Test-Time Scaling (TTS) improves large language models (LLMs) by allocating additional computation during inference, typically through parallel, sequential, or hybrid scaling. However, prior studies often assume fixed collaboration architectures (e.g., topologies) and single-model usage, overlooking that optimal architectures and model combinations can vary across tasks. Therefore, we study the novel problem of searching for compute-optimal model combinations and architectures in TTS under a fixed budget. We formalize it as a multi-LLM collaboration graph, where nodes encode roles and LLM model assignments, and edges capture information flow. This problem is challenging because (i) the combinatorial search space is prohibitively large, and (ii) task-specific requirements demand tailored designs. To address these, we reformulate the problem as probabilistic graph optimization and, through pilot experiments, derive three empirical insights into TTS collaboration graphs. Guided by these insights, we propose Agent-REINFORCE, an LLM-agent-augmented framework that mirrors the REINFORCE pipeline by mapping sampling-gradient-update to sampling-feedback-update, where feedback serves as a textual gradient to update the probabilistic graph and efficiently search for optimal multi-LLM collaboration graphs. Experiments show that Agent-REINFORCE outperforms both traditional and LLM-based baselines in sample efficiency and search performance, and effectively identifies optimal graphs under joint objectives of accuracy and inference latency.

Intelligent streetlight systems divide the streetlight network into multiple sectors, activating only the streetlights in the corresponding sectors when traffic elements pass by, rather than all streetlights, effectively reducing energy waste. This strategy requires streetlights to understand their neighbor relationships to illuminate only the streetlights in their respective sectors. However, manually configuring the neighbor relationships for a large number of streetlights in complex large-scale road streetlight networks is cumbersome and prone to errors. Due to the crisscrossing nature of roads, it is also difficult to determine the neighbor relationships using GPS or communication positioning. In response to these issues, this article proposes a systematic approach to model the streetlight network as a social network and construct a neighbor relationship probabilistic graph using IoT event records of streetlights detecting traffic elements. Based on this, a multi-objective genetic algorithm based probabilistic graph clustering method is designed to discover the neighbor relationships of streetlights. Considering the characteristic that pedestrians and vehicles usually move at a constant speed on a section of a road, speed consistency is introduced as an optimization objective, which, together with traditional similarity measures, forms a multi-objective function, enhancing the accuracy of neighbor relationship discovery. Extensive experiments on simulation datasets were conducted, comparing the proposed algorithm with other probabilistic graph clustering algorithms. The results demonstrate that the proposed algorithm can more accurately identify the neighbor relationships of streetlights compared to other algorithms, effectively achieving adaptive streetlight control for traffic elements.

In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, as suggested in Ple\v{c}ko and Meinshausen (2020) and optimal transport, as in De Lara et al. (2024). We extend "Knothe's rearrangement" Bonnotte (2013) and "triangular transport" Zech and Marzouk (2022a) to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss individual fairness. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.

One way to improve the estimation of time varying channels is to incorporate knowledge of previous observations. In this context, Dynamical VAEs (DVAEs) build a promising deep learning (DL) framework which is well suited to learn the distribution of time series data. We introduce a new DVAE architecture, called k-MemoryMarkovVAE (k-MMVAE), whose sparsity can be controlled by an additional memory parameter. Following the approach in [1] we derive a k-MMVAE aided channel estimator which takes temporal correlations of successive observations into account. The results are evaluated on simulated channels by QuaDRiGa and show that the k-MMVAE aided channel estimator clearly outperforms other machine learning (ML) aided estimators which are either memoryless or naively extended to time varying channels without major adaptions.

The sixth assessment of the international panel on climate change (IPCC) states that "cumulative net CO2 emissions over the last decade (2010-2019) are about the same size as the 11 remaining carbon budget likely to limit warming to 1.5C (medium confidence)." Such reports directly feed the public discourse, but nuances such as the degree of belief and of confidence are often lost. In this paper, we propose a formal account for allowing such degrees of belief and the associated confidence to be used to label arguments in abstract argumentation settings. Differently from other proposals in probabilistic argumentation, we focus on the task of probabilistic inference over a chosen query building upon Sato's distribution semantics which has been already shown to encompass a variety of cases including the semantics of Bayesian networks. Borrowing from the vast literature on such semantics, we examine how such tasks can be dealt with in practice when considering uncertain probabilities, and discuss the connections with existing proposals for probabilistic argumentation.

Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core decomposition algorithm based on graph peeling and Central Limit Theorem (CLT) that is capable of handling very large graphs. Their proposed peeling algorithm (PA) starts from the lowest degree vertices and recursively deletes these vertices, assigning core numbers, and updating the degree of neighbour vertices until it reached the maximum core. However, in many applications, particularly in biology, more valuable information can be obtained from dense sub-communities and we are not interested in small cores where vertices do not interact much with others. To make the previous PA focus more on dense subgraphs, we propose a multi-stage graph peeling algorithm (M-PA) that has a two-stage data screening procedure added before the previous PA. After removing vertices from the graph based on the user-defined thresholds, we can reduce the graph complexity largely and without affecting the vertices in subgraphs that we are interested in. We show that M-PA is more efficient than the previous PA and with the properly set filtering threshold, can produce very similar if not identical dense subgraphs to the previous PA (in terms of graph density and clustering coefficient).

In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable Explanation (MPE) task, the instance of MAP where the query variables are the complement of the evidence variables. We present a novel algorithm, included in the PITA reasoner, which tackles these tasks by representing each problem as a Binary Decision Diagram and applying a dynamic programming procedure on it. We compare our algorithm with the version of ProbLog that admits annotated disjunctions and can perform MAP and MPE inference. Experiments on several synthetic datasets show that PITA outperforms ProbLog in many cases. This paper is under consideration for acceptance in Theory and Practice of Logic Programming.

We consider a problem of stochastic online learning with general probabilistic graph feedback. Two cases are covered. (a) The one-step case where for each edge $(i,j)$ with probability $p_{ij}$ in the probabilistic feedback graph. After playing arm $i$ the learner observes a sample reward feedback of arm $j$ with independent probability $p_{ij}$. (b) The cascade case where after playing arm $i$ the learner observes feedback of all arms $j$ in a probabilistic cascade starting from $i$ -- for each $(i,j)$ with probability $p_{ij}$, if arm $i$ is played or observed, then a reward sample of arm $j$ would be observed with independent probability $p_{ij}$. Previous works mainly focus on deterministic graphs which corresponds to one-step case with $p_{ij} \in \{0,1\}$, an adversarial sequence of graphs with certain topology guarantees or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability.

The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based state estimation models currently used for data filtering, prediction and anomaly detection are hard to maintain and adapt to the ever-changing complex dynamics of the power system. A data-driven approach based on probabilistic graphs is proposed, where custom non-linear, localised models of the joint density of subset of system variables can be combined to model arbitrarily large and complex systems. The graphical model allows to naturally embed domain knowledge in the form of variables dependency structure or local quantitative relationships. A specific instance where neural-network models are used to represent the local joint densities is proposed, although the methodology generalises to other model classes. Accuracy and scalability are evaluated on a large-scale data set representative of the European transmission grid.

Probabilistic graphs model uncertainty by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. One of the main issues in probabilistic graphs is how to compute the connectivity of the network. The network reliability problem [4] is a generalization of the pairwise reachability, in which the goal is to determine the probability that all pairs of nodes are reachable from one another. Unlike a deterministic graph in which the reachability function is a binary value function indicating whether or not there is a path connecting two nodes, in the case of probabilistic graphs the function assumes probabilistic values. The concept of reachability in probabilistic graphs is used, along with its specialization, as a tool to compute how two nodes in the graph are likely to be connected. Reachability plays an important role in wide range of applications, such as in peer-to-peer networks [3, 18], for probabilistic-routing problem [2, 10], in road network [11], and in trust analysis in social networks [22].As adopted in these works, reachability is quite similar to the general concept of link prediction [9], whose task may be formalized as follows. Given a networked structure (V,E) made up of a set of data instances V and set of observed links E among some nodes in V, the task corresponds to predict how likely should exist an unobserved link between two nodes in the network. The extension to probabilistic graphs adds an important ingredient that should be adequately exploited.