We present an information-theoretic framework for discrete diffusion models that yields principled estimators of log-likelihood using score-matching losses. Inspired by the I-MMSE identity for the Gaussian setup, we derive analogous results for the discrete setting. Specifically, we introduce the Information-Minimum Denoising Score Entropy (I-MDSE) relation, which links mutual information between data and its diffused version to the minimum denoising score entropy (DSE) loss. We extend this theory to masked diffusion and establish the Information-Minimum Denoising Cross-Entropy (I-MDCE) relation, connecting cross-entropy losses to mutual information in discrete masked processes. These results provide a time-integral decomposition of the log-likelihood of the data in terms of optimal score-based losses, showing that commonly used losses such as DSE and DCE are not merely variational bounds but tight and principled estimators of log-likelihood. The I-MDCE decomposition further enables practical extensions, including time-free formula, conditional likelihood estimation in prompt-response tasks, and coupled Monte Carlo estimation of likelihood ratios. Experiments on synthetic and real-world data confirm the accuracy, variance stability, and utility of our estimators. The code is publicly available at https://github.com/Dongjae0324/infodis.

The theoretical analysis of Markov Decision Processes (MDPs) is commonly split into two cases - the average-reward case and the discounted-reward case - which, while sharing similarities, are typically analyzed separately. In this work, we extend a recently introduced geometric interpretation of MDPs for the discounted-reward case to the average-reward case, thereby unifying both. This allows us to extend a major result known for the discounted-reward case to the average-reward case: under a unique and ergodic optimal policy, the Value Iteration algorithm achieves a geometric convergence rate.

This paper studies group target trajectory intent as the outcome of a cooperative game where the complex-spatio trajectories are modeled using an NLP-based generative model. In our framework, the group intent is specified by the characteristic function of a cooperative game, and allocations for players in the cooperative game are specified by either the core, the Shapley value, or the nucleolus. The resulting allocations induce probability distributions that govern the coordinated spatio-temporal trajectories of the targets that reflect the group's underlying intent. We address two key questions: (1) How can the intent of a group trajectory be optimally formalized as the characteristic function of a cooperative game? (2) How can such intent be inferred from noisy observations of the targets? To answer the first question, we introduce a Fisher-information-based characteristic function of the cooperative game, which yields probability distributions that generate coordinated spatio-temporal patterns. As a generative model for these patterns, we develop an NLP-based generative model built on formal grammar, enabling the creation of realistic multi-target trajectory data. To answer the second question, we train a Graph Transformer Neural Network (GTNN) to infer group trajectory intent-expressed as the characteristic function of the cooperative game-from observational data with high accuracy. The self-attention function of the GTNN depends on the track estimates. Thus, the formulation and algorithms provide a multi-layer approach that spans target tracking (Bayesian signal processing) and the GTNN (for group intent inference).

Autonomous drone technology holds significant promise for enhancing search and rescue operations during evacuations by guiding humans toward safety and supporting broader emergency response efforts. However, their application in dynamic, real-time evacuation support remains limited. Existing models often overlook the psychological and emotional complexity of human behavior under extreme stress. In real-world fire scenarios, evacuees frequently deviate from designated safe routes due to panic and uncertainty. To address these challenges, this paper presents a multi-agent coordination framework in which autonomous Unmanned Aerial Vehicles (UAVs) assist human evacuees in real-time by locating, intercepting, and guiding them to safety under uncertain conditions. We model the problem as a Partially Observable Markov Decision Process (POMDP), where two heterogeneous UAV agents, a high-level rescuer (HLR) and a low-level rescuer (LLR), coordinate through shared observations and complementary capabilities. Human behavior is captured using an agent-based model grounded in empirical psychology, where panic dynamically affects decision-making and movement in response to environmental stimuli. The environment features stochastic fire spread, unknown evacuee locations, and limited visibility, requiring UAVs to plan over long horizons to search for humans and adapt in real-time. Our framework employs the Proximal Policy Optimization (PPO) algorithm with recurrent policies to enable robust decision-making in partially observable settings. Simulation results demonstrate that the UAV team can rapidly locate and intercept evacuees, significantly reducing the time required for them to reach safety compared to scenarios without UAV assistance.

