The classic Mallows model is a foundational tool for modeling user preferences. However, it has limitations in capturing real-world scenarios, where users often focus only on a limited set of preferred items and are indifferent to the rest. To address this, extensions such as the top-k Mallows model have been proposed, aligning better with practical applications. In this paper, we address several challenges related to the generalized top-k Mallows model, with a focus on analyzing buyer choices. Our key contributions are: (1) a novel sampling scheme tailored to generalized top-k Mallows models, (2) an efficient algorithm for computing choice probabilities under this model, and (3) an active learning algorithm for estimating the model parameters from observed choice data. These contributions provide new tools for analysis and prediction in critical decision-making scenarios. We present a rigorous mathematical analysis for the performance of our algorithms. Furthermore, through extensive experiments on synthetic data and real-world data, we demonstrate the scalability and accuracy of our proposed methods, and we compare the predictive power of Mallows model for top-k lists compared to the simpler Multinomial Logit model.

In-Image Machine Translation (IIMT) aims to translate images containing texts from one language to another. Current research of end-to-end IIMT mainly conducts on synthetic data, with simple background, single font, fixed text position, and bilingual translation, which can not fully reflect real world, causing a significant gap between the research and practical conditions. To facilitate research of IIMT in real-world scenarios, we explore Practical In-Image Multilingual Machine Translation (IIMMT). In order to convince the lack of publicly available data, we annotate the PRIM dataset, which contains real-world captured one-line text images with complex background, various fonts, diverse text positions, and supports multilingual translation directions. We propose an end-to-end model VisTrans to handle the challenge of practical conditions in PRIM, which processes visual text and background information in the image separately, ensuring the capability of multilingual translation while improving the visual quality. Experimental results indicate the VisTrans achieves a better translation quality and visual effect compared to other models. The code and dataset are available at: https://github.com/BITHLP/PRIM.

Complex chemical space and limited knowledge scope with biases holds immense challenge for human scientists, yet in automated materials discovery. Existing intelligent methods relies more on numerical computation, leading to inefficient exploration and results with hard-interpretability. To bridge this gap, we introduce a principles-guided material discovery system powered by language inferential multi-agent system (MAS), namely PriM. Our framework integrates automated hypothesis generation with experimental validation in a roundtable system of MAS, enabling systematic exploration while maintaining scientific rigor. Based on our framework, the case study of nano helix demonstrates higher materials exploration rate and property value while providing transparent reasoning pathways. This approach develops an automated-and-transparent paradigm for material discovery, with broad implications for rational design of functional materials. Code is publicly available at our \href{https://github.com/amair-lab/PriM}{GitHub}.

We seek to address a core challenge facing current Large Language Models (LLMs). LLMs have demonstrated superior performance in many tasks, yet continue to struggle with reasoning problems on explicit graphs that require multiple steps. To address this gap, we introduce a novel benchmark designed to evaluate LLM performance on classical algorithmic reasoning tasks on explicit graphs. Our benchmark encompasses five fundamental algorithms: Breadth-First Search (BFS) and Depth-First Search (DFS) for connectivity, Dijkstra's algorithm and Floyd-Warshall algorithm for all nodes shortest path, and Prim's Minimum Spanning Tree (MST-Prim's) algorithm. Through extensive experimentation, we assess the capabilities of state-of-the-art LLMs in executing these algorithms step-by-step and systematically evaluate their performance at each stage. Our findings highlight the persistent challenges LLMs face in this domain and underscore the necessity for advanced prompting techniques and algorithmic instruction to enhance their graph reasoning abilities. This work presents MAGMA, the first comprehensive benchmark focused on LLMs completing classical graph algorithms, and provides a critical step toward understanding and improving their structured problem-solving skills.

