Related papers: Exact Dual Geometry of SOC-ICNN Value Functions

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…

Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the…

We show that training deep neural networks (DNNs) with absolute value activation and arbitrary input dimension can be formulated as equivalent convex Lasso problems with novel features expressed using geometric algebra. This formulation…

Deep convolutional neural networks (CNNs) have been intensively used for multi-class segmentation of data from different modalities and achieved state-of-the-art performances. However, a common problem when dealing with large, high…

Image representations, from SIFT and Bag of Visual Words to Convolutional Neural Networks (CNNs), are a crucial component of almost any image understanding system. Nevertheless, our understanding of them remains limited. In this paper we…

Convex Shapes (CS) are common priors for optic disc and cup segmentation in eye fundus images. It is important to design proper techniques to represent convex shapes. So far, it is still a problem to guarantee that the output objects from a…

Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The…

In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the…

We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…

Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…

Neural implicit representations have emerged as a powerful paradigm for 3D reconstruction. However, despite their success, existing methods fail to capture fine geometric details and thin structures, especially in scenarios where only…

Deep Convolutional Neural Networks (DCNNs) have recently shown state of the art performance in high level vision tasks, such as image classification and object detection. This work brings together methods from DCNNs and probabilistic…

Hyperspectral Image Classification (HSIC) is a difficult task due to high inter and intra-class similarity and variability, nested regions, and overlapping. 2D Convolutional Neural Networks (CNN) emerged as a viable network whereas, 3D CNNs…

Input-convex neural networks (ICNNs) are widely used for log-concave density estimation, convex-potential normalizing flows, optimal transport, and transport-map inversion for high-dimensional Bayesian posteriors. These tasks share a…

The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit…

Deep learning is currently playing a crucial role toward higher levels of artificial intelligence. This paradigm allows neural networks to learn complex and abstract representations, that are progressively obtained by combining simpler…

Object detection is a challenging task in visual understanding domain, and even more so if the supervision is to be weak. Recently, few efforts to handle the task without expensive human annotations is established by promising deep neural…

We present a simple and effective architecture for fine-grained visual recognition called Bilinear Convolutional Neural Networks (B-CNNs). These networks represent an image as a pooled outer product of features derived from two CNNs and…

Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture…

While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…