Replace Euler-Maruyama in a reverse diffusion sampler with an interval transition that freezes the neural posterior-mean prediction but integrates the known linear drift and Gaussian noise exactly. The resulting exponential integrator should tolerate larger timesteps, particularly when the reverse dynamics are stiff in high-noise or strongly anisotropic directions.
Build an SPD classifier and residual head directly from Cholesky factors, using lower-triangular differences and matrix-power terms instead of generic eigendecomposition-based logarithm operators. This retains covariance geometry while making positive-definiteness automatic and backpropagation more numerically stable for minibatch training.
Replace or augment a dense attention similarity matrix with a Min-cone matrix generated by a monotone scalar sequence. The resulting matrix is positive semidefinite by construction, has only O(n) learned scalar parameters, and can be multiplied by values in O(n d) time using cumulative sums rather than forming an n-by-n matrix.
Replace scalar entropy penalties on attention maps with a matrix-valued heat-flow regularizer over a circular or periodic token coordinate. Each position stores a positive semidefinite matrix describing coupled heads, experts, or channels; heat smoothing is constrained by the sharp modified log-Sobolev and Bogoliubov–Kubo–Mori contraction rather than an arbitrary smoothing coefficient. This should suppress high-frequency routing noise while preserving positive matrix structure and reducing…
Apply a trainable scalar gate entrywise to a Min/Max structured affinity or covariance matrix while enforcing that the gate is nonnegative, nondecreasing, and convex. This preserves Loewner ordering on the structured cone and avoids unconstrained elementwise nonlinearities that can destroy PSD or order relations.
Add a certified perturbation margin to entropy-based losses so that the desired entropy remains valid after input augmentation, quantization, dropout, or attention noise. Instead of treating the entropy change caused by a perturbation as an uncontrolled empirical quantity, use the sharp modulus \(\Gamma_{\alpha,D}(\delta)\) to enforce a worst-case-safe entropy target.