Structure Before Flexibility: Mechanistically Testable Functional Conductances for Continuous-Time Network Dynamics

Continuous-time neural models can fit trajectories accurately while assigning the wrong contributions to individual interactions. We introduce SP-KAN-LTC, which fixes the conductance and driving-force factorization on each known edge and learns only a positive bounded state-dependent conductance, represented by a univariate spline network. A matched two-by-two factorization-by-function-class comparison shows that factorization contributes far more to mechanism recovery than the edge function class. In an eight-edge controlled benchmark with known mechanisms, SP-KAN-LTC reduces edge-current and intervention-effect error by a median of 99.8% and 99.5% relative to graph-matched and capacity-matched Current-KAN, with intervention rank correlation rising from -0.70 to +1.00. Within the matched perceptron family, the corresponding reductions are 99.1% and 98.9%, showing that the attribution failure is not specific to the spline parameterization. Against MLP-Conductance, the flexible spline edge contributes a smaller and conditional effect: no consistent advantage is established at four interactions, whereas intervention-effect error improves by 65.9% at eight. On measured electrophysiology, every factorized run recovers the independently recorded synaptic current more accurately than every unfactorized run, though SP-KAN-LTC does not consistently outperform the matched perceptron. Aliasing, driving-force misspecification, hidden interaction memory and held-out optogenetic transfer delimit the interpretation: accurate trajectories do not guarantee identifiable or structurally valid edge mechanisms, and external transfer is not demonstrated on C. elegans. The results support a structure-before-flexibility principle: constraining what an interaction is allowed to mean matters more for mechanistic fidelity than the flexibility used to parameterize it.