用神经网络权重直接读取量子场论的物理规律,实现可解释性生成。
Weight-Space Physics: Interpretable Hypernetworks for Lattice Quantum Field Theories

- 通过学习耦合常数到网络权重的映射,构建可解释的超网络生成器。
- 在6²到11²格点上准确捕捉相变点和有限尺寸效应,符合二维伊辛模型指数ν≈1。
- 权重空间本身可作为新物理观测量,适合研究复杂系统中的隐含规律。
格点场论是非微扰物理的核心工具,用于模拟强核力到材料临界现象等过程。其玻尔兹曼分布由耦合常数解析参数化,但裸参数对可观测量预测能力弱,通常需大量模拟才能提取物理。虽然归一化流已成为固定耦合下的有效采样方法,但难以解释网络学到了什么。我们提出将格点场论作为神经网络可解释性的测试平台:因目标物理已知且平滑变化,提供理想合成数据与真实答案。为此,我们引入基于联合嵌入预测架构的权重生成器JEPAWG,直接从耦合常数映射到流网络权重。在6²至11²格点标量理论中,JEPAWG潜空间恢复了底层流形的真实内在维数,精确定位相变点,并编码与二维伊辛模型指数ν≈1一致的有限尺寸位移,仅通过分析网络权重即可揭示物理结构。这暗示将网络权重视为新型物理可观测量的可能。作为生成器,JEPAWG还能有效插值与外推未见耦合,对多种子训练数据引入的权重空间不连续性保持鲁棒,优于主成分分析、自编码器和变分自编码器基线。
原文摘要 · Abstract (English)
Lattice field theory is the workhorse of non-perturbative physics, used to simulate phenomena from the strong nuclear force to critical phenomena in materials. Its Boltzmann distributions are parametrized analytically by coupling constants, but these bare parameters are weak predictors of observables -- extracting physics typically requires extensive simulation. While normalizing flows have emerged as effective samplers at fixed couplings, it remains difficult to interpret what these networks have learned. This raises a natural question: can the physics be read off directly from the flow network parameters themselves, and can those parameters be generated for unseen theories? We propose lattice field theory as a testbed for neural network interpretability: because the target physics is qualitatively well-understood and smoothly varying, it provides ideal synthetic data with known ground truth. To this end, we introduce JEPAWG, a Joint-Embedding Predictive Architecture-based Weight Generator that maps couplings directly to flow weights via a learned latent space. On a scalar theory at lattices of size $6^2$ to $11^2$, the JEPAWG latent space recovers the correct intrinsic dimension of the underlying manifold, locates the phase transition, and encodes a finite-size shift aligned with the 2D Ising exponent $ν\approx 1$, allowing us to uncover physical structure by studying the network weights alone. This suggests the fascinating idea of treating the network weights as a new type of physical observable. As a generator, JEPAWG also interpolates and extrapolates to unseen couplings effectively and remains robust to weight-space discontinuities introduced by multi-seed training data, outperforming PCA, AE, and VAE baselines.
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