Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Replace ordinary topology-sensitive message passing with scalar-gated aggregation followed by an explicit correction that aligns local node states with a graph-wide consensus component. The correction should make node embeddings less sensitive to line or edge removals while preserving local information needed for prediction. This is suitable for graph neural networks and graph-based world models exposed to changing graph sizes or sparsity patterns.
Use the recursive errors-in-variables subspace spectrum as a controller for the width of a latent SSM rather than fixing the state dimension in advance. Neurons or state channels are added when corrected covariance eigenvalues rise above the noise floor and pruned when they remain below it, producing a model-order-adaptive recurrent architecture for nonstationary streams.
Search sparse reservoir wiring in graph space rather than repeatedly testing every candidate with its full nonlinear dynamics. Use graph descriptors to predict validation accuracy and nonlinear feature selectivity, then spend exact simulations on candidates with high predicted performance or high surrogate uncertainty.