### Jackfoolery: The Presidential Campaign of the Eunuch, Jack Sullivan

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Global relationship between anatomical connectivity and activity propagation in the cerebral cortex. Computing and stability in cortical networks. Global and local synchrony of coupled neurons in small-world networks.

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Epilepsy as a Dynamic Disease Berlin: The columnar organization of the neocortex. Organization of excitable dynamics in hierarchical biological networks. Self-sustained dynamics and excitability of neural microcircuits. Power laws, Pareto distributions and Zipf's law.

Epidemic spreading in scale-free networks. A default mode of brain function: Neuroimage 37 , — Hierarchical organization of modularity in metabolic networks. Science , — Neuronal interconnection as a function of brain size. Dynamical reconnection and stability constraints on cortical network architecture. Self-sustained activity in a small-world network of excitable neurons. Modules are trained in order, so lower-layer weights W are known at each stage. The function performs the element-wise logistic sigmoid operation.

Each block estimates the same final label class y , and its estimate is concatenated with original input X to form the expanded input for the next block. Thus, the input to the first block contains the original data only, while downstream blocks' input adds the output of preceding blocks. Then learning the upper-layer weight matrix U given other weights in the network can be formulated as a convex optimization problem:.

Unlike other deep architectures, such as DBNs, the goal is not to discover the transformed feature representation. The structure of the hierarchy of this kind of architecture makes parallel learning straightforward, as a batch-mode optimization problem. This architecture is a DSN extension. It offers two important improvements: While parallelization and scalability are not considered seriously in conventional DNNs , [] [] [] all learning for DSN s and TDSN s is done in batch mode, to allow parallelization.

The basic architecture is suitable for diverse tasks such as classification and regression.

The need for deep learning with real-valued inputs, as in Gaussian restricted Boltzmann machines, led to the spike-and-slab RBM ss RBM , which models continuous-valued inputs with strictly binary latent variables. The difference is in the hidden layer, where each hidden unit has a binary spike variable and a real-valued slab variable.

A spike is a discrete probability mass at zero, while a slab is a density over continuous domain; [] their mixture forms a prior. One of these terms enables the model to form a conditional distribution of the spike variables by marginalizing out the slab variables given an observation. Compound hierarchical-deep models compose deep networks with non-parametric Bayesian models. However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input a distributed representation and must be adjusted together high degree of freedom.

Limiting the degree of freedom reduces the number of parameters to learn, facilitating learning of new classes from few examples.

Hierarchical Bayesian HB models allow learning from few examples, for example [] [] [] [] [] for computer vision, statistics and cognitive science. Compound HD architectures aim to integrate characteristics of both HB and deep networks. It is a full generative model , generalized from abstract concepts flowing through the layers of the model, which is able to synthesize new examples in novel classes that look "reasonably" natural.

All the levels are learned jointly by maximizing a joint log-probability score. A deep predictive coding network DPCN is a predictive coding scheme that uses top-down information to empirically adjust the priors needed for a bottom-up inference procedure by means of a deep, locally connected, generative model. This works by extracting sparse features from time-varying observations using a linear dynamical model. Then, a pooling strategy is used to learn invariant feature representations. These units compose to form a deep architecture and are trained by greedy layer-wise unsupervised learning.

The layers constitute a kind of Markov chain such that the states at any layer depend only on the preceding and succeeding layers.

DPCNs predict the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from previous states. DPCNs can be extended to form a convolutional network. Integrating external memory with Artificial neural networks dates to early research in distributed representations [] and Kohonen 's self-organizing maps.

For example, in sparse distributed memory or hierarchical temporal memory , the patterns encoded by neural networks are used as addresses for content-addressable memory , with "neurons" essentially serving as address encoders and decoders. However, the early controllers of such memories were not differentiable. Apart from long short-term memory LSTM , other approaches also added differentiable memory to recurrent functions. Neural Turing machines [] couple LSTM networks to external memory resources, with which they can interact by attentional processes. The combined system is analogous to a Turing machine but is differentiable end-to-end, allowing it to be efficiently trained by gradient descent.

Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting and associative recall from input and output examples. They out-performed Neural turing machines, long short-term memory systems and memory networks on sequence-processing tasks. Approaches that represent previous experiences directly and use a similar experience to form a local model are often called nearest neighbour or k-nearest neighbors methods. Documents similar to a query document can then be found by accessing all the addresses that differ by only a few bits from the address of the query document.

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Unlike sparse distributed memory that operates on bit addresses, semantic hashing works on 32 or bit addresses found in a conventional computer architecture. Memory networks [] [] are another extension to neural networks incorporating long-term memory. The long-term memory can be read and written to, with the goal of using it for prediction. These models have been applied in the context of question answering QA where the long-term memory effectively acts as a dynamic knowledge base and the output is a textual response.

