Types of artificial neural networks
There are many types of artificial neural networks (ANN).
Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research. Most artificial neural networks bear only some resemblance to their more complex biological counterparts, but are very effective at their intended tasks (e.g. classification or segmentation).
Neural networks can be hardware- (neurons are represented by physical components) or software-based (computer models), and can use a variety of topologies and learning algorithms.
- 1 Feedforward
- 2 Regulatory feedback
- 3 Radial basis function (RBF)
- 4 Recurrent neural network
- 5 Modular
- 6 Physical
- 7 Other types
- 8 Dynamic
- 9 Memory networks
- 10 See also
- 11 References
The feedforward neural network was the first and simplest type. In this network the information moves only from the input layer directly through any hidden layers to the output layer without cycles/loops. Feedforward networks can be constructed with various types of units, such as binary McCulloch-Pitts neurons, the simplest of which is the perceptron. Continuous neurons, frequently with sigmoidal activation, are used in the context of backpropagation.
An autoencoder, autoassociator or Diabolo network:19 is similar to the multilayer perceptron (MLP) – with an input layer, an output layer and one or more hidden layers connecting them. However, the output layer has the same number of units as the input layer. Its purpose is to reconstruct its own inputs (instead of emitting a target value). Therefore, autoencoders are unsupervised learning models. An autoencoder is used for unsupervised learning of efficient codings, typically for the purpose of dimensionality reduction and for learning generative models of data.
A probabilistic neural network (PNN) is a four-layer feedforward neural network. The layers are Input, hidden, pattern/summation and output. In the PNN algorithm, the parent probability distribution function (PDF) of each class is approximated by a Parzen window and a non-parametric function. Then, using PDF of each class, the class probability of a new input is estimated and Bayes’ rule is employed to allocate it to the class with the highest posterior probability. It was derived from the Bayesian network and a statistical algorithm called Kernel Fisher discriminant analysis. It is used for classification and pattern recognition.
A time delay neural network (TDNN) is a feedforward architecture for sequential data that recognizes features independent of sequence position. In order to achieve time-shift invariance, delays are added to the input so that multiple data points (points in time) are analyzed together.
In a convolutional neural network (CNN, or ConvNet or shift invariant or space invariant.) the unit connectivity pattern is inspired by the organization of the visual cortex. Units respond to stimuli in a restricted region of space known as the receptive field. Receptive fields partially overlap, over-covering the entire visual field. Unit response can be approximated mathematically by a convolution operation. They are variations of multilayer perceptrons that use minimal preprocessing. They have wide applications in image and video recognition, recommender systems and natural language processing.
Regulatory feedback networks started as a model to explain brain phenomena found during recognition including network-wide bursting and difficulty with similarity found universally in sensory recognition. A mechanism to perform optimization during recognition is created using inhibitory feedback connections back to the same inputs that activate them. This reduces requirements during learning and allows learning and updating to be easier while still being able to perform complex recognition.
Radial basis function (RBF)
Radial basis functions are functions that have a distance criterion with respect to a center. Radial basis functions have been applied as a replacement for the sigmoidal hidden layer transfer characteristic in multi-layer perceptrons. RBF networks have two layers: In the first, input is mapped onto each RBF in the 'hidden' layer. The RBF chosen is usually a Gaussian. In regression problems the output layer is a linear combination of hidden layer values representing mean predicted output. The interpretation of this output layer value is the same as a regression model in statistics. In classification problems the output layer is typically a sigmoid function of a linear combination of hidden layer values, representing a posterior probability. Performance in both cases is often improved by shrinkage techniques, known as ridge regression in classical statistics. This corresponds to a prior belief in small parameter values (and therefore smooth output functions) in a Bayesian framework.
RBF networks have the advantage of avoiding local minima in the same way as multi-layer perceptrons. This is because the only parameters that are adjusted in the learning process are the linear mapping from hidden layer to output layer. Linearity ensures that the error surface is quadratic and therefore has a single easily found minimum. In regression problems this can be found in one matrix operation. In classification problems the fixed non-linearity introduced by the sigmoid output function is most efficiently dealt with using iteratively re-weighted least squares.
