Recent work has shown that fast, compact low-bitwidth neural networks can be surprisingly accurate. These networks use homogeneous binarization: all parameters in each layer or (more commonly) the whole model have the same low bitwidth (e.g., 2 bits). However, modern hardware allows efficient designs where each arithmetic instruction can have a custom bitwidth, motivating heterogeneous binarization, where every parameter in the network may have a different bitwidth. In this paper, we show that it is feasible and useful to select bitwidths at the parameter granularity during training. For instance a heterogeneously quantized version of modern networks such as AlexNet and MobileNet, with the right mix of 1-, 2-and 3-bit parameters that average to just 1.4 bits can equal the accuracy of homogeneous 2-bit versions of these networks. Further, we provide analyses to show that the heterogeneously binarized systems yield FPGA-and ASIC-based implementations that are correspondingly more efficient in both circuit area and energy efficiency than their homogeneous counterparts.

The appendices of this supplemental material are focused on providing detailed proofs (Appendix A), per-layer derivations for activation errors (Appendix B), algorithm and implementationdetails(AppendixC),datasetsandhyperparameters(AppendixD),extended experimental data (Appendix E) and additional experiments (Appendix F) to accompany the main paper. A code example and trained models are available for CIFAR10/ResNet50 by accessing https://github.com/rdevans0/acgc. L and η depend on the model being trained and dataset, and are thus problem-dependent constants. Preliminary on Separation of Norms Given two, independent random vectorsA= (an) RN and B =(bn) RN, whereE[bn]=0 n. Given f which obeys (4), and a convex functionD( X) which bounds the gradient error from above for all X, θ, and X; provided that D( X) e2V2 the variance of the compressed gradients satisfies E[kˆ θf(θ,Xnt)k2] (1+e2)V2 (16) Proof.

Diffusion models have recently dominated image synthesis and other related generative tasks. However, the iterative denoising process is expensive in computations at inference time, making diffusion models less practical for low-latency and scalable real-world applications.

For training ResNet-50 on ImageNet, our 5-bit block Householder quantizer achieves only 0.5% validation accuracy loss relative to QA T, comparable to the existing INT8 baseline.

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.

Diffusion models have recently dominated image synthesis and other related generative tasks. However, the iterative denoising process is expensive in computations at inference time, making diffusion models less practical for low-latency and scalable real-world applications. Post-training quantization of diffusion models can significantly reduce the model size and accelerate the sampling process without requiring any re-training. Nonetheless, applying existing post-training quantization methods directly to low-bit diffusion models can significantly impair the quality of generated samples. Specifically, for each denoising step, quantization noise leads to deviations in the estimated mean and mismatches with the predetermined variance schedule. Moreover, as the sampling process proceeds, the quantization noise may accumulate, resulting in a low signal-to-noise ratio (SNR) during the later denoising steps. To address these challenges, we propose a unified formulation for the quantization noise and diffusion perturbed noise in the quantized denoising process.

How can we effectively handle queries for on-device large language models (LLMs) with varying runtime constraints, such as latency and accuracy? Multi-scale quantization addresses this challenge by enabling memory-efficient runtime model adaptation of LLMs through the overlaying of multiple model variants quantized to different bitwidths. Meanwhile, an important question still remains open-ended: how can models be properly configured to match a target precision or latency? While mixed-precision offers a promising solution, we take this further by leveraging the key observation that the sensitivity of each layer dynamically changes across decoding steps. Building on this insight, we introduce DP-LLM, a novel mechanism that dynamically assigns precision to each layer based on input values. Experimental results across multiple models and benchmarks demonstrate that DP-LLM achieves a superior performance-latency trade-off, outperforming prior approaches.

Mixture-of-Experts (MoE) models scale large language models through conditional computation, but inference becomes memory-bound once expert weights exceed the capacity of GPU memory. In this case, weights must be offloaded to external memory, and fetching them incurs costly and repeated transfers. We address this by adopting CXL-attached near-data processing (CXL-NDP) as the offloading tier to execute cold experts in place, converting expensive parameter movement into cheaper activation movement. Unlike prior GPU-NDP systems that are largely context-agnostic and reactive, we develop a context-aware MoE system that uses prefill-stage activation statistics to guide decoding-stage expert placement, dynamically pins hot experts in GPU-side HBM, and maps the remainder to CXL-NDP. To meet NDP's limited compute throughput, we introduce context-aware mixed-precision quantization that allocates per-expert bitwidths (1-4 bit) based on prefill stage. The resulting MoE inference system overlaps GPU and NDP execution while minimizing cross-device movement. The evaluation on the GPU-NDP system shows that our approach achieves up to an 8.7-fold decoding throughput improvement over the state-of-the-art method, while incurring only a 0.13% average accuracy drop.

Neural Information Processing Systems http://nips.cc/

Deploying continuous-control reinforcement learning policies on embedded hardware requires meeting tight latency and power budgets. Small FPGAs can deliver these, but only if costly floating-point pipelines are avoided. We study quantization-aware training (QA T) of policies for integer inference and we present a learning-to-hardware pipeline that automatically selects low-bit policies and synthesizes them to an Artix-7 FPGA. Across five MuJoCo tasks, we obtain policy networks that are competitive with full precision (FP32) policies but require as few as 3 or even only 2 bits per weight, and per internal activation value, as long as input precision is chosen carefully. On the target hardware, the selected policies achieve inference latencies on the order of microseconds and consume microjoules per action, favorably comparing to a quantized reference. Last, we observe that the quantized policies exhibit increased input noise robustness compared to the floating-point baseline.