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In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. Furthermore, the training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset. This structure is given in terms of signed volumes of triangles and parallelotopes generated by data vectors. The convex problem finds a small subset of samples via $\ell_1$ regularization to discover only relevant wedge product features. Our analysis provides a novel perspective on the inner workings of deep neural networks and sheds light on the role of the hidden layers.

In this letter, we present an extension to TensorNet, a state-of-the-art equivariant Cartesian tensor neural network potential, allowing it to handle charged molecules and spin states without architectural changes or increased costs. By incorporating these attributes, we address input degeneracy issues, enhancing the model's predictive accuracy across diverse chemical systems. This advancement significantly broadens TensorNet's applicability, maintaining its efficiency and accuracy.

In this paper we discuss a first attempt to build a language learning game for brazilian indigenous languages and the challenges around it. We present a design for the tool with gamification aspects. Then we describe a process to automatically generate language exercises and questions from a dependency treebank and a lexical database for Tupian languages. We discuss the limitations of our prototype highlighting ethical and practical implementation concerns. Finally, we conclude that new data gathering processes should be established in partnership with indigenous communities and oriented for educational purposes.

The Metaverse is at the vanguard of the impending digital revolution, with the potential to significantly transform industries and lifestyles. However, in 2023, skepticism surfaced within industrial and academic spheres, raising concerns that excitement may outpace actual technological progress. Interoperability, recognized as a major barrier to the Metaverse's full potential, is central to this debate. CoinMarketCap's report in February 2023 indicated that of over 240 metaverse initiatives, most existed in isolation, underscoring the interoperability challenge. Despite consensus on its critical role, there is a research gap in exploring the impact on the Metaverse, significance, and developmental extent. Our study bridges this gap via a systematic literature review and content analysis of the Web of Science (WoS) and Scopus databases, yielding 74 publications after a rigorous selection process. Interoperability, difficult to define due to varied contexts and lack of standardization, is central to the Metaverse, often seen as a digital ecosystem. Urs Gasser's framework, outlining technological, data, human, and institutional dimensions, systematically addresses interoperability complexities. Incorporating this framework, we dissect the literature for a comprehensive Metaverse interoperability overview. Our study seeks to establish benchmarks for future inquiries, navigating the complex field of Metaverse interoperability studies and contributing to academic advancement.

Detectives frequently engage in information detection and reasoning simultaneously when making decisions across various cases, especially when confronted with a vast amount of information. With the rapid development of large language models~(LLMs), evaluating how these models identify key information and reason to solve questions becomes increasingly relevant. We introduces the DetectBench, a reading comprehension dataset designed to assess a model's ability to jointly ability in key information detection and multi-hop reasoning when facing complex and implicit information. The DetectBench comprises 3,928 questions, each paired with a paragraph averaging 190 tokens in length. To enhance model's detective skills, we propose the Detective Thinking Framework. These methods encourage models to identify all possible clues within the context before reasoning. Our experiments reveal that existing models perform poorly in both information detection and multi-hop reasoning. However, the Detective Thinking Framework approach alleviates this issue.

In this paper, we seek to learn a robot policy guaranteed to satisfy state constraints. To encourage constraint satisfaction, existing RL algorithms typically rely on Constrained Markov Decision Processes and discourage constraint violations through reward shaping. However, such soft constraints cannot offer verifiable safety guarantees. To address this gap, we propose POLICEd RL, a novel RL algorithm explicitly designed to enforce affine hard constraints in closed-loop with a black-box environment. Our key insight is to force the learned policy to be affine around the unsafe set and use this affine region as a repulsive buffer to prevent trajectories from violating the constraint. We prove that such policies exist and guarantee constraint satisfaction. Our proposed framework is applicable to both systems with continuous and discrete state and action spaces and is agnostic to the choice of the RL training algorithm. Our results demonstrate the capacity of POLICEd RL to enforce hard constraints in robotic tasks while significantly outperforming existing methods.