RBF networks have the disadvantage of requiring good coverage of the input space by radial basis functions. RBF centres are determined with reference to the distribution of the input data, but without reference to the prediction task. As a result, representational resources may be wasted on areas of the input space that are irrelevant to the task. A common solution is to associate each data point with its own centre, although this can expand the linear system to be solved in the final layer and requires shrinkage techniques to avoid overfitting.
Associating each input datum with an RBF leads naturally to kernel methods such as support vector machines (SVM) and Gaussian processes (the RBF is the kernel function). All three approaches use a non-linear kernel function to project the input data into a space where the learning problem can be solved using a linear model. Like Gaussian processes, and unlike SVMs, RBF networks are typically trained in a maximum likelihood framework by maximizing the probability (minimizing the error). SVMs avoid overfitting by maximizing instead a margin. SVMs outperform RBF networks in most classification applications. In regression applications they can be competitive when the dimensionality of the input space is relatively small.
How RBF networks work
RBF neural networks are conceptually similar to K-Nearest Neighbor (k-NN) models. The basic idea is that similar inputs produce similar outputs.
In the case in of a training set has two predictor variables, x and y and the target variable has two categories, positive and negative. Given a new case with predictor values x=6, y=5.1, how is the target variable computed?
The nearest neighbor classification performed for this example depends on how many neighboring points are considered. If 1-NN is used and the closest point is negative, then the new point should be classified as negative. Alternatively, if 9-NN classification is used and the closest 9 points are considered, then the effect of the surrounding 8 positive points may outweigh the closest 9 (negative) point.
An RBF network positions neurons in the space described by the predictor variables (x,y in this example). This space has as many dimensions as predictor variables. The Euclidean distance is computed from the new point to the center of each neuron, and a radial basis function (RBF) (also called a kernel function) is applied to the distance to compute the weight (influence) for each neuron. The radial basis function is so named because the radius distance is the argument to the function.
Weight = RBF(distance)
Radial Basis Function
The value for the new point is found by summing the output values of the RBF functions multiplied by weights computed for each neuron.
The radial basis function for a neuron has a center and a radius (also called a spread). The radius may be different for each neuron, and, in RBF networks generated by DTREG, the radius may be different in each dimension.
With larger spread, neurons at a distance from a point have a greater influence.
RBF networks have three layers:
- Input layer: One neuron appears in the input layer for each predictor variable. In the case of categorical variables, N-1 neurons are used where N is the number of categories. The input neurons standardizes the value ranges by subtracting the median and dividing by the interquartile range. The input neurons then feed the values to each of the neurons in the hidden layer.
- Hidden layer: This layer has a variable number of neurons (determined by the training process). Each neuron consists of a radial basis function centered on a point with as many dimensions as predictor variables. The spread (radius) of the RBF function may be different for each dimension. The centers and spreads are determined by training. When presented with the x vector of input values from the input layer, a hidden neuron computes the Euclidean distance of the test case from the neuron’s center point and then applies the RBF kernel function to this distance using the spread values. The resulting value is passed to the summation layer.
- Summation layer: The value coming out of a neuron in the hidden layer is multiplied by a weight associated with the neuron and adds to the weighted values of other neurons. This sum becomes the output. For classification problems, one output is produced (with a separate set of weights and summation unit) for each target category. The value output for a category is the probability that the case being evaluated has that category.
The following parameters are determined by the training process:
- The number of neurons in the hidden layer
- The coordinates of the center of each hidden-layer RBF function
- The radius (spread) of each RBF function in each dimension
- The weights applied to the RBF function outputs as they pass to the summation layer
Various methods have been used to train RBF networks. One approach first uses K-means clustering to find cluster centers which are then used as the centers for the RBF functions. However, K-means clustering is computationally intensive and it often does not generate the optimal number of centers. Another approach is to use a random subset of the training points as the centers.
DTREG uses a training algorithm that uses an evolutionary approach to determine the optimal center points and spreads for each neuron. It determines when to stop adding neurons to the network by monitoring the estimated leave-one-out (LOO) error and terminating when the LOO error begins to increase because of overfitting.
The computation of the optimal weights between the neurons in the hidden layer and the summation layer is done using ridge regression. An iterative procedure computes the optimal regularization Lambda parameter that minimizes the generalized cross-validation (GCV) error.
GRNN is an associative memory neural network which is similar to the probabilistic neural network but it is used for regression and approximation not classification.
