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We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most major branches of modern mathematics -- from computationally intensive problems in number theory and real analysis to abstract questions in algebraic geometry and category theory. Solving a typical problem requires multiple hours of effort from a researcher in the relevant branch of mathematics, and for the upper end questions, multiple days. FrontierMath uses new, unpublished problems and automated verification to reliably evaluate models while minimizing risk of data contamination. Current state-of-the-art AI models solve under 2% of problems, revealing a vast gap between AI capabilities and the prowess of the mathematical community. As AI systems advance toward expert-level mathematical abilities, FrontierMath offers a rigorous testbed that quantifies their progress.

We introduce DexDiffuser, a novel dexterous grasping method that generates, evaluates, and refines grasps on partial object point clouds. DexDiffuser includes the conditional diffusion-based grasp sampler DexSampler and the dexterous grasp evaluator DexEvaluator. DexSampler generates high-quality grasps conditioned on object point clouds by iterative denoising of randomly sampled grasps. We also introduce two grasp refinement strategies: Evaluator-Guided Diffusion (EGD) and Evaluator-based Sampling Refinement (ESR). The experiment results demonstrate that DexDiffuser consistently outperforms the state-of-the-art multi-finger grasp generation method FFHNet with an, on average, 9.12% and 19.44% higher grasp success rate in simulation and real robot experiments, respectively. Supplementary materials are available at //yulihn.github.io/DexDiffuser_page/

In the realm of high-energy physics, the longevity of calorimeters is paramount. Our research introduces a deep learning strategy to refine the calibration process of calorimeters used in particle physics experiments. We develop a Wasserstein GAN inspired methodology that adeptly calibrates the misalignment in calorimeter data due to aging or other factors. Leveraging the Wasserstein distance for loss calculation, this innovative approach requires a significantly lower number of events and resources to achieve high precision, minimizing absolute errors effectively. Our work extends the operational lifespan of calorimeters, thereby ensuring the accuracy and reliability of data in the long term, and is particularly beneficial for experiments where data integrity is crucial for scientific discovery.

This study aims to optimize the existing retrieval-augmented generation model (RAG) by introducing a graph structure to improve the performance of the model in dealing with complex knowledge reasoning tasks. The traditional RAG model has the problem of insufficient processing efficiency when facing complex graph structure information (such as knowledge graphs, hierarchical relationships, etc.), which affects the quality and consistency of the generated results. This study proposes a scheme to process graph structure data by combining graph neural network (GNN), so that the model can capture the complex relationship between entities, thereby improving the knowledge consistency and reasoning ability of the generated text. The experiment used the Natural Questions (NQ) dataset and compared it with multiple existing generation models. The results show that the graph-based RAG model proposed in this paper is superior to the traditional generation model in terms of quality, knowledge consistency, and reasoning ability, especially when dealing with tasks that require multi-dimensional reasoning. Through the combination of the enhancement of the retrieval module and the graph neural network, the model in this study can better handle complex knowledge background information and has broad potential value in multiple practical application scenarios.

Past analyses of reinforcement learning from human feedback (RLHF) assume that the human evaluators fully observe the environment. What happens when human feedback is based only on partial observations? We formally define two failure cases: deceptive inflation and overjustification. Modeling the human as Boltzmann-rational w.r.t. a belief over trajectories, we prove conditions under which RLHF is guaranteed to result in policies that deceptively inflate their performance, overjustify their behavior to make an impression, or both. Under the new assumption that the human's partial observability is known and accounted for, we then analyze how much information the feedback process provides about the return function. We show that sometimes, the human's feedback determines the return function uniquely up to an additive constant, but in other realistic cases, there is irreducible ambiguity. We propose exploratory research directions to help tackle these challenges, experimentally validate both the theoretical concerns and potential mitigations, and caution against blindly applying RLHF in partially observable settings.

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

This paper introduces a new fundamental characteristic, \ie, the dynamic range, from real-world metric tools to deep visual recognition. In metrology, the dynamic range is a basic quality of a metric tool, indicating its flexibility to accommodate various scales. Larger dynamic range offers higher flexibility. In visual recognition, the multiple scale problem also exist. Different visual concepts may have different semantic scales. For example, ``Animal'' and ``Plants'' have a large semantic scale while ``Elk'' has a much smaller one. Under a small semantic scale, two different elks may look quite \emph{different} to each other . However, under a large semantic scale (\eg, animals and plants), these two elks should be measured as being \emph{similar}. %We argue that such flexibility is also important for deep metric learning, because different visual concepts indeed correspond to different semantic scales. Introducing the dynamic range to deep metric learning, we get a novel computer vision task, \ie, the Dynamic Metric Learning. It aims to learn a scalable metric space to accommodate visual concepts across multiple semantic scales. Based on three types of images, \emph{i.e.}, vehicle, animal and online products, we construct three datasets for Dynamic Metric Learning. We benchmark these datasets with popular deep metric learning methods and find Dynamic Metric Learning to be very challenging. The major difficulty lies in a conflict between different scales: the discriminative ability under a small scale usually compromises the discriminative ability under a large one, and vice versa. As a minor contribution, we propose Cross-Scale Learning (CSL) to alleviate such conflict. We show that CSL consistently improves the baseline on all the three datasets. The datasets and the code will be publicly available at //github.com/SupetZYK/DynamicMetricLearning.

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with an arbitrary depth. Although the primitive graph neural networks have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.