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Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes or at best marginally favorable compared to independent…

A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we…

We study the multiple manifold problem, a binary classification task modeled on applications in machine vision, in which a deep fully-connected neural network is trained to separate two low-dimensional submanifolds of the unit sphere. We…

We introduce a framework for reasoning about what meaning is captured by the neurons in a trained neural network. We provide a strategy for discovering meaning by training a second model (referred to as an observer model) to classify the…

Deep learning has achieved impressive prediction accuracies in a variety of scientific and industrial domains. However, the nested non-linear feature of deep learning makes the learning highly non-transparent, i.e., it is still unknown how…

Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of…

Incorporating prior knowledge into a data-driven modeling problem can drastically improve performance, reliability, and generalization outside of the training sample. The stronger the structural properties, the more effective these…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

This paper reviews recent studies in understanding neural-network representations and learning neural networks with interpretable/disentangled middle-layer representations. Although deep neural networks have exhibited superior performance…

Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete…

Deep neural networks have become increasingly successful at solving classic perception problems such as object recognition, semantic segmentation, and scene understanding, often reaching or surpassing human-level accuracy. This success is…

Modern convolutional neural networks (CNNs) are able to achieve human-level object classification accuracy on specific tasks, and currently outperform competing models in explaining complex human visual representations. However, the…

Scaling model capacity has been vital in the success of deep learning. For a typical network, necessary compute resources and training time grow dramatically with model size. Conditional computation is a promising way to increase the number…

Neural synchrony is hypothesized to play a crucial role in how the brain organizes visual scenes into structured representations, enabling the robust encoding of multiple objects within a scene. However, current deep learning models often…

This paper presents a novel deep learning architecture to classify structured objects in datasets with a large number of visually similar categories. We model sequences of images as linear-chain CRFs, and jointly learn the parameters from…

Multimodal problems are omnipresent in the real world: autonomous driving, robotic grasping, scene understanding, etc... We draw from the well-developed analysis of similarity to provide an example of a problem where neural networks are…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…

Deep Neural Networks have shown promising classification performance when predicting certain biomarkers from Whole Slide Images in digital pathology. However, the calibration of the networks' output probabilities is often not evaluated.…

Neural visual decoding is a central problem in brain computer interface research, aiming to reconstruct human visual perception and to elucidate the structure of neural representations. However, existing approaches overlook a fundamental…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…