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Large Width Limits Of Neural Networks
Artificial neural networks are a class of models used in machine learning, and inspired by biological neural networks. They are the core component of modern deep learning algorithms. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. Theoretical analysis of artificial neural networks sometimes considers the limiting case that layer width becomes large or infinite. This limit enables simple analytic statements to be made about neural network predictions, training dynamics, generalization, and loss surfaces. This wide layer limit is also of practical interest, since finite width neural networks often perform strictly better as layer width is increased. __TOC__ Theoretical approaches based on a large width limit * The Neural Network Gaussian Process (NNGP) corresponds to the infinite width limit of Bayesian neural networks, and to the distribution over func ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitely Wide Neural Network
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neural Network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called ''edges''. Neurons and edges typically have a ''weight'' that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold. Typically, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making pred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Circuit
A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Neural circuits interconnect to one another to form large scale brain networks. Biological neural networks have inspired the design of artificial neural networks, but artificial neural networks are usually not strict copies of their biological counterparts. Early study Early treatments of neural networks can be found in Herbert Spencer's ''Principles of Psychology'', 3rd edition (1872), Theodor Meynert's ''Psychiatry'' (1884), William James' ''Principles of Psychology'' (1890), and Sigmund Freud's Project for a Scientific Psychology (composed 1895). The first rule of neuronal learning was described by Hebb in 1949, in the Hebbian theory. Thus, Hebbian pairing of pre-synaptic and post-synaptic activity can substantially alter the dynamic characteristics of the synaptic connection and therefore either facilitate or inhibit signal transmission. In 1959, the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deep Learning
Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be Supervised learning, supervised, Semi-supervised learning, semi-supervised or Unsupervised learning, unsupervised. Deep-learning architectures such as #Deep_neural_networks, deep neural networks, deep belief networks, deep reinforcement learning, recurrent neural networks, convolutional neural networks and Transformer (machine learning model), Transformers have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, Climatology, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Artificial neural networks (ANNs) were inspired by information processing and distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Neuron
An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network. Artificial neurons are elementary units in an artificial neural network. The artificial neuron receives one or more inputs (representing excitatory postsynaptic potentials and inhibitory postsynaptic potentials at neural dendrites) and sums them to produce an output (or , representing a neuron's action potential which is transmitted along its axon). Usually each input is separately weighted, and the sum is passed through a non-linear function known as an activation function or transfer function. The transfer functions usually have a sigmoid shape, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions. They are also often monotonically increasing, continuous, differentiable and bounded. Non-monotonic, unbounded and oscillating activation functions with multiple zeros that outperform sigmoidal and ReLU like activatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deep Information Propagation
Deep or The Deep may refer to: Places United States * Deep Creek (Appomattox River tributary), Virginia * Deep Creek (Great Salt Lake), Idaho and Utah * Deep Creek (Mahantango Creek tributary), Pennsylvania * Deep Creek (Mojave River tributary), California * Deep Creek (Pine Creek tributary), Pennsylvania * Deep Creek (Soque River tributary), Georgia * Deep Creek (Texas), a tributary of the Colorado River The Colorado River ( es, Río Colorado) is one of the principal rivers (along with the Rio Grande) in the Southwestern United States and northern Mexico. The river drains an expansive, arid drainage basin, watershed that encompasses parts of ... * Deep Creek (Washington), a tributary of the Spokane River * Deep River (Indiana), a tributary of the Little Calumet River * Deep River (Iowa), a minor tributary of the English River * Deep River (North Carolina) * Deep River (Washington), a minor List of rivers of Washington#Lower Columbia Basin, tributary of the Columbia River ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Tangent Kernel
In the study of artificial neural networks (ANNs), the neural tangent kernel (NTK) is a kernel that describes the evolution of deep artificial neural networks during their training by gradient descent. It allows ANNs to be studied using theoretical tools from kernel methods. In general, a kernel is a positive-semidefinite symmetric function of two inputs which represents some notion of similarity between the two inputs. The NTK is a specific kernel derived from a given neural network; in general, when the neural network parameters change during training, the NTK evolves as well. However, in the limit of large layer width the NTK becomes constant, revealing a duality between training the wide neural network and kernel methods: gradient descent in the infinite-width limit is fully equivalent to kernel gradient descent with the NTK. As a result, using gradient descent to minimize least-square loss for neural networks yields the same mean estimator as ridgeless kernel regression with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deep Learning
Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be Supervised learning, supervised, Semi-supervised learning, semi-supervised or Unsupervised learning, unsupervised. Deep-learning architectures such as #Deep_neural_networks, deep neural networks, deep belief networks, deep reinforcement learning, recurrent neural networks, convolutional neural networks and Transformer (machine learning model), Transformers have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, Climatology, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Artificial neural networks (ANNs) were inspired by information processing and distr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
