用物理规律设计二值网络，压缩率低于1比特还保持精度。
Physics-Inspired Binary Neural Networks: Interpretable Compression with Theoretical Guarantees
- 结合数据驱动的全局一比特量化与物理先验的固定稀疏结构
- 压缩率低于1比特/权重，且在反问题任务中泛化性能更优
- 适合需要可解释性与低内存部署的科学计算场景
为何在已有问题结构先验的情况下，仍依赖密集网络再盲目稀疏化？许多逆问题可通过算法展开网络自然编码物理规律和稀疏性。本文提出物理启发的二值神经网络（PIBiNN），包含两个核心组件：(i) 数据驱动的一比特量化，采用单一全局缩放；(ii) 基于物理规律预定义的稀疏结构，训练中无需更新。该设计通过利用结构性零点，实现低于1比特/权重的压缩率，同时保留关键算子几何特性。相比三值或剪枝方案，本方法避免了随意稀疏化，降低元数据开销，并直接契合底层任务需求。实验表明，PIBiNN在内存效率和泛化能力上均优于主流基线，如三值量化与通道级量化。
原文摘要 · Abstract (English)
Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In this work, we propose a Physics-Inspired Binary Neural Network (PIBiNN) that combines two key components: (i) data-driven one-bit quantization with a single global scale, and (ii) problem-driven sparsity predefined by physics and requiring no updates during training. This design yields compression rates below one bit per weight by exploiting structural zeros, while preserving essential operator geometry. Unlike ternary or pruning-based schemes, our approach avoids ad-hoc sparsification, reduces metadata overhead, and aligns directly with the underlying task. Experiments suggest that PIBiNN achieves advantages in both memory efficiency and generalization compared to competitive baselines such as ternary and channel-wise quantization.
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