Recurrent neural network
Recurrent neural networks (RNN) propagate data forward, but also backwards, from later processing stages to earlier stages. RNN can be used as general sequence processors.
This architecture was developed in the 1980s. Its network creates a directed connection between every pair of units. Each has a time-varying, real-valued (more than just zero or one) activation (output). Each connection has a modifiable real-valued weight. Some of the nodes are called labeled nodes, some output nodes, the rest hidden nodes.
For supervised learning in discrete time settings, training sequences of real-valued input vectors become sequences of activations of the input nodes, one input vector at a time. At each time step, each non-input unit computes its current activation as a nonlinear function of the weighted sum of the activations of all units from which it receives connections. The system can explicitly activate (independent of incoming signals) some output units at certain time steps. For example, if the input sequence is a speech signal corresponding to a spoken digit, the final target output at the end of the sequence may be a label classifying the digit. For each sequence, its error is the sum of the deviations of all activations computed by the network from the corresponding target signals. For a training set of numerous sequences, the total error is the sum of the errors of all individual sequences.
To minimize total error, gradient descent can be used to change each weight in proportion to its derivative with respect to the error, provided the non-linear activation functions are differentiable. The standard method is called "backpropagation through time" or BPTT, a generalization of back-propagation for feedforward networks. A more computationally expensive online variant is called "Real-Time Recurrent Learning" or RTRL. Unlike BPTT this algorithm is local in time but not local in space. An online hybrid between BPTT and RTRL with intermediate complexity exists, with variants for continuous time. A major problem with gradient descent for standard RNN architectures is that error gradients vanish exponentially quickly with the size of the time lag between important events. The Long short-term memory architecture overcomes these problems.
In reinforcement learning settings, no teacher provides target signals. Instead a fitness function or reward function or utility function is occasionally used to evaluate performance, which influences its input stream through output units connected to actuators that affect the environment. Variants of evolutionary computation are often used to optimize the weight matrix.
The Hopfield network (like similar attractor-based networks) is of historic interest although it is not a general RNN, as it is not designed to process sequences of patterns. Instead it requires stationary inputs. It is an RNN in which all connections are symmetric. It guarantees that it will converge. If the connections are trained using Hebbian learning the Hopfield network can perform as robust content-addressable memory, resistant to connection alteration.
The Boltzmann machine can be thought of as a noisy Hopfield network. It is one of the first neural networks to demonstrate learning of latent variables (hidden units). Boltzmann machine learning was at first slow to simulate, but the contrastive divergence algorithm speeds up training for Boltzmann machines and Products of Experts.
The self-organizing map (SOM) uses unsupervised learning. A set of neurons learn to map points in an input space to coordinates in an output space. The input space can have different dimensions and topology from the output space, and SOM attempts to preserve these.
Learning vector quantization
Learning vector quantization (LVQ) can be interpreted as a neural network architecture. Prototypical representatives of the classes parameterize, together with an appropriate distance measure, in a distance-based classification scheme.
Simple recurrent networks have three layers, with the addition of a set of "context units" in the input layer. These units connect from the hidden layer or the output layer with a fixed weight of one. At each time step, the input is propagated in a standard feedforward fashion, and then a backpropagation-like learning rule is applied (not performing gradient descent). The fixed back connections leave a copy of the previous values of the hidden units in the context units (since they propagate over the connections before the learning rule is applied).
The echo state network (ESN) is a recurrent neural network with a sparsely connected random hidden layer. The weights of output neurons are the only part of the network that can change (be trained). ESN are good at reproducing certain time series. A variant for spiking neurons is known as liquid state machines.
Long short-term memory
The long short-term memory (LSTM) has no vanishing gradient problem. It works even when with long delays, and it can handle signals that have a mix of low and high frequency components. LSTM RNN outperformed other RNN and other sequence learning methods such as HMM in applications such as language learning and connected handwriting recognition.
Bi-directional RNN, or BRNN, use a finite sequence to predict or label each element of the sequence based on both the past and the future context of the element. This is done by adding the outputs of two RNN: one processing the sequence from left to right, the other one from right to left. The combined outputs are the predictions of the teacher-given target signals. This technique proved to be especially useful when combined with LSTM RNN.
