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).

The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase of training, it has been observed that the last-layer features collapse to their class-means and these class-means converge to the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is termed as Neural Collapse (NC). To theoretically understand this phenomenon, recent works employ a simplified unconstrained feature model to prove that NC emerges at the global solutions of the training problem. However, when the training dataset is class-imbalanced, some NC properties will no longer be true. For example, the class-means geometry will skew away from the simplex ETF when the loss converges. In this paper, we generalize NC to imbalanced regime for cross-entropy loss under the unconstrained ReLU feature model. We prove that, while the within-class features collapse property still holds in this setting, the class-means will converge to a structure consisting of orthogonal vectors with different lengths. Furthermore, we find that the classifier weights are aligned to the scaled and centered class-means with scaling factors depend on the number of training samples of each class, which generalizes NC in the class-balanced setting. We empirically prove our results through experiments on practical architectures and dataset.

Comparative opinion mining is a specialized field of sentiment analysis that aims to identify and extract sentiments expressed comparatively. To address this task, we propose an approach that consists of solving three sequential sub-tasks: (i) identifying comparative sentence, i.e., if a sentence has a comparative meaning, (ii) extracting comparative elements, i.e., what are comparison subjects, objects, aspects, predicates, and (iii) classifying comparison types which contribute to a deeper comprehension of user sentiments in Vietnamese product reviews. Our method is ranked fifth at the Vietnamese Language and Speech Processing (VLSP) 2023 challenge on Comparative Opinion Mining (ComOM) from Vietnamese Product Reviews.

Soft sensors that can discriminate shear and normal force could help provide machines the fine control desirable for safe and effective physical interactions with people. A capacitive sensor is made for this purpose, composed of patterned elastomer and containing both fixed and sliding pillars that allow the sensor to deform and buckle, much like skin itself. The sensor differentiates between simultaneously applied pressure and shear. In addition, finger proximity is detectable up to 15 mm, with a pressure and shear sensitivity of 1 kPa and a displacement resolution of 50 m. The operation is demonstrated on a simple gripper holding a cup. The combination of features and the straightforward fabrication method make this sensor a candidate for implementation as a sensing skin for humanoid robotics applications. Summary A 3-axis capacitive sensor with a dielectric composed of elastomer pillars creates a skinlike deformation that allows detection of approach, light touch, pressure and shear. MAIN TEXT Introduction To accommodate for complex interactions between humans and robots, it is important to design a method for touch identification that can be active on fingertips and other sensing surfaces. Ideally, the approach will be scalable to cover over most of a robot's surface area, forming an artificial or electronic skin (1, 2). Such a technology is also sought for neurally controlled prosthetic devices to enhance motor control (3, 4). The functional requirements of an artificial skin include the ability to sense and differentiate tactile stimuli such as light touch, pressure and shear (1). Having a smooth and soft skin, rather than a hard or bumpy surface, helps make the surface more lifelike, while the compliance allows for lower bandwidth control systems. There is a plethora of work on flexible touch and pressure sensors.

Despite the impressive performance of deep neural networks Modern deep neural networks have achieved impressive (DNNs) across areas of machine learning and artificial intelligence performance on tasks from image classification (Krizhevsky et al., 2012; Simonyan & Zisserman, to natural language processing. Surprisingly, 2015; Goodfellow et al., 2016; He et al., 2016b; Huang these complex systems with massive et al., 2017; Brown et al., 2020), the highly non-convex amounts of parameters exhibit the same structural nature of these systems, as well as their massive number of properties in their last-layer features and classifiers parameters, ranging from hundreds of millions to hundreds across canonical datasets when training until of billions, impose a significant barrier to having a concrete convergence. In particular, it has been observed theoretical understanding of how they work. Additionally, a that the last-layer features collapse to their classmeans, variety of optimization algorithms have been developed for and those class-means are the vertices of training DNNs, which makes it more challenging to analyze a simplex Equiangular Tight Frame (ETF). This the resulting trained networks and learned features (Ruder, phenomenon is known as Neural Collapse (N C). 2016). In particular, the modern practice of training DNNs Recent papers have theoretically shown that N C includes training the models far beyond zero error to achieve emerges in the global minimizers of training problems zero loss in the terminal phase of training (TPT) (Ma et al., with the simplified "unconstrained feature 2018; Belkin et al., 2019a;b).

The posterior collapse phenomenon in variational autoencoders (VAEs), 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 VAEs 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 VAEs performance, the theory for posterior collapse remains underdeveloped, especially beyond the standard VAEs. In this work, we advance the theoretical understanding of posterior collapse to two important and prevalent yet less studied classes of VAEs: conditional VAEs and hierarchical VAEs. Specifically, via a non-trivial theoretical analysis of linear conditional VAEs and hierarchical VAEs 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 VAEs and the effect of learnable encoder variance in the hierarchical VAEs. We empirically validate our theoretical findings for linear conditional and hierarchical VAEs and demonstrate that these results are also predictive for non-linear cases.

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.

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. Code for experiments in the paper is published at the following link https://github.com/ Despite the increasing importance of Wasserstein distance in applications, prior works have alluded to the concerns surrounding the high computational complexity of that distance. Additionally, it suffers from the curse of dimensionality, i.e., its sample complexity (the bounding gap of the distance between a probability measure and the empirical measures from its random samples) is of the order of O(n Over the years, numerous attempts have been made to improve the computational and sample complexities of the Wasserstein distance.

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.

Multi-head attention empowers the recent success of transformers, the state-of-the-art models that have achieved remarkable success in sequence modeling and beyond. These attention mechanisms compute the pairwise dot products between the queries and keys, which results from the use of unnormalized Gaussian kernels with the assumption that the queries follow a mixture of Gaussian distribution. There is no guarantee that this assumption is valid in practice. In response, we first interpret attention in transformers as a nonparametric kernel regression. We then propose the FourierFormer, a new class of transformers in which the dot-product kernels are replaced by the novel generalized Fourier integral kernels. Different from the dot-product kernels, where we need to choose a good covariance matrix to capture the dependency of the features of data, the generalized Fourier integral kernels can automatically capture such dependency and remove the need to tune the covariance matrix. We theoretically prove that our proposed Fourier integral kernels can efficiently approximate any key and query distributions. Compared to the conventional transformers with dot-product attention, FourierFormers attain better accuracy and reduce the redundancy between attention heads. We empirically corroborate the advantages of FourierFormers over the baseline transformers in a variety of practical applications including language modeling and image classification.