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 dense graph self-attention with two parallel branches: exact softmax attention only over graph neighbors and a global linear-attention branch that summarizes all nodes through feature-space statistics. A learned node-wise gate interpolates between the branches, allowing locally structured nodes to use sparse attention while retaining a global-information path.
Replace a stack of independently parameterized residual or MLP blocks with a small latent grid or vector repeatedly updated by one shared transition rule. Let the number of updates depend on the current latent state, so easy examples terminate early while hard examples receive more computation, potentially improving parameter efficiency and extrapolation.
Compress only the difference between the current client gradient and a persistent control variate, rather than compressing the full gradient. As the control variate tracks the client gradient, the residual shrinks and the same communication budget produces less compression noise than direct gradient quantization.
Replace sequential upward message passing in a tree-structured neural module with rake–compress contraction of quadratic latent-state messages. Each node stores a quadratic value function and each edge stores a linear transition or coupling triple; leaf elimination and unary-node compression are implemented as batched Schur complements, followed by a reverse pass that reconstructs node latents and edge outputs. The layer is exact for Gaussian or quadratic latent models and remains…
Train a mixture-of-experts router by solving its regularized nonnegative simplex least-squares subproblem with a matrix-free active-set conjugate-gradient method instead of projected gradient or Adam. The router coefficients remain exactly nonnegative and sum to one, while CG rapidly solves each free-set quadratic and the active-set pivots identify sparse expert assignments.
Replace full-history backpropagation through time for an online recurrent or state-space neural network with a fixed-length batch protocol. An encoder maps the most recent input-output window to the latent state at the beginning of each batch, after which the learned dynamics are rolled forward and updated recursively from the new batch only. This should prevent state drift across long streams while retaining adaptation to changing dynamics.
Treat unresolved inference items as active threats and allocate a fixed budget of C module evaluations per round. Each evaluation has an item-dependent probability of completing the item, while the scheduler observes only completion or failure after the round. Use fair allocation when completion probabilities are unknown or nearly homogeneous, then switch to a marginal-success greedy policy as feedback estimates become reliable.
Route tokens to experts using Laguerre cells defined by the minimum control energy needed to move a token embedding to each expert prototype, rather than by Euclidean distance or an unconstrained learned router logit. Per-expert dual weights deform the cells so that minibatch routing follows prescribed expert capacities, giving a geometrically interpretable alternative to auxiliary load-balancing losses.
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.