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The geometry of weight spaces and functional manifolds of neural networks play an important role towards 'understanding' the intricacies of ML. In this paper, we attempt to solve certain open questions in ML, by viewing them through the…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…
Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…
The geometric structure of an optimization landscape is argued to be fundamentally important to support the success of deep neural network learning. A direct computation of the landscape beyond two layers is hard. Therefore, to capture the…
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while…
Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…
This work starts with the intention of using mathematics to understand the intriguing vulnerability observed by ~\citet{szegedy2013} within artificial neural networks. Along the way, we will develop some novel tools with applications far…
Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
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…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…