A prevalent belief among optimization specialists is that linear convergence of gradient descent is contingent on the function growing quadratically away from its minimizers. In this work, we argue that this belief is inaccurate. We show that gradient descent with an adaptive stepsize converges at a local (nearly) linear rate on any smooth function that merely exhibits fourth-order growth away from its minimizer. The adaptive stepsize we propose arises from an intriguing decomposition theorem: any such function admits a smooth manifold around the optimal solution -- which we call the ravine -- so that the function grows at least quadratically away from the ravine and has constant order growth along it. The ravine allows one to interlace many short gradient steps with a single long Polyak gradient step, which together ensure rapid convergence to the minimizer. We illustrate the theory and algorithm on the problems of matrix sensing and factorization and learning a single neuron in the overparameterized regime.

In this paper, we propose a novel and generalizable zero-shot knowledge transfer framework that distills expert sports navigation strategies from web videos into robotic systems with adversarial constraints and out-of-distribution image trajectories. Our pipeline enables diffusion-based imitation learning by reconstructing the full 3D task space from multiple partial views, warping it into 2D image space, closing the planning loop within this 2D space, and transfer constrained motion of interest back to task space. Additionally, we demonstrate that the learned policy can serve as a local planner in conjunction with position control. We apply this framework in the wheelchair tennis navigation problem to guide the wheelchair into the ball-hitting region. Our pipeline achieves a navigation success rate of 97.67% in reaching real-world recorded tennis ball trajectories with a physical robot wheelchair, and achieve a success rate of 68.49% in a real-world, real-time experiment on a full-sized tennis court.

Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest descent direction, minimizing the output Kullback-Leibler divergence to exact MU inside a parameters' neighborhood. This probed direction decomposes into three components: weighted forgetting gradient ascent, fine-tuning retaining gradient descent, and a weight saliency matrix. Such decomposition derived from Euclidean metric encompasses most existing gradient-based MU methods. Nevertheless, adhering to Euclidean space may result in sub-optimal iterative trajectories due to the overlooked geometric structure of the output probability space. We suggest embedding the unlearning update into a manifold rendered by the remaining geometry, incorporating second-order Hessian from the remaining data. It helps prevent effective unlearning from interfering with the retained performance. However, computing the second-order Hessian for large-scale models is intractable. To efficiently leverage the benefits of Hessian modulation, we propose a fast-slow parameter update strategy to implicitly approximate the up-to-date salient unlearning direction. Free from specific modal constraints, our approach is adaptable across computer vision unlearning tasks, including classification and generation. Extensive experiments validate our efficacy and efficiency. Notably, our method successfully performs class-forgetting on ImageNet using DiT and forgets a class on CIFAR-10 using DDPM in just 50 steps, compared to thousands of steps required by previous methods.

Distribution system operators (DSOs) must cope with new challenges such as the reconstruction of distribution grids along climate neutrality pathways or the ability to manage and control consumption and generation in the grid. In order to meet the challenges, measurements within the distribution grid often form the basis for DSOs. Hence, it is an urgent problem that measurement devices are not installed in many low-voltage (LV) grids. In order to overcome this problem, we present an approach to estimate pseudo-measurements for non-measured LV feeders based on the metadata of the respective feeder using regression models. The feeder metadata comprise information about the number of grid connection points, the installed power of consumers and producers, and billing data in the downstream LV grid. Additionally, we use weather data, calendar data and timestamp information as model features. The existing measurements are used as model target. We extensively evaluate the estimated pseudo-measurements on a large real-world dataset with 2,323 LV feeders characterized by both consumption and feed-in. For this purpose, we introduce peak metrics inspired by the BigDEAL challenge for the peak magnitude, timing and shape for both consumption and feed-in. As regression models, we use XGBoost, a multilayer perceptron (MLP) and a linear regression (LR). We observe that XGBoost and MLP outperform the LR. Furthermore, the results show that the approach adapts to different weather, calendar and timestamp conditions and produces realistic load curves based on the feeder metadata. In the future, the approach can be adapted to other grid levels like substation transformers and can supplement research fields like load modeling, state estimation and LV load forecasting.

The rapid and accurate detection of biochemical compositions in fish is a crucial real-world task that facilitates optimal utilization and extraction of high-value products in the seafood industry. Raman spectroscopy provides a promising solution for quickly and non-destructively analyzing the biochemical composition of fish by associating Raman spectra with biochemical reference data using machine learning regression models. This paper investigates different regression models to address this task and proposes a new design of Convolutional Neural Networks (CNNs) for jointly predicting water, protein, and lipids yield. To the best of our knowledge, we are the first to conduct a successful study employing CNNs to analyze the biochemical composition of fish based on a very small Raman spectroscopic dataset. Our approach combines a tailored CNN architecture with the comprehensive data preparation procedure, effectively mitigating the challenges posed by extreme data scarcity. The results demonstrate that our CNN can significantly outperform two state-of-the-art CNN models and multiple traditional machine learning models, paving the way for accurate and automated analysis of fish biochemical composition.

