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Backpropagation Through Time
Backpropagation through time (BPTT) is a gradient-based technique for training certain types of recurrent neural networks. It can be used to train Elman networks. The algorithm was independently derived by numerous researchers. Algorithm The training data for a recurrent neural network is an ordered sequence of k input-output pairs, \langle \mathbf_0,\mathbf_0 \rangle, \langle\mathbf_1,\mathbf_1 \rangle,\langle\mathbf_2,\mathbf_2\rangle,...,\langle\mathbf_,\mathbf_\rangle. An initial value must be specified for the hidden state \mathbf_0. Typically, a vector of all zeros is used for this purpose. BPTT begins by unfolding a recurrent neural network in time. The unfolded network contains k inputs and outputs, but every copy of the network shares the same parameters. Then the backpropagation algorithm is used to find the gradient of the cost with respect to all the network parameters. Consider an example of a neural network that contains a recurrent layer f and a feedforward ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrent Neural Network
A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic behavior. Derived from feedforward neural networks, RNNs can use their internal state (memory) to process variable length sequences of inputs. This makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrent Neural Network
A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic behavior. Derived from feedforward neural networks, RNNs can use their internal state (memory) to process variable length sequences of inputs. This makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. Recurrent neural networks are theoretically Turing complete and can run arbitrary programs to process arbitrary sequences of inputs. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replace ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unfold Through Time
Unfold may refer to: Science * Unfoldable cardinal, in mathematics * Unfold (higher-order function), in computer science a family of anamorphism functions * Unfoldment (other), in spirituality and physics * Unfolded protein response, in biochemistry * Equilibrium unfolding, in biochemistry * Unfolded state (denatured protein), in biochemistry * Maximum variance unfolding Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. It is moti ... (semidefinite embedding), in computer science Music * ''Unfold'' (Marié Digby album), 2008 * ''Unfold'' (John O'Callaghan album), 2011 * ''Unfold'' (The Necks album), 2017 * "Unfold" (Porter Robinson song), 2021 * "Unfold", a song by De La Soul from the 2016 album '' And the Anonymous Nobody...'' See also * Fold (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backpropagation
In machine learning, backpropagation (backprop, BP) is a widely used algorithm for training feedforward neural network, feedforward artificial neural networks. Generalizations of backpropagation exist for other artificial neural networks (ANNs), and for functions generally. These classes of algorithms are all referred to generically as "backpropagation". In Artificial neural network#Learning, fitting a neural network, backpropagation computes the gradient of the loss function with respect to the Glossary of graph theory terms#weight, weights of the network for a single input–output example, and does so Algorithmic efficiency, efficiently, unlike a naive direct computation of the gradient with respect to each weight individually. This efficiency makes it feasible to use gradient methods for training multilayer networks, updating weights to minimize loss; gradient descent, or variants such as stochastic gradient descent, are commonly used. The backpropagation algorithm works by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feedforward Neural Network
A feedforward neural network (FNN) is an artificial neural network wherein connections between the nodes do ''not'' form a cycle. As such, it is different from its descendant: recurrent neural networks. The feedforward neural network was the first and simplest type of artificial neural network devised. In this network, the information moves in only one direction—forward—from the input nodes, through the hidden nodes (if any) and to the output nodes. There are no cycles or loops in the network. Single-layer perceptron The simplest kind of neural network is a ''single-layer perceptron'' network, which consists of a single layer of output nodes; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated in each node, and if the value is above some threshold (typically 0) the neuron fires and takes the activated value (typically 1); otherwise it takes the deactivated value (typically -1). Ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Programming
Evolutionary programming is one of the four major evolutionary algorithm paradigms. It is similar to genetic programming, but the structure of the program to be optimized is fixed, while its numerical parameters are allowed to evolve. It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence. Fogel used finite-state machines as predictors and evolved them. Currently evolutionary programming is a wide evolutionary computing dialect with no fixed structure or ( representation), in contrast with some of the other dialects. It has become harder to distinguish from evolutionary strategies. Its main variation operator is mutation; members of the population are viewed as part of a specific species rather than members of the same species therefore each parent generates an offspring, using a (μ + μ) survivor selection. See also * Artificial intelligence * Genetic algorithm * Genetic ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backpropagation Through Structure
Backpropagation through structure (BPTS) is a gradient-based technique for training recursive neural nets (a superset of recurrent neural nets) and is extensively described in a 1996 paper written by Christoph Goller and Andreas Küchler. References {{compu-ai-stub Artificial neural networks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
