For (i), we theoretically prove that the right sensitivity metric is the average Hessian trace, instead of just top Hessian eigenvalue.

Previous works re-design a small network for IoT devices, and then compress the network size by mixed-precision quantization.

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks. However, ultra low precision quantization could lead to significant degradation in model accuracy. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) they only use a heuristic metric based on top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) their approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) they do not consider mixed-precision activation quantization.

Mixed-Precision Quantization (MPQ) liberates the Deep Neural Networks (DNNs) from the Out-Of-Memory (OOM) bottleneck, which garnered increasing research attention. However, conventional methods either searched from costly differentiable optimization, which is neither efficient nor flexible, or learned a quantized DNN from the proxy (i.e., HAWQ) manually designed by human experts, which is labor-intensive and requires huge expert knowledge. Can we design a proxy without involving any human experts and training? In this paper, we provide an affirmative answer by proposing a novel Large Language Models (LLMs)-driven Training-free Automatic Proxy (dubbed TAP) discovery framework, which reforms the design paradigm of MPQ by utilizing LLMs to find superior TAP tailored for MPQ, automatically. In addition, to bridge the gap between black-box LLMs and the tough MPQ task, we ingeniously propose simple Direct Policy Optimization (DPO) based reinforcement learning to enhance LLMs' reasoning by optimizing prompts, which can construct a positive feedback loop between the LLM and the MPQ task, enabling LLMs to generate better TAP in the next evolution. Extensive experiments on mainstream benchmarks demonstrate that TAP achieves state-of-the-art performance. Finally, we truly believe that our TAP will significantly contribute to the MPQ community by providing a new perspective on LLM-driven design algorithms.

As Large Language Models (LLMs) continue to scale in parameter count, deploying them on commodity hardware has become increasingly challenging. Post-Training Quantization (PTQ) addresses this by reducing the precision of model weights, typically to 4-bit or lower. However, uniform quantization often leads to significant performance degradation due to the presence of ``outlier features'' -- weights that, while few in number, are critical for maintaining model accuracy. Current state-of-the-art methods such as AWQ (Activation-aware Weight Quantization) and SpQR (Sparse Quantization Representations) rely on calibration data to identify these salient weights via activation magnitudes or Hessian sensitivity. In scenarios where data privacy is paramount or calibration data is unavailable, these methods are inapplicable. In this work, we propose a data-free, structure-aware hypothesis: that the weights identified as Principal Components via Singular Value Decomposition (SVD) are intrinsically important to the model's downstream performance. We introduce a novel selection heuristic that preserves the top-$k$ weights aligned with the principal components in FP32, while aggressively quantizing the residual weights. We compare our method against activation-aware (AWQ) and second-order (SpQR) methods across GLUE benchmarks (MRPC, RTE, QNLI) using a DistilBERT backbone. Our experiments reveal that structural importance is highly correlated with functional importance. On the challenging RTE task, our SVD-based method achieves an accuracy of 66.06\%, outperforming both AWQ (65.34\%) and SpQR (65.34\%) at high protection budgets, validating that intrinsic matrix structure can serve as a robust proxy for weight saliency without the need for forward passes or calibration data.

Low-Rank Adaptation (LoRA) has become a popular technique for parameter-efficient fine-tuning of large language models (LLMs). In many real-world scenarios, multiple adapters are loaded simultaneously to enable LLM customization for personalized user experiences or to support a diverse range of tasks. Although each adapter is lightweight in isolation, their aggregate cost becomes substantial at scale. This makes it possible to quantize the important components to higher precision, while quantizing the rest to ultra-low bitwidth. We conduct comprehensive experiments with LLaMA 2-7B, LLaMA 2-13B, and Mistral 7B models on mathematical reasoning, coding, and summarization tasks. Large Language Models (LLMs) have achieved remarkable performance across a wide range of natural language tasks (Ouyang et al., 2022; Wang et al., 2022; Zhao et al., 2023), but fine-tuning LLMs for new applications remains computationally and memory intensive. To address this challenge, low-rank adaptation (LoRA; Hu et al., 2022) has emerged as a widely adopted method for parameter-efficient fine-tuning. LoRA introduces small, task-specific low-rank matrices, and during the adaptation, only these low-rank matrices are trained while the base model is frozen. An increasingly important use case of LoRA is LLM customization, as LLM providers (e.g., OpenAI and Google) allow users to personalize their own LLMs (OpenAI, 2025; Google Cloud, 2025).