Genetic Scale RNN
A RNN (often a LSTM) where a series is decomposed into a number of scales where every scale informs the primary length between two consecutive points. A first order scale consists of a normal RNN, a second order consists of all points separated by two indices and so on. The Nth order RNN connects the first and last node. The outputs from all the various scales are treated as a Committee of Machines and the associated scores are used genetically for the next iteration.
Biological studies have shown that the human brain operates as a collection of small networks. This realization gave birth to the concept of modular neural networks, in which several small networks cooperate or compete to solve problems.
Committee of machines
A committee of machines (CoM) is a collection of different neural networks that together "vote" on a given example. This generally gives a much better result than individual networks. Because neural networks suffer from local minima, starting with the same architecture and training but using randomly different initial weights often gives vastly different results. A CoM tends to stabilize the result.
The CoM is similar to the general machine learning bagging method, except that the necessary variety of machines in the committee is obtained by training from different starting weights rather than training on different randomly selected subsets of the training data.
The associative neural network (ASNN) is an extension of committee of machines that combines multiple feedforward neural networks and the k-nearest neighbor technique. It uses the correlation between ensemble responses as a measure of distance amid the analyzed cases for the kNN. This corrects the bias of the neural network ensemble. An associative neural network has a memory that can coincide with the training set. If new data become available, the network instantly improves its predictive ability and provides data approximation (self-learns) without retraining. Another important feature of ASNN is the possibility to interpret neural network results by analysis of correlations between data cases in the space of models.
A physical neural network includes electrically adjustable resistance material to simulate artificial synapses. Examples include the ADALINE memristor-based neural network. An optical neural network is a physical implementation of an artificial neural network with optical components.
Instantaneously trained neural networks (ITNN) were inspired by the phenomenon of short-term learning that seems to occur instantaneously. In these networks the weights of the hidden and the output layers are mapped directly from the training vector data. Ordinarily, they work on binary data, but versions for continuous data that require small additional processing exist.
Spiking neural networks (SNN) explicitly consider the timing of inputs. The network input and output are usually represented as a series of spikes (delta function or more complex shapes). SNN can process information in the time domain (signals that vary over time). They are often implemented as recurrent networks. SNN are also a form of pulse computer.
Spiking neural networks with axonal conduction delays exhibit polychronization, and hence could have a very large memory capacity.
SNN and the temporal correlations of neural assemblies in such networks—have been used to model figure/ground separation and region linking in the visual system.
A regulatory feedback network makes inferences using negative feedback. The feedback is used to find the optimal activation of units. It is most similar to a non-parametric method but is different from K-nearest neighbor in that it mathematically emulates feedforward networks.
The neocognitron is a hierarchical, multilayered network that was modeled after the visual cortex. It uses multiple types of units, (originally two, called simple and complex cells), as a cascading model for use in pattern recognition tasks. Local features are extracted by S-cells whose deformation is tolerated by C-cells. Local features in the input are integrated gradually and classified at higher layers. Among the various kinds of neocognitron are systems that can detect multiple patterns in the same input by using back propagation to achieve selective attention. It has been used for pattern recognition tasks and inspired convolutional neural networks.
Dynamic neural networks address nonlinear multivariate behaviour and include (learning of) time-dependent behaviour, such as transient phenomena and delay effects. Techniques to estimate a system process from observed data fall under the general category of system identification.
Cascade correlation is an architecture and supervised learning algorithm. Instead of just adjusting the weights in a network of fixed topology, Cascade-Correlation begins with a minimal network, then automatically trains and adds new hidden units one by one, creating a multi-layer structure. Once a new hidden unit has been added to the network, its input-side weights are frozen. This unit then becomes a permanent feature-detector in the network, available for producing outputs or for creating other, more complex feature detectors. The Cascade-Correlation architecture has several advantages: It learns quickly, determines its own size and topology, retains the structures it has built even if the training set changes and requires no backpropagation.
A neuro-fuzzy network is a fuzzy inference system in the body of an artificial neural network. Depending on the FIS type, several layers simulate the processes involved in a fuzzy inference-like fuzzification, inference, aggregation and defuzzification. Embedding an FIS in a general structure of an ANN has the benefit of using available ANN training methods to find the parameters of a fuzzy system.
