In industrial recommendation systems, multi-task learning (learning multiple tasks simultaneously on a single model) is a predominant approach to save training/serving resources and improve recommendation performance via knowledge transfer between the joint learning tasks. However, multi-task learning often suffers from negative transfer: one or several tasks are less optimized than training them separately. To carefully balance the optimization, we propose a gradient balancing approach called MultiBalance, which is suitable for industrial-scale multi-task recommendation systems. It balances the per-task gradients to alleviate the negative transfer, while saving the huge cost for grid search or manual explorations for appropriate task weights. Moreover, compared with prior work that normally balance the per-task gradients of shared parameters, MultiBalance is more efficient since only requiring to access per-task gradients with respect to the shared feature representations. We conduct experiments on Meta's large-scale ads and feeds multi-task recommendation system, and observe that MultiBalance achieves significant gains (e.g., 0.738% improvement for normalized entropy (NE)) with neutral training cost in Queries Per Second (QPS), which is significantly more efficient than prior methods that balance per-task gradients of shared parameters with 70~80% QPS degradation.

Sharpness-Aware Minimization (SAM) is an optimization technique designed to improve generalization by favoring flatter loss minima. To achieve this, SAM optimizes a modified objective that penalizes sharpness, using computationally efficient approximations. Interestingly, we find that more precise approximations of the proposed SAM objective degrade generalization performance, suggesting that the generalization benefits of SAM are rooted in these approximations rather than in the original intended mechanism. This highlights a gap in our understanding of SAM's effectiveness and calls for further investigation into the role of approximations in optimization.

Modern optimizers such as AdamW, equipped with momentum and adaptive learning rate, are designed to escape local minima and explore the vast parameter space. This exploration is beneficial for finding good loss basins when training from scratch. It is not necessarily ideal when resuming from a powerful foundation model because it can lead to large deviations from the pre-trained initialization and, consequently, worse robustness and generalization. At the same time, strong regularization on all parameters can lead to under-fitting. We hypothesize that selectively regularizing the parameter space is the key to fitting and retraining the pre-trained knowledge. This paper proposes a new weight decay technique, Selective Projection Decay (SPD), that selectively imposes a strong penalty on certain layers while allowing others to change freely. Intuitively, SPD expands and contracts the parameter search space for layers with consistent and inconsistent loss reduction, respectively. Experimentally, when equipped with SPD, Adam consistently provides better in-distribution generalization and out-of-distribution robustness performance on multiple popular vision and language benchmarks. Code available at~\url{https://github.com/GT-RIPL/Selective-Projection-Decay.git}

This paper introduces a novel kernel learning framework toward efficiently solving nonlinear partial differential equations (PDEs). In contrast to the state-of-the-art kernel solver that embeds differential operators within kernels, posing challenges with a large number of collocation points, our approach eliminates these operators from the kernel. We model the solution using a standard kernel interpolation form and differentiate the interpolant to compute the derivatives. Our framework obviates the need for complex Gram matrix construction between solutions and their derivatives, allowing for a straightforward implementation and scalable computation. As an instance, we allocate the collocation points on a grid and adopt a product kernel, which yields a Kronecker product structure in the interpolation. This structure enables us to avoid computing the full Gram matrix, reducing costs and scaling efficiently to a large number of collocation points. We provide a proof of the convergence and rate analysis of our method under appropriate regularity assumptions. In numerical experiments, we demonstrate the advantages of our method in solving several benchmark PDEs.

The rapid discovery of new chemical compounds is essential for advancing global health and developing treatments. While generative models show promise in creating novel molecules, challenges remain in ensuring the real-world applicability of these molecules and finding such molecules efficiently. To address this, we introduce Conditional Latent Space Molecular Scaffold Optimization (CLaSMO), which combines a Conditional Variational Autoencoder (CVAE) with Latent Space Bayesian Optimization (LSBO) to modify molecules strategically while maintaining similarity to the original input. Our LSBO setting improves the sample-efficiency of our optimization, and our modification approach helps us to obtain molecules with higher chances of real-world applicability. CLaSMO explores substructures of molecules in a sample-efficient manner by performing BO in the latent space of a CVAE conditioned on the atomic environment of the molecule to be optimized. Our experiments demonstrate that CLaSMO efficiently enhances target properties with minimal substructure modifications, achieving state-of-the-art results with a smaller model and dataset compared to existing methods. We also provide an open-source web application that enables chemical experts to apply CLaSMO in a Human-in-the-Loop setting.

