We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays and discretized multivariable functions taken, among others, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to $2^{1000}$. In numerical experiments, both on analytic model functions and on complex problems, PROTES outperforms popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution, and others).

--Graphs serve as versatile data structures in numerous real-world domains--including social networks, molecular biology, and knowledge graphs--by capturing intricate relational information among entities. Among graph-based learning techniques, Graph Contrastive Learning (GCL) has gained significant attention for its ability to derive robust, self-supervised graph representations through the contrasting of positive and negative sample pairs. However, a critical challenge lies in ensuring high-quality positive pairs so that the intrinsic semantic and structural properties of the original graph are preserved rather than distorted. T o address this issue, we propose SRGCL (Self-Reinforced Graph Contrastive Learning), a novel framework that leverages the model's own encoder to dynamically evaluate and select high-quality positive pairs. We designed an unified positive pair generator employing multiple augmentation strategies, and a selector guided by the manifold hypothesis to maintain the underlying geometry of the latent space. By adopting a probabilistic mechanism for selecting positive pairs, SRGCL iteratively refines its assessment of pair quality as the encoder's representational power improves. Extensive experiments on diverse graph-level classification tasks demonstrate that SRGCL, as a plug-in module, consistently outperforms state-of-the-art GCL methods, underscoring its adaptability and efficacy across various domains. Graphs, as powerful and flexible data structures, have become a cornerstone in numerous real-world applications, ranging from social networks [1] and biochemical molecule modeling [2] to knowledge graphs [3] and recommendation systems [4].

We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays and discretized multivariable functions taken, among others, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to 2 {1000} . In numerical experiments, both on analytic model functions and on complex problems, PROTES outperforms popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution, and others).