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pro vyhledávání: '"68q17"'
Autor:
Mańdziuk, Tomasz, Ventura, Emanuele
One of the fundamental open problems in the field of tensors is the border Comon's conjecture: given a symmetric tensor $F\in(\mathbb{C}^n)^{\otimes d}$ for $d\geq 3$, its border and symmetric border ranks are equal. In this paper, we prove the conje
Externí odkaz:
http://arxiv.org/abs/2411.05721
Autor:
Kapron, Bruce M., Samieefar, Koosha
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game theory, we sp
Externí odkaz:
http://arxiv.org/abs/2411.04392
Autor:
Sobczyk, Aleksandros
Optimizing data movements during program executions is essential for achieving high performance in modern computing systems. This has been classically modeled with the Red-Blue Pebble Game and its variants. In the existing models, it is typically ass
Externí odkaz:
http://arxiv.org/abs/2410.22237
Non-Gaussian Component Analysis (NGCA) is the statistical task of finding a non-Gaussian direction in a high-dimensional dataset. Specifically, given i.i.d.\ samples from a distribution $P^A_{v}$ on $\mathbb{R}^n$ that behaves like a known distributi
Externí odkaz:
http://arxiv.org/abs/2410.21426
Autor:
Pintore, Moreno, Després, Bruno
Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We analyse three existing upper bounds written for the $l^2$ norm. We highlig
Externí odkaz:
http://arxiv.org/abs/2410.21053
Autor:
Toint, Philippe L.
The adaptive regularization algorithm for unconstrained nonconvex optimization was shown in Nesterov and Polyak (2006) and Cartis, Gould and Toint (2011) to require, under standard assumptions, at most $\mathcal{O}(\epsilon^{3/(3-q)})$ evaluations of
Externí odkaz:
http://arxiv.org/abs/2409.16047
Autor:
Cooper, Martin, Amgoud, Leila
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead to an exp
Externí odkaz:
http://arxiv.org/abs/2409.12154
Autor:
Jagiełła, Jakub, Jelisiejew, Joachim
We give a self-contained classification of $1_*$-generic minimal border rank tensors in $C^m \otimes C^m \otimes C^m$ for $m \leq 5$. Together with previous results, this gives a classification of all minimal border rank tensors in $C^m \otimes C^m \
Externí odkaz:
http://arxiv.org/abs/2409.06025
The well-studied red-blue pebble game models the execution of an arbitrary computational DAG by a single processor over a two-level memory hierarchy. We present a natural generalization to a multiprocessor setting where each processor has its own lim
Externí odkaz:
http://arxiv.org/abs/2409.03898
We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the reques
Externí odkaz:
http://arxiv.org/abs/2408.09124