Generalized Category Discovery (GCD) focuses on classifying known categories while simultaneously discovering novel categories from unlabeled data. However, previous GCD methods face challenges due to inconsistent optimization objectives and category confusion. This leads to feature overlap and ultimately hinders performance on novel categories. To address these issues, we propose the Neural Collapse-inspired Generalized Category Discovery (NC-GCD) framework. By pre-assigning and fixing Equiangular Tight Frame (ETF) prototypes, our method ensures an optimal geometric structure and a consistent optimization objective for both known and novel categories. We introduce a Consistent ETF Alignment Loss that unifies supervised and unsupervised ETF alignment and enhances category separability. Additionally, a Semantic Consistency Matcher (SCM) is designed to maintain stable and consistent label assignments across clustering iterations.

Continuously extending combinatorial optimization objectives is a powerful technique commonly applied to the optimization of set functions. However, few such methods exist for extending functions on permutations, despite the fact that many combinatorial optimization problems, such as the quadratic assignment problem (QAP) and the traveling salesperson problem (TSP), are inherently optimization over permutations.

While the continuous Entropic Optimal Transport (EOT) field has been actively developing in recent years, it became evident that the classic EOT problem is prone to different issues like the sensitivity to outliers and imbalance of classes in the source and target measures. This fact inspired the development of solvers that deal with the *unbalanced* EOT (UEOT) problem $-$ the generalization of EOT allowing for mitigating the mentioned issues by relaxing the marginal constraints. Surprisingly, it turns out that the existing solvers are either based on heuristic principles or heavy-weighted with complex optimization objectives involving several neural networks. We address this challenge and propose a novel theoretically-justified, lightweight, unbalanced EOT solver. Our advancement consists of developing a novel view on the optimization of the UEOT problem yielding tractable and a non-minimax optimization objective. We show that combined with a light parametrization recently proposed in the field our objective leads to a fast, simple, and effective solver which allows solving the continuous UEOT problem in minutes on CPU. We prove that our solver provides a universal approximation of UEOT solutions and obtain its generalization bounds. We give illustrative examples of the solver's performance.

The objective of dataset condensation is to ensure that the model trained with the synthetic dataset can perform comparably to the model trained with full datasets. However, existing methods predominantly concentrate on classification tasks, posing challenges in their adaptation to time series forecasting (TS-forecasting).

Insuch applications, a team of agents aim to maximize a joint expected utility through a single global reward.