Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks

Tree tensor networks (TTNs) offer powerful models for image classification. While these TTN image classifiers already show excellent performance on classical hardware, embedding them into quantum neural networks (QNNs) may further improve the performance by leveraging quantum resources. However, embedding TTN classifiers into QNNs for multiclass classification remains challenging. Key obstacles are the highorder gate operations required for large bond dimensions and the mid-circuit postselection with exponentially low success rates necessary for the exact embedding. In this work, to address these challenges, we propose forest tensor network (FTN)-classifiers, which aggregate multiple small-bond-dimension TTNs. This allows us to handle multiclass classification without requiring large gates in the embedded circuits. We then remove the overhead of mid-circuit postselection by extending the adiabatic encoding framework to our setting and smoothly encode the FTN-classifiers into a quantum forest tensor network (qFTN)- classifiers. Numerical experiments on MNIST and CIFAR-10 demonstrate that we can successfully train FTN-classifiers and encode them into qFTN-classifiers, while maintaining or even improving the performance of the pre-trained FTN-classifiers. These results suggest that synergy between TTN classification models and QNNs can provide a robust and scalable framework for multiclass quantum-enhanced image classification.

Learning Dynamic Graphs via Tensorized and Lightweight Graph Convolutional Networks

A dynamic graph (DG) is frequently encountered in numerous real-world scenarios. Consequently, A dynamic graph convolutional network (DGCN) has been successfully applied to perform precise representation learning on a DG. However, conventional DGCNs typically consist of a static GCN coupled with a sequence neural network (SNN) to model spatial and temporal patterns separately. This decoupled modeling mechanism inherently disrupts the intricate spatio-temporal dependencies. To address the issue, this study proposes a novel Tensorized Lightweight Graph Convolutional Network (TLGCN) for accurate dynamic graph learning. It mainly contains the following two key concepts: a) designing a novel spatio-temporal information propagation method for joint propagation of spatio-temporal information based on the tensor M-product framework; b) proposing a tensorized lightweight graph convolutional network based on the above method, which significantly reduces the memory occupation of the model by omitting complex feature transformation and nonlinear activation. Numerical experiments on four real-world datasets demonstrate that the proposed TLGCN outperforms the state-of-the-art models in the weight estimation task on DGs.

Least-Squares-Embedded Optimization for Accelerated Convergence of PINNs in Acoustic Wavefield Simulations

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from slow convergence and instability, particularly for high-frequency wavefields. For scattered acoustic wavefield simulation based on Helmholtz equation, we derive a hybrid optimization framework that accelerates training convergence by embedding a least-squares (LS) solver directly into the GD loss function. This formulation enables optimal updates for the linear output layer. Our method is applicable with or without perfectly matched layers (PML), and we provide practical tensor-based implementations for both scenarios. Numerical experiments on benchmark velocity models demonstrate that our approach achieves faster convergence, higher accuracy, and improved stability compared to conventional PINN training. In particular, our results show that the LS-enhanced method converges rapidly even in cases where standard GD-based training fails. The LS solver operates on a small normal matrix, ensuring minimal computational overhead and making the method scalable for large-scale wavefield simulations.

High-performance training and inference for deep equivariant interatomic potentials

Machine learning interatomic potentials, particularly those based on deep equivariant neural networks, have demonstrated state-of-the-art accuracy and computational efficiency in atomistic modeling tasks like molecular dynamics and high-throughput screening. The size of datasets and demands of downstream workflows are growing rapidly, making robust and scalable software essential. This work presents a major overhaul of the NequIP framework focusing on multi-node parallelism, computational performance, and extensibility. The redesigned framework supports distributed training on large datasets and removes barriers preventing full utilization of the PyTorch 2.0 compiler at train time. We demonstrate this acceleration in a case study by training Allegro models on the SPICE 2 dataset of organic molecular systems. For inference, we introduce the first end-to-end infrastructure that uses the PyTorch Ahead-of-Time Inductor compiler for machine learning interatomic potentials. Additionally, we implement a custom kernel for the Allegro model's most expensive operation, the tensor product. Together, these advancements speed up molecular dynamics calculations on system sizes of practical relevance by up to a factor of 18.