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of GEPs and are widely used in statistical data processing. In this work, we study GEPs under generative priors, assuming that the underlying leading generalized eigenvector lies within the range of a Lipschitz continuous generative model. Under appropriate conditions, we show that any optimal solution to the corresponding optimization problems attains the optimal statistical rate. Moreover, from a computational perspective, we propose an iterative algorithm called the Projected Rayleigh Flow Method (PRFM) to approximate the optimal solution. We theoretically demonstrate that under suitable assumptions, PRFM converges linearly to an estimated vector that achieves the optimal statistical rate. Numerical results are provided to demonstrate the effectiveness of the proposed method.

Financial AI empowers sophisticated approaches to financial market forecasting, portfolio optimization, and automated trading. This survey provides a systematic analysis of these developments across three primary dimensions: predictive models that capture complex market dynamics, decision-making frameworks that optimize trading and investment strategies, and knowledge augmentation systems that leverage unstructured financial information. We examine significant innovations including foundation models for financial time series, graph-based architectures for market relationship modeling, and hierarchical frameworks for portfolio optimization. Analysis reveals crucial trade-offs between model sophistication and practical constraints, particularly in high-frequency trading applications. We identify critical gaps and open challenges between theoretical advances and industrial implementation, outlining open challenges and opportunities for improving both model performance and practical applicability.

Designing devices for novel applications is oftentimes a time rigorous and resource-constrained process that requires utilizing computationally intensive simulations, device fabrication, and testing of the physical components in the application-specific environment. At the same time, customizing device characteristics to a particular application can allow for significant performance improvements. Automated codesign strategies are becoming increasingly popular with advancements in the artificial intelligence (AI) field that provide useful machine learning algorithms and frameworks [1-4]. Such codesign provides new opportunities to automatically customize devices for application-specific needs to maximize performance--whether that involves a particular capability, energy usage, latency, throughput, or even combinations of metrics. The operation of emerging devices, such as magnetic tunnel junctions (MTJs) [5-8], can be simulated using physics-based models that capture key behaviors based on materials and device properties.

This paper studies a new latency optimization problem in unmanned aerial vehicles (UAVs)-enabled federated learning (FL) with integrated sensing and communication. In this setup, distributed UAVs participate in model training using sensed data and collaborate with a base station (BS) serving as FL aggregator to build a global model. The objective is to minimize the FL system latency over UAV networks by jointly optimizing UAVs' trajectory and resource allocation of both UAVs and the BS. The formulated optimization problem is troublesome to solve due to its non-convexity. Hence, we develop a simple yet efficient iterative algorithm to find a high-quality approximate solution, by leveraging block coordinate descent and successive convex approximation techniques. Simulation results demonstrate the effectiveness of our proposed joint optimization strategy under practical parameter settings, saving the system latency up to 68.54\% compared to benchmark schemes.

Dynamical systems (DSs) provide a framework for high flexibility, robustness, and control reliability and are widely used in motion planning and physical human-robot interaction. The properties of the DS directly determine the robot's specific motion patterns and the performance of the closed-loop control system. In this paper, we establish a quantitative relationship between stiffness properties and DS. We propose a stiffness encoding framework to modulate DS properties by embedding specific stiffnesses. In particular, from the perspective of the closed-loop control system's passivity, a conservative DS is learned by encoding a conservative stiffness. The generated DS has a symmetric attraction behavior and a variable stiffness profile. The proposed method is applicable to demonstration trajectories belonging to different manifolds and types (e.g., closed and self-intersecting trajectories), and the closed-loop control system is always guaranteed to be passive in different cases. For controllers tracking the general DS, the passivity of the system needs to be guaranteed by the energy tank. We further propose a generic vector field decomposition strategy based on conservative stiffness, which effectively slows down the decay rate of energy in the energy tank and improves the stability margin of the control system. Finally, a series of simulations in various scenarios and experiments on planar and curved motion tasks demonstrate the validity of our theory and methodology.