Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

This paper investigates regularized stochastic gradient descent (SGD) algorithms for estimating nonlinear operators from a Polish space to a separable Hilbert space. We assume that the regression operator lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued kernel. Two significant settings are considered: an online setting with polynomially decaying step sizes and regularization parameters, and a finite-horizon setting with constant step sizes and regularization parameters. We introduce regularity conditions on the structure and smoothness of the target operator and the input random variables. Under these conditions, we provide a dimension-free convergence analysis for the prediction and estimation errors, deriving both expectation and high-probability error bounds. Our analysis demonstrates that these convergence rates are nearly optimal. Furthermore, we present a new technique for deriving bounds with high probability for general SGD schemes, which also ensures almost-sure convergence. Finally, we discuss potential extensions to more general operator-valued kernels and the encoder-decoder framework.

RiskNet: Interaction-Aware Risk Forecasting for Autonomous Driving in Long-Tail Scenarios

Ensuring the safety of autonomous vehicles (AVs) in long-tail scenarios remains a critical challenge, particularly under high uncertainty and complex multi-agent interactions. To address this, we propose RiskNet, an interaction-aware risk forecasting framework, which integrates deterministic risk modeling with probabilistic behavior prediction for comprehensive risk assessment. At its core, RiskNet employs a field-theoretic model that captures interactions among ego vehicle, surrounding agents, and infrastructure via interaction fields and force. This model supports multidimensional risk evaluation across diverse scenarios (highways, intersections, and roundabouts), and shows robustness under high-risk and long-tail settings. To capture the behavioral uncertainty, we incorporate a graph neural network (GNN)-based trajectory prediction module, which learns multi-modal future motion distributions. Coupled with the deterministic risk field, it enables dynamic, probabilistic risk inference across time, enabling proactive safety assessment under uncertainty. Evaluations on the highD, inD, and rounD datasets, spanning lane changes, turns, and complex merges, demonstrate that our method significantly outperforms traditional approaches (e.g., TTC, THW, RSS, NC Field) in terms of accuracy, responsiveness, and directional sensitivity, while maintaining strong generalization across scenarios. This framework supports real-time, scenario-adaptive risk forecasting and demonstrates strong generalization across uncertain driving environments. It offers a unified foundation for safety-critical decision-making in long-tail scenarios.

Spectral Algorithms under Covariate Shift

Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world scenarios where the distributions of training and test data may differ, we conduct a rigorous investigation into the convergence behavior of spectral algorithms under distribution shifts, specifically within the framework of reproducing kernel Hilbert spaces. Our study focuses on the case of covariate shift. In this scenario, the marginal distributions of the input data differ between the training and test datasets, while the conditional distribution of the output given the input remains unchanged. Under this setting, we analyze the generalization error of spectral algorithms and show that they achieve minimax optimality when the density ratios between the training and test distributions are uniformly bounded. However, we also identify a critical limitation: when the density ratios are unbounded, the spectral algorithms may become suboptimal. To address this limitation, we propose a weighted spectral algorithm that incorporates density ratio information into the learning process. Our theoretical analysis shows that this weighted approach achieves optimal capacity-independent convergence rates. Furthermore, by introducing a weight clipping technique, we demonstrate that the convergence rates of the weighted spectral algorithm can approach the optimal capacity-dependent convergence rates arbitrarily closely. This improvement resolves the suboptimality issue in unbounded density ratio scenarios and advances the state-of-the-art by refining existing theoretical results.

OrchMLLM: Orchestrate Multimodal Data with Batch Post-Balancing to Accelerate Multimodal Large Language Model Training

Multimodal large language models (MLLMs), such as GPT-4o, are garnering significant attention. During the exploration of MLLM training, we identified Modality Composition Incoherence, a phenomenon that the proportion of a certain modality varies dramatically across different examples. It exacerbates the challenges of addressing mini-batch imbalances, which lead to uneven GPU utilization between Data Parallel (DP) instances and severely degrades the efficiency and scalability of MLLM training, ultimately affecting training speed and hindering further research on MLLMs. To address these challenges, we introduce OrchMLLM, a comprehensive framework designed to mitigate the inefficiencies in MLLM training caused by Modality Composition Incoherence. First, we propose Batch Post-Balancing Dispatcher, a technique that efficiently eliminates mini-batch imbalances in sequential data. Additionally, we integrate MLLM Global Orchestrator into the training framework to orchestrate multimodal data and tackle the issues arising from Modality Composition Incoherence. We evaluate OrchMLLM across various MLLM sizes, demonstrating its efficiency and scalability. Experimental results reveal that OrchMLLM achieves a Model FLOPs Utilization (MFU) of $41.6\%$ when training an 84B MLLM with three modalities on $2560$ H100 GPUs, outperforming Megatron-LM by up to $3.1\times$ in throughput.

