Multi-task learning enables the acquisition of task-generic knowledge by training multiple tasks within a unified architecture. However, training all tasks together in a single architecture can lead to performance degradation, known as negative transfer, which is a main concern in multi-task learning. Previous works have addressed this issue by optimizing the multi-task network through gradient manipulation or weighted loss adjustments. However, their optimization strategy focuses on addressing task imbalance in shared parameters, neglecting the learning of task-specific parameters. As a result, they show limitations in mitigating negative transfer, since the learning of shared space and task-specific information influences each other during optimization. To address this, we propose a different approach to enhance multi-task performance by selectively grouping tasks and updating them for each batch during optimization. We introduce an algorithm that adaptively determines how to effectively group tasks and update them during the learning process. To track inter-task relations and optimize multi-task networks simultaneously, we propose proximal inter-task affinity, which can be measured during the optimization process. We provide a theoretical analysis on how dividing tasks into multiple groups and updating them sequentially significantly affects multi-task performance by enhancing the learning of task-specific parameters. Our methods substantially outperform previous multi-task optimization approaches and are scalable to different architectures and various numbers of tasks. Multi-task learning (MTL) stands out as a key approach for crafting efficient and robust deep learning models that can adeptly manage numerous tasks within a unified architecture (Caruana, 1997).

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly through the connection to PAC-Bayes analysis. A second line of work has provided algorithm-specific generalization bounds through stability arguments or using mutual information bounds, and has shown that the bounds are tight in practice, but unfortunately these bounds do not directly apply to approximate Bayesian algorithms. This paper fills this gap by developing algorithm-specific stability based generalization bounds for a class of approximate Bayesian algorithms that includes VI, specifically when using stochastic gradient descent to optimize their objective. As in the non-Bayesian case, the generalization error is bounded by by expected parameter differences on a perturbed dataset. The new approach complements PAC-Bayes analysis and can provide tighter bounds in some cases. An experimental illustration shows that the new approach yields non-vacuous bounds on modern neural network architectures and datasets and that it can shed light on performance differences between variant approximate Bayesian algorithms.

A neural stochastic differential equation (SDE) is an SDE with drift and diffusion terms parametrized by neural networks. The training procedure for neural SDEs consists of optimizing the SDE vector field (neural network) parameters to minimize the expected value of an objective functional on infinite-dimensional path-space. Existing training techniques focus on methods to efficiently compute path-wise gradients of the objective functional with respect to these parameters, then pair this with Monte-Carlo simulation to estimate the expectation, and stochastic gradient descent to optimize. In this work we introduce a novel training technique which bypasses and improves upon Monte-Carlo simulation; we extend results in the theory of Wiener-space cubature to approximate the expected objective functional by a weighted sum of deterministic ODE solutions. This allows us to compute gradients by efficient ODE adjoint methods. Furthermore, we exploit a high-order recombination scheme to drastically reduce the number of ODE solutions necessary to achieve a reasonable approximation. We show that this Wiener-space cubature approach can surpass the O(1/sqrt(n)) rate of Monte-Carlo simulation, or the O(log(n)/n) rate of quasi-Monte-Carlo, to achieve a O(1/n) rate under reasonable assumptions.

The goal in thinning is to summarize a dataset using a small set of representative points. Remarkably, sub-Gaussian thinning algorithms like Kernel Halving and Compress can match the quality of uniform subsampling while substantially reducing the number of summary points. However, existing guarantees cover only a restricted range of distributions and kernel-based quality measures and suffer from pessimistic dimension dependence. To address these deficiencies, we introduce a new low-rank analysis of sub-Gaussian thinning that applies to any distribution and any kernel, guaranteeing high-quality compression whenever the kernel or data matrix is approximately low-rank. To demonstrate the broad applicability of the techniques, we design practical sub-Gaussian thinning approaches that improve upon the best known guarantees for approximating attention in transformers, accelerating stochastic gradient training through reordering, and distinguishing distributions in near-linear time.

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables efficient optimization, it is of limited applicability to many practical problems. To bridge this gap and better understand the practical success of optimization algorithms in nonconvex settings, we introduce a novel unified parametric assumption. Our assumption is general enough to encompass a broad class of nonconvex functions while also being specific enough to enable the derivation of a unified convergence theorem for gradient-based methods. Notably, by tuning the parameters of our assumption, we demonstrate its versatility in recovering several existing function classes as special cases and in identifying functions amenable to efficient optimization. We derive our convergence theorem for both deterministic and stochastic optimization, and conduct experiments to verify that our assumption can hold practically over optimization trajectories.

