Related papers: Visualizing Loss Functions as Topological Landscap…

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…

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…

3D human pose estimation from a single image is a challenging problem, especially for in-the-wild settings due to the lack of 3D annotated data. We propose two anatomically inspired loss functions and use them with a weakly-supervised…

Some recent visual-based relocalization algorithms rely on deep learning methods to perform camera pose regression from image data. This paper focuses on the loss functions that embed the error between two poses to perform deep learning…

Convolutional Neural Networks (CNNs) are widely used for image classification in a variety of fields, including medical imaging. While most studies deploy cross-entropy as the loss function in such tasks, a growing number of approaches have…

Due to the success of deep learning to solving a variety of challenging machine learning tasks, there is a rising interest in understanding loss functions for training neural networks from a theoretical aspect. Particularly, the properties…

A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…

Parts of the brain that carry sensory tasks are organized topographically: nearby neurons are responsive to the same properties of input signals. Thus, in this work, inspired by the neuroscience literature, we proposed a new topographic…

The field of neuroscience and the development of artificial neural networks (ANNs) have mutually influenced each other, drawing from and contributing to many concepts initially developed in statistical mechanics. Notably, Hopfield networks…

Topological consistency plays a crucial role in the task of boundary segmentation for reticular images, such as cell membrane segmentation in neuron electron microscopic images, grain boundary segmentation in material microscopic images and…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…

Neural networks are powerful models that solve a variety of complex real-world problems. However, the stochastic nature of training and large number of parameters in a typical neural model makes them difficult to evaluate via inspection.…

A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

We analyze the loss landscape and expressiveness of practical deep convolutional neural networks (CNNs) with shared weights and max pooling layers. We show that such CNNs produce linearly independent features at a "wide" layer which has…

Autonomous robots navigating in off-road terrain like forests open new opportunities for automation. While off-road navigation has been studied, existing work often relies on clearly delineated pathways. We present a method allowing for…

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights. We introduce a natural distinction between pure critical…

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as…

Massive semantically labeled datasets are readily available for 2D images, however, are much harder to achieve for 3D scenes. Objects in 3D repositories like ShapeNet are labeled, but regrettably only in isolation, so without context. 3D…

The clear understanding of the non-convex landscape of neural network is a complex incomplete problem. This paper studies the landscape of linear (residual) network, the simplified version of the nonlinear network. By treating the gradient…