Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Attach a learned controller to a physical or simulated plant and use a continuous safety certificate to compute a conservative remaining-time budget before the current action or latent prediction can become unsafe. Compile this spatial margin into a unit-rate temporal contract, allowing asynchronous inference, batching, or early execution without online rollout integration; trigger a new network evaluation only when the countdown reaches a guard threshold.
Treat a change in a neural network mask, expert set, layer width, or adapter configuration as an optimal transition problem rather than an instantaneous switch. A cheap planner proposes a short sequence of topology masks and parameter interpolations, while an expensive forward-pass feasibility filter rejects each candidate intermediate model if it violates accuracy, activation, norm, latency, or memory limits. This permits dynamic pruning and MoE reconfiguration with a certificate that the…
Replace selected dense neural-network operators by low-rank factors whose rank is selected by a randomized residual test at a user-specified tolerance. Construct candidate bases in large blocks for efficient matrix operations, then prune the block to the smallest rank that passes the residual criterion instead of treating the block size as the final rank.
Remove a latent relay or hub token from an attention or graph layer and replace its two-hop influence by direct effective edges between retained tokens. The correction is a normalized rank-one update, so it can preserve hub-mediated communication while reducing the number of stored and processed states.
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.