Research ideas

Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.

2 ideas found

Status: Mechanism works Solves: Memory Clear all

✓ Mechanism works 2026

Dirichlet-to-Neumann Graph Pooling

Replace a large graph submodule by a compact boundary response operator that maps boundary node features to induced boundary fluxes after the interior has been eliminated. Stack these operators recursively to obtain a hierarchical graph neural network whose coarse-level computation preserves long-range effects of discarded vertices more faithfully than average pooling or simple node clustering.

Useful7/10

Difficulty6/10

Novelty6/10

Architecture Memory Scalability Accuracy

Paper: Gluing Formula for the Pseudo-Determinant of Graph Laplacian and Applications to Counting of Spanning Trees arXiv:2608.26458

✓ Mechanism works 2026

Modular collision-free sparse attention

Replace dense attention between grid-arranged tokens by a deterministic block-sparse pattern generated from modular permutations. In each block, connect row token i to column token p(i)=2i modulo B; because i, i-p(i), and i+p(i) are injective modulo B when gcd(B,6)=1, the pattern avoids repeated horizontal, vertical, and diagonal projections. Use shifted permutations across heads to increase receptive-field coverage while retaining structured sparsity.

Useful6/10

Difficulty4/10

Novelty6/10

Architecture Speedup Memory Scalability

Paper: Closing the gap and settling the problem of queens on an $n\times n$ board, each attacking at most one other arXiv:2608.27432