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 independent noisy evaluations in a stochastic fixed-point solver with a recursive estimator whose increment is a clipped oracle difference. For a contractive or nearly nonexpansive implicit layer, this should suppress heavy-tailed minibatch noise without clipping the fixed-point signal itself, producing more reliable residual decrease and fewer expensive oracle evaluations.
Treat a neural hidden-state process as a finite or discretized continuous-time Markov chain and define a target event as first entry into a target state set. Instead of estimating the derivative of the mean hitting time by expensive long rollouts, build an auxiliary regenerative chain that resets to the source state after reaching the target and estimate the same response from its stationary distribution. Penalize disagreement between this response prediction and short empirical perturbation…
Replace magnitude pruning in a trained recurrent network with stochastic pruning probabilities computed from weight magnitudes and the covariance of neuron activities under injected noise. Connections whose endpoints fluctuate in a sign-compatible way receive higher retention probability, while retained weights are rescaled to preserve average recurrent strength. The method uses local weights and activity covariance, avoiding Hessian construction and expensive global saliency optimization.
Use Halpern iteration to solve a non-expansive neural equilibrium layer from temporally correlated samples, and estimate its stochastic operator with a PAGE-style refresh/difference estimator. The anchor supplies a vanishing but explicit stabilizing force, while same-state differences reuse consecutive Markov samples and should reduce the number of full oracle evaluations required for a target fixed-point residual.
Add a small constrained equilibrium layer whose response depends on the current neural state and recent exogenous history, then cache responses keyed by a learned history embedding. For a new history, reuse a cached response only when an empirical Wasserstein distance to the cached history is below a threshold; otherwise run a few inner optimization iterations. The paper's local Holder and trajectory-stability results motivate graceful degradation rather than catastrophic errors for nearby…
Use a multiplicative renewal clock to decide when a neural module is updated, rather than updating at every wall-clock tick or using a fixed iteration schedule. The resulting computation allocates many updates early and increasingly long intervals between later updates, while preserving a tunable stochastic distribution of update times; this is intended for anytime recurrent refinement, continual learning, or adaptive inference where late updates have diminishing marginal value.
Add a cheap spectral gate to a state-space model or recurrent event detector that decides whether multi-step lookahead can change the threshold decision. If the learned threshold readout is approximately a nonnegative left eigenvector of the transition matrix, use the current state only; otherwise activate predictive heads and search over a small horizon. This avoids unnecessary rollout computation while preserving early-warning behavior in oscillatory or rotating dynamics.
Construct a branching residual network whose active computational paths reproduce according to a fixed offspring/connectivity law, while a controller can only remove paths using an age- or depth-dependent hazard \(u(a)\). Use the resulting bound as a diagnostic and gating schedule: removal can suppress unstable activity and reduce compute, but it should not be expected to cross the reproduction-driven propagation barrier unless the network's expansion operator is also changed.