Tan N. Nguyen

Ngoc-Vuong Ho, Tan Nguyen, Gia-Han Diep et al.

Medical image analysis using deep learning has recently been prevalent, showing great performance for various downstream tasks including medical image segmentation and its sibling, volumetric image segmentation. Particularly, a typical volumetric segmentation network strongly relies on a voxel grid representation which treats volumetric data as a stack of individual voxel `slices', which allows learning to segment a voxel grid to be as straightforward as extending existing image-based segmentation networks to the 3D domain. However, using a voxel grid representation requires a large memory footprint, expensive test-time and limiting the scalability of the solutions. In this paper, we propose Point-Unet, a novel method that incorporates the efficiency of deep learning with 3D point clouds into volumetric segmentation. Our key idea is to first predict the regions of interest in the volume by learning an attentional probability map, which is then used for sampling the volume into a sparse point cloud that is subsequently segmented using a point-based neural network. We have conducted the experiments on the medical volumetric segmentation task with both a small-scale dataset Pancreas and large-scale datasets BraTS18, BraTS19, and BraTS20 challenges. A comprehensive benchmark on different metrics has shown that our context-aware Point-Unet robustly outperforms the SOTA voxel-based networks at both accuracies, memory usage during training, and time consumption during testing. Our code is available at https://github.com/VinAIResearch/Point-Unet.

Khang Nguyen, Hieu Nong, Vinh Nguyen et al.

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Tan Nguyen, Richard G. Baraniuk, Robert M. Kirby et al.

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear attention and hashing tricks; efficient transformers have been proposed to reduce the quadratic complexity of transformers but significantly degrade the accuracy. In response, we first interpret the linear attention and residual connections in computing the attention map as gradient descent steps. We then introduce momentum into these components and propose the \emph{momentum transformer}, which utilizes momentum to improve the accuracy of linear transformers while maintaining linear memory and computational complexities. Furthermore, we develop an adaptive strategy to compute the momentum value for our model based on the optimal momentum for quadratic optimization. This adaptive momentum eliminates the need to search for the optimal momentum value and further enhances the performance of the momentum transformer. A range of experiments on both autoregressive and non-autoregressive tasks, including image generation and machine translation, demonstrate that the momentum transformer outperforms popular linear transformers in training efficiency and accuracy.

Hien Dang, Tho Tran, Stanley Osher et al.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Khai Nguyen, Tongzheng Ren, Huy Nguyen et al.

Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is the average of transportation cost between one-dimensional representations (projections) of original measures that are obtained by Radon Transform (RT). Despite its efficiency in the number of supports, estimating the sliced Wasserstein requires a relatively large number of projections in high-dimensional settings. Therefore, for applications where the number of supports is relatively small compared with the dimension, e.g., several deep learning applications where the mini-batch approaches are utilized, the complexities from matrix multiplication of Radon Transform become the main computational bottleneck. To address this issue, we propose to derive projections by linearly and randomly combining a smaller number of projections which are named bottleneck projections. We explain the usage of these projections by introducing Hierarchical Radon Transform (HRT) which is constructed by applying Radon Transform variants recursively. We then formulate the approach into a new metric between measures, named Hierarchical Sliced Wasserstein (HSW) distance. By proving the injectivity of HRT, we derive the metricity of HSW. Moreover, we investigate the theoretical properties of HSW including its connection to SW variants and its computational and sample complexities. Finally, we compare the computational cost and generative quality of HSW with the conventional SW on the task of deep generative modeling using various benchmark datasets including CIFAR10, CelebA, and Tiny ImageNet.

Hien Dang, Tho Tran, Tan Nguyen et al.

The posterior collapse phenomenon in variational autoencoder (VAE), where the variational posterior distribution closely matches the prior distribution, can hinder the quality of the learned latent variables. As a consequence of posterior collapse, the latent variables extracted by the encoder in VAE preserve less information from the input data and thus fail to produce meaningful representations as input to the reconstruction process in the decoder. While this phenomenon has been an actively addressed topic related to VAE performance, the theory for posterior collapse remains underdeveloped, especially beyond the standard VAE. In this work, we advance the theoretical understanding of posterior collapse to two important and prevalent yet less studied classes of VAE: conditional VAE and hierarchical VAE. Specifically, via a non-trivial theoretical analysis of linear conditional VAE and hierarchical VAE with two levels of latent, we prove that the cause of posterior collapses in these models includes the correlation between the input and output of the conditional VAE and the effect of learnable encoder variance in the hierarchical VAE. We empirically validate our theoretical findings for linear conditional and hierarchical VAE and demonstrate that these results are also predictive for non-linear cases with extensive experiments.

Anh Do, Duy Dinh, Tan Nguyen et al.

Generative Flow Networks (GFlowNets) are recently proposed models for learning stochastic policies that generate compositional objects by sequences of actions with the probability proportional to a given reward function. The central problem of GFlowNets is to improve their exploration and generalization. In this work, we propose a novel path regularization method based on optimal transport theory that places prior constraints on the underlying structure of the GFlowNets. The prior is designed to help the GFlowNets better discover the latent structure of the target distribution or enhance its ability to explore the environment in the context of active learning. The path regularization controls the flow in GFlowNets to generate more diverse and novel candidates via maximizing the optimal transport distances between two forward policies or to improve the generalization via minimizing the optimal transport distances. In addition, we derive an efficient implementation of the regularization by finding its closed form solutions in specific cases and a meaningful upper bound that can be used as an approximation to minimize the regularization term. We empirically demonstrate the advantage of our path regularization on a wide range of tasks, including synthetic hypergrid environment modeling, discrete probabilistic modeling, and biological sequence design.

Tan Nguyen, Coy D. Heldermon, Corey Toler-Franklin

We present a novel method that extends the self-attention mechanism of a vision transformer (ViT) for more accurate object detection across diverse datasets. ViTs show strong capability for image understanding tasks such as object detection, segmentation, and classification. This is due in part to their ability to leverage global information from interactions among visual tokens. However, the self-attention mechanism in ViTs are limited because they do not allow visual tokens to exchange local or global information with neighboring features before computing global attention. This is problematic because tokens are treated in isolation when attending (matching) to other tokens, and valuable spatial relationships are overlooked. This isolation is further compounded by dot-product similarity operations that make tokens from different semantic classes appear visually similar. To address these limitations, we introduce two modifications to the traditional self-attention framework; a novel aggressive convolution pooling strategy for local feature mixing, and a new conceptual attention transformation to facilitate interaction and feature exchange between semantic concepts. Experimental results demonstrate that local and global information exchange among visual features before self-attention significantly improves performance on challenging object detection tasks and generalizes across multiple benchmark datasets and challenging medical datasets. We publish source code and a novel dataset of cancerous tumors (chimeric cell clusters).

Bao Wang, Hedi Xia, Tan Nguyen et al.

We present and review an algorithmic and theoretical framework for improving neural network architecture design via momentum. As case studies, we consider how momentum can improve the architecture design for recurrent neural networks (RNNs), neural ordinary differential equations (ODEs), and transformers. We show that integrating momentum into neural network architectures has several remarkable theoretical and empirical benefits, including 1) integrating momentum into RNNs and neural ODEs can overcome the vanishing gradient issues in training RNNs and neural ODEs, resulting in effective learning long-term dependencies. 2) momentum in neural ODEs can reduce the stiffness of the ODE dynamics, which significantly enhances the computational efficiency in training and testing. 3) momentum can improve the efficiency and accuracy of transformers.