit group-wise PTQ, BenQ consistently improves over uniform RTN and trades wins with NF4 across architectures and tasks, while remaining substantially simpler than optimization-based methods. We additionally report dynamic activation quantization as an exploratory stress test: the results show that log-spaced grids can reduce RTN failures in some families, but also reveal that outlier handling remains essential for reliable low-bit activation PTQ. Code is available at https://github.com/ufopcsilab/benford-quant.