不同神经网络架构在科学建模中迁移能力差异显著，需控制实验评估。
Architecture Shapes Transfer Specificity in Implicit Neural Representations
- 通过可控测试对比三种隐式神经表示架构的迁移特性。
- 傅里叶特征迁移最强（33.1倍），但ReLU最专注特定任务（仅0.41倍随机迁移）。
- 架构选择应基于明确控制条件，而非仅看迁移增益大小。
坐标网络中的迁移性能常以热启动增益衡量，但该增益反映的是源任务特异性结构还是通用权重复用尚不明确。本文在三类隐式神经表示（INR）——SIREN、ReLU MLP 和傅里叶特征MLP——中开展系统研究，采用受控解析测试、二维柱塞腔纳维-斯托克斯基准和一维偏微分方程（热传导、黏性伯格斯、聚焦立方非线性薛定谔方程）参考解套件。解析测试使用独立种子随机对照，PDE基准则采用同族源对照与辅助消融实验。结果表明，迁移幅度与迁移特异性可清晰分离：在10种子的一维几何测试中，傅里叶特征迁移最强（33.1×），其次为SIREN（23.0×）和ReLU（10.7×），但ReLU更具选择性——其随机对照迁移仅为0.41×，而SIREN高达14.24×。在双参数一维族测试中，ReLU在默认设置下表现最佳，傅里叶特征需带宽调优后才提升。在纳维-斯托克斯及更广义一维PDE套件中，无单一架构在所有方程上占优，但规律一致：SIREN多为广泛权重复用，而ReLU及部分方程中傅里叶特征更具源任务选择性。静态诊断工具效果有限，且实证中拒绝了启发式缩放律 $A_{\text{transfer}} \propto 1/Δt^2$。研究将迁移特异性定位为坐标网络的重要诊断指标，并建议科学机器学习中的架构选择应置于明确控制条件下评估，而非仅依赖迁移幅度。
原文摘要 · Abstract (English)
Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using controlled analytic tests, a 2D lid-driven-cavity Navier--Stokes benchmark, and 1D PDE reference-solution suites for heat, viscous Burgers, and focusing cubic NLS. The analytic tests use independent-seed random controls, while the PDE benchmarks use alternate same-family source controls and auxiliary ablations. Across settings, transfer magnitude and transfer specificity separate clearly. In a 10-seed controlled 1D geometric test, Fourier Features show the largest structured transfer ($33.1\times$), followed by SIREN ($23.0\times$) and ReLU ($10.7\times$), but ReLU is far more selective: random-control transfer is $0.41\times$ for ReLU versus $14.24\times$ for SIREN. On a controlled two-parameter 1D family, the ranking changes: ReLU gives the clearest structured-versus-control separation at default settings, whereas Fourier Features improve only after bandwidth retuning. In Navier--Stokes and the broader 1D PDE suite, no single architecture dominates every equation, yet the same pattern remains: SIREN often reuses weights broadly, whereas ReLU and, in some equations, Fourier Features are more source-selective. Static diagnostics remain weak, and the heuristic scaling law $A_{\text{transfer}} \propto 1/Δt^2$ is rejected in the implemented 1D audit. These results position transfer specificity as a useful diagnostic for coordinate networks and suggest that architecture selection in scientific machine learning should be evaluated under explicit control conditions, not by transfer magnitude alone.
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