Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions, derivations, and proofs, in contrast to the experimental sciences which rely on the modelling of data with error-bars. In this Perspective, we categorize the approaches to mathematical discovery as "top-down", "bottom-up" and "meta-mathematics", as inspired by historical examples. We review some of the progress over the last few years, comparing and contrasting both the advances and the short-comings in each approach. We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.

This paper analyzes Large Language Models (LLMs) with regard to their programming exercise generation capabilities. Through a survey study, we defined the state of the art, extracted their strengths and weaknesses and finally proposed an evaluation matrix, helping researchers and educators to decide which LLM is the best fitting for the programming exercise generation use case. We also found that multiple LLMs are capable of producing useful programming exercises. Nevertheless, there exist challenges like the ease with which LLMs might solve exercises generated by LLMs. This paper contributes to the ongoing discourse on the integration of LLMs in education.

The success of Artificial Intelligence (AI) in multiple disciplines and vertical domains in recent years has promoted the evolution of mobile networking and the future Internet toward an AI-integrated Internet-of-Things (IoT) era. Nevertheless, most AI techniques rely on data generated by physical devices (e.g., mobile devices and network nodes) or specific applications (e.g., fitness trackers and mobile gaming). To bypass this circumvent, Generative AI (GAI), a.k.a. AI-generated content (AIGC), has emerged as a powerful AI paradigm; thanks to its ability to efficiently learn complex data distributions and generate synthetic data to represent the original data in various forms. This impressive feature is projected to transform the management of mobile networking and diversify the current services and applications provided. On this basis, this work presents a concise tutorial on the role of GAIs in mobile and wireless networking. In particular, this survey first provides the fundamentals of GAI and representative GAI models, serving as an essential preliminary to the understanding of the applications of GAI in mobile and wireless networking. Then, this work provides a comprehensive review of state-of-the-art studies and GAI applications in network management, wireless security, semantic communication, and lessons learned from the open literature. Finally, this work summarizes the current research on GAI for mobile and wireless networking by outlining important challenges that need to be resolved to facilitate the development and applicability of GAI in this edge-cutting area.

Spiking Neural Networks (SNNs) have attracted great attention for their energy-efficient operations and biologically inspired structures, offering potential advantages over Artificial Neural Networks (ANNs) in terms of energy efficiency and interpretability. Nonetheless, similar to ANNs, the robustness of SNNs remains a challenge, especially when facing adversarial attacks. Existing techniques, whether adapted from ANNs or specifically designed for SNNs, exhibit limitations in training SNNs or defending against strong attacks. In this paper, we propose a novel approach to enhance the robustness of SNNs through gradient sparsity regularization. We observe that SNNs exhibit greater resilience to random perturbations compared to adversarial perturbations, even at larger scales. Motivated by this, we aim to narrow the gap between SNNs under adversarial and random perturbations, thereby improving their overall robustness. To achieve this, we theoretically prove that this performance gap is upper bounded by the gradient sparsity of the probability associated with the true label concerning the input image, laying the groundwork for a practical strategy to train robust SNNs by regularizing the gradient sparsity. We validate the effectiveness of our approach through extensive experiments on both image-based and event-based datasets. The results demonstrate notable improvements in the robustness of SNNs. Our work highlights the importance of gradient sparsity in SNNs and its role in enhancing robustness.

Federated Learning (FL) is a promising paradigm that offers significant advancements in privacy-preserving, decentralized machine learning by enabling collaborative training of models across distributed devices without centralizing data. However, the practical deployment of FL systems faces a significant bottleneck: the communication overhead caused by frequently exchanging large model updates between numerous devices and a central server. This communication inefficiency can hinder training speed, model performance, and the overall feasibility of real-world FL applications. In this survey, we investigate various strategies and advancements made in communication-efficient FL, highlighting their impact and potential to overcome the communication challenges inherent in FL systems. Specifically, we define measures for communication efficiency, analyze sources of communication inefficiency in FL systems, and provide a taxonomy and comprehensive review of state-of-the-art communication-efficient FL methods. Additionally, we discuss promising future research directions for enhancing the communication efficiency of FL systems. By addressing the communication bottleneck, FL can be effectively applied and enable scalable and practical deployment across diverse applications that require privacy-preserving, decentralized machine learning, such as IoT, healthcare, or finance.

