Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors, which limits the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.

Large Language Models (LLMs) often exhibit limited logical coherence, mapping premises to conclusions without adherence to explicit inference rules. We propose Proof-Carrying Reasoning with LLMs (PCRLLM), a framework that constrains reasoning to single-step inferences while preserving natural language formulations. Each output explicitly specifies premises, rules, and conclusions, thereby enabling verification against a target logic. This mechanism mitigates trustworthiness concerns by supporting chain-level validation even in black-box settings. Moreover, PCRLLM facilitates systematic multi-LLM collaboration, allowing intermediate steps to be compared and integrated under formal rules. Finally, we introduce a benchmark schema for generating large-scale step-level reasoning data, combining natural language expressiveness with formal rigor.

This brief study focuses on the application of autoencoders to improve the quality of low-amplitude signals, such as gravitational events. A pre-existing autoencoder was trained using cosmic event data, optimizing its architecture and parameters. The results show a significant increase in the signal-to-noise ratio of the processed signals, demonstrating the potential of autoencoders in the analysis of small signals with multiple sources of interference.

Sequence learning is an essential aspect of intelligence. In Artificial Intelligence, sequence prediction task is usually used to test a sequence learning model. In this paper, a model of sequence learning, which is interpretable through Non-Axiomatic Logic, is designed and tested. The learning mechanism is composed of three steps, hypothesizing, revising, and recycling, which enable the model to work under the Assumption of Insufficient Knowledge and Resources. Synthetic datasets for sequence prediction task are generated to test the capacity of the model. The results show that the model works well within different levels of difficulty. In addition, since the model adopts concept-centered representation, it theoretically does not suffer from catastrophic forgetting, and the practical results also support this property. This paper shows the potential of learning sequences in a logical way.

Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are based on the use of the Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative approach called Node-Average Likelihood (NAL) that is competitive with EM but computationally more efficient; and proved its consistency and model identifiability for discrete BNs. In this paper, we give general sufficient conditions for the consistency of NAL; and we prove consistency and identifiability for conditional Gaussian BNs, which include discrete and Gaussian BNs as special cases. Hence NAL has a wider applicability than originally stated in Balov (2013).

This work presents a new application of a mathematical theory of psychological behavior from Usher and McClelland and the random utility model from McFadden, to the web user behavior. The model describes the stochastic behavior of a general kind of web users, consisting of the probability of following a hyperlink for a specific length of time. The simulation experiment together with the artificial agent illustrates behavioral patterns characteristic of human subjects.