In this paper, we first identify activation shift, a simple but remarkable phenomenon in a neural network in which the preactivation value of a neuron has non-zero mean that depends on the angle between the weight vector of the neuron and the mean of the activation vector in the previous layer. We then propose linearly constrained weights (LCW) to reduce the activation shift in both fully connected and convolutional layers. The impact of reducing the activation shift in a neural network is studied from the perspective of how the variance of variables in the network changes through layer operations in both forward and backward chains. We also discuss its relationship to the vanishing gradient problem. Experimental results show that LCW enables a deep feedforward network with sigmoid activation functions to be trained efficiently by resolving the vanishing gradient problem. Moreover, combined with batch normalization, LCW improves generalization performance of both feedforward and convolutional networks.

In this article, we review the literature on statistical theories of neural networks from three perspectives. In the first part, results on excess risks for neural networks are reviewed in the nonparametric framework of regression or classification. These results rely on explicit constructions of neural networks, leading to fast convergence rates of excess risks, in that tools from the approximation theory are adopted. Through these constructions, the width and depth of the networks can be expressed in terms of sample size, data dimension, and function smoothness. Nonetheless, their underlying analysis only applies to the global minimizer in the highly non-convex landscape of deep neural networks. This motivates us to review the training dynamics of neural networks in the second part. Specifically, we review papers that attempt to answer ``how the neural network trained via gradient-based methods finds the solution that can generalize well on unseen data.'' In particular, two well-known paradigms are reviewed: the Neural Tangent Kernel (NTK) paradigm, and Mean-Field (MF) paradigm. In the last part, we review the most recent theoretical advancements in generative models including Generative Adversarial Networks (GANs), diffusion models, and in-context learning (ICL) in the Large Language Models (LLMs). The former two models are known to be the main pillars of the modern generative AI era, while ICL is a strong capability of LLMs in learning from a few examples in the context. Finally, we conclude the paper by suggesting several promising directions for deep learning theory.

With the advent of 5G commercialization, the need for more reliable, faster, and intelligent telecommunication systems are envisaged for the next generation beyond 5G (B5G) radio access technologies. Artificial Intelligence (AI) and Machine Learning (ML) are not just immensely popular in the service layer applications but also have been proposed as essential enablers in many aspects of B5G networks, from IoT devices and edge computing to cloud-based infrastructures. However, most of the existing surveys in B5G security focus on the performance of AI/ML models and their accuracy, but they often overlook the accountability and trustworthiness of the models' decisions. Explainable AI (XAI) methods are promising techniques that would allow system developers to identify the internal workings of AI/ML black-box models. The goal of using XAI in the security domain of B5G is to allow the decision-making processes of the security of systems to be transparent and comprehensible to stakeholders making the systems accountable for automated actions. In every facet of the forthcoming B5G era, including B5G technologies such as RAN, zero-touch network management, E2E slicing, this survey emphasizes the role of XAI in them and the use cases that the general users would ultimately enjoy. Furthermore, we presented the lessons learned from recent efforts and future research directions on top of the currently conducted projects involving XAI.

Convolutional networks (ConvNets) have achieved great successes in various challenging vision tasks. However, the performance of ConvNets would degrade when encountering the domain shift. The domain adaptation is more significant while challenging in the field of biomedical image analysis, where cross-modality data have largely different distributions. Given that annotating the medical data is especially expensive, the supervised transfer learning approaches are not quite optimal. In this paper, we propose an unsupervised domain adaptation framework with adversarial learning for cross-modality biomedical image segmentations. Specifically, our model is based on a dilated fully convolutional network for pixel-wise prediction. Moreover, we build a plug-and-play domain adaptation module (DAM) to map the target input to features which are aligned with source domain feature space. A domain critic module (DCM) is set up for discriminating the feature space of both domains. We optimize the DAM and DCM via an adversarial loss without using any target domain label. Our proposed method is validated by adapting a ConvNet trained with MRI images to unpaired CT data for cardiac structures segmentations, and achieved very promising results.