The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parameters, and training hybrid models that combine differential equations with data-driven approaches. Furthermore, recognizing the strong synergies between inverse methods and machine learning offers the opportunity to establish a coherent framework applicable to both fields. Differentiating functions based on the numerical solution of differential equations is non-trivial. Numerous methods based on a wide variety of paradigms have been proposed in the literature, each with pros and cons specific to the type of problem investigated. Here, we provide a comprehensive review of existing techniques to compute derivatives of numerical solutions of differential equations. We first discuss the importance of gradients of solutions of differential equations in a variety of scientific domains. Second, we lay out the mathematical foundations of the various approaches and compare them with each other. Third, we cover the computational considerations and explore the solutions available in modern scientific software. Last but not least, we provide best-practices and recommendations for practitioners. We hope that this work accelerates the fusion of scientific models and data, and fosters a modern approach to scientific modelling.

Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers engaged in the search of algorithms and architectures capable of processing sequences of patterns, retaining information about the past inputs while still leveraging the upcoming data, without losing precious long-term dependencies and correlations. While such an ultimate goal is inspired by the human hallmark of continuous real-time processing of sensory information, several solutions simplified the learning paradigm by artificially limiting the processed context or dealing with sequences of limited length, given in advance. These solutions were further emphasized by the large ubiquity of Transformers, that have initially shaded the role of Recurrent Neural Nets. However, recurrent networks are facing a strong recent revival due to the growing popularity of (deep) State-Space models and novel instances of large-context Transformers, which are both based on recurrent computations to go beyond several limits of currently ubiquitous technologies. In fact, the fast development of Large Language Models enhanced the interest in efficient solutions to process data over time. This survey provides an in-depth summary of the latest approaches that are based on recurrent models for sequential data processing. A complete taxonomy over the latest trends in architectural and algorithmic solutions is reported and discussed, guiding researchers in this appealing research field. The emerging picture suggests that there is room for thinking of novel routes, constituted by learning algorithms which depart from the standard Backpropagation Through Time, towards a more realistic scenario where patterns are effectively processed online, leveraging local-forward computations, opening to further research on this topic.

Reservoir Computing with Cellular Automata (ReCA) is a relatively novel and promising approach. It consists of 3 steps: an encoding scheme to inject the problem into the CA, the CA iterations step itself and a simple classifying step, typically a linear classifier. This paper demonstrates that the ReCA concept is effective even in arguably the simplest implementation of a ReCA system. However, we also report a failed attempt on the UCR Time Series Classification Archive where ReCA seems to work, but only because of the encoding scheme itself, not in any part due to the CA. This highlights the need for ablation testing, i.e., comparing internally with sub-parts of one model, but also raises an open question on what kind of tasks ReCA is best suited for.

A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing localized discrepancy distance, where discrepancy is computed with respect to a fixed output classifier. These results imply a broad set of new, efficient learning algorithms in the recently introduced model of Testable Learning with Distribution Shift (TDS learning) due to Klivans et al. (2023). Our approach generalizes and improves all prior work on TDS learning: (1) we obtain universal learners that succeed simultaneously for large classes of test distributions, (2) achieve near-optimal error rates, and (3) give exponential improvements for constant depth circuits. Our methods further extend to semi-parametric settings and imply the first positive results for low-dimensional convex sets. Additionally, we separate learning and testing phases and obtain algorithms that run in fully polynomial time at test time.

We consider the problem of user-adaptive 3D gaze estimation. The performance of person-independent gaze estimation is limited due to interpersonal anatomical differences. Our goal is to provide a personalized gaze estimation model specifically adapted to a target user. Previous work on user-adaptive gaze estimation requires some labeled images of the target person data to fine-tune the model at test time. However, this can be unrealistic in real-world applications, since it is cumbersome for an end-user to provide labeled images. In addition, previous work requires the training data to have both gaze labels and person IDs. This data requirement makes it infeasible to use some of the available data. To tackle these challenges, this paper proposes a new problem called efficient label-free user adaptation in gaze estimation. Our model only needs a few unlabeled images of a target user for the model adaptation. During offline training, we have some labeled source data without person IDs and some unlabeled person-specific data. Our proposed method uses a meta-learning approach to learn how to adapt to a new user with only a few unlabeled images. Our key technical innovation is to use a generalization bound from domain adaptation to define the loss function in meta-learning, so that our method can effectively make use of both the labeled source data and the unlabeled person-specific data during training. Extensive experiments validate the effectiveness of our method on several challenging benchmarks.