Cooperative Multi-Agent Reinforcement Learning (MARL) algorithms, trained only to optimize task reward, can lead to a concentration of power where the failure or adversarial intent of a single agent could decimate the reward of every agent in the system. In the context of teams of people, it is often useful to explicitly consider how power is distributed to ensure no person becomes a single point of failure. Here, we argue that explicitly regularizing the concentration of power in cooperative RL systems can result in systems which are more robust to single agent failure, adversarial attacks, and incentive changes of co-players. To this end, we define a practical pairwise measure of power that captures the ability of any co-player to influence the ego agent's reward, and then propose a power-regularized objective which balances task reward and power concentration. Given this new objective, we show that there always exists an equilibrium where every agent is playing a power-regularized best-response balancing power and task reward. Moreover, we present two algorithms for training agents towards this power-regularized objective: Sample Based Power Regularization (SBPR), which injects adversarial data during training; and Power Regularization via Intrinsic Motivation (PRIM), which adds an intrinsic motivation to regulate power to the training objective. Our experiments demonstrate that both algorithms successfully balance task reward and power, leading to lower power behavior than the baseline of task-only reward and avoid catastrophic events in case an agent in the system goes off-policy.

We address the problem of computing a single linkage dendrogram. A possible approach is to: (i) Form an edge weighted graph $G$ over the data, with edge weights reflecting dissimilarities. (ii) Calculate the MST $T$ of $G$. (iii) Break the longest edge of $T$ thereby splitting it into subtrees $T_L$, $T_R$. (iv) Apply the splitting process recursively to the subtrees. This approach has the attractive feature that Prim's algorithm for MST construction calculates distances as needed, and hence there is no need to ever store the inter-point distance matrix. The recursive partitioning algorithm requires us to determine the vertices (and edges) of $T_L$ and $T_R$. We show how this can be done easily and efficiently using information generated by Prim's algorithm without any additional computational cost.

Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without explicit guidance on how to structure their problem-solving. Here, instead, we focus on learning in the space of algorithms: we train several state-of-the-art GNN architectures to imitate individual steps of classical graph algorithms, parallel (breadth-first search, Bellman-Ford) as well as sequential (Prim's algorithm). As graph algorithms usually rely on making discrete decisions within neighbourhoods, we hypothesise that maximisation-based message passing neural networks are best-suited for such objectives, and validate this claim empirically. We also demonstrate how learning in the space of algorithms can yield new opportunities for positive transfer between tasks---showing how learning a shortest-path algorithm can be substantially improved when simultaneously learning a reachability algorithm.

Scenario discovery is the process of finding areas of interest, commonly referred to as scenarios, in data spaces resulting from simulations. For instance, one might search for conditions - which are inputs of the simulation model - where the system under investigation is unstable. A commonly used algorithm for scenario discovery is PRIM. It yields scenarios in the form of hyper-rectangles which are human-comprehensible. When the simulation model has many inputs, and the simulations are computationally expensive, PRIM may not produce good results, given the affordable volume of data. So we propose a new procedure for scenario discovery - we train an intermediate statistical model which generalizes fast, and use it to label (a lot of) data for PRIM. We provide the statistical intuition behind our idea. Our experimental study shows that this method is much better than PRIM itself. Specifically, our method reduces the number of simulations runs necessary by 75% on average.

This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices are approximately distributed according to a Poisson distribution, the number of clusters is estimated by thresholding the Prim's trajectory. The corresponding cluster centroids are then computed in order to initialize the generalized Lloyd's algorithm, also known as $K$-means, which allows to circumvent initialization problems. Some results are derived for evaluating the false positive rate of our cluster detection algorithm, with the help of approximations relevant in Euclidean spaces. Metrics used for measuring similarity between multi-dimensional data points are based on symmetrical divergences. The use of these informational divergences together with the proposed method leads to better results, compared to other clustering methods for the problem of astrophysical data processing. Some applications of this method in the multi/hyper-spectral imagery domain to a satellite view of Paris and to an image of the Mars planet are also presented. In order to demonstrate the usefulness of divergences in our problem, the method with informational divergence as similarity measure is compared with the same method using classical metrics. In the astrophysics application, we also compare the method with the spectral clustering algorithms.