Gradient Knows Best: Mixed-Precision Quantization via Gradient-Guided Bit Allocation for Super-Resolution

HAMP-LIC: Hessian-Aware Mixed-Precision Post-Training Quantization for Learned Image Compression

Use this plain-text version for the arXiv abstract field: Learned image compression (LIC) models achieve strong rate-distortion performance but are hindered by high computational complexity and encoding-decoding mismatches across heterogeneous hardware platforms. Uniform fixed-precision quantization alleviates these issues but suffers severe quality degradation at low bit widths because it ignores differences in the quantization sensitivities of individual layers. To enable efficient and accurate low-bit deployment of pretrained LIC models, we propose HAMP-LIC, a Hessian-aware mixed-precision post-training quantization (PTQ) framework with a four-stage optimization strategy. First, block-wise sensitivity is estimated from the Hessian trace to capture second-order importance. Second, a task-aware refinement module adjusts these sensitivities by jointly considering quantization distortion and rate-distortion performance. Third, guided by the refined sensitivity profile, bit widths are allocated under a global model-size constraint to balance efficiency and reconstruction quality. Finally, block-wise reconstruction using a small calibration set further suppresses quantization error. Experiments on representative LIC models, including Minnen2018 and Cheng2020, demonstrate that HAMP-LIC achieves up to 4.85x model compression with as little as 0.59% BD-rate loss. It consistently outperforms existing fixed- and mixed-precision PTQ methods across multiple datasets while completely eliminating cross-platform encoding-decoding errors.

Sensitivity-Guided Mixed-Precision Post-Training Quantization for MambaVision

Hybrid vision backbones such as MambaVision combine convolutional layers, Mamba blocks (based on selective state space models), and self-attention within a single architecture. However, the heterogeneous operator composition of such models poses new challenges for post-training quantization (PTQ): uniform bit-width assignment causes catastrophic accuracy collapse due to widely varying per-block quantization sensitivity. In this work, we present a systematic per-block sensitivity analysis of MambaVision, revealing that mixer blocks (Mamba and attention) are remarkably robust to quantization down to 4-bit weights and 4-bit activations (average accuracy drop of only $\text{0. 0 6 \%})$, while a small number of bottleneck blocks (stem and downsampling layers) are extremely fragile under the same conditions. Based on these findings, we propose a sensitivity-guided mixed-precision assignment strategy that keeps critical blocks at 16-bit floating point, quantizes robust mixer blocks to 4-bit weights and 4-bit activations, and applies 8-bit weights and 8-bit activations to moderately sensitive blocks. Our best configuration achieves 80.66% Top-1 accuracy on ImageNet-1K with GPTQ (-3.29% from 16-bit floating point), recovering +4.68% over uniform 8-bit quantization at a comparable average bit-width of 8.14 bits, while reducing model size by 53.3% and bit operations by 70.8%. We further provide a Hessian mismatch analysis explaining the counterintuitive finding that GPTQ underperforms round-to-nearest under uniform quantization but recovers its advantage under mixed-precision, where 16-bit floating point bottleneck blocks act as error propagation firewalls.

Efficient Tuning Before Low-Bit Post-Training Quantization for Stochastic Gradient Descent-optimized Models

Efficient Tuning Before Quantization (ETBQ) is proposed, a pre-conditioning tuning stage for Stochastic Gradient Descent (SGD)-optimized models before PTQ, which improves low-bit PTQ across diverse tasks.

SoftWater: Class-Aware Rate Allocation for Softmax Quantization

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.

SeGO: Sensitivity-Aware Golden Optimization for Large-Scale VLM Quantization

HyQuant: Hybrid-Precision Quantization for LLM Attention

Across diverse tasks, models, and datasets, HyQuant maintains nearly lossless accuracy with an extremely simple design, demonstrating the efficiency and practical feasibility of hybrid quantization for LLM attention.