Establish depth-dependent lower bounds for shared-weight TTFS networks

Establish a lower bound for shared-weight feedforward TTFS spiking neural networks that grows exponentially with network depth, or determine whether such depth-dependent exponential growth is attainable under the shared-weight constraint.

Background

For arbitrary positive weights, the paper constructs a folding mechanism that produces exponentially many causal regions with depth. In the shared-weight setting, however, the authors prove an obstruction showing that their two-layer multi-fold construction has monotone relative output timing and therefore cannot generate the required alternating sawtooth.

The obstruction does not exclude other mechanisms, so the existence of exponential-in-depth lower bounds for shared-weight networks remains unresolved.