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 fixed DCT or Fourier transform in transform coding with a trainable isometric tensor-network transform whose local gates are learned once on a dataset. Retain the k coefficients with largest magnitude and reconstruct with the exact adjoint transform; the transform remains norm-preserving and fast while adapting its coefficient ordering to the data distribution.
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 ordinary per-channel or per-token KV quantization with a structured orthogonal transform followed by blockwise 3-bit quantization. Use a normalized Walsh-Hadamard transform and small SO(4) rotations to spread outliers across coordinates, quantize the transformed vectors, and exploit orthogonality to rotate queries and attention outputs so unquantized attention remains mathematically equivalent.
Attach a certificate to a cached transformer KV state or recurrent latent state and refresh it only while its predicted certificate remains inside a latency-contracted admissible region. The controller uses a bound on certificate drift to guarantee that the state will remain admissible throughout the next sampling, communication, and execution delay, reducing unnecessary recomputation while exposing a measurable refresh boundary.