Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many real-world settings. For instance, in genomics, cyclic regulatory networks are common, and measurements are often corrupted by instrumental noise. To address these challenges, we propose RECLAIM, a causal discovery framework that natively handles both cycles and measurement noise. RECLAIM learns the causal graph structure by maximizing the likelihood of the observed measurements via expectation-maximization (EM), using residual normalizing flows for tractable likelihood computation. We consider two measurement models: (i) Gaussian additive noise, and (ii) a linear measurement system with additive Gaussian noise. We provide theoretical consistency guarantees for both the settings. Experiments on synthetic data and real-world protein signaling datasets demonstrate the efficacy of the proposed method.

Neural Information Processing Systems http://nips.cc/

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Modern deep learning techniques focus on extracting intricate information from data to achieve accurate predictions. However, the training datasets may be crowdsourced and include sensitive information, such as personal contact details, financial data, and medical records. As a result, there is a growing emphasis on developing privacy-preserving training algorithms for neural networks that maintain good performance while preserving privacy. In this paper, we investigate the generalization and privacy performances of the differentially private gradient descent (DP-GD) algorithm, which is a private variant of the gradient descent (GD) by incorporating additional noise into the gradients during each iteration. Moreover, we identify a concrete learning task where DP-GD can achieve superior generalization performance compared to GD in training two-layer Huberized ReLU convolutional neural networks (CNNs). Specifically, we demonstrate that, under mild conditions, a small signal-to-noise ratio can result in GD producing training models with poor test accuracy, whereas DP-GD can yield training models with good test accuracy and privacy guarantees if the signal-to-noise ratio is not too small. This indicates that DP-GD has the potential to enhance model performance while ensuring privacy protection in certain learning tasks. Numerical simulations are further conducted to support our theoretical results.