The rapid scaling of language models (LMs) has resulted in unprecedented computational, memory, and energy requirements, making their training and deployment increasingly unsustainable. Quantization has emerged as an essential compression technique to reduce model size, alleviate memory bottlenecks, and accelerate inference. However, while uniform low-bit quantization (e.g., INT8, INT4) provides significant efficiency gains, it can degrade accuracy in sensitive components of transformer-based LMs. Mixed-precision quantization offers a promising alternative by selectively allocating precision across layers or within tensors to balance efficiency and accuracy. This survey provides a comprehensive overview of Mixed-Precision quantization frameworks for LMs (MXPLMs). We first review quantization fundamentals, including uniform and non-uniform quantizers, quantization granularity, and methods widely used in post-training quantization. We then categorize and compare recent MXPLM frameworks according to their bit allocation strategies and precision configurations across weights, activations, and key-value caches. A comparative analysis highlights differences in perplexity, zero-shot task performance, and deployment trade-offs. Furthermore, we contrast MXPLMs with earlier mixed-precision quantization methods for deep neural networks, identifying strategies that transfer and those that face challenges in the LM setting. Finally, we summarize open issues and future directions, including hardware-aware design, activation quantization, and scalable optimization methods for billion-parameter models. By consolidating recent advances, this work serves as a reference for understanding the current landscape and research prospects of mixed-precision quantization for large-scale language models.

With the advancement of mobile device capabilities, deploying reranking models directly on devices has become feasible, enabling real-time contextual recommendations. When migrating models from cloud to devices, resource heterogeneity inevitably necessitates model compression. Recent quantization methods show promise for efficient deployment, yet they overlook device-specific user interests, resulting in compromised recommendation accuracy. While on-device finetuning captures personalized user preference, it imposes additional computational burden through local retraining. To address these challenges, we propose a framework for \underline{\textbf{C}}ustomizing \underline{\textbf{H}}ybrid-precision \underline{\textbf{O}}n-device model for sequential \underline{\textbf{R}}ecommendation with \underline{\textbf{D}}evice-cloud collaboration (\textbf{CHORD}), leveraging channel-wise mixed-precision quantization to simultaneously achieve personalization and resource-adaptive deployment. CHORD distributes randomly initialized models across heterogeneous devices and identifies user-specific critical parameters through auxiliary hypernetwork modules on the cloud. Our parameter sensitivity analysis operates across multiple granularities (layer, filter, and element levels), enabling precise mapping from user profiles to quantization strategy. Through on-device mixed-precision quantization, CHORD delivers dynamic model adaptation and accelerated inference without backpropagation, eliminating costly retraining cycles. We minimize communication overhead by encoding quantization strategies using only 2 bits per channel instead of 32-bit weights. Experiments on three real-world datasets with two popular backbones (SASRec and Caser) demonstrate the accuracy, efficiency, and adaptivity of CHORD.

The Mixture of Experts (MoE) architecture is an important method for scaling Large Language Models (LLMs). It increases model capacity while keeping computation cost low. However, the ultra-large MoE models still have hundreds of billions of parameters, requiring massive memory/storage and leading to difficulties for deployment on resource-constrained edge platforms. Pruning or quantization alone can hardly address the issue, because of the super-aggressive compression ratio with significantly degraded accuracy and output quality. To facilitate the deployment of ultra-large MoEs on edge platforms, we propose a collaborative compression framework by combining expert pruning, mixed-precision quantization, and activation optimization. It can effectively reduce the storage footprint of the ultra-large MoE DeepSeek-V3 from 1.3TB to 103GB, while preserving high output quality with better accuracy than traditional uniform low-bit quantization methods. To the best of our knowledge, we are the first to deploy a compressed model from the ultra-large DeepSeek-V3 on the platform with a strict 128GB total memory limit. Our comprehensive experiments on multiple benchmarks under various memory constraints demonstrate the effectiveness of our method with smaller model sizes and higher accuracy than uniform low-bit quantization methods.