Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the sufficient network complexity to ensure closed-loop guarantees remains a fundamental open problem. This involves a critical precision-complexity trade-off: undersized networks may fail to capture the MPC policy, while oversized ones may outweigh the benefits of ReLU network approximation. In this work, we project the MPC actions onto a tightened constraint set to satisfy the hard constraints, and establish a state-dependent Lipschitz continuity property for the optimal MPC cost function, which enables sharp convergence analysis of the closed-loop system. For the first time, we derive explicit bounds on ReLU network width and depth for approximating MPC policies with closed-loop guarantees. To reduce network complexity for the convergence to user-specified target sets, we propose a non-uniform error framework with a state-aware scaling function to adaptively adjust both the input and output of the ReLU network. Our contributions provide a foundational step toward certifiable ReLU NN-based MPC.
Man Liu, Xingchen Liu, Hairui Zhao, Guangming Tan, Dingwen Tao
原文摘要
The rapid scaling of large language models (LLMs) has made communication overhead a critical bottleneck in distributed model-parallel training. Although existing low-precision compression methods can effectively reduce communication costs, further reducing the communication footprint to ultra-low-bit formats such as FP4 introduces new challenges, including limited numerical range, sub-byte storage overhead, and increased computational cost from fine-grained quantization. In this paper, we present \textbf{FP4Quant}, a micro-grouped FP4 compression framework for efficient model-parallel LLM training. FP4Quant integrates a micro-grouped dual-scale FP4 quantization mechanism to preserve local tensor distribution characteristics, a warp-cooperative FP4 packing scheme to enable efficient sub-byte data representation, and a hybrid two-level FWHT pipeline to mitigate quantization errors with GPU-aware execution optimization. Experiments on NVIDIA H100 GPUs with Qwen-7B demonstrate up to 1.56$\times$ end-to-end throughput improvement over BF16, revealing a trade-off between throughput and model quality.