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Applications of Binary Neural Networks (BNNs) are promising for embedded systems with hard constraints on computing power. Contrary to conventional neural networks with the floating-point datatype, BNNs use binarized weights and activations…

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

In this work, we investigate the structure and representation capacity of sinusoidal MLPs - multilayer perceptron networks that use sine as the activation function. These neural networks (known as neural fields) have become fundamental in…

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…

We resolve a problem of finding the Poincare symmetries from hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Robotic and animal mapping systems share many of the same objectives and challenges, but differ in one key aspect: where much of the research in robotic mapping has focused on solving the data association problem, the grid cell neurons…

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for representing signals such as images, 3D shapes, signed distance fields, and radiance fields. While significant progress has been made in architecture design…

Deep Neural Networks (DNNs) face interpretability challenges due to their opaque internal representations. While Feature Map Convergence Evaluation (FMCE) quantifies module-level convergence via Feature Map Convergence Scores (FMCS), it…

We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn…

In the present paper, we study the Poincare map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global…

The performance and efficiency of running large-scale datasets on traditional computing systems exhibit critical bottlenecks due to the existing "power wall" and "memory wall" problems. To resolve those problems, processing-in-memory (PIM)…

Compute-in-memory (CIM) has shown significant potential in efficiently accelerating deep neural networks (DNNs) at the edge, particularly in speeding up quantized models for inference applications. Recently, there has been growing interest…

With the wide and deep adoption of deep learning models in real applications, there is an increasing need to model and learn the representations of the neural networks themselves. These models can be used to estimate attributes of different…

We propose a heuristic algorithm for fast computation of the Poincar\'{e} series $P_n(t)$ of the invariants of binary forms of degree $n$, viewed as rational functions. The algorithm is based on certain polynomial identities which remain to…

The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…

We present MorphNet, an approach to automate the design of neural network structures. MorphNet iteratively shrinks and expands a network, shrinking via a resource-weighted sparsifying regularizer on activations and expanding via a uniform…

One of the most computationally intensive parts in modern recognition systems is an inference of deep neural networks that are used for image classification, segmentation, enhancement, and recognition. The growing popularity of edge…

We showcase a topological mapping framework for a challenging indoor warehouse setting. At the most abstract level, the warehouse is represented as a Topological Graph where the nodes of the graph represent a particular warehouse…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…