The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Having a clean dataset has been the foundational assumption of most natural language processing (NLP) systems. However, properly written text is rarely found in real-world scenarios and hence, oftentimes invalidates the aforementioned foundational assumption. Recently, Large language models (LLMs) have shown impressive performance, but can they handle the inevitable noise in real-world data? This work tackles this critical question by investigating LLMs' resilience against morphological variations in text. To that end, we artificially introduce varying levels of noise into a diverse set of datasets and systematically evaluate LLMs' robustness against the corrupt variations of the original text. Our findings show that contrary to popular beliefs, generative LLMs are quiet robust to noisy perturbations in text. This is a departure from pre-trained models like BERT or RoBERTa whose performance has been shown to be sensitive to deteriorating noisy text. Additionally, we test LLMs' resilience on multiple real-world benchmarks that closely mimic commonly found errors in the wild. With minimal prompting, LLMs achieve a new state-of-the-art on the benchmark tasks of Grammar Error Correction (GEC) and Lexical Semantic Change (LSC). To empower future research, we also release a dataset annotated by humans stating their preference for LLM vs. human-corrected outputs along with the code to reproduce our results.

As AI systems appear to exhibit ever-increasing capability and generality, assessing their true potential and safety becomes paramount. This paper contends that the prevalent evaluation methods for these systems are fundamentally inadequate, heightening the risks and potential hazards associated with AI. I argue that a reformation is required in the way we evaluate AI systems and that we should look towards cognitive sciences for inspiration in our approaches, which have a longstanding tradition of assessing general intelligence across diverse species. We will identify some of the difficulties that need to be overcome when applying cognitively-inspired approaches to general-purpose AI systems and also analyse the emerging area of "Evals". The paper concludes by identifying promising research pathways that could refine AI evaluation, advancing it towards a rigorous scientific domain that contributes to the development of safe AI systems.

Large language models (LLMs) present an opportunity to scale high-quality personalized education to all. A promising approach towards this means is to build dialog tutoring models that scaffold students' problem-solving. However, even though existing LLMs perform well in solving reasoning questions, they struggle to precisely detect student's errors and tailor their feedback to these errors. Inspired by real-world teaching practice where teachers identify student errors and customize their response based on them, we focus on verifying student solutions and show how grounding to such verification improves the overall quality of tutor response generation. We collect a dataset of 1K stepwise math reasoning chains with the first error step annotated by teachers. We show empirically that finding the mistake in a student solution is challenging for current models. We propose and evaluate several verifiers for detecting these errors. Using both automatic and human evaluation we show that the student solution verifiers steer the generation model towards highly targeted responses to student errors which are more often correct with less hallucinations compared to existing baselines.

Different from human nature, it is still common practice today for vision tasks to train deep learning models only initially and on fixed datasets. A variety of approaches have recently addressed handling continual data streams. However, extending these methods to manage out-of-distribution (OOD) scenarios has not effectively been investigated. On the other hand, it has recently been shown that non-continual neural mesh models exhibit strong performance in generalizing to such OOD scenarios. To leverage this decisive property in a continual learning setting, we propose incremental neural mesh models that can be extended with new meshes over time. In addition, we present a latent space initialization strategy that enables us to allocate feature space for future unseen classes in advance and a positional regularization term that forces the features of the different classes to consistently stay in respective latent space regions. We demonstrate the effectiveness of our method through extensive experiments on the Pascal3D and ObjectNet3D datasets and show that our approach outperforms the baselines for classification by 2 6% in the in-domain and by 6 50% in the OOD setting. Our work also presents the first incremental learning approach for pose estimation. Our code and model can be found at github.com/Fischer-Tom/iNeMo.

Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was limited to verifying low-dimensional dynamical systems -- this is because the computational complexity of the dynamic programming approach it relied on grows exponentially with the number of system states. To address this limitation, in recent years, there have been methods that compute the reachability value function simultaneously with learning control policies to scale HJ reachability analysis while still maintaining a reliable estimate of the true reachable set. These HJ reachability approximations are used to improve the safety, and even reward performance, of learned control policies and can solve challenging tasks such as those with dynamic obstacles and/or with lidar-based or vision-based observations. In this survey paper, we review the recent developments in the field of HJ reachability estimation in reinforcement learning that would provide a foundational basis for further research into reliability in high-dimensional systems.

This paper proposes LCFL, a novel clustering metric for evaluating clients' data distributions in federated learning. LCFL aligns with federated learning requirements, accurately assessing client-to-client variations in data distribution. It offers advantages over existing clustered federated learning methods, addressing privacy concerns, improving applicability to non-convex models, and providing more accurate classification results. LCFL does not require prior knowledge of clients' data distributions. We provide a rigorous mathematical analysis, demonstrating the correctness and feasibility of our framework. Numerical experiments with neural network instances highlight the superior performance of LCFL over baselines on several clustered federated learning benchmarks.

Powerful foundation models, including large language models (LLMs), with Transformer architectures have ushered in a new era of Generative AI across various industries. Industry and research community have witnessed a large number of new applications, based on those foundation models. Such applications include question and answer, customer services, image and video generation, and code completions, among others. However, as the number of model parameters reaches to hundreds of billions, their deployment incurs prohibitive inference costs and high latency in real-world scenarios. As a result, the demand for cost-effective and fast inference using AI accelerators is ever more higher. To this end, our tutorial offers a comprehensive discussion on complementary inference optimization techniques using AI accelerators. Beginning with an overview of basic Transformer architectures and deep learning system frameworks, we deep dive into system optimization techniques for fast and memory-efficient attention computations and discuss how they can be implemented efficiently on AI accelerators. Next, we describe architectural elements that are key for fast transformer inference. Finally, we examine various model compression and fast decoding strategies in the same context.

Large Language Models (LLMs) are frequently updated due to data or architecture changes to improve their performance. When updating models, developers often focus on increasing overall performance metrics with less emphasis on being compatible with previous model versions. However, users often build a mental model of the functionality and capabilities of a particular machine learning model they are interacting with. They have to adapt their mental model with every update -- a draining task that can lead to user dissatisfaction. In practice, fine-tuned downstream task adapters rely on pretrained LLM base models. When these base models are updated, these user-facing downstream task models experience instance regression or negative flips -- previously correct instances are now predicted incorrectly. This happens even when the downstream task training procedures remain identical. Our work aims to provide seamless model updates to a user in two ways. First, we provide evaluation metrics for a notion of compatibility to prior model versions, specifically for generative tasks but also applicable for discriminative tasks. We observe regression and inconsistencies between different model versions on a diverse set of tasks and model updates. Second, we propose a training strategy to minimize the number of inconsistencies in model updates, involving training of a compatibility model that can enhance task fine-tuned language models. We reduce negative flips -- instances where a prior model version was correct, but a new model incorrect -- by up to 40% from Llama 1 to Llama 2.

Alberto Carvalho said he is moving foward with his venture into artificial intelligence -- a platform designed to help students and families navigate the complexities of the district -- despite the collapse of the company that designed an AI chatbot. In his first extended interview about what happened, the L.A. schools chief described a fully functional AI-driven platform that is in place and owned by the district -- with everything but a chatbot for now. But parents and teachers are questioning this characterization, because the platform is not available across the school system and its signature feature is sidelined. They said they have no idea how or how well it works, how to access it or what it is supposed to do. Their only information, they said, came from splashy media events.