Synaptic DynamicsII:Supervised Learning The Backpropagation Algorithm and Spport Vector Machines JingLIU 2004.11.3
Synaptic DynamicsII : Supervised Learning The Backpropagation Algorithm and Spport Vector Machines JingLIU 2004.11.3
History of BP Algorithm Rumelhart [1986]popularized the BP algorithm in the Paralle/Distributed Processing edited volume in the late 1980's. ■ BP algorithm overcame the limitations of the perceptron algorithm,limitations that Minsky and Papert[1969]had carefully enumerated. BP's popularity begot waves of criticism.BP algorithm often failed to converge,and at best converged to local error minima. The wave of criticism challenged BP's historical priority. The wave of criticism challenge whether the BP learning was new.The algorithm not offer a new kind of learning
History of BP Algorithm ◼ Rumelhart [1986]popularized the BP algorithm in the Parallel Distributed Processing edited volume in the late 1980’s. ◼ BP algorithm overcame the limitations of the perceptron algorithm, limitations that Minsky and Papert[1969] had carefully enumerated. ◼ BP’s popularity begot waves of criticism. BP algorithm often failed to converge, and at best converged to local error minima. ◼ The wave of criticism challenged BP’s historical priority. ◼ The wave of criticism challenge whether the BP learning was new. The algorithm not offer a new kind of learning
Multilayer feedforward NNs Output layer Hidden layer Input layer ■■■■■■■■■■■■■
Multilayer feedforward NNs
Feedforward Sigmoidal Representation Theorems Feedforward sigmoidal architectures can in principle represent any Borel-measurable function to any desired accuracy-if the network contains enough hidden"neurons between the input and output neuronal fields. So the MLP can solve the problems of nonlinear separable problems and function approximate
Feedforward Sigmoidal Representation Theorems ◼ Feedforward sigmoidal architectures can in principle represent any Borel-measurable function to any desired accuracy—if the network contains enough “hidden” neurons between the input and output neuronal fields. ◼ So the MLP can solve the problems of nonlinear separable problems and function approximate
Feedforward Sigmoidal Representation Theorems We can explain the theorem in the following two aspects: To improve the NNs'classification ability,we must use multilayer networks,at least one hidden layers. One the other hand,when feedforward-sigmoidal neural networks finely approximate complicated functions,the networks may suffer a like "explosion"of hidden neurons and interconnecting synapses
Feedforward Sigmoidal Representation Theorems ◼ We can explain the theorem in the following two aspects: ◼ To improve the NNs’ classification ability, we must use multilayer networks, at least one hidden layers. ◼ One the other hand, when feedforward –sigmoidal neural networks finely approximate complicated functions, the networks may suffer a like “explosion” of hidden neurons and interconnecting synapses