We study two-step recurrences with positive step sizes and nonnegative momentum coefficients whose terminal residual is the Chebyshev minimax polynomial on a prescribed spectral interval $[\mu,L]$. These recurrences have the same terminal error on a fixed quadratic, but their first-order responses to stepwise Hessian p...
Dmitry Pasechnyuk-Vilensky, Martin Takác· 0 citations
Second-order methods for smooth monotone variational inequalities reach the optimal rate $O(T^{-3/2})$, but a distributed exact Jacobian costs $d$ times more communication than an operator value. We show that similarity does part of the work for free: if the server's Jacobian differs from the global one by at most $\be...
Ewsey R. Obzherin, Roman M. Mozhaev, A. Gasnikov et al.· 0 citations
We study second-order methods for convex stochastic optimization, where gradients and Hessians are available only through stochastic estimates with variances $\sigma_1^2$ and $\sigma_2^2$, respectively. First, we propose the Stochastic Contracting Cubic Newton method. At each iteration, it minimizes a cubic model with...
A. Agafonov, Аслан Нажмудинович Ашабоков, D. Kamzolov et al.· 0 citations
We consider distributed stochastic convex optimization with a fixed budget of $N$ independent samples split among $m$ workers. Sample average approximation reduces the problem to a regularized finite-sum problem whose local Hessians are statistically similar. This allows the Hessian of the local objective at the server...
Yury A. Sokolov, Maxim Mashtaler, A. Gasnikov et al.· 0 citations
Across seven frontier and open models, simulation is far ahead of planning for every model, near saturation for the strongest and well short of it for the weakest, and the length of the required solution, not grid size or obstacle count, governs planning failure.
Idriss Malek, Omar Choukrani, D. Orel et al.· 0 citations
Under finite-dimensional strong-monotonicity and admissible-lift assumptions, the corresponding represented hypothesis classes coincide among resolvent feed-forward networks, graph-stationary networks, supra-graph stationary systems, and sheaf-based architectures with unitary connection.
Dmitry Pasechnyuk-Vilensky, Martin Takác· 0 citations
This work introduces Oscillatory Predictive Learning (OPL), a two-stage framework that combines Artificial Kuramoto Oscillatory Neurons (AKOrN) with predictive self-supervised pretraining using X-PhiNet and compares it with other randomized adversarial defense methods that provide precise, reproducible, and strong atta...
M. Habibi, Klea Ziu, Martin Takác et al.· 0 citations
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