Related papers: Permutation Binary Neural Networks: Analysis of Pe…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
There is a concerted effort to build domain-general artificial intelligence in the form of universal neural network models with sufficient computational flexibility to solve a wide variety of cognitive tasks but without requiring…
Symmetry in the parameter space of deep neural networks (DNNs) has proven beneficial for various deep learning applications. A well-known example is the permutation symmetry in Multi-Layer Perceptrons (MLPs), where permuting the rows of…
Self-gravitating bodies can have an arbitrarily complex shape, which implies a much richer multipolar structure than that of a black hole in General Relativity. With this motivation, we study the corrections to the dynamics of a binary…
Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses -- so-called neuromorphic systems -- is a viable computational substrate. Since neuromorphic systems have been…
Artificial intelligence based on artificial neural networks, which are originally inspired by the biological architectures of human brain, has mostly been realized using software but executed on conventional von Neumann computers, where the…
These notes were written during the 9th and 10th sessions of the subject Dynamical Systems II coursed at DTU (Denmark) during the Winter Semester 2015-2016, and later extended in February 2017. They aim to provide students with a…
The ability to process time-series at low energy cost is critical for many applications. Recurrent neural network, which can perform such tasks, are computationally expensive when implementing in software on conventional computers. Here we…
Modern nuclear data evaluation increasingly requires not only accurate scattering calculations, but also efficient methods for uncertainty quantification and parameter optimization, tasks that benefit from differentiable solvers amenable to…
Functional brain networks can change rapidly as a function of stimuli or cognitive shifts. Tracking dynamic functional connectivity is particularly challenging as it requires estimating the structure of the network at each moment as well as…
Learning image transformations is essential to the idea of mental simulation as a method of cognitive inference. We take a connectionist modeling approach, using planar neural networks to learn fundamental imagery transformations, like…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing…
How to effectively approximate real-valued parameters with binary codes plays a central role in neural network binarization. In this work, we reveal an important fact that binarizing different layers has a widely-varied effect on the…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional…
Causal relationship recognition is a fundamental operation in neural networks aimed at learning behavior, action planning, and inferring external world dynamics. This operation is particularly crucial for reinforcement learning (RL). In the…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…
Several algebro-geometric properties of commutative rings of partial differential operators as well as several geometric constructions are investigated. In particular, we show how to associate a geometric data by a commutative ring of…
Orbital parameters of binary radio pulsars reveal the history of the pulsars' formation and evolution including dynamic interactions with other objects. Advanced technology has enabled us to determine these orbital parameters accurately in…