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 a dense token-mixing, MLP, or low-rank-adapter projection with a Bernoulli-signed sparse matrix normalized by the paper's predicted operator scale. Estimate the active representation dimension and use the effective scale to detect regimes in which extreme sparsity is likely to cause unstable amplification or dead rows.
Replace an ordinary group-L1 penalty on structured neural components with a powered ratio-of-norms penalty applied to their nonnegative importance magnitudes. The ratio encourages importance to concentrate on a small number of heads, channels, or experts while being less sensitive to arbitrary rescaling of the underlying weights. After training, components with small importance can be physically removed and the model can be fine-tuned.
Add a local Jacobian spectral regularizer and an initialization sweep to steer a looped transformer away from uncontrolled near-unit dynamics. The goal is to prevent examples from entering a fold-critical regime with very long relaxation times, or alternatively to deliberately target a controlled critical regime when adaptive test-time compute is useful.
Use attention-graph hitting times to identify tokens whose information has not mixed through the network, then route only those tokens through additional Transformer blocks. Tokens with fast reachability exit early, while slow or isolated tokens receive more computation.
Augment a causal sequence model with a small hierarchy of prefix summaries weighted by powers of the logarithmic rank of each preceding token. The summaries retain order-sensitive deviations from a baseline representation while costing O(KNd) for sequence length N, hierarchy width K, and hidden dimension d, instead of O(N^2d) dense attention.
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.
Replace an unconstrained relative-position attention-bias table by a learnable two-dimensional Fourier representation, or regularize the bias toward a small Fourier ratio. The ratio favors coefficient concentration without depending on the absolute scale of the bias, allowing the trained bias to be reconstructed from a small number of dominant frequencies.
Replace a dense channel-mixing matrix in a sequence layer with alternating diagonal propagation and sparse unipotent Stokes jumps. The diagonal part carries independently controlled exponential phases, while the unipotent factors implement cheap residual-like mode conversion without changing determinant or requiring a dense matrix multiply. Constrain the phase magnitudes and jump coefficients during training to obtain a reversible, norm-monitorable mixer.
Replace an unrestricted collection of nested dyadic attention windows on a 2D token grid by a sparse antichain: no selected window may contain another selected window. Use the paper's exponential occupancy guarantee to control how many attention blocks reuse the same token, and add a differentiable log-moment penalty during training when exact antichain selection is relaxed. The expected benefit is bounded peak KV reuse and more predictable sparse-attention cost without discarding multiscale…