arXiv subjects

Riccardo Rende

Publications and source records attributed to Riccardo Rende.

21 records · Page 2Linked to original sources

arXiv2024

A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States

Neural-network architectures have been increasingly used to represent quantum many-body wave functions. These networks require a large number of variational parameters and are challenging to optimize using traditional methods, as gradient descent. Stochastic Reconfiguration (SR) has been effective with a limited number of parameters, but becomes impractical beyond a few thousand parameters. Here, we leverage a simple linear algebra identity to show that SR can be employed even in the deep learning scenario. We demonstrate the effectiveness of our method by optimizing a Deep Transformer architecture with $3 \times 10^5$ parameters, achieving state-of-the-art ground-state energy in the $J_1$-$J_2$ Heisenberg model at $J_2/J_1=0.5$ on the $10\times10$ square lattice, a challenging benchmark in highly-frustrated magnetism. This work marks a significant step forward in the scalability and efficiency of SR for Neural-Network Quantum States, making them a promising method to investigate unknown quantum phases of matter, where other methods struggle.

cond-mat.str-el↗

arXiv2024

Mapping of attention mechanisms to a generalized Potts model

Transformers are neural networks that revolutionized natural language processing and machine learning. They process sequences of inputs, like words, using a mechanism called self-attention, which is trained via masked language modeling (MLM). In MLM, a word is randomly masked in an input sequence, and the network is trained to predict the missing word. Despite the practical success of transformers, it remains unclear what type of data distribution self-attention can learn efficiently. Here, we show analytically that if one decouples the treatment of word positions and embeddings, a single layer of self-attention learns the conditionals of a generalized Potts model with interactions between sites and Potts colors. Moreover, we show that training this neural network is exactly equivalent to solving the inverse Potts problem by the so-called pseudo-likelihood method, well known in statistical physics. Using this mapping, we compute the generalization error of self-attention in a model scenario analytically using the replica method.

cond-mat.dis-nn↗

arXiv2023

Transformer variational wave functions for frustrated quantum spin systems

The Transformer architecture has become the state-of-art model for natural language processing tasks and, more recently, also for computer vision tasks, thus defining the Vision Transformer (ViT) architecture. The key feature is the ability to describe long-range correlations among the elements of the input sequences, through the so-called self-attention mechanism. Here, we propose an adaptation of the ViT architecture with complex parameters to define a new class of variational neural-network states for quantum many-body systems, the ViT wave function. We apply this idea to the one-dimensional $J_1$-$J_2$ Heisenberg model, demonstrating that a relatively simple parametrization gets excellent results for both gapped and gapless phases. In this case, excellent accuracies are obtained by a relatively shallow architecture, with a single layer of self-attention, thus largely simplifying the original architecture. Still, the optimization of a deeper structure is possible and can be used for more challenging models, most notably highly-frustrated systems in two dimensions. The success of the ViT wave function relies on mixing both local and global operations, thus enabling the study of large systems with high accuracy.

cond-mat.dis-nn↗