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Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…

Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

The rapid progress of Artificial Intelligence research came with the development of increasingly complex deep learning models, leading to growing challenges in terms of computational complexity, energy efficiency and interpretability. In…

In a previous work, we proposed a geometric framework to study a deep neural network, seen as sequence of maps between manifolds, employing singular Riemannian geometry. In this paper, we present an application of this framework, proposing…

Detection of cell nuclei in microscopic images is a challenging research topic, because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell…

Models for image representation learning are typically designed for either recognition or generation. Various forms of contrastive learning help models learn to convert images to embeddings that are useful for classification, detection, and…

Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…

Networks are ubiquitous structure that describes complex relationships between different entities in the real world. As a critical component of prediction task over nodes in networks, learning the feature representation of nodes has become…

In the field of pattern recognition research, the method of using deep neural networks based on improved computing hardware recently attracted attention because of their superior accuracy compared to conventional methods. Deep neural…

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…

Cell nuclei detection is a challenging research topic because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic…

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…

The great success of deep learning has stimulated avid research activities in verifying the power of depth in theory, a common consensus of which is that deep net are versatile in approximating and learning numerous functions. Such a…

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data…

Deep convolutional neural networks (CNNs) trained on objects and scenes have shown intriguing ability to predict some response properties of visual cortical neurons. However, the factors and computations that give rise to such ability, and…

This paper proposes a novel approach to pattern classification using a probabilistic neural network model. The strategy is based on a compact-sized probabilistic neural network capable of continuous incremental learning and unlearning…

Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional…

Intermediate features at different layers of a deep neural network are known to be discriminative for visual patterns of different complexities. However, most existing works ignore such cross-layer heterogeneities when classifying samples…