Grounding 3D scene affordance aims to locate interactive regions in 3D environments, which is crucial for embodied agents to interact intelligently with their surroundings. Most existing approaches achieve this by mapping semantics to 3D instances based on static geometric structure and visual appearance. This passive strategy limits the agent's ability to actively perceive and engage with the environment, making it reliant on predefined semantic instructions. In contrast, humans develop complex interaction skills by observing and imitating how others interact with their surroundings. To empower the model with such abilities, we introduce a novel task: grounding 3D scene affordance from egocentric interactions, where the goal is to identify the corresponding affordance regions in a 3D scene based on an egocentric video of an interaction. This task faces the challenges of spatial complexity and alignment complexity across multiple sources. To address these challenges, we propose the Egocentric Interaction-driven 3D Scene Affordance Grounding (Ego-SAG) framework, which utilizes interaction intent to guide the model in focusing on interaction-relevant sub-regions and aligns affordance features from different sources through a bidirectional query decoder mechanism. Furthermore, we introduce the Egocentric Video-3D Scene Affordance Dataset (VSAD), covering a wide range of common interaction types and diverse 3D environments to support this task. Extensive experiments on VSAD validate both the feasibility of the proposed task and the effectiveness of our approach.

Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix Completion (SMC) methods have been proposed, but they suffer from high computation complexity due to the Singular Value Decomposition (SVD) operation. To reduce the computation complexity, Matrix Factorization (MF) techniques are more explicit and frequently applied to provide a low-rank solution, but the exact low-rank optimal solution can not be guaranteed since it suffers from a non-convex structure. In this paper, we introduce a novel SMC framework that offers a more reliable and efficient solution. Specifically, beyond simply utilizing the unique Positive Semi-definiteness (PSD) property to guide the completion process, our approach further complements a carefully designed rank-minimization regularizer, aiming to achieve an optimal and low-rank solution. Based on the key insights that the underlying PSD property and Low-Rank property improve the SMC performance, we present two novel, scalable, and effective algorithms, SMCNN and SMCNmF, which investigate the PSD property to guide the estimation process and incorporate nonconvex low-rank regularizer to ensure the low-rank solution. Theoretical analysis ensures better estimation performance and convergence speed. Empirical results on real-world datasets demonstrate the superiority and efficiency of our proposed methods compared to various baseline methods.

Labor market forecasting on talent demand and supply is essential for business management and economic development. With accurate and timely forecasts, employers can adapt their recruitment strategies to align with the evolving labor market, and employees can have proactive career path planning according to future demand and supply. However, previous studies ignore the interconnection between demand-supply sequences among different companies and positions for predicting variations. Moreover, companies are reluctant to share their private human resource data for global labor market analysis due to concerns over jeopardizing competitive advantage, security threats, and potential ethical or legal violations. To this end, in this paper, we formulate the Federated Labor Market Forecasting (FedLMF) problem and propose a Meta-personalized Convergence-aware Clustered Federated Learning (MPCAC-FL) framework to provide accurate and timely collaborative talent demand and supply prediction in a privacy-preserving way. First, we design a graph-based sequential model to capture the inherent correlation between demand and supply sequences and company-position pairs. Second, we adopt meta-learning techniques to learn effective initial model parameters that can be shared across companies, allowing personalized models to be optimized for forecasting company-specific demand and supply, even when companies have heterogeneous data. Third, we devise a Convergence-aware Clustering algorithm to dynamically divide companies into groups according to model similarity and apply federated aggregation in each group. The heterogeneity can be alleviated for more stable convergence and better performance. Extensive experiments demonstrate that MPCAC-FL outperforms compared baselines on three real-world datasets and achieves over 97% of the state-of-the-art model, i.e., DH-GEM, without exposing private company data.

Protein-ligand binding [Clyde et al., 2023] refers to the process as shown in Figure 1 by which ligands--usually small molecules, ions, or proteins--generate signals by binding to the active sites of target proteins through intermolecular forces. This binding typically changes the conformation of target proteins, which then results in the realization, modulation, or alteration of protein functions. Therefore, protein-ligand binding plays a central role in most, if not all, important life processes. For example, oxygen molecules are bound and carried through the human body by proteins like hemoglobin, and then utilized for energy production, while nonsteroidal anti-inflammatory drugs (NSAIDs) like ibuprofen work by inhibiting the functionality of the cyclooxygenase (COX) enzyme that thus reducing the release of pain-causing substances in the body. The concept and importance of binding affinity prediction were first addressed in Böhm [1994]: given the 3D structures of a target protein and a potential ligand, the objective is to predict the binding constant of such a complex, along with the most probable binding pose candidates. The prediction of the binding site (the set of protein residues that have at least one non-hydrogen atom within 4.0 Å of a ligand's non-hydrogen atom [Khazanov and Carlson, 2013]) and affinity (binding constants such as inhibition or dissociation constants, or the concentration at 50% inhibition) are usually divided into two separate but related stages [Ballester and Mitchell, 2010a]. One notable motivation for constructing a good binding affinity predictor (or scoring function, as called in some earlier work) is the essential role that it plays in drug discovery [Liu et al., 2023, 2024a] and virtual screening [Meng et al., 2011, Pinzi and Rastelli, 2019, Sadybekov and Katritch, 2023]. Traditional drug discovery essentially involves a process of trial and error.

Survival analysis plays a crucial role in estimating the likelihood of future events for patients by modeling time-to-event data, particularly in healthcare settings where predictions about outcomes such as death and disease recurrence are essential. However, this analysis poses challenges due to the presence of censored data, where time-to-event information is missing for certain data points. Yet, censored data can offer valuable insights, provided we appropriately incorporate the censoring time during modeling. In this paper, we propose SurvCORN, a novel method utilizing conditional ordinal ranking networks to predict survival curves directly. Additionally, we introduce SurvMAE, a metric designed to evaluate the accuracy of model predictions in estimating time-to-event outcomes. Through empirical evaluation on two real-world cancer datasets, we demonstrate SurvCORN's ability to maintain accurate ordering between patient outcomes while improving individual time-to-event predictions. Our contributions extend recent advancements in ordinal regression to survival analysis, offering valuable insights into accurate prognosis in healthcare settings.