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While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited. In particular, it remains elusive how to design provably efficient quantum RL algorithms that can address the…

Image super-resolution (SR) in resource-constrained scenarios demands lightweight models balancing performance and latency. Convolutional neural networks (CNNs) offer low latency but lack non-local feature capture, while Transformers excel…

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

Optimization techniques in deep learning are predominantly led by first-order gradient methodologies, such as SGD. However, neural network training can greatly benefit from the rapid convergence characteristics of second-order optimization.…

This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…

Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to…

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank…

The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…

Recent developments in applied mathematics increasingly employ machine learning (ML)-particularly supervised learning-to accelerate numerical computations, such as solving nonlinear partial differential equations. In this work, we extend…

We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…

We demonstrate that distributed block coordinate descent can quickly solve kernel regression and classification problems with millions of data points. Armed with this capability, we conduct a thorough comparison between the full kernel, the…

Kernel-based methods are heavily used in machine learning. However, they suffer from $O(N^2)$ complexity in the number $N$ of considered data points. In this paper, we propose an approximation procedure, which reduces this complexity to…

Constraint ordering plays a critical role in the efficiency of Mixed-Integer Linear Programming (MILP) solvers, particularly for large-scale problems where poorly ordered constraints trigger increased LP iterations and suboptimal search…

Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size,…

Large Language Models (LLMs) achieve superior performance through Chain-of-Thought (CoT) reasoning, but these token-level reasoning chains are computationally expensive and inefficient. In this paper, we introduce Compressed Latent…

Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising…