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Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…

Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical…

Empirical evidence shows that deep vision networks often represent concepts as directions in latent space with concept information written along directional components in the vector representation of the input. However, the mechanism to…

The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to…

The Lucid methods described by Olah et al. (2018) provide a way to inspect the inner workings of neural networks trained on image classification tasks using feature visualization. Such methods have generally been applied to networks trained…

Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…

Convolutional Neural Networks (CNNs) trained with the Softmax loss are widely used classification models for several vision tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning…

Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the…

Expressivity is one of the most significant issues in assessing neural networks. In this paper, we provide a quantitative analysis of the expressivity for the deep neural network (DNN) from its dynamic model, where the Hilbert space is…

This paper introduces a hypothesis space for deep learning based on deep neural networks (DNNs). By treating a DNN as a function of two variables - the input variable and the parameter variable - we consider the set of DNNs where the…

Deep neural networks process data through a cascade of representations: input features, hidden activations, logits, and loss. While perturbations at the input, logit, and label levels have been systematically studied, the intermediate…

Deep learning models suffer from opaqueness. For Convolutional Neural Networks (CNNs), current research strategies for explaining models focus on the target classes within the associated training dataset. As a result, the understanding of…

In network representation learning we learn how to represent heterogeneous information networks in a low-dimensional space so as to facilitate effective search, classification, and prediction solutions. Previous network representation…

We present an algorithm for extracting key-point descriptors using deep convolutional neural networks (CNN). Unlike many existing deep CNNs, our model computes local features around a given point in an image. We also present a face…

As a non-linear extension of the classic Linear Discriminant Analysis(LDA), Deep Linear Discriminant Analysis(DLDA) replaces the original Categorical Cross Entropy(CCE) loss function with eigenvalue-based loss function to make a deep neural…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

This paper aims to explain how a deep neural network (DNN) gradually extracts new knowledge and forgets noisy features through layers in forward propagation. Up to now, although the definition of knowledge encoded by the DNN has not reached…

We introduce Deep Inception Networks (DINs), a family of Deep Learning models that provide a general framework for end-to-end systematic trading strategies. DINs extract time series (TS) and cross sectional (CS) features directly from daily…

Implicit neural representation (INR) characterizes the attributes of a signal as a function of corresponding coordinates which emerges as a sharp weapon for solving inverse problems. However, the expressive power of INR is limited by the…

To characterize the function space explored by neural networks (NNs) is an important aspect of learning theory. In this work, noticing that a multi-layer NN generates implicitly a hierarchy of reproducing kernel Hilbert spaces (RKHSs) -…