Determine the mechanism governing region-complexity dynamics during training

Determine the mechanism responsible for the observed sharp early decrease and subsequent partial recovery of causal-region complexity during training of positive-weight TTFS spiking neural networks and matched ReLU networks.

Background

The experiments report that the estimated number of regions decreases sharply during the early stages of training and then partially recovers. The paper notes that this behavior is qualitatively similar to observations for artificial neural networks but does not explain its cause.

Because the phenomenon concerns the evolution of causal-region complexity under optimization, resolving it would connect the paper’s geometric theory to the training dynamics of TTFS networks.

References

The specific mechanism leading to this dynamics is still unknown, although some advances are being pursued in .

— Polyhedral Geometry of Time-to-First-Spike Neural Networks  (2609.11227 - Singh et al., 10 Sep 2026) in Appendix, Experimental details, paragraph “Number of regions during training”

These extensions would describe variability around a regional partition, but leave open how that partition itself emerges and changes during learning.

— Neural networks as decision trees: an analytical solution for learning and neural selectivity  (2610.08228 - Tissot et al., 6 Oct 2026) in Discussion, paragraph “Extending activation-region analysis to biological dynamics”