相关论文: Toward Trainability of Deep Quantum Neural Network…

In recent years, deep learning has had a profound impact on machine learning and artificial intelligence. At the same time, algorithms for quantum computers have been shown to efficiently solve some problems that are intractable on…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in…

Quantum circuit Born machines are generative models which represent the probability distribution of classical dataset as quantum pure states. Computational complexity considerations of the quantum sampling problem suggest that the quantum…

Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or…

Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits…

In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term…

Quantum neural networks (QNNs) use parameterized quantum circuits with data-dependent inputs and generate outputs through the evaluation of expectation values. Calculating these expectation values necessitates repeated circuit evaluations,…

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a…

Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence…

Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to…

Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential…

Giving provable guarantees for learning neural networks is a core challenge of machine learning theory. Most prior work gives parameter recovery guarantees for one hidden layer networks, however, the networks used in practice have multiple…

Neural networks are more expressive when they have multiple layers. In turn, conventional training methods are only successful if the depth does not lead to numerical issues such as exploding or vanishing gradients, which occur less…

Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a global optimizer with perfect fit (zero-loss) in many…

Our understanding of learning dynamics of deep neural networks (DNNs) remains incomplete. Recent research has begun to uncover the mathematical principles underlying these networks, including the phenomenon of "Neural Collapse", where…

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum…

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more…

A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called Quantum Machine Learning (QML), aims to achieve a speedup over traditional machine learning for data…

We study the role of depth in training randomly initialized overparameterized neural networks. We give a general result showing that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of…