MoE Parallel Folding: Heterogeneous Parallelism Mappings for Efficient Large-Scale MoE Model Training with Megatron Core

Mixture of Experts (MoE) models enhance neural network scalability by dynamically selecting relevant experts per input token, enabling larger model sizes while maintaining manageable computation costs. However, efficient training of large-scale MoE models across thousands of GPUs presents significant challenges due to limitations in existing parallelism strategies. We introduce an end-to-end training framework for large-scale MoE models that utilizes five-dimensional hybrid parallelism: Tensor Parallelism, Expert Parallelism, Context Parallelism, Data Parallelism, and Pipeline Parallelism. Central to our approach is MoE Parallel Folding, a novel strategy that decouples the parallelization of attention and MoE layers in Transformer models, allowing each layer type to adopt optimal parallel configurations. Additionally, we develop a flexible token-level dispatcher that supports both token-dropping and token-dropless MoE training across all five dimensions of parallelism. This dispatcher accommodates dynamic tensor shapes and coordinates different parallelism schemes for Attention and MoE layers, facilitating complex parallelism implementations. Our experiments demonstrate significant improvements in training efficiency and scalability. We achieve up to 49.3% Model Flops Utilization (MFU) for the Mixtral 8x22B model and 39.0% MFU for the Qwen2-57B-A14B model on H100 GPUs, outperforming existing methods. The framework scales efficiently up to 1,024 GPUs and maintains high performance with sequence lengths up to 128K tokens, validating its effectiveness for large-scale MoE model training. The code is available in Megatron-Core.

Multiscale Tensor Summation Factorization as a New Neural Network Layer (MTS Layer) for Multidimensional Data Processing

Multilayer perceptrons (MLP), or fully connected artificial neural networks, are known for performing vector-matrix multiplications using learnable weight matrices; however, their practical application in many machine learning tasks, especially in computer vision, can be limited due to the high dimensionality of input-output pairs at each layer. To improve efficiency, convolutional operators have been utilized to facilitate weight sharing and local connections, yet they are constrained by limited receptive fields. In this paper, we introduce Multiscale Tensor Summation (MTS) Factorization, a novel neural network operator that implements tensor summation at multiple scales, where each tensor to be summed is obtained through Tucker-decomposition-like mode products. Unlike other tensor decomposition methods in the literature, MTS is not introduced as a network compression tool; instead, as a new backbone neural layer. MTS not only reduces the number of parameters required while enhancing the efficiency of weight optimization compared to traditional dense layers (i.e., unfactorized weight matrices in MLP layers), but it also demonstrates clear advantages over convolutional layers. The proof-of-concept experimental comparison of the proposed MTS networks with MLPs and Convolutional Neural Networks (CNNs) demonstrates their effectiveness across various tasks, such as classification, compression, and signal restoration. Additionally, when integrated with modern non-linear units such as the multi-head gate (MHG), also introduced in this study, the corresponding neural network, MTSNet, demonstrates a more favorable complexity-performance tradeoff compared to state-of-the-art transformers in various computer vision applications. The software implementation of the MTS layer and the corresponding MTS-based networks, MTSNets, is shared at https://github.com/mehmetyamac/MTSNet.

DenSe-AdViT: A novel Vision Transformer for Dense SAR Object Detection

Vision Transformer (ViT) has achieved remarkable results in object detection for synthetic aperture radar (SAR) images, owing to its exceptional ability to extract global features. However, it struggles with the extraction of multi-scale local features, leading to limited performance in detecting small targets, especially when they are densely arranged. Therefore, we propose Density-Sensitive Vision Transformer with Adaptive Tokens (DenSe-AdViT) for dense SAR target detection. We design a Density-Aware Module (DAM) as a preliminary component that generates a density tensor based on target distribution. It is guided by a meticulously crafted objective metric, enabling precise and effective capture of the spatial distribution and density of objects. To integrate the multi-scale information enhanced by convolutional neural networks (CNNs) with the global features derived from the Transformer, Density-Enhanced Fusion Module (DEFM) is proposed. It effectively refines attention toward target-survival regions with the assist of density mask and the multiple sources features. Notably, our DenSe-AdViT achieves 79.8% mAP on the RSDD dataset and 92.5% on the SIVED dataset, both of which feature a large number of densely distributed vehicle targets.

