How structural constraints bound attainable network configurations

Determine precisely how structural constraints in neural networks bound the range of attainable structural and dynamical configurations during learning, for example under spatial embedding and network communicability penalties in recurrent architectures, in order to characterize the limits on network structure and function imposed by such constraints.

Background

The study investigates spatially embedded recurrent neural networks (seRNNs) that incorporate structural constraints reflecting spatial wiring costs and communication efficiency. Prior work shows that such constraints can align model structure and function with biological observations, but the general principles by which constraints limit learned configurations are not fully characterized.

The authors analyze entropic measures of weights and eigenspectra across both rate and spiking RNNs to assess how constraints shape topology and dynamics. They explicitly note that the general mechanism by which structural constraints bound attainable configurations remains unknown, motivating their investigation.

References

But it remains unclear precisely how - in general - structural constraints bound the range of attainable configurations.

— Spatial embedding promotes a specific form of modularity with low entropy and heterogeneous spectral dynamics  (2409.17693 - Sheeran et al., 2024) in Abstract, page 1

This metric extraction task, although the metric being not inherently guaranteed to be the one that correctly represents the geometry of the system due to the blackbox aproach of LNN's, remains a worthwhile endeavor. And converging to a desired form of Lagrangian whether by further conditioning the Lagrangian model or adding regularizations could make it possible to extract interpretable metric elements, which remains as a future work.

— Learning Schwarzschild Geodesic Motion with Lagrangian Neural Networks  (2610.13234 - Caglar et al., 9 Oct 2026) in Section 6, “Future Work and Limitations,” subsection “Inequivalent Lagrangians” (Section 6.2)