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 or augment a deterministic recurrent hidden state with a stochastic Markov transition, then explicitly measure its entropy production and output memory time. Penalize operating points where the target changes faster than the hidden state can track at the available dissipation, while allowing the model to satisfy the bound either by increasing transition activity or by developing a longer-lived memory mode.
Replace correlation-based memory pruning in an RNN or state-space model by measuring how hidden-state history changes the response to individual past input events. Train a compressed memory coordinate only if it preserves the event-consequence kernel for the target observable, such as future loss, prediction, or control return. A memory representation is accepted when the conditional variance of this kernel within compressed-state groups is small, even if dwell-time or autocorrelation…
Paper: The Memory Hidden in Response Fluctuations: Trajectory-Level Fluctuation-Response Theory and Inequalities for Non-Markovian Jump DynamicsarXiv:2608.20328
Replace or augment a recurrent hidden coordinate with a nonnegative bistable autocatalytic state driven by an external control signal. The cell retains information through metastable low and high states, while a periodic or slowly varying control produces a controlled phase lag and hysteresis useful for temporal regime detection. Explicit noise can be injected to test whether it enhances switching near the predicted intermediate-frequency regime.
Replace dense pairwise interactions between all forecast horizons with nested time-shell summaries. For sorted horizons, the readout at shell j receives a cumulative embedding of all coefficients or queries assigned to later horizons, reproducing the paper's dependence on products such as \(\Pi_j=\prod_{l>j}e^{\alpha_l}=e^{\sum_{l>j}\alpha_l}\). This gives an \(O(Kd)\) multi-horizon interaction instead of an \(O(K^2d)\) temporal attention block and should work best for weak-memory…
Replace unconstrained low-rank compression of a neural state with an augmented basis that always contains vectors representing known conserved quantities or diagnostically important linear statistics. After each learned transition, project the state back onto the affine constraint set with an exact minimum-norm correction, preventing rank truncation and model error from accumulating in those statistics.
Replace a single recurrent state with two coupled one-dimensional latent chains whose relative alignment is periodically shifted during inference. Ferromagnetic coupling preserves locally coherent patterns, while controlled sliding produces a nonequilibrium friction effect that can make global magnetization substantially longer-lived than in a static noisy chain. The shift velocity acts as a measurable memory-control parameter rather than an unconstrained architectural hyperparameter.
Split a recurrent or state-space model into a persistent slow state and a fast internal state. Every r recurrent steps, preserve the slow state but reset or contract the fast state toward a learned reference, reproducing selective restart rather than a destructive global reset. The expected benefit is suppression of long-range oscillatory and error correlations while retaining trajectory-level information.