Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Use the weighted quadrature identity as a training or inference constraint for a compressed activation path: retain only a minimal set of binary evaluations and compute normalization or residual-energy statistics exactly on the modeled Rademacher component. This provides a zero-variance alternative to random activation subsampling for the represented subspace.
Encode a neural-network checkpoint into a k by k matrix with k=n-t, and assign worker i both a row fragment and a column fragment. When a worker fails, a replacement obtains only the row and column fragments needed to reconstruct its assigned state, instead of downloading the complete checkpoint from all workers.
Replace raw braid-generator sequences by sequences of positive simple Garside factors obtained from the left-greedy normal form. Because powers of \(\Delta\) lie in the Hilden subgroup, they can be removed while preserving the relevant double-coset presentation, reducing non-uniqueness and often shortening the sequence. Feed the resulting factor tokens to a Transformer or sequence classifier, and train it to be invariant to inserted removable \(\Delta\)-powers.
Use an approximate decision diagram to select a structured subset of neurons, channels, attention heads, or attention edges when their quadratic interactions are sparse or inverse-sparse. Merge states that agree on a local interaction boundary and accept a tunable epsilon loss in the pruning objective, obtaining a representation whose size is linear in model width for fixed accuracy tolerance.
Represent candidate two-dimensional attention windows as dyadic rectangles and penalize local regions where many deeply embedded windows overlap. Use complementary horizontal and vertical depth exponents rather than independently penalizing one coordinate. The resulting router should reduce pathological concentration of sparse attention computation while preserving access to multiscale context.
Represent an intermediate feature as a low-rank PSD matrix and compress it using nonnegative measurements \(\langle A_i,X\rangle\), while penalizing the empirical ratio between maximum and minimum measurement distortion over low-rank feature pairs. This directly discourages collapsed directions and excessively amplified directions in a covariance or Gram-feature bottleneck.
Compress the hidden state of a stable neural state-space layer using low-rank controllability and observability Gramians. States that are difficult to excite from the input or weakly visible at the output are removed, producing a smaller recurrent state with a principled input-output preservation criterion.
Construct a sparse attention support by solving multiple small perturbed assignment problems between query and key embeddings and taking the union of the selected optimal matchings. Use the resulting spanning tree as the only set of cross-token edges, with edge biases determined by empirical assignment frequency.