Tensor product network

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A tensor product network, in artificial neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable assignment. Orthonormal vectors are chosen to model the ideas (such as variable names and target assignments), and the tensor product of these vectors construct a network whose mathematical properties allow the user to easily extract the association from it.

Artificial neural network computational model used in machine learning, computer science and other research disciplines, which is based on a large collection of connected simple units called artificial neurons, loosely analogous to axons in a biological brain

Artificial neural networks (ANN) or connectionist systems are computing systems inspired by the biological neural networks that constitute animal brains. The neural network itself is not an algorithm, but rather a framework for many different machine learning algorithms to work together and process complex data inputs. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge about cats, for example, that they have fur, tails, whiskers and cat-like faces. Instead, they automatically generate identifying characteristics from the learning material that they process.

Tensor geometric object

In mathematics, a tensor is a geometric object that maps in a multi-linear manner geometric vectors, scalars, and other tensors to a resulting tensor. Vectors and scalars which are often used in elementary physics and engineering applications, are considered as the simplest tensors. Vectors from the dual space of the vector space, which supplies the geometric vectors, are also included as tensors. Geometric in this context is chiefly meant to emphasize independence of any selection of a coordinate system.

In computer programming, a variable or scalar is a storage location paired with an associated symbolic name, which contains some known or unknown quantity of information referred to as a value. The variable name is the usual way to reference the stored value, in addition to referring to the variable itself, depending on the context. This separation of name and content allows the name to be used independently of the exact information it represents. The identifier in computer source code can be bound to a value during run time, and the value of the variable may thus change during the course of program execution.

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Canonical may refer to:

In mathematics, the symmetric algebra S(V) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.

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Tensor network theory Theory of brain function that provides a mathematical model of the transformation of sensory space-time coordinates into motor coordinates and vice versa by cerebellar neuronal networks.

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In mathematics, the tensor product (TP) model transformation was proposed by Baranyi and Yam as key concept for higher order singular value decomposition of functions. It transforms a function into TP function form if such a transformation is possible. If an exact transformation is not possible, then the method determines a TP function that is an approximation of the given function. Hence, the TP model transformation can provide a trade-off between approximation accuracy and complexity.

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