Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.
Construct two latent variables X and Y with exactly the same marginal distribution, while forcing their difference X-Y to follow a chosen centered noise or residual law. Insert the pair into a residual, VAE, or diffusion block so that the model receives the desired perturbation without changing the marginal latent distribution at either endpoint. This creates a controlled alternative to independently sampled noise, especially when marginal drift in repeated stochastic layers is harmful.
Calibrate the maximum attention logit in each head against the log-correlated extreme-value law instead of applying fixed clipping or a fixed max-norm penalty. Penalize only maxima that exceed the predicted log N minus three-quarter log log N baseline by an unusually large order-one fluctuation, allowing ordinary sharp attention while suppressing rare pathological spikes.
Replace the usual uniform expert-load target in sparse MoE training with a random, heavy-tailed capacity allocation generated by a conditioned Poisson point process. The constant profile reproduces a Poisson–Dirichlet-like allocation, while a profile such as \(\phi_\gamma(x)=1+e^{-\beta\gamma x}\) deliberately changes the frequency of large versus small expert allocations.
Add a mean-field stochastic binary recurrent layer with an explicit susceptibility controller. The layer estimates the response statistic \(\chi=\beta^2N^{-1}\sum_i\operatorname{sech}^4(u_i)\) and either penalizes or clips it below \(1-\delta\), preventing the high-gain regime in which replicas with identical weights develop strongly divergent states. The expected benefit is more stable long-horizon recurrence and lower variance across stochastic forward passes.
Replace explicitly stored independent random positional features with deterministic multiplicative phase features generated from a small table of random phases indexed by primes. Restrict positions to integers whose prime factors exceed a slowly growing threshold, because the paper's central-limit result says periodic weighted sums over these rough integers recover Gaussian behavior despite strong multiplicative dependence.