We study the canonical statistical task of computing the principal component from n i.i.d.

Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their inherent inability to effectively address long-range dependencies in time series data, primarily due to using fixed-size inputs for prediction. Furthermore, they typically sacrifice essential temporal correlation among consecutive training samples by shuffling them into mini-batches. To overcome these limitations, we introduce a fast and effective Spectral Attention mechanism, which preserves temporal correlations among samples and facilitates the handling of long-range information while maintaining the base model structure. Spectral Attention preserves longperiod trends through a low-pass filter and facilitates gradient to flow between samples. Spectral Attention can be seamlessly integrated into most sequence models, allowing models with fixed-sized look-back windows to capture longrange dependencies over thousands of steps. Through extensive experiments on 11 real-world time series datasets using 7 recent forecasting models, we consistently demonstrate the efficacy of our Spectral Attention mechanism, achieving state-ofthe-art results.

Graph Anomaly Detection (GAD) aims to identify uncommon, deviated, or suspicious objects within graph-structured data. Existing methods generally focus on a single graph object type (node, edge, graph, etc.) and often overlook the inherent connections among different object types of graph anomalies. For instance, a money laundering transaction might involve an abnormal account and the broader community it interacts with. To address this, we present UniGAD, the first unified framework for detecting anomalies at node, edge, and graph levels jointly. Specifically, we develop the Maximum Rayleigh Quotient Subgraph Sampler (MRQSampler) that unifies multi-level formats by transferring objects at each level into graph-level tasks on subgraphs. We theoretically prove that MRQSampler maximizes the accumulated spectral energy of subgraphs (i.e., the Rayleigh quotient) to preserve the most significant anomaly information. To further unify multi-level training, we introduce a novel GraphStitch Network to integrate information across different levels, adjust the amount of sharing required at each level, and harmonize conflicting training goals. Comprehensive experiments show that UniGAD outperforms both existing GAD methods specialized for a single task and graph prompt-based approaches for multiple tasks, while also providing robust zero-shot task transferability.

To facilitate these annotations, we used both our user application and Label Studio.

Following step-by-step procedures is an essential component of various activities carried out by individuals in their daily lives. These procedures serve as a guiding framework that helps to achieve goals efficiently, whether it is assembling furniture or preparing a recipe. However, the complexity and duration of procedural activities inherently increase the likelihood of making errors. Understanding such procedural activities from a sequence of frames is a challenging task that demands an accurate interpretation of visual information and the ability to reason about the structure of the activity. To this end, we collect a new egocentric 4D dataset CaptainCook4D comprising 384 recordings (94.5 hours) of people performing recipes in real kitchen environments. This dataset consists of two distinct types of activities: one in which participants adhere to the provided recipe instructions and another in which they deviate and induce errors. We provide 5.3K step annotations and 10K finegrained action annotations and benchmark the dataset for the following tasks: error recognition, multi-step localization and procedure learning

Unsupervised Environment Design (UED) formalizes the problem of autocurricula through interactive training between a teacher agent and a student agent. The teacher generates new training environments with high learning potential, curating an adaptive curriculum that strengthens the student's ability to handle unseen scenarios. Existing UED methods mainly rely on regret, a metric that measures the difference between the agent's optimal and actual performance, to guide curriculum design. Regret-driven methods generate curricula that progressively increase environment complexity for the student but overlook environment novelty-a critical element for enhancing an agent's generalizability. Measuring environment novelty is especially challenging due to the underspecified nature of environment parameters in UED, and existing approaches face significant limitations. To address this, this paper introduces the Coverage-based Evaluation of Novelty In Environment (CENIE) framework. CENIE proposes a scalable, domainagnostic, and curriculum-aware approach to quantifying environment novelty by leveraging the student's state-action space coverage from previous curriculum experiences. We then propose an implementation of CENIE that models this coverage and measures environment novelty using Gaussian Mixture Models.

We study the batched best arm identification (BBAI) problem, where the learner's goal is to identify the best arm while switching the policy as less as possible. In particular, we aim to find the best arm with probability 1 δ for some small constant δ > 0 while minimizing both the sample complexity (total number of arm pulls) and the batch complexity (total number of batches). We propose the three-batch best arm identification (Tri-BBAI) algorithm, which is the first batched algorithm that achieves the optimal sample complexity in the asymptotic setting (i.e., δ 0) and runs in 3 batches in expectation. Based on Tri-BBAI, we further propose the almost optimal batched best arm identification (Opt-BBAI) algorithm, which is the first algorithm that achieves the near-optimal sample and batch complexity in the non-asymptotic setting (i.e., δ is finite), while enjoying the same batch and sample complexity as Tri-BBAI when δ tends to zero. Moreover, in the non-asymptotic setting, the complexity of previous batch algorithms is usually conditioned on the event that the best arm is returned (with a probability of at least 1 δ), which is potentially unbounded in cases where a sub-optimal arm is returned. In contrast, the complexity of Opt-BBAI does not rely on such an event. This is achieved through a novel procedure that we design for checking whether the best arm is eliminated, which is of independent interest.