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Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are interested in finding a surrogate that provides valid predictions of any potential future model evaluations, we introduce an online learning method empowered by optimizer-driven sampling. The method has two advantages over current approaches. First, it ensures that all turning points on the model response surface are included in the training data. Second, after any new model evaluations, surrogates are tested and "retrained" (updated) if the "score" drops below a validity threshold. Tests on benchmark functions reveal that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema, even when the scoring metric favors overall accuracy. We apply our method to simulations of nuclear matter to demonstrate that highly accurate surrogates for the nuclear equation of state can be reliably auto-generated from expensive calculations using a few model evaluations.

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these approaches are evaluated on the same two datasets. We find that all techniques are capable of accurately reproducing the particle-level spectra across complex observables. Given that these approaches are conceptually diverse, they offer an exciting toolkit for a new class of measurements that can probe the Standard Model with an unprecedented level of detail and may enable sensitivity to new phenomena.

As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating process changes, leading to a deviation in the model's performance. The prediction interval, which captures the range of likely outcomes for a given prediction, serves as a crucial tool for characterizing uncertainties induced by their underlying distribution. In this paper, we propose methodologies for aggregating prediction intervals to obtain one with minimal width and adequate coverage on the target domain under unsupervised domain shift, under which we have labeled samples from a related source domain and unlabeled covariates from the target domain. Our analysis encompasses scenarios where the source and the target domain are related via i) a bounded density ratio, and ii) a measure-preserving transformation. Our proposed methodologies are computationally efficient and easy to implement. Beyond illustrating the performance of our method through a real-world dataset, we also delve into the theoretical details. This includes establishing rigorous theoretical guarantees, coupled with finite sample bounds, regarding the coverage and width of our prediction intervals. Our approach excels in practical applications and is underpinned by a solid theoretical framework, ensuring its reliability and effectiveness across diverse contexts.

Graph self-supervised learning has sparked a research surge in training informative representations without accessing any labeled data. However, our understanding of graph self-supervised learning remains limited, and the inherent relationships between various self-supervised tasks are still unexplored. Our paper aims to provide a fresh understanding of graph self-supervised learning based on task correlations. Specifically, we evaluate the performance of the representations trained by one specific task on other tasks and define correlation values to quantify task correlations. Through this process, we unveil the task correlations between various self-supervised tasks and can measure their expressive capabilities, which are closely related to downstream performance. By analyzing the correlation values between tasks across various datasets, we reveal the complexity of task correlations and the limitations of existing multi-task learning methods. To obtain more capable representations, we propose Graph Task Correlation Modeling (GraphTCM) to illustrate the task correlations and utilize it to enhance graph self-supervised training. The experimental results indicate that our method significantly outperforms existing methods across various downstream tasks.

We propose the idea of using Kuramoto models (including their higher-dimensional generalizations) for machine learning over non-Euclidean data sets. These models are systems of matrix ODE's describing collective motions (swarming dynamics) of abstract particles (generalized oscillators) on spheres, homogeneous spaces and Lie groups. Such models have been extensively studied from the beginning of XXI century both in statistical physics and control theory. They provide a suitable framework for encoding maps between various manifolds and are capable of learning over spherical and hyperbolic geometries. In addition, they can learn coupled actions of transformation groups (such as special orthogonal, unitary and Lorentz groups). Furthermore, we overview families of probability distributions that provide appropriate statistical models for probabilistic modeling and inference in Geometric Deep Learning. We argue in favor of using statistical models which arise in different Kuramoto models in the continuum limit of particles. The most convenient families of probability distributions are those which are invariant with respect to actions of certain symmetry groups.

Since the seminal work by Angluin, active learning of automata, by membership and equivalence queries, has been extensively studied and several generalisations have been developed to learn various extensions of automata. For weighted automata, restricted cases have been tackled in the literature and in this paper we chart the boundaries of the Angluin approach (using a class of hypothesis automata constructed from membership and equivalence queries) applied to learning weighted automata over a general semiring. We show precisely the theoretical limitations of this approach and classify functions with respect to how guessable they are (corresponding to the existence and abundance of solutions of certain systems of equations). We provide a syntactic description of the boundary condition for a correct hypothesis of the prescribed form to exist. Of course, from an algorithmic standpoint, knowing that (many) solutions exist need not translate into an effective algorithm to find one; we conclude with a discussion of some known conditions (and variants thereof) that suffice to ensure this, illustrating the ideas over several familiar semirings (including the natural numbers) and pose some open questions for future research.

Ensuring data privacy in machine learning models is critical, particularly in distributed settings where model gradients are typically shared among multiple parties to allow collaborative learning. Motivated by the increasing success of recovering input data from the gradients of classical models, this study addresses a central question: How hard is it to recover the input data from the gradients of quantum machine learning models? Focusing on variational quantum circuits (VQC) as learning models, we uncover the crucial role played by the dynamical Lie algebra (DLA) of the VQC ansatz in determining privacy vulnerabilities. While the DLA has previously been linked to the classical simulatability and trainability of VQC models, this work, for the first time, establishes its connection to the privacy of VQC models. In particular, we show that properties conducive to the trainability of VQCs, such as a polynomial-sized DLA, also facilitate the extraction of detailed snapshots of the input. We term this a weak privacy breach, as the snapshots enable training VQC models for distinct learning tasks without direct access to the original input. Further, we investigate the conditions for a strong privacy breach where the original input data can be recovered from these snapshots by classical or quantum-assisted polynomial time methods. We establish conditions on the encoding map such as classical simulatability, overlap with DLA basis, and its Fourier frequency characteristics that enable such a privacy breach of VQC models. Our findings thus play a crucial role in detailing the prospects of quantum privacy advantage by guiding the requirements for designing quantum machine learning models that balance trainability with robust privacy protection.

We present an active automata learning algorithm which learns a decomposition of a finite state machine, based on projecting onto individual outputs. This is dual to a recent compositional learning algorithm by Labbaf et al. (2023). When projecting the outputs to a smaller set, the model itself is reduced in size. By having several such projections, we do not lose any information and the full system can be reconstructed. Depending on the structure of the system this reduces the number of queries drastically, as shown by a preliminary evaluation of the algorithm.

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory for its occurring mechanism in deep learning remains yet to be established. In this study, we revisited the phenomenon of double descent and discussed the conditions of its occurrence. This paper introduces the concept of class-activation matrices and a methodology for estimating the effective complexity of functions, on which we unveil that over-parameterized models exhibit more distinct and simpler class patterns in hidden activations compared to under-parameterized ones. We further looked into the interpolation of noisy labelled data among clean representations and demonstrated overfitting w.r.t. expressive capacity. By comprehensively analysing hypotheses and presenting corresponding empirical evidence that either validates or contradicts these hypotheses, we aim to provide fresh insights into the phenomenon of double descent and benign over-parameterization and facilitate future explorations. By comprehensively studying different hypotheses and the corresponding empirical evidence either supports or challenges these hypotheses, our goal is to offer new insights into the phenomena of double descent and benign over-parameterization, thereby enabling further explorations in the field. The source code is available at //github.com/Yufei-Gu-451/sparse-generalization.git.