Influence Maximization in Temporal Social Networks with a Cold-Start Problem: A Supervised Approach

Influence Maximization (IM) in temporal graphs focuses on identifying influential "seeds" that are pivotal for maximizing network expansion. We advocate defining these seeds through Influence Propagation Paths (IPPs), which is essential for scaling up the network. Our focus lies in efficiently labeling IPPs and accurately predicting these seeds, while addressing the often-overlooked cold-start issue prevalent in temporal networks. Our strategy introduces a motif-based labeling method and a tensorized Temporal Graph Network (TGN) tailored for multi-relational temporal graphs, bolstering prediction accuracy and computational efficiency. Moreover, we augment cold-start nodes with new neighbors from historical data sharing similar IPPs. The recommendation system within an online team-based gaming environment presents subtle impact on the social network, forming multi-relational (i.e., weak and strong) temporal graphs for our empirical IM study. We conduct offline experiments to assess prediction accuracy and model training efficiency, complemented by online A/B testing to validate practical network growth and the effectiveness in addressing the cold-start issue.

HyperKING: Quantum-Classical Generative Adversarial Networks for Hyperspectral Image Restoration

Quantum machine intelligence starts showing its impact on satellite remote sensing (SRS). Also, recent literature exhibits that quantum generative intelligences encompass superior potential than their classical counterpart, motivating us to develop quantum generative adversarial networks (GANs) for SRS. However, existing quantum GANs are restricted by the limited quantum bit (qubit) resources of current quantum computers and process merely a small 2x2 grayscale image, far from being applicable to SRS. Recently, the novel concept of hybrid quantum-classical GAN, a quantum generator with a classical discriminator, has upgraded the order to 28x28 (still grayscale), whereas it is still insufficient for SRS. This motivates us to design a radically new hybrid framework, where both generator and discriminator are hybrid architectures. We demonstrate this feasibility, leading to a breakthrough of processing 128x128 hyperspectral images for SRS. Specifically, we design the quantum part with mathematically provable quantum full expressibility (FE) to address core signal processing tasks, wherein the FE property allows the quantum network to realize any valid quantum operator with appropriate training. The classical part, composed of convolutional layers, treats the read-in (compressing the optical information into limited qubits) and read-out (addressing the quantum collapse effect) procedures. The proposed innovative hybrid quantum GAN, named Hyperspectral Knot-like IntelligeNt dIscrimiNator and Generator (HyperKING), where knot partly symbolizes the quantum entanglement and partly the compressed quantum domain in the central part of the network architecture. HyperKING significantly surpasses the classical approaches in hyperspectral tensor completion, mixed noise removal (about 3dB improvement), and blind source separation results.

Adiabatic Encoding of Pre-trained MPS Classifiers into Quantum Circuits

Although Quantum Neural Networks (QNNs) offer powerful methods for classification tasks, the training of QNNs faces two major training obstacles: barren plateaus and local minima. A promising solution is to first train a tensor-network (TN) model classically and then embed it into a QNN.\ However, embedding TN-classifiers into quantum circuits generally requires postselection whose success probability may decay exponentially with the system size. We propose an \emph{adiabatic encoding} framework that encodes pre-trained MPS-classifiers into quantum MPS (qMPS) circuits with postselection, and gradually removes the postselection while retaining performance. We prove that training qMPS-classifiers from scratch on a certain artificial dataset is exponentially hard due to barren plateaus, but our adiabatic encoding circumvents this issue. Additional numerical experiments on binary MNIST also confirm its robustness.