Related papers: Universal scaling laws in quantum-probabilistic ma…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and…
The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy…
Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…
Classical statistical learning theory predicts that overparameterized models should exhibit severe overfitting, yet modern deep neural networks with far more parameters than training samples consistently generalize well. This contradiction…
Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…
Neural scaling laws and double-descent phenomena suggest that deep-network training obeys a simple macroscopic structure despite highly nonlinear optimization dynamics. We derive such structure directly from gradient descent in function…
Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…
Tensor-network Born machines (TNBMs) are quantum-inspired generative models for learning data distributions. Using tensor-network contraction and optimization techniques, the model learns an efficient representation of the target…
Predicting material properties is crucial for designing better batteries, semiconductors, and medical devices. Deep learning helps scientists quickly find promising materials by predicting their energy, forces, and stresses. Companies scale…
Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit…
Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla…
We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are…
Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In…
We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behavior. The conjecture is verified for free fermions, Heisenberg and quantum Ising ladders. Our results…
Tensor network quantum machine learning (QML) models are promising applications on near-term quantum hardware. While decoherence of qubits is expected to decrease the performance of QML models, it is unclear to what extent the diminished…
Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding…
Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum inspired generative models, such as Born machines based on the matrix product state framework, have…