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Modern Hopfield Network
Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron i is defined by a time-dependent variable V_i, which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons. In the original Hopfield model of associative memory, the variables were binary, and the dynamics were described by a one-at-a-time update of the state of the neurons. An energy function quadratic in the V_i was defined, and the dynamics consisted of changing the activity of each single neuron i only if doing so would lower the total energy of the system. This same idea was extended to the case of V_i being a continuous variable representing the output of neuron i, and V_i being a monotonic function of an input current. The dynamic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrent Neural Networks
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] |
Energy Function
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to stimuli such as touch, sound, or light that affect the cells of the sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is a compact structure, and the axon and dend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Order Differential Equations
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Activation Function
In artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs. A standard integrated circuit can be seen as a digital network of activation functions that can be "ON" (1) or "OFF" (0), depending on input. This is similar to the linear perceptron in neural networks. However, only ''nonlinear'' activation functions allow such networks to compute nontrivial problems using only a small number of nodes, and such activation functions are called nonlinearities. Classification of activation functions The most common activation functions can be divided in three categories: ridge functions, radial functions and fold functions. An activation function f is saturating if \lim_ , \nabla f(v), = 0. It is nonsaturating if it is not saturating. Non-saturating activation functions, such as ReLU, may be better than saturating activation functions, as they don't suffer from vanishing gradient. Ridge activation functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Hopfield Network
Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron i is defined by a time-dependent variable V_i, which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons. In the original Hopfield model of associative memory, the variables were binary, and the dynamics were described by a one-at-a-time update of the state of the neurons. An energy function quadratic in the V_i was defined, and the dynamics consisted of changing the activity of each single neuron i only if doing so would lower the total energy of the system. This same idea was extended to the case of V_i being a continuous variable representing the output of neuron i, and V_i being a monotonic function of an input current. The dynamic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Theory Of Modern Hopfield Networks
Effectiveness is the capability of producing a desired result or the ability to produce desired output. When something is deemed effective, it means it has an intended or expected outcome, or produces a deep, vivid impression. Etymology The origin of the word "effective" stems from the Latin word effectīvus, which means creative, productive or effective. It surfaced in Middle English between 1300 and 1400 A.D. Usage In mathematics and logic, ''effective'' is used to describe metalogical methods that fit the criteria of an effective procedure. In group theory, a group element acts ''effectively'' (or ''faithfully'') on a point, if that point is not fixed by the action. In physics, an effective theory is, similar to a phenomenological theory, a framework intended to explain certain (observed) effects without the claim that the theory correctly models the underlying (unobserved) processes. In heat transfer, ''effectiveness'' is a measure of the performance of a heat exchang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HAM Full Connect
Ham is pork from a leg cut that has been preserved by wet or dry curing, with or without smoking."Bacon: Bacon and Ham Curing" in ''Chambers's Encyclopædia''. London: George Newnes, 1961, Vol. 2, p. 39. As a processed meat, the term "ham" includes both whole cuts of meat and ones that have been mechanically formed. Ham is made around the world, including a number of regional specialties, such as Westphalian ham and some varieties of Spanish ''jamón''. In addition, numerous ham products have specific geographical naming protection, such as prosciutto di Parma in Europe, and Smithfield ham in the US. History The preserving of pork leg as ham has a long history, with traces of production of cured ham among the Etruscan civilization known in the 6th and 5th century BC. Cato the Elder wrote about the "salting of hams" in his ' tome around 160 BC. There are claims that the Chinese were the first people to mention the production of cured ham. ' claims an origin from Gaul. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hierarchical Associative Memory
A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science, organizational theory, systems theory, systematic biology, and the social sciences (especially political philosophy). A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy that are not linked vertically to one a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
