Related papers: The algebra and the geometry aspect of Deep learni…

Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals…

Learning on 3D structures of large biomolecules is emerging as a distinct area in machine learning, but there has yet to emerge a unifying network architecture that simultaneously leverages the graph-structured and geometric aspects of the…

Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…

Despite the extreme popularity of deep learning in science and industry, its formal understanding is limited. This thesis puts forth notions of rank as key for developing a theory of deep learning, focusing on the fundamental aspects of…

We model human and animal learning by computing with high-dimensional vectors (H = 10,000 for example). The architecture resembles traditional (von Neumann) computing with numbers, but the instructions refer to vectors and operate on them…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…

Recently, growth in our understanding of the computations performed in both biological and artificial neural networks has largely been driven by either low-level mechanistic studies or global normative approaches. However, concrete…

In this paper, we explore the algebra of quantum idempotents and the quantization of fermions which gives rise to a Hilbert space equal to the Grassmann algebra associated with the Lie algebra. Since idempotents carry representations of the…

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…

Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Modern deep learning treats neural networks primarily as endpoint functions from inputs to outputs. Inspired by the shift from force to geometry in physics, we ask whether a network should instead be understood through the geometry of its…

A technical note aiming to offer deeper intuition for the LayerNorm function common in deep neural networks. LayerNorm is defined relative to a distinguished 'neural' basis, but it does more than just normalize the corresponding vector…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…

By bridging deep networks and physics, the programme of geometrization of deep networks was proposed as a framework for the interpretability of deep learning systems. Following this programme we can apply two key ideas of physics, the…

Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…