Product assortment selection is a critical challenge facing physical retailers. Effectively aligning inventory with the preferences of shoppers can increase sales and decrease out-of-stocks. However, in real-world settings the problem is challenging due to the combinatorial explosion of product assortment possibilities. Consumer preferences are typically heterogeneous across space and time, making inventory-preference alignment challenging. Additionally, existing strategies rely on syndicated data, which tends to be aggregated, low resolution, and suffer from high latency. To solve these challenges, we introduce a real-time recommendation system, which we call EdgeRec3D. Our system utilizes recent advances in 3D computer vision for perception and automatic, fine grained sales estimation. These perceptual components run on the edge of the network and facilitate real-time reward signals. Additionally, we develop a Bayesian payoff model to account for noisy estimates from 3D LIDAR data. We rely on spatial clustering to allow the system to adapt to heterogeneous consumer preferences, and a graph-based candidate generation algorithm to address the combinatorial search problem. We test our system in real-world stores across two, 6-8 week A/B tests with beverage products and demonstrate a 35% and 27% increase in sales respectively. Finally, we monitor the deployed system for a period of 28 weeks with an observational study and show a 9.4% increase in sales.

Learning-based intelligent energy management systems for plug-in hybrid electric vehicles (PHEVs) are crucial for achieving efficient energy utilization. However, their application faces system reliability challenges in the real world, which prevents widespread acceptance by original equipment manufacturers (OEMs). This paper begins by establishing a PHEV model based on physical and datadriven models, focusing on the high-fidelity training environment. It then proposes a real-vehicle application-oriented control framework, combining horizon-extended reinforcement learning (RL)- based energy management with the equivalent consumption minimization strategy (ECMS) to enhance practical applicability, and improves the flawed method of equivalent factor evaluation based on instantaneous driving cycle and powertrain states found in existing research. Finally, comprehensive simulation and hardware-in-the-loop validation are carried out which demonstrates the advantages of the proposed control framework in fuel economy over adaptive-ECMS and rule-based strategies. Compared to conventional RL architectures that directly control powertrain components, the proposed control method not only achieves similar optimality but also significantly enhances the disturbance resistance of the energy management system, providing an effective control framework for RL-based energy management strategies aimed at real-vehicle applications by OEMs.

Active learning is an iterative labeling process that is used to obtain a small labeled subset, despite the absence of labeled data, thereby enabling to train a model for supervised tasks such as text classification. While active learning has made considerable progress in recent years due to improvements provided by pre-trained language models, there is untapped potential in the often neglected unlabeled portion of the data, although it is available in considerably larger quantities than the usually small set of labeled data. Here we investigate how self-training, a semi-supervised approach where a model is used to obtain pseudo-labels from the unlabeled data, can be used to improve the efficiency of active learning for text classification. Starting with an extensive reproduction of four previous self-training approaches, some of which are evaluated for the first time in the context of active learning or natural language processing, we devise HAST, a new and effective self-training strategy, which is evaluated on four text classification benchmarks, on which it outperforms the reproduced self-training approaches and reaches classification results comparable to previous experiments for three out of four datasets, using only 25% of the data.

As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We focus here on lifting two explicit algorithms: mirror descent and preconditioned gradient descent. These algorithms have been introduced to better capture the geometry of the function to minimize and are provably convergent under appropriate (namely relative) smoothness and convexity conditions. Adapting these notions to the Wasserstein space, we prove guarantees of convergence of some Wasserstein-gradient-based discrete-time schemes for new pairings of objective functionals and regularizers. The difficulty here is to carefully select along which curves the functionals should be smooth and convex. We illustrate the advantages of adapting the geometry induced by the regularizer on ill-conditioned optimization tasks, and showcase the improvement of choosing different discrepancies and geometries in a computational biology task of aligning single-cells.

Clustering is a cornerstone of contemporary machine learning and data analysis. A successful clustering algorithm partitions data elements so that similar items reside within the same group, while dissimilar items are separated. Introduced in 2004 by Bansal, Blum and Chawla Bansal et al. ((2004)), the correlation clustering objective offers a natural approach to model this problem. Due to its concise and elegant formulation, this problem has drawn significant interest from researchers and practitioners, leading to applications across diverse domains. These include ensemble clustering identification ((Bonchi et al., 2013)), duplicate detection ((Arasu et al., 2009)), community mining ((Chen et al., 2012)), disambiguation tasks ((Kalashnikov et al., 2008)), automated labeling ((Agrawal et al., 2009; Chakrabarti et al., 2008)), and many more. In the correlation clustering problem we are given a graph where each edge has either a positive or negative label, and where a positive edge (u, v) indicates that u, v are similar elements (and a negative edge (u, v) indicates that u, v are dissimilar), the objective is to compute a partition of the graph that minimizes the number of negative edges within clusters plus positive edges between clusters. Since the problem is NP-hard, researchers have focused on designing approximation algorithms. The algorithm proposed by Cao et al. ((2024)) achieves an approximation ratio of 1.43 + ϵ, improving upon the previous 1.73 + ϵ and 1.994 + ϵ achieved by Cohen-Addad et al. ((2023, 2022b)). Prior to these developments, the best approximation guarantee of 2.06 was attained by the algorithm of Chawla et al. ((2015)).