In recent years, the application of deep networks has revolutionized the field of machine learning, particularly in tasks involving complex data such as images and natural language. These models, typically trained using stochastic gradient descent, have demonstrated remarkable performance on various benchmarks, raising questions about the underlying mechanisms that contribute to their success. Despite their practical efficacy, the theoretical understanding of these models remains relatively limited, creating a pressing need for deeper insights into their generalization abilities. The classical theory shows that the latter is a consequence of regularization, which is the way to impose a priori knowledge into the model and to favour "simple" solutions. While usually regularization is achieved either by choosing simple models or explicitly adding a penalty term to the empirical risk during training, this is not the case for deep neural networks, which are trained simply by minimizing the empirical risk. A new perspective has then emerged in the recent literature, which relates regularization directly to the optimization procedure (gradient based methods). The main idea is to show that the training dynamics themselves exhibit self regularizing properties, by inducing an implicit regularization (bias) which prefers generalizing solutions (see [Vardi, 2023] for an extended review of the importance of implicit bias in machine learning). In this context, a common approach is to study simplified models that approximate the networks used in practice. Analyzing the implicit bias of optimization algorithms for such networks is facilitated but still might give some insights on the good performance of neural networks in various scenarios.

To efficiently deal with high-dimensional datasets in many areas, unsupervised feature selection (UFS) has become a rising technique for dimension reduction. Even though there are many UFS methods, most of them only consider the global structure of datasets by embedding a single sparse regularization or constraint. In this paper, we introduce a novel bi-sparse UFS method, called BSUFS, to simultaneously characterize both global and local structures. The core idea of BSUFS is to incorporate $\ell_{2,p}$-norm and $\ell_q$-norm into the classical principal component analysis (PCA), which enables our proposed method to select relevant features and filter out irrelevant noise accurately. Here, the parameters $p$ and $q$ are within the range of [0,1). Therefore, BSUFS not only constructs a unified framework for bi-sparse optimization, but also includes some existing works as special cases. To solve the resulting non-convex model, we propose an efficient proximal alternating minimization (PAM) algorithm using Riemannian manifold optimization and sparse optimization techniques. Theoretically, PAM is proven to have global convergence, i.e., for any random initial point, the generated sequence converges to a critical point that satisfies the first-order optimality condition. Extensive numerical experiments on synthetic and real-world datasets demonstrate the effectiveness of our proposed BSUFS. Specifically, the average accuracy (ACC) is improved by at least 4.71% and the normalized mutual information (NMI) is improved by at least 3.14% on average compared to the existing UFS competitors. The results validate the advantages of bi-sparse optimization in feature selection and show its potential for other fields in image processing. Our code will be available at https://github.com/xianchaoxiu.

Recent interest in mobile manipulation has resulted in a wide range of new robot designs. A large family of these designs focuses on modular platforms that combine existing mobile bases with static manipulator arms. They combine these modules by mounting the arm in a tabletop configuration. However, the operating workspaces and heights for common mobile manipulation tasks, such as opening articulated objects, significantly differ from tabletop manipulation tasks. As a result, these standard arm mounting configurations can result in kinematics with restricted joint ranges and motions. To address these problems, we present the first Concurrent Design approach for mobile manipulators to optimize key arm-mounting parameters. Our approach directly targets task performance across representative household tasks by training a powerful multitask-capable reinforcement learning policy in an inner loop while optimizing over a distribution of design configurations guided by Bayesian Optimization and HyperBand (BOHB) in an outer loop. This results in novel designs that significantly improve performance across both seen and unseen test tasks, and outperform designs generated by heuristic-based performance indices that are cheaper to evaluate but only weakly correlated with the motions of interest. We evaluate the physical feasibility of the resulting designs and show that they are practical and remain modular, affordable, and compatible with existing commercial components. We open-source the approach and generated designs to facilitate further improvements of these platforms.

We develop a model-free approach to optimally control stochastic, Markovian systems subject to a reach-avoid constraint. Specifically, the state trajectory must remain within a safe set while reaching a target set within a finite time horizon. Due to the time-dependent nature of these constraints, we show that, in general, the optimal policy for this constrained stochastic control problem is non-Markovian, which increases the computational complexity. To address this challenge, we apply the state-augmentation technique from arXiv:2402.19360, reformulating the problem as a constrained Markov decision process (CMDP) on an extended state space. This transformation allows us to search for a Markovian policy, avoiding the complexity of non-Markovian policies. To learn the optimal policy without a system model, and using only trajectory data, we develop a log-barrier policy gradient approach. We prove that under suitable assumptions, the policy parameters converge to the optimal parameters, while ensuring that the system trajectories satisfy the stochastic reach-avoid constraint with high probability.

In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge. Several techniques have been developed to overcome this problem. These include communication compression and implementation of local steps, which work particularly well when there is similarity of local data samples. In this paper, we study the synergy of these approaches for efficient distributed optimization. We propose the first theoretically grounded accelerated algorithms utilizing unbiased and biased compression under data similarity, leveraging variance reduction and error feedback frameworks. Our results are of record and confirmed by experiments on different average losses and datasets.

