A typical solution isdirect democracywhich decides based on amajority vote, the so called "wisdom of the crowd."

In practical situations, the clustering result must be stable against points missing in the input data so that we can make trustworthy andconsistentdecisions.

Optimal transport (OT) is a widely used technique in machine learning, graphics, and vision that aligns two distributions or datasets using their relative geometry. In symmetry-rich settings, however, OT alignments based solely on pairwise geometric distances between raw features can ignore the intrinsic coherence structure of the data. We introduce Bis-pectral Optimal Transport, a symmetry-aware extension of discrete OT that compares elements using their representation using the bispectrum, a group Fourier invariant that preserves all signal structure while removing only the variation due to group actions. Empirically, we demonstrate that the transport plans computed with Bispectral OT achieve greater class preservation accuracy than naive feature OT on benchmark datasets transformed with visual symmetries, improving the quality of meaningful correspondences that capture the underlying semantic label structure in the dataset while removing nuisance variation not affecting class or content.

Current frameworks for training offensive penetration testing agents with deep reinforcement learning struggle to produce agents that perform well in real-world scenarios, due to the reality gap in simulation-based frameworks and the lack of scalability in emulation-based frameworks. Additionally, existing frameworks often use an unrealistic metric that measures the agents' performance on the training data. NASimEmu, a new framework introduced in this paper, addresses these issues by providing both a simulator and an emulator with a shared interface. This approach allows agents to be trained in simulation and deployed in the emulator, thus verifying the realism of the used abstraction. Our framework promotes the development of general agents that can transfer to novel scenarios unseen during their training. For the simulation part, we adopt an existing simulator NASim and enhance its realism. The emulator is implemented with industry-level tools, such as Vagrant, VirtualBox, and Metasploit. Experiments demonstrate that a simulation-trained agent can be deployed in emulation, and we show how to use the framework to train a general agent that transfers into novel, structurally different scenarios. NASimEmu is available as open-source.

Finding an optimal set of nodes, called key players, whose activation (or removal) would maximally enhance (or degrade) certain network functionality, is a fundamental class of problems in network science. Potential applications include network immunization, epidemic control, drug design, and viral marketing. Due to their general NP-hard nature, those problems typically cannot be solved by exact algorithms with polynomial time complexity. Many approximate and heuristic strategies have been proposed to deal with specific application scenarios. Yet, we still lack a unified framework to efficiently solve this class of problems.

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In a real-time interactive environment like customer support--where any mistakes have real business costs--any technology affecting customer interactions must be transparent and controllable. Machine learning is not infallible; the decisions artificial intelligence makes will not be 100-percent correct, 100-percent of the time. Therefore, it's important for support leaders to have insights into these decisions, as well as the opportunity to regulate them on a case-by-case basis. Only then can they control the risk--and the cost--of a potential failure.