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: Scalability ML: Transformer Clear all

✓ Mechanism works 2026

Degree-Corrected Hierarchical Router

Replace a flat MoE or graph-pooling assignment with recursive partitions selected by interaction evidence after removing each item’s expected degree effect. Tokens, nodes, or examples that are frequently active for purely popularity-related reasons should not automatically form an expert or cluster. Recursion stops when a candidate split has nonpositive degree-corrected evidence, producing an adaptive hierarchy rather than a fixed number of equally sized groups.

Useful6/10

Difficulty6/10

Novelty7/10

Architecture Accuracy Stability Scalability

Paper: Community structure of the pseudofractal web arXiv:2607.03010

✓ 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