arXiv subjects

Tiago de Souza Farias

Publications and source records attributed to Tiago de Souza Farias.

8 recordsLinked to original sources

arXiv2025

Introdução a rede neural para Físicos

As técnicas de aprendizado de máquina emergiram no contexto científico e se desenvolveram como ferramentas poderosas para enfrentar uma ampla gama de desafios na sociedade. A integração dessas técnicas com a física tem conduzido a abordagens inovadoras na compreensão, controle e simulação de fenômenos físicos. Este artigo visa proporcionar uma introdução prática às redes neurais e seus conceitos fundamentais, destacando perspectivas recentes dos avanços na interseção entre modelos de aprendizado de máquina e sistemas físicos. Além disso, apresentamos um material prático para orientar o leitor em seus primeiros passos na aplicação de redes neurais para resolver problemas físicos. Como exemplo ilustrativo, fornecemos quatro aplicações de complexidades crescentes para o problema de um pêndulo simples, a saber: fit de parâmetros da Equação Diferencial Ordinária (EDO) do pêndulo para aproximação de ângulo pequeno; Physics Informed Neural Networks (PINNs) para encontrar soluções da EDO do pêndulo em ângulo pequeno; Autoencoders em conjunto de dados de imagens do pêndulo para estimação de dimensionalidade do espaço de parâmetros do problema físico; uso de arquiteturas Sparse Identification of Non-Linear Dynamics (SINDy) para descoberta de modelos e expressões analíticas para o problema do pêndulo não linear (ângulos grandes).

physics.class-ph↗

arXiv2025

QuForge: A Library for Qudits Simulation

Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer separated components. In this article, we present QuForge, a Python-based library designed to simulate quantum circuits with qudits. This library provides the necessary quantum gates for implementing quantum algorithms, tailored to any chosen qudit dimension. Built on top of differentiable frameworks, QuForge supports execution on accelerating devices such as GPUs and TPUs, significantly speeding up simulations. It also supports sparse operations, leading to a reduction in memory consumption compared to other libraries. Additionally, by constructing quantum circuits as differentiable graphs, QuForge facilitates the implementation of quantum machine learning algorithms, enhancing the capabilities and flexibility of quantum computing research.

quant-ph↗

arXiv2025

A short review on qudit quantum machine learning

As quantum devices scale toward practical machine learning applications, the binary qubit paradigm faces expressivity and resource efficiency limitations. Multi-level quantum systems, or qudits, offer a promising alternative by harnessing a larger Hilbert space, enabling richer data embeddings, more compact variational circuits, and support for multi-valued problem structures. In this work, we review the role of qudits in quantum machine learning techniques, mainly variational quantum algorithms and quantum neural networks. Drawing on recent experimental demonstrations, including high-level superconducting transmons, qutrit-based combinatorial optimization, and single-qudit classifiers, we highlight how qudit architectures can reduce circuit depth and parameter counts while maintaining competitive fidelity. We further assess the evolving software ecosystem, from specialized simulators and differentiable-programming libraries to extensions of mainstream frameworks. We also identify key challenges in control complexity, noise management, and tooling maturity.

quant-ph↗

arXiv2025

Barren plateaus are amplified by the dimension of qudits

Variational Quantum Algorithms (VQAs) have emerged as pivotal strategies for attaining quantum advantage in diverse scientific and technological domains, notably within Quantum Neural Networks. However, despite their potential, VQAs encounter significant obstacles, chief among them being the vanishing gradient problem, commonly referred to as barren plateaus. In this article, through meticulous analysis, we demonstrate that existing literature implicitly suggests the intrinsic influence of qudit dimensionality on barren plateaus. To instantiate these findings, we present numerical results that exemplify the impact of qudit dimensionality on barren plateaus. Therefore, despite the proposition of various error mitigation techniques, our results call for further scrutiny about their efficacy in the context of VQAs with qudits.

quant-ph↗

arXiv2025

MixFunn: A Neural Network for Differential Equations with Improved Generalization and Interpretability

We introduce MixFunn, a novel neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability. The architecture comprises two key components: the mixed-function neuron, which integrates multiple parameterized nonlinear functions to improve representational flexibility, and the second-order neuron, which combines a linear transformation of its inputs with a quadratic term to capture cross-combinations of input variables. These features significantly enhance the expressive power of the network, enabling it to achieve comparable or superior results with drastically fewer parameters and a reduction of up to four orders of magnitude compared to conventional approaches. We applied MixFunn in a physics-informed setting to solve differential equations in classical mechanics, quantum mechanics, and fluid dynamics, demonstrating its effectiveness in achieving higher accuracy and improved generalization to regions outside the training domain relative to standard machine learning models. Furthermore, the architecture facilitates the extraction of interpretable analytical expressions, offering valuable insights into the underlying solutions.

cs.LG↗

arXiv2024

A differentiable programming framework for spin models

We introduce a novel framework for simulating spin models using differentiable programming, an approach that leverages the advancements in machine learning and computational efficiency. We focus on three distinct spin systems: the Ising model, the Potts model, and the Cellular Potts model, demonstrating the practicality and scalability of our framework in modeling these complex systems. Additionally, this framework allows for the optimization of spin models, which can adjust the parameters of a system by a defined objective function. In order to simulate these models, we adapt the Metropolis-Hastings algorithm to a differentiable programming paradigm, employing batched tensors for simulating spin lattices. This adaptation not only facilitates the integration with existing deep learning tools but also significantly enhances computational speed through parallel processing capabilities, as it can be implemented on different hardware architectures, including GPUs and TPUs.

cond-mat.stat-mech↗

arXiv2023

Feature Alignment as a Generative Process

Reversibility in artificial neural networks allows us to retrieve the input given an output. We present feature alignment, a method for approximating reversibility in arbitrary neural networks. We train a network by minimizing the distance between the output of a data point and the random output with respect to a random input. We applied the technique to the MNIST, CIFAR-10, CelebA and STL-10 image datasets. We demonstrate that this method can roughly recover images from just their latent representation without the need of a decoder. By utilizing the formulation of variational autoencoders, we demonstrate that it is possible to produce new images that are statistically comparable to the training data. Furthermore, we demonstrate that the quality of the images can be improved by coupling a generator and a discriminator together. In addition, we show how this method, with a few minor modifications, can be used to train networks locally, which has the potential to save computational memory resources.

cs.LG↗

arXiv2018

Gradient target propagation

We report a learning rule for neural networks that computes how much each neuron should contribute to minimize a giving cost function via the estimation of its target value. By theoretical analysis, we show that this learning rule contains backpropagation, Hebian learning, and additional terms. We also give a general technique for weights initialization. Our results are at least as good as those obtained with backpropagation. The neural networks are trained and tested in three problems: MNIST, MNIST-Fashion, and CIFAR-10 datasets. The associated code is available at https://github.com/tiago939/target.

cs.LG↗