Related papers: Nilpotent Feed Forward Network Dynamics
A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent…
Front form dynamics is not a manifestly rotational invariant formalism. In particular, the requirement of an invariance under rotations around the transverse axes is difficult to fulfill.In the present work it is investigated, to which…
Modern machine learning models are able to outperform humans on a variety of non-trivial tasks. However, as the complexity of the models increases, they consume significant amounts of power and still struggle to generalize effectively to…
We analyze renormalizability properties of noncommutative (NC) theories with a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model which is renormalizable at all orders of the loop expansion. We show that this…
Incorporating the Forward Forward algorithm into neural network training represents a transformative shift from traditional methods, introducing a dual forward mechanism that streamlines the learning process by bypassing the complexities of…
We use the method of equivariant moving frames to revisit the problem of normal forms and equivalence of nondegenerate real hypersurfaces M \subset C^2 under the pseudo-group action of holomorphic transformations. The moving frame…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…
In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into…
The paper proposes representation functionals in a dual paradigm where learning jointly concerns both linear convolutional weights and parametric forms of nonlinear activation functions. The nonlinear forms proposed for performing the…
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of…
Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of…
We revisit the problem of introducing an a priori control for devices that can be modeled via a symplectic map in a neighborhood of an elliptic equilibrium. Using a technique based on Lie transform methods we produce a normal form algorithm…
We use string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. We obtain concise geometric expressions for the objects describing bulk and boundary…
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…
We investigate deformations of four-dimensional N=(1,1) euclidean superspace induced by nonanticommuting fermionic coordinates. We essentially use the harmonic superspace approach and consider nilpotent bi-differential Poisson operators…
Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ($\approx$ hydrodynamic modes) of the underlying physical system, much more than quasi one- and…
We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations…
We investigate the hexagon formalism in the planar 4d conformal fishnet theory. This theory arises from N=4 SYM by a deformation that preserves both conformal symmetry and integrability. Based on this relation, we obtain the hexagon form…