As machine learning (ML) systems are increasingly adopted across industries, addressing fairness and bias has become essential. While many solutions focus on ethical challenges in ML, recent studies highlight that data itself is a major source of bias. Pre-processing techniques, which mitigate bias before training, are effective but may impact model performance and pose integration difficulties. In contrast, fairness-aware Data Preparation practices are both familiar to practitioners and easier to implement, providing a more accessible approach to reducing bias. Objective. This registered report proposes an empirical evaluation of how optimally selected fairness-aware practices, applied in early ML lifecycle stages, can enhance both fairness and performance, potentially outperforming standard pre-processing bias mitigation methods. Method. To this end, we will introduce FATE, an optimization technique for selecting 'Data Preparation' pipelines that optimize fairness and performance. Using FATE, we will analyze the fairness-performance trade-off, comparing pipelines selected by FATE with results by pre-processing bias mitigation techniques.

We analyze the convergence of Gauss-Newton dynamics for training neural networks with smooth activation functions. In the underparameterized regime, the Gauss-Newton gradient flow induces a Riemannian gradient flow on a low-dimensional, smooth, embedded submanifold of the Euclidean output space. Using tools from Riemannian optimization, we prove \emph{last-iterate} convergence of the Riemannian gradient flow to the optimal in-class predictor at an \emph{exponential rate} that is independent of the conditioning of the Gram matrix, \emph{without} requiring explicit regularization. We further characterize the critical impacts of the neural network scaling factor and the initialization on the convergence behavior. In the overparameterized regime, we show that the Levenberg-Marquardt dynamics with an appropriately chosen damping factor yields robustness to ill-conditioned kernels, analogous to the underparameterized regime. These findings demonstrate the potential of Gauss-Newton methods for efficiently optimizing neural networks, particularly in ill-conditioned problems where kernel and Gram matrices have small singular values.

Data-based methods have gained increasing importance in engineering, especially but not only driven by successes with deep artificial neural networks. Success stories are prevalent, e.g., in areas such as data-driven modeling, control and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems, e.g., in mechanics and dynamics, where design so far requires a lot of specialized knowledge. However, research-wise, compared to established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Possible ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice. The analysis, discussions, and examples are based on the research experience made in a priority program of the German research foundation focusing on research on artificially intelligent design assistants in mechanics and dynamics.

Producing optimized and accurate transmission spectra of exoplanets from telescope data has traditionally been a manual and labor-intensive procedure. Here we present the results of the first attempt to improve and standardize this procedure using artificial intelligence (AI) based processing of light curves and spectroscopic data from transiting exoplanets observed with the Hubble Space Telescope's (HST) Wide Field Camera 3 (WFC3) instrument. We implement an AI-based parameter optimizer that autonomously operates the Eureka pipeline to produce homogeneous transmission spectra of publicly available HST WFC3 datasets, spanning exoplanet types from hot Jupiters to sub-Neptunes. Surveying 42 exoplanets with temperatures between 280 and 2580 Kelvin, we confirm modeled relationships between the amplitude of the water band at 1.4um in hot Jupiters and their equilibrium temperatures. We also identify a similar, novel trend in Neptune/sub-Neptune atmospheres, but shifted to cooler temperatures. Excitingly, a planet mass versus equilibrium temperature diagram reveals a "Clear Sky Corridor," where planets between 700 and 1700 Kelvin (depending on the mass) show stronger 1.4um H2O band measurements. This novel trend points to metallicity as a potentially important driver of aerosol formation. As we unveil and include these new discoveries into our understanding of aerosol formation, we enter a thrilling future for the study of exoplanet atmospheres. With HST sculpting this foundational understanding for aerosol formation in various exoplanet types, ranging from Jupiters to sub-Neptunes, we present a compelling platform for the James Webb Space Telescope (JWST) to discover similar atmospheric trends for more planets across a broader wavelength range.

Assignment problems are a classic combinatorial optimization problem in which a group of agents must be assigned to a group of tasks such that maximum utility is achieved while satisfying assignment constraints. Given the utility of each agent completing each task, polynomial-time algorithms exist to solve a single assignment problem in its simplest form. However, in many modern-day applications such as satellite constellations, power grids, and mobile robot scheduling, assignment problems unfold over time, with the utility for a given assignment depending heavily on the state of the system. We apply multi-agent reinforcement learning to this problem, learning the value of assignments by bootstrapping from a known polynomial-time greedy solver and then learning from further experience. We then choose assignments using a distributed optimal assignment mechanism rather than by selecting them directly. We demonstrate that this algorithm is theoretically justified and avoids pitfalls experienced by other RL algorithms in this setting. Finally, we show that our algorithm significantly outperforms other methods in the literature, even while scaling to realistic scenarios with hundreds of agents and tasks.