Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Add a fixed or weakly learned interface-localized branch to a sequence model. Set the critical mass term to zero and make the transport coefficient change sign across a learnable interface, producing a localized mode that pools information near a detected transition rather than averaging uniformly over the sequence.
Calibrate the scales of several additive self-adjoint residual or attention operators so their aggregate spectrum has a controlled higher-moment Berry–Esseen certificate. Penalize unusually large normalized (2+δ)-moments, which should reduce spectral outliers and make the summed operator closer to a predictable semicircle-shaped spectrum.
Add a centro-affine Dirichlet penalty to a neural module whose inputs or outputs lie on a sphere, such as normalized embeddings or attention directions. The penalty measures intrinsic variation under an unconditional convex-body metric while projecting out the constant and coordinate-affine modes excluded by the theorem.
Treat a spatial feature map or lattice-indexed embedding as a function on a d-dimensional discrete grid and penalize excessive concentration near a chosen anchor using the inverse-radial Hardy weight. Calibrate the penalty with the theorem's high-dimensional scaling 2^ell d^ell instead of selecting an arbitrary spatial L2 coefficient.