In this paper, we explore the fundamental role of the Monge-Amp\`ere equation in deep learning, particularly in the context of Boltzmann machines and energy-based models. We first review the structure of Boltzmann learning and its relation to free energy minimization. We then establish a connection between optimal transport theory and deep learning, demonstrating how the Monge-Amp\`ere equation governs probability transformations in generative models. Additionally, we provide insights from quantum geometry, showing that the space of covariance matrices arising in the learning process coincides with the Connes-Araki-Haagerup (CAH) cone in von Neumann algebra theory. Furthermore, we introduce an alternative approach based on renormalization group (RG) flow, which, while distinct from the optimal transport perspective, reveals another manifestation of the Monge-Amp\`ere domain in learning dynamics. This dual perspective offers a deeper mathematical understanding of hierarchical feature learning, bridging concepts from statistical mechanics, quantum geometry, and deep learning theory.

As deep learning models grow in complexity, achieving model-agnostic interpretability becomes increasingly vital. In this work, we employ post-hoc conceptual contrastive edits to expose noteworthy patterns and biases imprinted in representations of retrieval models. We systematically design optimal and controllable contrastive interventions targeting various parts of speech, and effectively apply them to explain both linguistic and visiolinguistic pre-trained models in a black-box manner. Additionally, we introduce a novel metric to assess the per-word impact of contrastive interventions on model outcomes, providing a comprehensive evaluation of each intervention's effectiveness.

Traditional 3D Gaussian Splatting techniques rely on images captured from multiple viewpoints to achieve optimal performance, but this dependence limits their use in scenarios where only a single image is available. In this work, we introduce FlashDreamer, a novel approach for reconstructing a complete 3D scene from a single image, significantly reducing the need for multi-view inputs. Our approach leverages a pre-trained vision-language model to generate descriptive prompts for the scene, guiding a diffusion model to produce images from various perspectives, which are then fused to form a cohesive 3D reconstruction. Extensive experiments show that our method effectively and robustly expands single-image inputs into a comprehensive 3D scene, extending monocular 3D reconstruction capabilities without further training.

Brain foundation models (BFMs) have emerged as a transformative paradigm in computational neuroscience, offering a revolutionary framework for processing diverse neural signals across different brain-related tasks. These models leverage large-scale pre-training techniques, allowing them to generalize effectively across multiple scenarios, tasks, and modalities, thus overcoming the traditional limitations faced by conventional artificial intelligence (AI) approaches in understanding complex brain data. By tapping into the power of pretrained models, BFMs provide a means to process neural data in a more unified manner, enabling advanced analysis and discovery in the field of neuroscience. In this survey, we define BFMs for the first time, providing a clear and concise framework for constructing and utilizing these models in various applications. We also examine the key principles and methodologies for developing these models, shedding light on how they transform the landscape of neural signal processing. This survey presents a comprehensive review of the latest advancements in BFMs, covering the most recent methodological innovations, novel views of application areas, and challenges in the field. Notably, we highlight the future directions and key challenges that need to be addressed to fully realize the potential of BFMs. These challenges include improving the quality of brain data, optimizing model architecture for better generalization, increasing training efficiency, and enhancing the interpretability and robustness of BFMs in real-world applications.

One of the main barriers to adoption of Machine Learning (ML) is that ML models can fail unexpectedly. In this work, we aim to provide practitioners a guide to better understand why ML models fail and equip them with techniques they can use to reason about failure. Specifically, we discuss failure as either being caused by lack of reliability or lack of robustness. Differentiating the causes of failure in this way allows us to formally define why models fail from first principles and tie these definitions to engineering concepts and real-world deployment settings. Throughout the document we provide 1) a summary of important theoretic concepts in reliability and robustness, 2) a sampling current techniques that practitioners can utilize to reason about ML model reliability and robustness, and 3) examples that show how these concepts and techniques can apply to real-world settings.

V ehicle Top Tag Assisted V ehicle-Road Cooperative Localization For Autonomous Public Buses Hao Li, Yifei Sun, Bo Liu, Linbin Wang Abstract -- Accurate vehicle localization is indispensable to autonomous vehicles, but is difficult to realize in complicated application scenarios. Intersection scenarios that suffer from environmental shielding and crowded dynamic objects are especially crucial and challenging. T o handle difficult intersection scenarios, the methodology of vehicle top tag assisted vehicle-road cooperative localization or for short vehicle top tag assisted localization is proposed. The proposed methodology has merits of satisfying all the feasibility, reliability, explainability, society and economy concerns. Concrete solutions of vehicle top tag detection and vehicle top tag localization that instantiate the core part of the proposed methodology are presented. Simulation results are provided to demonstrate effectiveness of the presented solutions. The proposed methodology of vehicle top tag assisted localization also has the potential to be extended to a much wider range of practical applications than our intended ones involving autonomous public buses. State-of-the-art (SOT A) vehicle localization systems normally rely on certain exteroceptive sensors such as GNSS, LiDAR, and vision system (or camera), augmented by proprioceptive sensors such as IMU. Relevant methods can be mainly categorized into GNSS based ones, LiDAR based ones, and vision based ones. These categories of vehicle localization methods are not mutually exclusive.