This paper investigates the convergence properties of the hypergradient descent method (HDM), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochastic first-order methods. We provide the first rigorous convergence analysis of HDM using the online learning framework of [Gao24] and apply this analysis to develop new state-of-the-art adaptive gradient methods with empirical and theoretical support. Notably, HDM automatically identifies the optimal stepsize for the local optimization landscape and achieves local superlinear convergence. Our analysis explains the instability of HDM reported in the literature and proposes efficient strategies to address it. We also develop two HDM variants with heavy-ball and Nesterov momentum. Experiments on deterministic convex problems show HDM with heavy-ball momentum (HDM-HB) exhibits robust performance and significantly outperforms other adaptive first-order methods. Moreover, HDM-HB often matches the performance of L-BFGS, an efficient and practical quasi-Newton method, using less memory and cheaper iterations.

Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can be applied effectively only when the class of policies being optimized over satisfies strong closure conditions, which is typically not the case when working with parametric policy classes in large-scale environments. In this work, we develop a theoretical framework for PMD for general policy classes where we replace the closure conditions with a strictly weaker variational gradient dominance assumption, and obtain upper bounds on the rate of convergence to the best-in-class policy. Our main result leverages a novel notion of smoothness with respect to a local norm induced by the occupancy measure of the current policy, and casts PMD as a particular instance of smooth non-convex optimization in non-Euclidean space.

Weight averaging has become a standard technique for enhancing model performance. However, methods such as Stochastic Weight Averaging (SWA) and Latest Weight Averaging (LAWA) often require manually designed procedures to sample from the training trajectory, and the results depend heavily on hyperparameter tuning. To minimize human effort, this paper proposes a simple yet efficient algorithm called Selective Weight Averaging (SeWA), which adaptively selects checkpoints during the final stages of training for averaging. Based on SeWA, we show that only a few points are needed to achieve better generalization and faster convergence. Theoretically, solving the discrete subset selection problem is inherently challenging. To address this, we transform it into a continuous probabilistic optimization framework and employ the Gumbel-Softmax estimator to learn the non-differentiable mask for each checkpoint. Further, we theoretically derive the SeWA's stability-based generalization bounds, which are sharper than that of SGD under both convex and non-convex assumptions. Finally, solid extended experiments in various domains, including behavior cloning, image classification, and text classification, further validate the effectiveness of our approach.

Recent breakthroughs in artificial intelligence (AI), wireless communications, and sensing technologies have accelerated the evolution of edge intelligence. However, conventional systems still grapple with issues such as low communication efficiency, redundant data acquisition, and poor model generalization. To overcome these challenges, we propose an innovative framework that enhances edge intelligence through AI-in-the-loop joint sensing and communication (JSAC). This framework features an AI-driven closed-loop control architecture that jointly optimizes system resources, thereby delivering superior system-level performance. A key contribution of our work is establishing an explicit relationship between validation loss and the system's tunable parameters. This insight enables dynamic reduction of the generalization error through AI-driven closed-loop control. Specifically, for sensing control, we introduce an adaptive data collection strategy based on gradient importance sampling, allowing edge devices to autonomously decide when to terminate data acquisition and how to allocate sample weights based on real-time model feedback. For communication control, drawing inspiration from stochastic gradient Langevin dynamics (SGLD), our joint optimization of transmission power and batch size converts channel and data noise into gradient perturbations that help mitigate overfitting. Experimental evaluations demonstrate that our framework reduces communication energy consumption by up to 77 percent and sensing costs measured by the number of collected samples by up to 52 percent while significantly improving model generalization -- with up to 58 percent reductions of the final validation loss. It validates that the proposed scheme can harvest the mutual benefit of AI and JSAC systems by incorporating the model itself into the control loop of the system.

In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a specific learning algorithm. Here, the exact algorithm running using a specific model parameterization often offers a crucial implicit regularization effect, leading to good generalization. To characterize the scaling law, previous theoretical studies mainly focus on linear models, whereas, feature learning, a notable process that contributes to the remarkable empirical success of neural networks, is regretfully vacant. This paper studies the scaling law over a linear regression with the model being quadratically parameterized. We consider infinitely dimensional data and slope ground truth, both signals exhibiting certain power-law decay rates. We study convergence rates for Stochastic Gradient Descent and demonstrate the learning rates for variables will automatically adapt to the ground truth. As a result, in the canonical linear regression, we provide explicit separations for generalization curves between SGD with and without feature learning, and the information-theoretical lower bound that is agnostic to parametrization method and the algorithm. Our analysis for decaying ground truth provides a new characterization for the learning dynamic of the model.