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Understanding internal feature representations of deep neural networks (DNNs) is a fundamental step toward model interpretability. Inspired by neuroscience methods that probe biological neurons using visual stimuli, recent deep learning…
In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…
We present a methodology to learn explicit Model Predictive Control (eMPC) laws from sample data points with tunable complexity. The learning process is cast in a special Neural Network setting where the coefficients of two linear layers…
This paper investigates controller identification given data from a Model Predictive Controller (MPC) with constraints. We propose an approach for learning MPC that explicitly uses the gradient information in the training process. This is…
Deep neural networks are widely used for nonlinear function approximation with applications ranging from computer vision to control. Although these networks involve the composition of simple arithmetic operations, it can be very challenging…
We use deep sparsely connected neural networks to measure the complexity of a function class in $L^2(\mathbb R^d)$ by restricting connectivity and memory requirement for storing the neural networks. We also introduce representation system -…
Although deep neural networks (DNNs) achieve high predictive accuracy, their confidence estimates are often unreliable, potentially compromising user trust in their decisions. This has motivated research on calibrated models, where…
An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The…
Recent years have produced great advances in training large, deep neural networks (DNNs), including notable successes in training convolutional neural networks (convnets) to recognize natural images. However, our understanding of how these…
Adaptive inference is a promising technique to improve the computational efficiency of deep models at test time. In contrast to static models which use the same computation graph for all instances, adaptive networks can dynamically adjust…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
The effectiveness of deep neural architectures has been widely supported in terms of both experimental and foundational principles. There is also clear evidence that the activation function (e.g. the rectifier and the LSTM units) plays a…
Neural networks are a convenient way to automatically fit functions that are too complex to be described by hand. The downside of this approach is that it leads to build a black-box without understanding what happened inside. Finding the…
We contribute to a better understanding of the class of functions that can be represented by a neural network with ReLU activations and a given architecture. Using techniques from mixed-integer optimization, polyhedral theory, and tropical…
As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In…
We propose a novel explanation method that explains the decisions of a deep neural network by investigating how the intermediate representations at each layer of the deep network were refined during the training process. This way we can a)…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…
Deep Learning has a hierarchical network architecture to represent the complicated feature of input patterns. We have developed the adaptive structure learning method of Deep Belief Network (DBN) that can discover an optimal number of…
Deep reinforcement learning, applied to vision-based problems like Atari games, maps pixels directly to actions; internally, the deep neural network bears the responsibility of both extracting useful information and making decisions based…