DEPT: Deep Extreme Point Tracing for Ultrasound Image Segmentation

Automatic medical image segmentation plays a crucial role in computer aided diagnosis. However, fully supervised learning approaches often require extensive and labor-intensive annotation efforts. To address this challenge, weakly supervised learning methods, particularly those using extreme points as supervisory signals, have the potential to offer an effective solution. In this paper, we introduce Deep Extreme Point Tracing (DEPT) integrated with Feature-Guided Extreme Point Masking (FGEPM) algorithm for ultrasound image segmentation. Notably, our method generates pseudo labels by identifying the lowest-cost path that connects all extreme points on the feature map-based cost matrix. Additionally, an iterative training strategy is proposed to refine pseudo labels progressively, enabling continuous network improvement. Experimental results on two public datasets demonstrate the effectiveness of our proposed method. The performance of our method approaches that of the fully supervised method and outperforms several existing weakly supervised methods.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D CNNs, comprising multi-channel convolutional layers with zero-padding and ReLU activations, followed by a fully connected layer. We propose a fully constructive approach for building 2D CNNs to approximate Korobov functions and provide rigorous analysis of the complexity of the constructed networks. Our results demonstrate that 2D CNNs achieve near-optimal approximation rates under the continuous weight selection model, significantly alleviating the curse of dimensionality. This work provides a solid theoretical foundation for 2D CNNs and illustrates their potential for broader applications in function approximation.

CLAD: Constrained Latent Action Diffusion for Vision-Language Procedure Planning

We propose CLAD -- a Constrained Latent Action Diffusion model for vision-language procedure planning in instructional videos. Procedure planning is the challenging task of predicting intermediate actions given a visual observation of a start and a goal state. However, future interactive AI systems must also be able to plan procedures using multi-modal input, e.g., where visual observations are augmented with language descriptions. To tackle this vision-language procedure planning task, our method uses a Variational Autoencoder (VAE) to learn the latent representation of actions and observations as constraints and integrate them into the diffusion process. This approach exploits that the latent space of diffusion models already has semantics that can be used. We use the latent constraints to steer the diffusion model to better generate actions. We report extensive experiments on the popular CrossTask, Coin, and NIV datasets and show that our method outperforms state-of-the-art methods by a large margin. By evaluating ablated versions of our method, we further show that the proposed integration of the action and observation representations learnt in the VAE latent space is key to these performance improvements.

A Synergy Scoring Filter for Unsupervised Anomaly Detection with Noisy Data

Noise-inclusive fully unsupervised anomaly detection (FUAD) holds significant practical relevance. Although various methods exist to address this problem, they are limited in both performance and scalability. Our work seeks to overcome these obstacles, enabling broader adaptability of unsupervised anomaly detection (UAD) models to FUAD. To achieve this, we introduce the Synergy Scoring Filter (SSFilter), the first fully unsupervised anomaly detection approach to leverage sample-level filtering. SSFilter facilitates end-to-end robust training and applies filtering to the complete training set post-training, offering a model-agnostic solution for FUAD. Specifically, SSFilter integrates a batch-level anomaly scoring mechanism based on mutual patch comparison and utilizes regression errors in anomalous regions, alongside prediction uncertainty, to estimate sample-level uncertainty scores that calibrate the anomaly scoring mechanism. This design produces a synergistic, robust filtering approach. Furthermore, we propose a realistic anomaly synthesis method and an integrity enhancement strategy to improve model training and mitigate missed noisy samples. Our method establishes state-of-the-art performance on the FUAD benchmark of the recent large-scale industrial anomaly detection dataset, Real-IAD. Additionally, dataset-level filtering enhances the performance of various UAD methods on the FUAD benchmark, and the high scalability of our approach significantly boosts its practical applicability.

Unlocking the Potential of Classic GNNs for Graph-level Tasks: Simple Architectures Meet Excellence

Message-passing Graph Neural Networks (GNNs) are often criticized for their limited expressiveness, issues like over-smoothing and over-squashing, and challenges in capturing long-range dependencies, while Graph Transformers (GTs) are considered superior due to their global attention mechanisms. Literature frequently suggests that GTs outperform GNNs, particularly in graph-level tasks such as graph classification and regression. In this study, we explore the untapped potential of GNNs through an enhanced framework, GNN+, which integrates six widely used techniques: edge feature integration, normalization, dropout, residual connections, feed-forward networks, and positional encoding, to effectively tackle graph-level tasks. We conduct a systematic evaluation of three classic GNNs, namely GCN, GIN, and GatedGCN, enhanced by the GNN+ framework across 14 well-known graph-level datasets. Our results show that, contrary to the prevailing belief, classic GNNs excel in graph-level tasks, securing top three rankings across all datasets and achieving first place in eight, while also demonstrating greater efficiency than GTs. This highlights the potential of simple GNN architectures, challenging the belief that complex mechanisms in GTs are essential for superior graph-level performance.

EmbodiedEval: Evaluate Multimodal LLMs as Embodied Agents

Multimodal Large Language Models (MLLMs) have shown significant advancements, providing a promising future for embodied agents. Existing benchmarks for evaluating MLLMs primarily utilize static images or videos, limiting assessments to non-interactive scenarios. Meanwhile, existing embodied AI benchmarks are task-specific and not diverse enough, which do not adequately evaluate the embodied capabilities of MLLMs. To address this, we propose EmbodiedEval, a comprehensive and interactive evaluation benchmark for MLLMs with embodied tasks. EmbodiedEval features 328 distinct tasks within 125 varied 3D scenes, each of which is rigorously selected and annotated. It covers a broad spectrum of existing embodied AI tasks with significantly enhanced diversity, all within a unified simulation and evaluation framework tailored for MLLMs. The tasks are organized into five categories: navigation, object interaction, social interaction, attribute question answering, and spatial question answering to assess different capabilities of the agents. We evaluated the state-of-the-art MLLMs on EmbodiedEval and found that they have a significant shortfall compared to human level on embodied tasks. Our analysis demonstrates the limitations of existing MLLMs in embodied capabilities, providing insights for their future development. We open-source all evaluation data and simulation framework at https://github.com/thunlp/EmbodiedEval.