可序列学习与在可微电阻网络中的灾难性遗忘
Sequential Learning and Catastrophic Forgetting in Differentiable Resistor Networks
AI总结：
研究可微电阻网络中可序列学习与灾难性遗忘现象，通过任务冲突和适应度调整揭示物理机制，展示拓扑结构对遗忘-适应平衡的影响。
摘要：
可微物理网络提供了一个简单设置，通过可训练参数与物理平衡约束的相互作用研究学习。我们研究了由基尔霍夫定律约束的可微电阻网络中的可序列学习。尽管通过梯度调整边导纳可以学习个体输入-输出映射，但对冲突任务的连续训练会导致灾难性遗忘。我们显示遗忘受任务冲突和对新任务适应度的影响。均匀锚定和归一化梯度加权锚定仅通过增加新任务的最终损失来减少遗忘，给出清晰的遗忘-适应权衡。我们还显示遗忘与高电流边的局部导纳变化有关，给出物理解释为主导传输路径的重新配置。更广泛的随机任务集合显示，最强的遗忘发生在第二任务反转第一任务施加的输出顺序时。最后，跨Erdős-Rényi、小世界、无标度和随机几何图集合的比较显示拓扑结构改变遗忘-适应平衡。这些结果将可微电阻网络定位为紧凑、物理可解释的连续学习研究测试床。
英文摘要：
Differentiable physical networks provide a simple setting in which learning can be studied through the interaction between trainable parameters and physical equilibrium constraints. We investigate sequential learning in differentiable resistor networks governed by Kirchhoff's laws. Although individual input--output mappings can be learned by gradient-based adjustment of edge conductances, sequential training on conflicting tasks produces catastrophic forgetting. We show that forgetting is controlled by task conflict and by the degree of adaptation to the new task. Uniform anchoring and normalised gradient-weighted anchoring reduce forgetting only by increasing the final loss on the new task, giving a clear forgetting--adaptation trade-off. We also show that forgetting is associated with localised conductance changes on high-current edges, giving a physical interpretation as reconfiguration of dominant transport pathways. Broader random-task ensembles show that the strongest forgetting occurs when the second task reverses the output ordering imposed by the first task. Finally, comparisons across Erdős--Rényi, small-world, scale-free, and random-geometric graph ensembles show that topology changes the forgetting--adaptation balance. These results position differentiable resistor networks as compact, physically interpretable testbeds for studying continual learning in tunable matter.
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