Compositional pattern-producing networks (CPPNs) are a variation of artificial neural networks which differ in their set of activation functions and how they are applied. While typical artificial neural networks often contain only sigmoid functions (and sometimes Gaussian functions), CPPNs can include both types of functions and many others. Furthermore, unlike typical artificial neural networks, CPPNs are applied across the entire space of possible inputs so that they can represent a complete image. Since they are compositions of functions, CPPNs in effect encode images at infinite resolution and can be sampled for a particular display at whatever resolution is optimal.
One-shot associative memory
This type of network can add new patterns without re-training. It is done by creating a specific memory structure, which assigns each new pattern to an orthogonal plane using adjacently connected hierarchical arrays. The network offers real-time pattern recognition and high scalability; this requires parallel processing and is thus best suited for platforms such as wireless sensor networks, grid computing, and GPGPUs.
Hierarchical temporal memory
Hierarchical temporal memory (HTM) models some of the structural and algorithmic properties of the neocortex. HTM is a biomimetic model based on memory-prediction theory. HTM is a method for discovering and inferring the high-level causes of observed input patterns and sequences, thus building an increasingly complex model of the world.
HTM combines existing ideas to mimic the neocortex with a simple design that provides many capabilities. HTM combines and extends approaches used in Bayesian networks, spatial and temporal clustering algorithms, while using a tree-shaped hierarchy of nodes that is common in neural networks.
Holographic associative memory
Holographic Associative Memory (HAM) is an analog, correlation-based, associative, stimulus-response system. Information is mapped onto the phase orientation of complex numbers. The memory is effective for associative memory tasks, generalization and pattern recognition with changeable attention. Dynamic search localization is central to biological memory. In visual perception, humans focus on specific objects in a pattern. Humans can change focus from object to object without learning. HAM can mimic this ability by creating explicit representations for focus. It uses a bi-modal representation of pattern and a hologram-like complex spherical weight state-space. HAMs are useful for optical realization because the underlying hyper-spherical computations can be implemented with optical computation.
- Adaptive resonance theory
- Artificial life
- Autoassociative memory
- Biologically inspired computing
- Blue brain
- Connectionist expert system
- Counterpropagation network
- Decision tree
- Expert system
- Genetic algorithm
- In Situ Adaptive Tabulation
- Linear discriminant analysis
- Logistic regression
- Multilayer perceptron
- Neural gas
- Neuroevolution, NeuroEvolution of Augmented Topologies (NEAT)
- Ni1000 chip
- Optical neural network
- Particle swarm optimization
- Predictive analytics
- Principal components analysis
- Simulated annealing
- Systolic array
- Time delay neural network (TDNN)
- University Of Southern California. (2004, June 16). Gray Matters: New Clues Into How Neurons Process Information. ScienceDaily Quote: "... "It's amazing that after a hundred years of modern neuroscience research, we still don't know the basic information processing functions of a neuron," said Bartlett Mel..."
- Weizmann Institute of Science. (2007, April 2). It's Only A Game Of Chance: Leading Theory Of Perception Called Into Question. ScienceDaily Quote: "..."Since the 1980s, many neuroscientists believed they possessed the key for finally beginning to understand the workings of the brain. But we have provided strong evidence to suggest that the brain may not encode information using precise patterns of activity."..."
- University Of California - Los Angeles (2004, December 14). UCLA Neuroscientist Gains Insights Into Human Brain From Study Of Marine Snail. ScienceDaily Quote: "..."Our work implies that the brain mechanisms for forming these kinds of associations might be extremely similar in snails and higher organisms...We don't fully understand even very simple kinds of learning in these animals."..."
- Yale University. (2006, April 13). Brain Communicates In Analog And Digital Modes Simultaneously. ScienceDaily Quote: "...McCormick said future investigations and models of neuronal operation in the brain will need to take into account the mixed analog-digital nature of communication. Only with a thorough understanding of this mixed mode of signal transmission will a truly in depth understanding of the brain and its disorders be achieved, he said..."
- Bengio, Y. (2009). "Learning Deep Architectures for AI" (PDF). Foundations and Trends in Machine Learning. 2: 1–127. CiteSeerX 10.1.1.701.9550. doi:10.1561/2200000006.
