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Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…
Generative adversarial networks, which can generate metasurfaces based on a training set of high performance device layouts, have the potential to significantly reduce the computational cost of the metasurface design process. However, basic…
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic models, such as neural networks with polynomial activations,…
Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…
Recent analysis of deep neural networks has revealed their vulnerability to carefully structured adversarial examples. Many effective algorithms exist to craft these adversarial examples, but performant defenses seem to be far away. In this…
Despite significant advances, deep networks remain highly susceptible to adversarial attack. One fundamental challenge is that small input perturbations can often produce large movements in the network's final-layer feature space. In this…
Deep neural networks are learning models having achieved state of the art performance in many fields like prediction, computer vision, language processing and so on. However, it has been shown that certain inputs exist which would not trick…
We study the natural gradient method for learning in deep Bayesian networks, including neural networks. There are two natural geometries associated with such learning systems consisting of visible and hidden units. One geometry is related…
Neural networks have been shown vulnerable to a variety of adversarial algorithms. A crucial step to understanding the rationale for this lack of robustness is to assess the potential of the neural networks' representation to encode the…
Deep neural networks achieve remarkable performance in multiple fields. However, after proper training they suffer from an inherent vulnerability against adversarial examples (AEs). In this work we shed light on inner representations of the…
There have been several attempts to mathematically understand neural networks and many more from biological and computational perspectives. The field has exploded in the last decade, yet neural networks are still treated much like a black…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…
Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…
Hypercomplex algebras have recently been gaining prominence in the field of deep learning owing to the advantages of their division algebras over real vector spaces and their superior results when dealing with multidimensional signals in…
One of the main challenges in modern deep learning is to understand why such over-parameterized models perform so well when trained on finite data. A way to analyze this generalization concept is through the properties of the associated…
As humans, we inherently perceive images based on their predominant features, and ignore noise embedded within lower bit planes. On the contrary, Deep Neural Networks are known to confidently misclassify images corrupted with meticulously…
Injecting adversarial examples during training, known as adversarial training, can improve robustness against one-step attacks, but not for unknown iterative attacks. To address this challenge, we first show iteratively generated…
Deep Learning has become one of the primary research areas in developing intelligent machines. Most of the well-known applications (such as Speech Recognition, Image Processing and NLP) of AI are driven by Deep Learning. Deep Learning…
Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by…
As hyperbolic deep learning grows in popularity, so does the need for adversarial robustness in the context of such a non-Euclidean geometry. To this end, this paper proposes hyperbolic alternatives to the commonly used FGM and PGD…