Symmetry-Induced Non-Identifiability in Neural Circuit Inference

Inferring synaptic weights from neural activity is commonly framed as a data-driven problem, yet inferred connectivity can become largely independent of spike inputs even when models are trained on them. Using a graph-based inference framework, we show that positional encoding alone can recover stable connectivity structure, with inferred weights remaining consistent when spike inputs are removed at test time. We interpret this as symmetry-induced degeneracy, where invariances render multiple connectivity configurations observationally equivalent and can dominate over activity-dependent evidence. These findings highlight the strong influence of inductive bias and suggest that neural circuit inference should be understood as learning within a symmetry-constrained weight space.