Sequential Learning and Catastrophic Forgetting in Differentiable Resistor Networks

arXiv cs.LG / 5/5/2026

📰 NewsIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper studies sequential learning in differentiable resistor networks where trainable edge conductances are optimized under Kirchhoff’s-law equilibrium constraints using gradient-based methods.
It finds that training on conflicting tasks leads to catastrophic forgetting even though each individual input–output mapping can be learned successfully.
The authors show that forgetting depends on both task conflict and how strongly the system adapts to the new task, and that anchoring methods can reduce forgetting only by worsening final performance on the new task.
Forgetting is linked to localized changes in conductance on high-current edges, suggesting a physical reconfiguration of the network’s dominant transport pathways.
Results across random-task setups and multiple graph-topology ensembles indicate that the strongest forgetting occurs when the second task reverses the output ordering from the first task, and that network topology shifts the forgetting–adaptation trade-off.

Abstract

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 Erd\H{o}s--R\'enyi, 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.