- Modeling word perception using the Elman network, Liou, C.-Y., Huang, J.-C. and Yang, W.-C., Neurocomputing, Volume 71, 3150–3157 (2008), doi:10.1016/j.neucom.2008.04.030
- Autoencoder for Words, Liou, C.-Y., Cheng, C.-W., Liou, J.-W., and Liou, D.-R., Neurocomputing, Volume 139, 84–96 (2014), doi:10.1016/j.neucom.2013.09.055
- Auto-Encoding Variational Bayes, Kingma, D.P. and Welling, M., ArXiv e-prints, 2013 arxiv
.org /abs /1312 .6114
- Generating Faces with Torch, Boesen A., Larsen L. and Sonderby S.K., 2015 torch
.ch /blog /2015 /11 /13 /gan .html
- "Competitive probabilistic neural network (PDF Download Available)". ResearchGate. Retrieved 2017-03-16.
- "Archived copy". Archived from the original on 2010-12-18. Retrieved 2012-03-22.CS1 maint: Archived copy as title (link)
- "Archived copy" (PDF). Archived from the original (PDF) on 2012-01-31. Retrieved 2012-03-22.CS1 maint: Archived copy as title (link)
- TDNN Fundamentals, Kapitel aus dem Online Handbuch des SNNS
- Zhang, Wei (1988). "Shift-invariant pattern recognition neural network and its optical architecture". Proceedings of Annual Conference of the Japan Society of Applied Physics.
- Zhang, Wei (1990). "Parallel distributed processing model with local space-invariant interconnections and its optical architecture". Applied Optics. 29 (32): 4790–7. doi:10.1364/ao.29.004790. PMID 20577468.
- "Convolutional Neural Networks (LeNet) – DeepLearning 0.1 documentation". DeepLearning 0.1. LISA Lab. Retrieved 31 August 2013.
- LeCun, Yann. "LeNet-5, convolutional neural networks". Retrieved 16 November 2013.
- van den Oord, Aaron; Dieleman, Sander; Schrauwen, Benjamin (2013-01-01). Burges, C. J. C.; Bottou, L.; Welling, M.; Ghahramani, Z.; Weinberger, K. Q., eds. Deep content-based music recommendation (PDF). Curran Associates, Inc. pp. 2643–2651.
- Collobert, Ronan; Weston, Jason (2008-01-01). A Unified Architecture for Natural Language Processing: Deep Neural Networks with Multitask Learning. Proceedings of the 25th International Conference on Machine Learning. ICML '08. New York, NY, USA: ACM. pp. 160–167. doi:10.1145/1390156.1390177. ISBN 978-1-60558-205-4.
- P. J. Werbos. Generalization of backpropagation with application to a recurrent gas market model. Neural Networks, 1, 1988.
- David E. Rumelhart; Geoffrey E. Hinton; Ronald J. Williams. Learning Internal Representations by Error Propagation.
- A. J. Robinson and F. Fallside. The utility driven dynamic error propagation network. Technical Report CUED/F-INFENG/TR.1, Cambridge University Engineering Department, 1987.
- R. J. Williams and D. Zipser. Gradient-based learning algorithms for recurrent networks and their computational complexity. In Back-propagation: Theory, Architectures and Applications. Hillsdale, NJ: Erlbaum, 1994.
- Schmidhuber, J. (1989). "A local learning algorithm for dynamic feedforward and recurrent networks". Connection Science. 1 (4): 403–412. doi:10.1080/09540098908915650.
- Neural and Adaptive Systems: Fundamentals through Simulation. J.C. Principe, N.R. Euliano, W.C. Lefebvre
- Schmidhuber, J. (1992). "A fixed size storage O(n3) time complexity learning algorithm for fully recurrent continually running networks". Neural Computation. 4 (2): 243–248. doi:10.1162/neco.19184.108.40.206.
- R. J. Williams. Complexity of exact gradient computation algorithms for recurrent neural networks. Technical Report Technical Report NU-CCS-89-27, Boston: Northeastern University, College of Computer Science, 1989.
- Pearlmutter, B. A. (1989). "Learning state space trajectories in recurrent neural networks". Neural Computation. 1 (2): 263–269. doi:10.1162/neco.19220.127.116.113.
- S. Hochreiter. Untersuchungen zu dynamischen neuronalen Netzen. Diploma thesis, Institut f. Informatik, Technische Univ. Munich, 1991.
