Related papers: Generalization and Overfitting in Matrix Product S…

As data-driven methods rise in popularity in materials science applications, a key question is how these machine learning models can be used to understand microstructure. Given the importance of process-structure-property relations…

A challenge in multi-agent reinforcement learning is to be able to generalize over intractable state-action spaces. Inspired from Tesseract [Mahajan et al., 2021], this position paper investigates generalisation in state-action space over…

In classical Machine Learning, "overfitting" is the phenomenon occurring when a given model learns the training data excessively well, and it thus performs poorly on unseen data. A commonly employed technique in Machine Learning is the so…

Adversarial training is a widely used method to improve the robustness of deep neural networks (DNNs) over adversarial perturbations. However, it is empirically observed that adversarial training on over-parameterized networks often suffers…

Matrix product state (MPS) offers a framework for encoding classical data into quantum states, enabling the efficient utilization of quantum resources for data representation and processing. This research paper investigates techniques to…

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

Recent results suggest that the use of ensembles in Statistical Mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to the ones of the ensemble. Nevertheless, it…

Classical learning theory describes a well-characterised U-shaped relationship between model complexity and prediction error, reflecting a transition from underfitting in underparameterised regimes to overfitting as complexity grows. Recent…

An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of…

Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made…

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In…

In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…

Matrix product states (MPS) are a central language for one-dimensional quantum matter and a practical target for near-term quantum simulators and variational algorithms. Yet, while substantial effort has focused on preparing MPS with…

Feature learning strength (FLS), i.e., the inverse of the effective output scaling of a model, plays a critical role in shaping the optimization dynamics of neural nets. While its impact has been extensively studied under the asymptotic…

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with…

We present a tensorization algorithm for constructing tensor train/matrix product state (MPS) representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function…

Multi-task learning (MTL) is a machine learning paradigm that aims to improve the generalization performance of a model on multiple related tasks by training it simultaneously on those tasks. Unlike MTL, where the model has instant access…

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…

Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the…