Online communities play a critical role in shaping societal discourse and influencing collective behavior in the real world. The tendency for people to connect with others who share similar characteristics and views, known as homophily, plays a key role in the formation of echo chambers which further amplify polarization and division. Existing works examining homophily in online communities traditionally infer it using content- or adjacency-based approaches, such as constructing explicit interaction networks or performing topic analysis. These methods fall short for platforms where interaction networks cannot be easily constructed and fail to capture the complex nature of user interactions across the platform. This work introduces a novel approach for quantifying user homophily. We first use an Inverse Reinforcement Learning (IRL) framework to infer users' policies, then use these policies as a measure of behavioral homophily. We apply our method to Reddit, conducting a case study across 5.9 million interactions over six years, demonstrating how this approach uncovers distinct behavioral patterns and user roles that vary across different communities. We further validate our behavioral homophily measure against traditional content-based homophily, offering a powerful method for analyzing social media dynamics and their broader societal implications. We find, among others, that users can behave very similarly (high behavioral homophily) when discussing entirely different topics like soccer vs e-sports (low topical homophily), and that there is an entire class of users on Reddit whose purpose seems to be to disagree with others.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present \texttt{BFS-Prover}, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. \texttt{BFS-Prover} achieves a score of $71.31$ on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman Majorization-Minimization (VBMM) algorithm, extends the Bregman Proximal Gradient method by allowing the Bregman function used in the divergence to adaptively vary at each iteration, provided it satisfies a majorizing condition on the objective function. This adaptive framework enables the algorithm to approximate the objective more precisely at each iteration, thereby allowing for accelerated convergence compared to the traditional Bregman Proximal Gradient descent. We establish the convergence of the VBMM algorithm to a minimizer under mild assumptions on the family of metrics used. Furthermore, we introduce a novel application of both the Bregman Proximal Gradient method and the VBMM algorithm to the estimation of the multidimensional parameters of a Dirichlet distribution through the maximization of its log-likelihood. Numerical experiments confirm that the VBMM algorithm outperforms existing approaches in terms of convergence speed.

T he past century ha s witnessed incredible technological change . The many benefits and conveniences o f technology are accompanied by new complexities and human challenges that affect work, home, social, and civic realms. Th ere is a w idening gap "between a growing complexity of our own making and a lagging development of our own capacities" (Botkin et al., 1998) . Now, artificial intelligence promises to increase the rate of scientific discovery and innovation exponentially, creating new changes and p otential complexities to which humans must adapt (Friedman, 2017) . On the other hand, new AI tools, especially generative AI models, may help people to engage with the growing volume and complexity of information in their reasoning tasks such as decisionmaking and problem solving.

The increasing complexity of software systems has driven significant advancements in program analysis, as traditional methods unable to meet the demands of modern software development. To address these limitations, deep learning techniques, particularly Large Language Models (LLMs), have gained attention due to their context-aware capabilities in code comprehension. Recognizing the potential of LLMs, researchers have extensively explored their application in program analysis since their introduction. Despite existing surveys on LLM applications in cybersecurity, comprehensive reviews specifically addressing their role in program analysis remain scarce. In this survey, we systematically review the application of LLMs in program analysis, categorizing the existing work into static analysis, dynamic analysis, and hybrid approaches. Moreover, by examining and synthesizing recent studies, we identify future directions and challenges in the field. This survey aims to demonstrate the potential of LLMs in advancing program analysis practices and offer actionable insights for security researchers seeking to enhance detection frameworks or develop domain-specific models.

Large Language Models (LLM)-based systems, i.e. interconnected elements that include an LLM as a central component (e.g., conversational agents), are typically monolithic static architectures that rely on a single LLM for all user queries. However, they often require different preprocessing strategies, levels of reasoning, or knowledge. Generalist LLMs (e.g. GPT-4) trained on very large multi-topic corpora can perform well in a variety of tasks. They require significant financial, energy, and hardware resources that may not be justified for basic tasks. This implies potentially investing in unnecessary costs for a given query. To overcome this problem, a routing mechanism routes user queries to the most suitable components, such as smaller LLMs or experts in specific topics. This approach may improve response quality while minimising costs. Routing can be expanded to other components of the conversational agent architecture, such as the selection of optimal embedding strategies. This paper explores key considerations for integrating routing into LLM-based systems, focusing on resource management, cost definition, and strategy selection. Our main contributions include a formalisation of the problem, a novel taxonomy of existing approaches emphasising relevance and resource efficiency, and a comparative analysis of these strategies in relation to industry practices. Finally, we identify critical challenges and directions for future research.

