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 explicit thresholding of a large structured routing-logit tensor with the paper's cubic sign iteration applied directly to its TT cores. The resulting approximate sign field can be converted into binary expert gates or binary activation masks without materializing all tensor entries, enabling routing over exponentially large Cartesian index spaces. Use TT rounding after each Hadamard product to prevent rank explosion, and compare the method against dense thresholding on smaller…
Represent a 3D neural field using high-order polynomial coefficients attached to an adaptively refined tetrahedral mesh, with a small MLP predicting residual corrections from local coordinates. Refine only tetrahedra whose prediction, rendering, or PDE residual is large, and use globally ordered vertices so neighboring tetrahedra share identical face and edge coefficients without hanging-node constraint solves.
Replace a dense block of a large neural-network weight matrix with an adaptively constructed cross approximation, but prevent premature termination using residual checks on O(m+n) additional diagonal-like entries. Accept a rank only after the probe residual has remained below tolerance for several consecutive iterations; otherwise continue adding pivots.