Gal Vinograd

Yossi Arjevani, Gal Vinograd

We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points represented by Puiseux series in the problem dimension, and so obtain precise analytic estimates on the objective function value and the Hessian spectrum. The results enable an analytic characterization of various obstructions to local optimization methods, revealing, in particular, a complex array of saddles and minima that differ in their symmetry, structure, and analytic properties. A notable phenomenon, observed for all critical points considered, concerns the index of the Hessian increasing with the objective function value.

Gal Vinograd, Idan Achituve, Ethan Fetaya

We present EDDY (Exact-marginal Diversification via Divergence-free dYnamics), a guidance mechanism for diffusion and flow matching models that promotes diversity among samples generated while maintaining quality. EDDY exploits symmetries of the Fokker-Planck equation, using drift perturbations that change particle trajectories while preserving the evolving marginal distribution. We instantiate this principle through kernel-based anti-symmetric pairwise matrix fields, constructed from the repulsive directions. The resulting divergence-free dynamics promote diversity at the joint particle level while preserving each particle's marginal distribution without any additional training. As computing the guidance can be computationally expensive in cases such as text-to-image generation with perceptual embeddings, we propose practical approximations as an effective and efficient solution. Experiments on synthetic distributions and text-to-image generation show that EDDY improves diversity while maintaining strong distributional fidelity compared to common baselines.