Related papers: Input Convex Neural Networks
In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…
This paper presents a novel framework of neural networks for isotropic hyperelasticity that enforces necessary physical and mathematical constraints while simultaneously satisfying the universal approximation theorem. The two key…
Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…
With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a…
Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…
Deep convolutional neural networks, assisted by architectural design strategies, make extensive use of data augmentation techniques and layers with a high number of feature maps to embed object transformations. That is highly inefficient…
Connected decision boundaries are useful in several tasks like image segmentation, clustering, alpha-shape or defining a region in nD-space. However, the machine learning literature lacks methods for generating connected decision boundaries…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
This paper addresses the analysis and design of quadratic neural networks, which have been recently introduced in the literature, and their applications to regression, classification, system identification and control of dynamical systems.…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
Deep neural networks are an extremely successful and widely used technique for various pattern recognition and machine learning tasks. Due to power and resource constraints, these computationally intensive networks are difficult to…
A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic…
Deep convolutional network has been the state-of-the-art approach for a wide variety of tasks over the last few years. Its successes have, in many cases, turned it into the default model in quite a few domains. In this work, we will…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
Currently, increasingly deeper neural networks have been applied to improve their accuracy. In contrast, We propose a novel wider Convolutional Neural Networks (CNN) architecture, motivated by the Multi-column Deep Neural Networks and the…