Look up tensor in Wiktionary, the free dictionary.
A tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.
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Tensor may also refer to:
A tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.
Tensor may also refer to:
In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H, or in blackboard bold by Quaternions are not a field, because multiplication of quaternions is not, in general, commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form
In mathematics, vector algebra may mean:
Processor may refer to:
Adaptive resonance theory (ART) is a theory developed by Stephen Grossberg and Gail Carpenter on aspects of how the brain processes information. It describes a number of artificial neural network models which use supervised and unsupervised learning methods, and address problems such as pattern recognition and prediction.
A scalar is an element of a field which is used to define a vector space. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication, in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers. Then scalars of that vector space will be elements of the associated field.
William Rowan Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton's original treatment of quaternions, using his notation and terms. Hamilton's treatment is more geometric than the modern approach, which emphasizes quaternions' algebraic properties. Mathematically, quaternions discussed differ from the modern definition only by the terminology which is used.
In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. They find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations.
Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality reduction can be performed on a data tensor that contains a collection of observations have been vectorized, or observations that are treated as matrices and concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D).
Deep learning is a subset of machine learning methods based on neural networks with representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised.
Google Brain was a deep learning artificial intelligence research team that served as the sole AI branch of Google before being incorporated under the newer umbrella of Google AI, a research division at Google dedicated to artificial intelligence. Formed in 2011, it combined open-ended machine learning research with information systems and large-scale computing resources. It created tools such as TensorFlow, which allow neural networks to be used by the public, and multiple internal AI research projects, and aimed to create research opportunities in machine learning and natural language processing. It was merged into former Google sister company DeepMind to form Google DeepMind in April 2023.
Torch is an open-source machine learning library, a scientific computing framework, and a scripting language based on Lua. It provides LuaJIT interfaces to deep learning algorithms implemented in C. It was created by the Idiap Research Institute at EPFL. Torch development moved in 2017 to PyTorch, a port of the library to Python.
Eclipse Deeplearning4j is a programming library written in Java for the Java virtual machine (JVM). It is a framework with wide support for deep learning algorithms. Deeplearning4j includes implementations of the restricted Boltzmann machine, deep belief net, deep autoencoder, stacked denoising autoencoder and recursive neural tensor network, word2vec, doc2vec, and GloVe. These algorithms all include distributed parallel versions that integrate with Apache Hadoop and Spark.
Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus. Once trained, such a model can detect synonymous words or suggest additional words for a partial sentence. Word2vec was developed by Tomáš Mikolov and colleagues at Google and published in 2013.
TensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks.
An AI accelerator, deep learning processor or neural processing unit (NPU) is a class of specialized hardware accelerator or computer system designed to accelerate artificial intelligence and machine learning applications, including artificial neural networks and computer vision. Typical applications include algorithms for robotics, Internet of Things, and other data-intensive or sensor-driven tasks. They are often manycore designs and generally focus on low-precision arithmetic, novel dataflow architectures or in-memory computing capability. As of 2024, a typical AI integrated circuit chip contains tens of billions of MOSFETs.
PyTorch is a machine learning library based on the Torch library, used for applications such as computer vision and natural language processing, originally developed by Meta AI and now part of the Linux Foundation umbrella. It is recognized as one of the two most popular machine learning libraries alongside TensorFlow, offering free and open-source software released under the modified BSD license. Although the Python interface is more polished and the primary focus of development, PyTorch also has a C++ interface.
Region-based Convolutional Neural Networks (R-CNN) are a family of machine learning models for computer vision, and specifically object detection and localization. The original goal of R-CNN was to take an input image and produce a set of bounding boxes as output, where each bounding box contains an object and also the category of the object. In general, R-CNN architectures perform selective search over feature maps outputted by a CNN.
Google JAX is a machine learning framework for transforming numerical functions. It is described as bringing together a modified version of autograd and TensorFlow's XLA. It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary functions of JAX are:
Tensor informally refers in machine learning to two different concepts that organize and represent data. Data may be organized in a multidimensional array (M-way array) that is informally referred to as a "data tensor"; however in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor") may be analyzed either by artificial neural networks or tensor methods.