The fields of MPC and RL consider two successful control techniques for Markov decision processes. Both approaches are derived from similar fundamental principles, and both are widely used in practical applications, including robotics, process control, energy systems, and autonomous driving. Despite their similarities, MPC and RL follow distinct paradigms that emerged from diverse communities and different requirements. Various technical discrepancies, particularly the role of an environment model as part of the algorithm, lead to methodologies with nearly complementary advantages. Due to their orthogonal benefits, research interest in combination methods has recently increased significantly, leading to a large and growing set of complex ideas leveraging MPC and RL. This work illuminates the differences, similarities, and fundamentals that allow for different combination algorithms and categorizes existing work accordingly. Particularly, we focus on the versatile actor-critic RL approach as a basis for our categorization and examine how the online optimization approach of MPC can be used to improve the overall closed-loop performance of a policy.

The alteration of the climate in various areas of the world is of increasing concern since climate stability is a necessary condition for human survival as well as every living organism. The main reason of climate change is the greenhouse effect caused by the accumulation of carbon dioxide in the atmosphere. In this paper, we design a networked system underpinned by compartmental dynamical thermodynamics to circulate the atmospheric carbon dioxide. Specifically, in the carbon dioxide emitter compartment, we develop an initial-condition-dependent finite-time stabilizing controller that guarantees stability within a desired time leveraging the system property of affinity in the control. Then, to compensate for carbon emissions we show that a cultivation of microalgae with a volume 625 times bigger than the one of the carbon emitter is required. To increase the carbon uptake of the microalgae, we implement the nonaffine-in-the-control microalgae dynamical equations as an environment of a state-of-the-art library for reinforcement learning (RL), namely, Stable-Baselines3, and then, through the library, we test the performance of eight RL algorithms for training a controller that maximizes the microalgae absorption of carbon through the light intensity. All the eight controllers increased the carbon absorption of the cultivation during a training of 200,000 time steps with a maximum episode length of 200 time steps and with no termination conditions. This work is a first step towards approaching net zero as a classical and learning-based network control problem. The source code is publicly available.

This technology has important applications in many challenges of the industry such as content moderation, tracing AI-generated content, and monitoring the usage of AI models. The contributions of this thesis include the development of new watermarking techniques for images, audio, and text. We first introduce methods for active moderation of images on social platforms. We then develop specific techniques for AI-generated content. We specifically demonstrate methods to adapt latent generative models to embed watermarks in all generated content, identify watermarked sections in speech, and improve watermarking in large language models with tests that ensure low false positive rates. Furthermore, we explore the use of digital watermarking to detect model misuse, including the detection of watermarks in language models fine-tuned on watermarked text, and introduce training-free watermarks for the weights of large transformers. Through these contributions, the thesis provides effective solutions for the challenges posed by the increasing use of generative AI models and the need for model monitoring and content moderation. It finally examines the challenges and limitations of watermarking techniques and discuss potential future directions for research in this area.

Scientific reasoning, the process through which humans apply logic, evidence, and critical thinking to explore and interpret scientific phenomena, is essential in advancing knowledge reasoning across diverse fields. However, despite significant progress, current scientific reasoning models still struggle with generalization across domains and often fall short of multimodal perception. Multimodal Large Language Models (MLLMs), which integrate text, images, and other modalities, present an exciting opportunity to overcome these limitations and enhance scientific reasoning. Therefore, this position paper argues that MLLMs can significantly advance scientific reasoning across disciplines such as mathematics, physics, chemistry, and biology. First, we propose a four-stage research roadmap of scientific reasoning capabilities, and highlight the current state of MLLM applications in scientific reasoning, noting their ability to integrate and reason over diverse data types. Second, we summarize the key challenges that remain obstacles to achieving MLLM's full potential. To address these challenges, we propose actionable insights and suggestions for the future. Overall, our work offers a novel perspective on MLLM integration with scientific reasoning, providing the LLM community with a valuable vision for achieving Artificial General Intelligence (AGI).