arXiv subjects

Letao Wang

Publications and source records attributed to Letao Wang.

4 recordsLinked to original sources

arXiv2026

Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks

Partial differential equations (PDEs) play a crucial role in financial mathematics, particularly in portfolio optimization, and solving them using classical numerical or neural network methods has always posed significant challenges. Here, we investigate the potential role of quantum circuits for solving PDEs. We design a parameterized quantum circuit (PQC) for implementing a polynomial based on tensor rank decomposition, reducing the quantum resource complexity from exponential to polynomial when the corresponding tensor rank is moderate. Building on this circuit, we develop a Quantum Physics-Informed Neural Network (QPINN) and a Quantum-inspired PINN, both of which guarantee the existence of an approximation of the PDE solution, and this approximation can be represented as a polynomial that incorporates tensor rank decomposition. Numerical experiments are conducted on the Hamilton--Jacobi--Bellman (HJB) PDE arising from the Merton portfolio optimization problem, which determines the optimal investment fraction between a risky and a risk-free asset. The results show that our quantum models achieve lower losses and approximation errors than a classical fully connected PINN while using substantially fewer trainable parameters. Our quantum models further outperform a classical PINN constructed to share a similar inductive bias, providing experimental evidence of quantum-induced improvement in the tested settings and highlighting a resource-efficient pathway toward classical and near-term quantum solvers for PDEs with exploitable solution structure.

quant-ph↗

arXiv2025

Understanding SOAP from the Perspective of Gradient Whitening

Shampoo with Adam in the Preconditioner's eigenbasis (SOAP) has recently emerged as a promising optimization algorithm for neural network training, achieving superior training efficiency over both Adam and Shampoo in language modeling tasks. In this work, we analyze Adam, Shampoo, and SOAP from the perspective of gradient whitening, interpreting their preconditioners as approximations to the whitening matrix, which captures second-order curvature information. We further establish a theoretical equivalence between idealized versions of SOAP and Shampoo under the Kronecker product assumption. To empirically evaluate these insights, we reproduce the language modeling experiments using nanoGPT and grayscale image colorization. Our results show that SOAP exhibits similar convergence rate as Shampoo, and no significant advantage over both Adam and Shampoo in the final loss achieved, which aligns with their equivalence in theory.

cs.LG↗

arXiv2024

Subspace Preserving Quantum Convolutional Neural Network Architectures

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can offer polynomial speed-up and can be used to mimic classical machine learning algorithms. In this work, we propose a novel convolutional neural network architecture model based on Hamming weight preserving quantum circuits. In particular, we introduce convolutional layers, and measurement based pooling layers that preserve the symmetries of the quantum states while realizing non-linearity using gates that are not subspace preserving. Our proposal offers significant polynomial running time advantages over classical deep-learning architecture. We provide an open source simulation library for Hamming weight preserving quantum circuits that can simulate our techniques more efficiently with GPU-oriented libraries. Using this code, we provide examples of architectures that highlight great performances on complex image classification tasks with a limited number of qubits, and with fewer parameters than classical deep-learning architectures.

quant-ph↗

arXiv2022

SimVQA: Exploring Simulated Environments for Visual Question Answering

Existing work on VQA explores data augmentation to achieve better generalization by perturbing the images in the dataset or modifying the existing questions and answers. While these methods exhibit good performance, the diversity of the questions and answers are constrained by the available image set. In this work we explore using synthetic computer-generated data to fully control the visual and language space, allowing us to provide more diverse scenarios. We quantify the effect of synthetic data in real-world VQA benchmarks and to which extent it produces results that generalize to real data. By exploiting 3D and physics simulation platforms, we provide a pipeline to generate synthetic data to expand and replace type-specific questions and answers without risking the exposure of sensitive or personal data that might be present in real images. We offer a comprehensive analysis while expanding existing hyper-realistic datasets to be used for VQA. We also propose Feature Swapping (F-SWAP) -- where we randomly switch object-level features during training to make a VQA model more domain invariant. We show that F-SWAP is effective for enhancing a currently existing VQA dataset of real images without compromising on the accuracy to answer existing questions in the dataset.

cs.CV↗