Related papers: Mnesors for automatic control
Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…
Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…
The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…
Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to…
The paper presents a hybrid system controller, incorporating a neural and an LQG controller. The neural controller has been optimized by genetic algorithms directly on the inverted pendulum system. The failure free optimization process…
Vision of ferromagnet/semiconductor hybrid as a strongly coupled but flexible spin system is presented. We analyze the experiments and argue that contrary to the common sense the nonmagnetic semiconductor plays a crucial role in…
The large dimensionality of environments is the limiting factor in applying optimal control to open quantum systems beyond Markovian approximations. Multiple methods exist to simulate non-Markovian open systems which effectively reduce the…
This paper presents an intelligent controller for uncertain underactuated nonlinear systems. The adopted approach is based on sliding mode control and enhanced by an artificial neural network to cope with modeling inaccuracies and external…
A denotational semantics of quantum Turing machines having a quantum control is defined in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore-Penrose generalized inverse, a new additive trace is…
The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used…
In recent years several classes of structured matrices are extended to classes of tensors in the context of tensor complementarity problem. The tensor complementarity problem is a class of nonlinear complementarity problem where the…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
Efficient, low-loss, and versatile optical modulators are a critical ingredient for practical integrated photonic systems. Modulators based on micro-electromechanical systems (MEMS) have unique advantages over more traditional thermal,…
We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defined on bordisms that are 2-framed. Accordingly we do not need…
The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of…
In this paper the Mechanical Neural Network(MNN) is introduced, a physical implementation of a multilayer perceptron(MLP) with ReLU activation functions, two input neurons, four hidden neurons and two output neurons. This physical model of…
For simulations where the forward and the inverse directions have a physics meaning, invertible neural networks are especially useful. A conditional INN can invert a detector simulation in terms of high-level observables, specifically for…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a…
The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…