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The rapid expansion of Internet of Things (IoT) ecosystems has led to increasingly complex and heterogeneous network topologies. Traditional network monitoring and visualization tools rely on aggregated metrics or static representations,…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…
Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…
We study image segmentation using spatiotemporal dynamics in a recurrent neural network where the state of each unit is given by a complex number. We show that this network generates sophisticated spatiotemporal dynamics that can…
While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying…
One of the most impactful findings in computational neuroscience over the past decade is that the object recognition accuracy of deep neural networks (DNNs) correlates with their ability to predict neural responses to natural images in the…
The objective of this paper is a model that is able to discover, track and segment multiple moving objects in a video. We make four contributions: First, we introduce an object-centric segmentation model with a depth-ordered layer…
Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…
The attributes of object contours has great significance for instance segmentation task. However, most of the current popular deep neural networks do not pay much attention to the object edge information. Inspired by the human annotation…
Various factors, such as identities, views (poses), and illuminations, are coupled in face images. Disentangling the identity and view representations is a major challenge in face recognition. Existing face recognition systems either use…
Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…
Both humans and deep learning models can recognize objects from 3D shapes depicted with sparse visual information, such as a set of points randomly sampled from the surfaces of 3D objects (termed a point cloud). Although deep learning…
We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
We propose an algorithm grounded in dynamical systems theory that generalizes manifold learning from a global state representation, to a network of local interacting manifolds termed a Generative Manifold Network (GMN). Manifolds are…
Humans perceive and interact with hundreds of objects every day. In doing so, they need to employ mental models of these objects and often exploit symmetries in the object's shape and appearance in order to learn generalizable and…
We examine how the saccade mechanism from biological vision can be used to make deep neural networks more efficient for classification and object detection problems. Our proposed approach is based on the ideas of attention-driven visual…
Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…