Multi-environment POMDPs (ME-POMDPs) extend standard POMDPs with discrete model uncertainty. ME-POMDPs represent a finite set of POMDPs that share the same state, action, and observation spaces, but may arbitrarily vary in their transition, observation, and reward models. Such models arise, for instance, when multiple domain experts disagree on how to model a problem. The goal is to find a single policy that is robust against any choice of POMDP within the set, i.e., a policy that maximizes the worst-case reward across all POMDPs. We generalize and expand on existing work in the following way. First, we show that ME-POMDPs can be generalized to POMDPs with sets of initial beliefs, which we call adversarial-belief POMDPs (AB-POMDPs). Second, we show that any arbitrary ME-POMDP can be reduced to a ME-POMDP that only varies in its transition and reward functions or only in its observation and reward functions, while preserving (optimal) policies. We then devise exact and approximate (point-based) algorithms to compute robust policies for AB-POMDPs, and thus ME-POMDPs. We demonstrate that we can compute policies for standard POMDP benchmarks extended to the multi-environment setting.

This paper presents an approach for accelerated learning of optimal plans for a given task represented using Linear Temporal Logic (LTL) in multi-agent systems. Given a set of options (temporally abstract actions) available to each agent, we convert the task specification into the corresponding Buchi Automaton and proceed with a model-free approach which collects transition samples and constructs a product Semi Markov Decision Process (SMDP) on-the-fly. Value-based Reinforcement Learning algorithms can then be used to synthesize a correct-by-design controller without learning the underlying transition model of the multi-agent system. The exponential sample complexity due to multiple agents is dealt with using a novel reward shaping approach. We test the proposed algorithm in a deterministic gridworld simulation for different tasks and find that the reward shaping results in significant reduction in convergence times. We also infer that using options becomes increasing more relevant as the state and action space increases in multi-agent systems.

We analyse financial stability and welfare impacts associated with the introduction of a Central Bank Digital Currency (CBDC) in a macroeconomic agent-based model. The model considers firms, banks, and households interacting on labour, goods, credit, and interbank markets. Households move their liquidity from deposits to CBDC based on the perceived riskiness of their banks. We find that the introduction of CBDC exacerbates bank-runs and may lead to financial instability phenomena. The effect can be changed by introducing a limit on CBDC holdings. The adoption of CBDC has little effect on macroeconomic variables but the interest rate on loans to firms goes up and credit goes down in a limited way. CBDC leads to a redistribution of wealth from firms and banks to households with a higher bank default rate. CBDC may have negative welfare effects, but a bound on holding enables a welfare improvement.

Reinforcement Learning (RL) from raw visual input has achieved impressive successes in recent years, yet it remains fragile to out-of-distribution variations such as changes in lighting, color, and viewpoint. Point Cloud Reinforcement Learning (PC-RL) offers a promising alternative by mitigating appearance-based brittleness, but its sensitivity to camera pose mismatches continues to undermine reliability in realistic settings. To address this challenge, we propose PCA Point Cloud (PPC), a canonicalization framework specifically tailored for downstream robotic control. PPC maps point clouds under arbitrary rigid-body transformations to a unique canonical pose, aligning observations to a consistent frame, thereby substantially decreasing viewpoint-induced inconsistencies. In our experiments, we show that PPC improves robustness to unseen camera poses across challenging robotic tasks, providing a principled alternative to domain randomization.

The p-persistent CSMA protocol is central to random-access MAC analysis, but predicting saturation throughput in heterogeneous multi-hop wireless networks remains a hard problem. Simplified models that assume a single, shared interference domain can underestimate throughput by 48-62% in sparse topologies. Exact Markov-chain analyses are accurate but scale exponentially in computation time, making them impractical for large networks. These computational barriers motivate structural machine learning approaches like GNNs for scalable throughput prediction in general network topologies. Yet off-the-shelf GNNs struggle here: a standard GCN yields 63.94% normalized mean absolute error (NMAE) on heterogeneous networks because symmetric normalization conflates a node's direct interference with higher-order, cascading effects that pertain to how interference propagates over the network graph. Building on these insights, we propose the Decoupled Graph Convolutional Network (D-GCN), a novel architecture that explicitly separates processing of a node's own transmission probability from neighbor interference effects. D-GCN replaces mean aggregation with learnable attention, yielding interpretable, per-neighbor contribution weights while capturing complex multihop interference patterns. D-GCN attains 3.3% NMAE, outperforms strong baselines, remains tractable even when exact analytical methods become computationally infeasible, and enables gradient-based network optimization that achieves within 1% of theoretical optima.

Large Language Models (LLMs) are being increasingly used as synthetic agents in social science, in applications ranging from augmenting survey responses to powering multi-agent simulations. This paper outlines cautions that should be taken when interpreting LLM outputs and proposes a pragmatic reframing for the social sciences in which LLMs are used as high-capacity pattern matchers for quasi-predictive interpolation under explicit scope conditions and not as substitutes for probabilistic inference. Practical guardrails such as independent draws, preregistered human baselines, reliability-aware validation, and subgroup calibration, are introduced so that researchers may engage in useful prototyping and forecasting while avoiding category errors.