In the dynamic field of nuclear magnetic resonance (NMR) spectroscopy, artificial intelligence (AI) has ushered in a transformative era for molecular studies. AI-driven NMR prediction, powered by advanced machine learning and predictive algorithms, has fundamentally reshaped the interpretation of NMR spectra. This innovation empowers us to forecast spectral patterns swiftly and accurately across a broad spectrum of molecular structures. Furthermore, the advent of generative modeling offers a groundbreaking approach, making it feasible to make informed prediction of 2D NMR from chemical language (such as SMILES, IUPAC Name). Our method mirrors the multifaceted nature of NMR imaging experiments, producing 2D NMRs for the same molecule based on different conditions, such as solvents and temperatures. Our methodology is versatile, catering to both monosaccharide-derived small molecules, oligosaccharides and large polysaccharides. A deeper exploration of the discrepancies in these predictions can provide insights into the influence of elements such as functional groups, repeating units, and the modification of the monomers on the outcomes. Given the complex nature involved in the generation of 2D NMRs, our objective is to fully leverage the potential of AI to enhance the precision, efficiency, and comprehensibility of NMR spectral analysis, ultimately advancing both the field of NMR spectroscopy and the broader realm of molecular research.

Large language models (LLMs) are vulnerable when trained on datasets containing harmful content, which leads to potential jailbreaking attacks in two scenarios: the integration of harmful texts within crowdsourced data used for pre-training and direct tampering with LLMs through fine-tuning. In both scenarios, adversaries can compromise the safety alignment of LLMs, exacerbating malfunctions. Motivated by the need to mitigate these adversarial influences, our research aims to enhance safety alignment by either neutralizing the impact of malicious texts in pre-training datasets or increasing the difficulty of jailbreaking during downstream fine-tuning. In this paper, we propose a data curation framework designed to counter adversarial impacts in both scenarios. Our method operates under the assumption that we have no prior knowledge of attack details, focusing solely on curating clean texts. We introduce an iterative process aimed at revising texts to reduce their perplexity as perceived by LLMs, while simultaneously preserving their text quality. By pre-training or fine-tuning LLMs with curated clean texts, we observe a notable improvement in LLM robustness regarding safety alignment against harmful queries. For instance, when pre-training LLMs using a crowdsourced dataset containing 5\% harmful instances, adding an equivalent amount of curated texts significantly mitigates the likelihood of providing harmful responses in LLMs and reduces the attack success rate by 71\%. Our study represents a significant step towards mitigating the risks associated with training-based jailbreaking and fortifying the secure utilization of LLMs.

One emergent ability of large language models (LLMs) is that query-specific examples can be included in the prompt at inference time. In this work, we use active learning for adaptive prompt design and call it Active In-context Prompt Design (AIPD). We design the LLM prompt by adaptively choosing few-shot examples from a training set to optimize performance on a test set. The training examples are initially unlabeled and we obtain the label of the most informative ones, which maximally reduces uncertainty in the LLM prediction. We propose two algorithms, GO and SAL, which differ in how the few-shot examples are chosen. We analyze these algorithms in linear models: first GO and then use its equivalence with SAL. We experiment with many different tasks in small, medium-sized, and large language models; and show that GO and SAL outperform other methods for choosing few-shot examples in the LLM prompt at inference time.

Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable spaces effectively. To Address these challenges, we introduce a hybrid Reinforcement Learning (RL) framework that synergizes RL for discrete variable selection with Bayesian Optimization for continuous variable adjustment. This framework stands out by its strategic integration of RL and continuous optimization techniques, enabling it to dynamically adapt to the problem's mixed-variable nature. By employing RL for exploring discrete decision spaces and Bayesian Optimization to refine continuous parameters, our approach not only demonstrates flexibility but also enhances optimization performance. Our experiments on synthetic functions and real-world machine learning hyperparameter tuning tasks reveal that our method consistently outperforms traditional RL, random search, and standalone Bayesian optimization in terms of effectiveness and efficiency.

The role of natural language constraints in Safe Multi-agent Reinforcement Learning (MARL) is crucial, yet often overlooked. While Safe MARL has vast potential, especially in fields like robotics and autonomous vehicles, its full potential is limited by the need to define constraints in pre-designed mathematical terms, which requires extensive domain expertise and reinforcement learning knowledge, hindering its broader adoption. To address this limitation and make Safe MARL more accessible and adaptable, we propose a novel approach named Safe Multi-agent Reinforcement Learning with Natural Language constraints (SMALL). Our method leverages fine-tuned language models to interpret and process free-form textual constraints, converting them into semantic embeddings that capture the essence of prohibited states and behaviours. These embeddings are then integrated into the multi-agent policy learning process, enabling agents to learn policies that minimize constraint violations while optimizing rewards. To evaluate the effectiveness of SMALL, we introduce the LaMaSafe, a multi-task benchmark designed to assess the performance of multiple agents in adhering to natural language constraints. Empirical evaluations across various environments demonstrate that SMALL achieves comparable rewards and significantly fewer constraint violations, highlighting its effectiveness in understanding and enforcing natural language constraints.