Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Construct a sparse attention mask from a fixed regular candidate graph and one scalar random label per token, retaining edge $(u,v)$ when $x_u+x_v\geq\tau$. Unlike independent random pruning, this produces correlated neighborhoods and a controllable distribution of token degrees, potentially giving some tokens broad receptive fields while retaining a fixed sparse budget.
Replace a dense token or channel mixing matrix by a fixed sparse directed graph whose states are ordered pairs of symbols and whose transitions advance through a cyclic phase. Each state has exactly two allowed successors, obtained by appending a symbol different from the previous two, producing a strongly connected, vertex-transitive sparse mixer with shared local dynamics. The prescribed phase structure prevents arbitrary short-cycle routing and can act as an anti-collapse inductive bias in…
Represent each matroid circuit as a structured hyperedge and perform message passing from circuit embeddings back to their constituent elements. Tie all circuit-update parameters that lie in the same automorphism orbit, so relabelings preserving the matroid produce exactly relabeled hidden states rather than requiring the network to learn this symmetry from data.
Build a sparse neural mixing layer from colored directed strands rather than a dense all-to-all matrix. Feature channels are assigned ordered colors, local trivalent junctions conserve every color, and an edge width is the weighted sum of the colors carried by that edge; a differentiable penalty favors monotone, crossing-free routings that define a canonical leading term. This creates a structured routing prior that can be compared directly against dense attention and unconstrained sparse…
Replace an unconstrained pairwise attention score with an intersection of coordinate-wise threshold or interval compatibility heads. Each head is a supergraph that permits pairs satisfying one constraint, while the final attention edge exists only when every head permits the pair. This provides an interpretable inductive bias for multi-constraint relations and prevents the model from approximating a conjunction using a single unstable nonlinear score.
Represent a population of N circular latent states using a three-parameter Möbius transformation applied to fixed uniform reference phases, rather than learning N unrelated angles. The resulting states remain on the circle by construction and can model concentrated or nearly uniform phase populations through a single concentration parameter.
Replace independently sampled random-walk paths used for GNN neighbor or subgraph sampling by persistent rotor walks on the training graph. Each node stores a pointer into a fixed cyclic ordering of its outgoing neighbors; every visit advances the pointer and selects the next neighbor, producing deterministic coverage with no repeated random choices. Use several short rotor trajectories per seed and periodically reinitialize only the rotors in an encountered subgraph.
Add a curvature-aware structural regularizer to a graph neural network or learned graph-rewiring module. The regularizer raises low-curvature edges toward the sharp 1/2 threshold, which is predicted to suppress first-dimensional cycle-space structure and reduce redundant or conflicting message-passing routes without explicitly computing graph homology.