Neural networks are widely used, yet their analysis and verification remain challenging. In this work, we present a Lean 4 formalization of neural networks, covering both deterministic and stochastic models. We first formalize Hopfield networks, recurrent networks that store patterns as stable states. We prove convergence and the correctness of Hebbian learning, a training rule that updates network parameters to encode patterns, here limited to the case of pairwise-orthogonal patterns. We then consider stochastic networks, where updates are probabilistic and convergence is to a stationary distribution. As a canonical example, we formalize the dynamics of Boltzmann machines and prove their ergodicity, showing convergence to a unique stationary distribution using a new formalization of the Perron-Frobenius theorem.

When should an autonomous agent commit resources to a task? We introduce the Agent Capability Problem (ACP), a framework for predicting whether an agent can solve a problem under resource constraints. Rather than relying on empirical heuristics, ACP frames problem-solving as information acquisition: an agent requires $\Itotal$ bits to identify a solution and gains $\Istep$ bits per action at cost $\Cstep$, yielding an effective cost $\Ceff = (\Itotal/\Istep), \Cstep$ that predicts resource requirements before search. We prove that $\Ceff$ lower-bounds expected cost and provide tight probabilistic upper bounds. Experimental validation shows that ACP predictions closely track actual agent performance, consistently bounding search effort while improving efficiency over greedy and random strategies. The framework generalizes across LLM-based and agentic workflows, linking principles from active learning, Bayesian optimization, and reinforcement learning through a unified information-theoretic lens. \

Abstract--We investigate model-based reinforcement learning in contextual Markov decision processes (C-MDPs) in which the context is unobserved and induces confounding in the offline dataset. In such settings, conventional model-learning methods are fundamentally inconsistent, as the transition and reward mechanisms generated under a behavioral policy do not correspond to the interventional quantities required for evaluating a state-based policy. T o address this issue, we adapt a proximal off-policy evaluation approach that identifies the confounded reward expectation using only observable state-action-reward trajectories under mild invertibility conditions on proxy variables. When combined with a behavior-averaged transition model, this construction yields a surrogate MDP whose Bellman operator is well defined and consistent for state-based policies, and which integrates seamlessly with the maximum causal entropy (MaxCausalEnt) model-learning framework. The proposed formulation enables principled model learning and planning in confounded environments where contextual information is unobserved, unavailable, or impractical to collect.

We revisit the classic ski rental problem through the lens of Bayesian decision-making and machine-learned predictions. While traditional algorithms minimize worst-case cost without assumptions, and recent learning-augmented approaches leverage noisy forecasts with robustness guarantees, our work unifies these perspectives. We propose a discrete Bayesian framework that maintains exact posterior distributions over the time horizon, enabling principled uncertainty quantification and seamless incorporation of expert priors. Our algorithm achieves prior-dependent competitive guarantees and gracefully interpolates between worst-case and fully-informed settings. Our extensive experimental evaluation demonstrates superior empirical performance across diverse scenarios, achieving near-optimal results under accurate priors while maintaining robust worst-case guarantees. This framework naturally extends to incorporate multiple predictions, non-uniform priors, and contextual information, highlighting the practical advantages of Bayesian reasoning in online decision problems with imperfect predictions.

This work aims to learn the directed acyclic graph (DAG) that captures the instantaneous dependencies underlying a multivariate time series. The observed data follow a linear structural vector autoregressive model (SVARM) with both instantaneous and time-lagged dependencies, where the instantaneous structure is modeled by a DAG to reflect potential causal relationships. While recent continuous relaxation approaches impose acyclicity through smooth constraint functions involving powers of the adjacency matrix, they lead to non-convex optimization problems that are challenging to solve. In contrast, we assume that the underlying DAG has only non-negative edge weights, and leverage this additional structure to impose acyclicity via a convex constraint. This enables us to cast the problem of non-negative DAG recovery from multivariate time-series data as a convex optimization problem in abstract form, which we solve using the method of multipliers. Crucially, the convex formulation guarantees global optimality of the solution. Finally, we assess the performance of the proposed method on synthetic time-series data, where it outperforms existing alternatives.

Integrating autonomous mobile robots into human environments requires human-like decision-making and energy-efficient, event-based computation. Despite progress, neuromorphic methods are rarely applied to Deep Reinforcement Learning (DRL) navigation approaches due to unstable training. We address this gap with a hybrid socially integrated DRL actor-critic approach that combines Spiking Neural Networks (SNNs) in the actor with Artificial Neural Networks (ANNs) in the critic and a neuromorphic feature extractor to capture temporal crowd dynamics and human-robot interactions. Our approach enhances social navigation performance and reduces estimated energy consumption by approximately 1.69 orders of magnitude.

