Kernel methods augmented with random features give scalable algorithms for learning from big data.

The performance of large language models (LLMs) on verifiable tasks is usually measured by pass@k, the probability of answering a question correctly at least once in k trials. At a fixed budget, a more suitable metric is coverage@cost, the average number of unique questions answered as a function of the total number of attempts. We connect the two metrics and show that the empirically-observed power-law behavior in pass@k leads to a sublinear growth of the coverage@cost (diminishing returns). To solve this problem, we propose Reset-and-Discard (ReD), a query method of LLMs that increases coverage@cost for any given budget, regardless of the pass@k form. Moreover, given a pass@k, we can quantitatively predict the savings in the total number of attempts using ReD. If pass@k is not available for the model, ReD can infer its power-law exponent. Experiments on three LLMs using HumanEval demonstrate that ReD substantially reduces the required attempts, tokens, and USD cost to reach a desired coverage, while also offering an efficient way to measure inference power-laws.

Recent advancements highlight the pivotal role of quantum machine learning (QML) [4, 13] in processing quantum data derived from quantum systems [14]. A fundamental task in QML is generating quantum data by learning the underlying distribution, essential for understanding quantum systems, synthesizing new samples, and advancing applications in quantum chemistry and materials science. However, extending classical generative approaches to quantum data presents significant challenges, as quantum distributions exhibit superposition, entanglement, and non-locality that classical models struggle to replicate efficiently. Quantum generative models such as quantum generative adversarial networks [24, 42] and quantum variational autoencoders [20, 38] can be used to prepare a fixed single quantum state [21, 28, 37], but are inefficient for generating ensembles of quantum states [3] due to the need for training deep parameterized quantum circuits (PQCs). The quantum denoising diffusion probabilistic model [40] offers a promising approach that employs intermediate training steps to smoothly interpolate between the target distribution and noise, thereby enabling efficient training.

Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks.

This work presents a machine learning approach based on support vector machines (SVMs) for quantum entanglement detection. Particularly, we focus in bipartite systems of dimensions 3x3, 4x4, and 5x5, where the positive partial transpose criterion (PPT) provides only partial characterization. Using SVMs with quantum-inspired kernels we develop a classification scheme that distinguishes between separable states, PPT-detectable entangled states, and entangled states that evade PPT detection. Our method achieves increasing accuracy with system dimension, reaching 80%, 90%, and nearly 100% for 3x3, 4x4, and 5x5 systems, respectively. Our results show that principal component analysis significantly enhances performance for small training sets. The study reveals important practical considerations regarding purity biases in the generation of data for this problem and examines the challenges of implementing these techniques on near-term quantum hardware. Our results establish machine learning as a powerful complement to traditional entanglement detection methods, particularly for higher-dimensional systems where conventional approaches become inadequate. The findings highlight key directions for future research, including hybrid quantum-classical implementations and improved data generation protocols to overcome current limitations.

The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.

The integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems, in which accurate physical properties are extracted from complex data sets. This is particularly relevant for quantum chromodynamics (QCD), the theory of strong interactions, with its inherent limitations in observational data and demanding computational approaches. This perspective highlights advances and potential of physics-driven learning methods, focusing on predictions of physical quantities towards QCD physics, and drawing connections to machine learning(ML). It is shown that the fusion of ML and physics can lead to more efficient and reliable problem-solving strategies. Key ideas of ML, methodology of embedding physics priors, and generative models as inverse modelling of physical probability distributions are introduced. Specific applications cover first-principle lattice calculations, and QCD physics of hadrons, neutron stars, and heavy-ion collisions. These examples provide a structured and concise overview of how incorporating prior knowledge such as symmetry, continuity and equations into deep learning designs can address diverse inverse problems across different physical sciences.

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT based electron dynamics simulations using autoregressive neural operators as time-propagators for the electron density. By leveraging physics-informed constraints and high-resolution training data, our model achieves superior accuracy and computational speed compared to traditional numerical solvers. We demonstrate the effectiveness of our model on a class of one-dimensional diatomic molecules. This method has potential in enabling real-time, on-the-fly modeling of laser-irradiated molecules and materials with varying experimental parameters.

The next generation of searches for neutrinoless double beta decay (0{\nu}\b{eta}\b{eta}) are poised to answer deep questions on the nature of neutrinos and the source of the Universe's matter-antimatter asymmetry. They will be looking for event rates of less than one event per ton of instrumented isotope per year. To claim discovery, accurate and efficient simulations of detector events that mimic 0{\nu}\b{eta}\b{eta} is critical. Traditional Monte Carlo (MC) simulations can be supplemented by machine-learning-based generative models. In this work, we describe the performance of generative models designed for monolithic liquid scintillator detectors like KamLAND to produce highly accurate simulation data without a predefined physics model. We demonstrate its ability to recover low-level features and perform interpolation. In the future, the results of these generative models can be used to improve event classification and background rejection by providing high-quality abundant generated data.

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the material's synthesis or operating conditions. These conditions dictate thermodynamic driving forces and kinetic rates responsible for yielding the observed surface structure and morphology. Computational surface science methods have long been applied to connect thermochemical conditions to surface phase stability, particularly in the heterogeneous catalysis and thin film growth communities. This review provides a brief introduction to first-principles approaches to compute surface phase diagrams before introducing emerging data-driven approaches. The remainder of the review focuses on the application of machine learning, predominantly in the form of learned interatomic potentials, to study complex surfaces. As machine learning algorithms and large datasets on which to train them become more commonplace in materials science, computational methods are poised to become even more predictive and powerful for modeling the complexities of inorganic surfaces at the nanoscale.