--Graph Neural Networks (GNNs) have achieved significant success in machine learning, with wide applications in social networks, bioinformatics, knowledge graphs, and other fields. Most research assumes ideal closed-set environments. However, in real-world open-set environments, graph learning models face challenges in robustness and reliability due to unseen classes. This highlights the need for Graph Open-Set Recognition (GOSR) methods to address these issues and ensure effective GNN application in practical scenarios. Research in GOSR is in its early stages, with a lack of a comprehensive benchmark spanning diverse tasks and datasets to evaluate methods. Moreover, traditional methods, Graph Out-of-Distribution Detection (GOODD), GOSR, and Graph Anomaly Detection (GAD) have mostly evolved in isolation, with little exploration of their interconnections or potential applications to GOSR. T o fill these gaps, we introduce G-OSR, a comprehensive benchmark for evaluating GOSR methods at both the node and graph levels, using datasets from multiple domains to ensure fair and standardized comparisons of effectiveness and efficiency across traditional, GOODD, GOSR, and GAD methods. The results offer critical insights into the generalizability and limitations of current GOSR methods and provide valuable resources for advancing research in this field through systematic analysis of diverse approaches. RAPH learning, as a significant research direction in machine learning, has been widely applied in social network analysis, recommendation systems, bioinformatics, knowledge graphs, traffic planning, and the fields of chemistry and materials science [1]. Graph Neural Networks (GNNs) have demonstrated superior performance in various node classification and graph classification tasks [2]. These methods typically follow a closed-set setting, which assumes that all test classes are among the seen classes accessible during training [3]. However, in real-world scenarios, due to undersampling, out-of-distribution, or anomalous samples, it is highly likely to encounter samples belonging to novel unseen classes, which can significantly impact the safety and robustness of models [4], as illustrated in Figure 1. Guangyao Chen is with Cornell University, Ithaca, NY, USA. Wentao Zhang is with Peking University, Beijing, China. Zhongyi Han is with King Abdullah University of Science and Technology, Thuwal, Saudi Arabia. Rundong He and Yilong Yin are the corresponding authors. Closed-set classification cannot identify unseen classes, while open-set recognition can identify unseen classes and classify nodes belonging to seen classes.

Adversarial attacks have emerged as a major challenge to the trustworthy deployment of machine learning models, particularly in computer vision applications. These attacks have a varied level of potency and can be implemented in both white box and black box approaches. Practical attacks include methods to manipulate the physical world and enforce adversarial behaviour by the corresponding target neural network models. Multiple different approaches to mitigate different kinds of such attacks are available in the literature, each with their own advantages and limitations. In this survey, we present a comprehensive systematization of knowledge on adversarial defenses, focusing on two key computer vision tasks: image classification and object detection. We review the state-of-the-art adversarial defense techniques and categorize them for easier comparison. In addition, we provide a schematic representation of these categories within the context of the overall machine learning pipeline, facilitating clearer understanding and benchmarking of defenses. Furthermore, we map these defenses to the types of adversarial attacks and datasets where they are most effective, offering practical insights for researchers and practitioners. This study is necessary for understanding the scope of how the available defenses are able to address the adversarial threats, and their shortcomings as well, which is necessary for driving the research in this area in the most appropriate direction, with the aim of building trustworthy AI systems for regular practical use-cases.

This paper reviews statistical methods for hypothesis testing and clustering in network models. We analyze the method by Bickel et al. (2016) for deriving the asymptotic null distribution of the largest eigenvalue, noting its slow convergence and the need for bootstrap corrections. The SCORE method by Jin et al. (2015) and the NCV method by Chen et al. (2018) are evaluated for their efficacy in clustering within Degree-Corrected Block Models, with NCV facing challenges due to its time-intensive nature. We suggest exploring eigenvector entry distributions as a potential efficiency improvement.

Temporal networks have gained significant prominence in the past decade for modelling dynamic interactions within complex systems. A key challenge in this domain is Temporal Link Prediction (TLP), which aims to forecast future connections by analysing historical network structures across various applications including social network analysis. While existing surveys have addressed specific aspects of TLP, they typically lack a comprehensive framework that distinguishes between representation and inference methods. This survey bridges this gap by introducing a novel taxonomy that explicitly examines representation and inference from existing methods, providing a novel classification of approaches for TLP. We analyse how different representation techniques capture temporal and structural dynamics, examining their compatibility with various inference methods for both transductive and inductive prediction tasks. Our taxonomy not only clarifies the methodological landscape but also reveals promising unexplored combinations of existing techniques. This taxonomy provides a systematic foundation for emerging challenges in TLP, including model explainability and scalable architectures for complex temporal networks.