Simultaneous localization and mapping (SLAM) plays a fundamental role in extended reality (XR) applications. As the standards for immersion in XR continue to increase, the demands for SLAM benchmarking have become more stringent. Trajectory accuracy is the key metric, and marker-based optical motion capture (MoCap) systems are widely used to generate ground truth (GT) because of their drift-free and relatively accurate measurements. However, the precision of MoCap-based GT is limited by two factors: the spatiotemporal calibration with the device under test (DUT) and the inherent jitter in the MoCap measurements. These limitations hinder accurate SLAM benchmarking, particularly for key metrics like rotation error and inter-frame jitter, which are critical for immersive XR experiences. This paper presents a novel continuous-time maximum likelihood estimator to address these challenges. The proposed method integrates auxiliary inertial measurement unit (IMU) data to compensate for MoCap jitter. Additionally, a variable time synchronization method and a pose residual based on screw congruence constraints are proposed, enabling precise spatiotemporal calibration across multiple sensors and the DUT. Experimental results demonstrate that our approach outperforms existing methods, achieving the precision necessary for comprehensive benchmarking of state-of-the-art SLAM algorithms in XR applications. Furthermore, we thoroughly validate the practicality of our method by benchmarking several leading XR devices and open-source SLAM algorithms. The code is publicly available at https://github.com/ylab-xrpg/xr-hpgt.

Vehicle collisions remain a major challenge in large-scale mixed traffic systems, especially when human-driven vehicles (HVs) and robotic vehicles (RVs) interact under dynamic and uncertain conditions. Although Multi-Agent Reinforcement Learning (MARL) offers promising capabilities for traffic signal control, ensuring safety in such environments remains difficult. As a direct indicator of traffic risk, the collision rate must be well understood and incorporated into traffic control design. This study investigates the primary factors influencing collision rates in a MARL-governed Mixed Traffic Control (MTC) network. We examine three dimensions: total vehicle count, signalized versus unsignalized intersection configurations, and turning-movement strategies. Through controlled simulation experiments, we evaluate how each factor affects collision likelihood. The results show that collision rates are sensitive to traffic density, the level of signal coordination, and turning-control design. These findings provide practical insights for improving the safety and robustness of MARL-based mixed traffic control systems, supporting the development of intelligent transportation systems in which both efficiency and safety are jointly optimized.

Crowd navigation has garnered considerable research interest in recent years, especially with the proliferating application of deep reinforcement learning (DRL) techniques. Many studies, however, do not sufficiently analyze the relative priorities among evaluation metrics, which compromises the fair assessment of methods with divergent objectives. Furthermore, trajectory-continuity metrics, specifically those requiring $C^2$ smoothness, are rarely incorporated. Current DRL approaches generally prioritize efficiency and proximal comfort, often neglecting trajectory optimization or addressing it only through simplistic, unvalidated smoothness reward. Nevertheless, effective trajectory optimization is essential to ensure naturalness, enhance comfort, and maximize the energy efficiency of any navigation system. To address these gaps, this paper proposes a unified framework that enables the fair and transparent assessment of navigation methods by examining the prioritization and joint evaluation of multiple optimization objectives. We further propose a novel reward-shaping strategy that explicitly emphasizes trajectory-curvature optimization. The resulting trajectory quality and adaptability are significantly enhanced across multi-scale scenarios. Through extensive 2D and 3D experiments, we demonstrate that the proposed method achieves superior performance compared to state-of-the-art approaches.

The increasing complexity of cyber threats in distributed environments demands advanced frameworks for real-time detection and response across multimodal data streams. This paper introduces AgenticCyber, a generative AI powered multi-agent system that orchestrates specialized agents to monitor cloud logs, surveillance videos, and environmental audio concurrently. The solution achieves 96.2% F1-score in threat detection, reduces response latency to 420 ms, and enables adaptive security posture management using multimodal language models like Google's Gemini coupled with LangChain for agent orchestration. Benchmark datasets, such as AWS CloudTrail logs, UCF-Crime video frames, and UrbanSound8K audio clips, show greater performance over standard intrusion detection systems, reducing mean time to respond (MTTR) by 65% and improving situational awareness. This work introduces a scalable, modular proactive cybersecurity architecture for enterprise networks and IoT ecosystems that overcomes siloed security technologies with cross-modal reasoning and automated remediation.