- S. Hochreiter, Y. Bengio, P. Frasconi, and J. Schmidhuber. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies. In S. C. Kremer and J. F. Kolen, editors, A Field Guide to Dynamical Recurrent Neural Networks. IEEE Press, 2001.
- Hochreiter, S.; Schmidhuber, J. (1997). "Long short-term memory". Neural Computation. 9 (8): 1735–1780. doi:10.1162/neco.1918.104.22.1685.
- Neural Networks as Cybernetic Systems 2nd and revised edition, Holk Cruse 
- Jaeger, H.; Harnessing (2004). "Predicting chaotic systems and saving energy in wireless communication". Science. 304 (5667): 78–80. CiteSeerX 10.1.1.719.2301. doi:10.1126/science.1091277. PMID 15064413.
- W. Maass, T. Natschläger, and H. Markram. A fresh look at real-time computation in generic recurrent neural circuits. Technical report, Institute for Theoretical Computer Science, TU Graz, 2002.
- F. A. Gers and J. Schmidhuber. LSTM recurrent networks learn simple context free and context sensitive languages IEEE Transactions on Neural Networks 12(6):1333–1340, 2001.
- A. Graves, J. Schmidhuber. Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks. Advances in Neural Information Processing Systems 22, NIPS'22, p 545-552, Vancouver, MIT Press, 2009.
- Schuster, Mike; Paliwal, Kuldip K. (1997). "Bidirectional recurrent neural networks". IEEE Transactions on Signal Processing. 45 (11): 2673–2681. CiteSeerX 10.1.1.331.9441. doi:10.1109/78.650093.
- Graves, A.; Schmidhuber, J. (2005). "Framewise phoneme classification with bidirectional LSTM and other neural network architectures". Neural Networks. 18 (5–6): 602–610. CiteSeerX 10.1.1.331.5800. doi:10.1016/j.neunet.2005.06.042. PMID 16112549.
- Schmidhuber, J. (1992). "Learning complex, extended sequences using the principle of history compression". Neural Computation. 4 (2): 234–242. doi:10.1162/neco.1922.214.171.124.
- Dynamic Representation of Movement Primitives in an Evolved Recurrent Neural Network
- "Associative Neural Network". www.vcclab.org. Retrieved 2017-06-17.
- Anderson, James A.; Rosenfeld, Edward (2000). Talking Nets: An Oral History of Neural Networks. ISBN 9780262511117.
- Gerstner; Kistler. "Spiking Neuron Models: Single Neurons, Populations, Plasticity". icwww.epfl.ch. Retrieved 2017-06-18. Freely available online textbook
- Izhikevich EM (February 2006). "Polychronization: computation with spikes". Neural Computation. 18 (2): 245–82. doi:10.1162/089976606775093882. PMID 16378515.
- Achler T., Omar C., Amir E., "Shedding Weights: More With Less", IEEE Proc. International Joint Conference on Neural Networks, 2008
- David H. Hubel and Torsten N. Wiesel (2005). Brain and visual perception: the story of a 25-year collaboration. Oxford University Press US. p. 106. ISBN 978-0-19-517618-6.
- Hubel, DH; Wiesel, TN (October 1959). "Receptive fields of single neurones in the cat's striate cortex". J. Physiol. 148 (3): 574–91. doi:10.1113/jphysiol.1959.sp006308. PMC 1363130. PMID 14403679.
- Fukushima 1987, p. 83.
- Fukushima 1987, p. 84.
- Fukushima 2007
- Fukushima 1987, pp.81, 85
- LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey (2015). "Deep learning". Nature. 521 (7553): 436–444. doi:10.1038/nature14539. PMID 26017442.
- Fahlman, Scott E.; Lebiere, Christian (August 29, 1991). "The Cascade-Correlation Learning Architecture" (PDF). Carnegie Mellon University. Retrieved 4 October 2014.
- B.B. Nasution, A.I. Khan, A Hierarchical Graph Neuron Scheme for Real-Time Pattern Recognition, IEEE Transactions on Neural Networks, vol 19(2), 212-229, Feb. 2008
- Sutherland, John G. (1 January 1990). "A holographic model of memory, learning and expression". International Journal of Neural Systems. 01 (3): 259–267. doi:10.1142/S0129065790000163.