That can analyze large volumes of data and identify objects at the actual speed of light. Deep neural networks can be potentially improved by deepening and parameter reduction, while maintaining trainability. While training extremely deep e. Such systems operate on probability distribution vectors stored in memory cells and registers.

Thus, the model is fully differentiable and trains end-to-end. The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently — unlike models like LSTM, whose number of parameters grows quadratically with memory size. Encoder—decoder frameworks are based on neural networks that map highly structured input to highly structured output. The approach arose in the context of machine translation , [] [] [] where the input and output are written sentences in two natural languages.

Multilayer kernel machines MKM are a way of learning highly nonlinear functions by iterative application of weakly nonlinear kernels.

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They use the kernel principal component analysis KPCA , [] as a method for the unsupervised greedy layer-wise pre-training step of deep learning. For the sake of dimensionality reduction of the updated representation in each layer, a supervised strategy selects the best informative features among features extracted by KPCA. A more straightforward way to use kernel machines for deep learning was developed for spoken language understanding.

The number of levels in the deep convex network is a hyper-parameter of the overall system, to be determined by cross validation. Neural architecture search NAS uses machine learning to automate the design of Artificial neural networks. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset and use the results as feedback to teach the NAS network. ANN capabilities fall within the following broad categories: Because of their ability to reproduce and model nonlinear processes, Artificial neural networks have found many applications in a wide range of disciplines.

Application areas include system identification and control vehicle control, trajectory prediction, [] process control , natural resource management , quantum chemistry , [] game-playing and decision making backgammon , chess , poker , pattern recognition radar systems, face identification , signal classification, [] object recognition and more , sequence recognition gesture, speech, handwritten and printed text recognition , medical diagnosis , finance [] e. Artificial neural networks have been used to diagnose cancers, including lung cancer , [] prostate cancer , colorectal cancer [] and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.

Artificial neural networks have been used to accelerate reliability analysis of infrastructures subject to natural disasters.

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Artificial neural networks have also been used for building black-box models in geoscience: Many types of models are used, defined at different levels of abstraction and modeling different aspects of neural systems. They range from models of the short-term behavior of individual neurons , [] models of how the dynamics of neural circuitry arise from interactions between individual neurons and finally to models of how behavior can arise from abstract neural modules that represent complete subsystems.

These include models of the long-term, and short-term plasticity, of neural systems and their relations to learning and memory from the individual neuron to the system level. The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.

A specific recurrent architecture with rational valued weights as opposed to full precision real number -valued weights has the full power of a universal Turing machine , [] using a finite number of neurons and standard linear connections. Further, the use of irrational values for weights results in a machine with super-Turing power. Models' "capacity" property roughly corresponds to their ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.

Models may not consistently converge on a single solution, firstly because many local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical. However, for CMAC neural network, a recursive least squares algorithm was introduced to train it, and this algorithm can be guaranteed to converge in one step. Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training.

This arises in convoluted or over-specified systems when the capacity of the network significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use cross-validation and similar techniques to check for the presence of over-training and optimally select hyperparameters to minimize the generalization error. The second is to use some form of regularization.

This concept emerges in a probabilistic Bayesian framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: Supervised neural networks that use a mean squared error MSE cost function can use formal statistical methods to determine the confidence of the trained model.

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This value can then be used to calculate the confidence interval of the output of the network, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified. By assigning a softmax activation function , a generalization of the logistic function , on the output layer of the neural network or a softmax component in a component-based neural network for categorical target variables, the outputs can be interpreted as posterior probabilities.

This is very useful in classification as it gives a certainty measure on classifications. A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation. Improving the training efficiency and convergence capability has always been an ongoing research area for neural network. For example, by introducing a recursive least squares algorithm for CMAC neural network, the training process only takes one step to converge. No neural network has solved computationally difficult problems such as the n-Queens problem, the travelling salesman problem , or the problem of factoring large integers.

A fundamental objection is that they do not reflect how real neurons function. Back propagation is a critical part of most artificial neural networks, although no such mechanism exists in biological neural networks. Sensor neurons fire action potentials more frequently with sensor activation and muscle cells pull more strongly when their associated motor neurons receive action potentials more frequently. The motivation behind Artificial neural networks is not necessarily to strictly replicate neural function, but to use biological neural networks as an inspiration.

A central claim of Artificial neural networks is therefore that it embodies some new and powerful general principle for processing information. Unfortunately, these general principles are ill-defined. It is often claimed that they are emergent from the network itself. This allows simple statistical association the basic function of artificial neural networks to be described as learning or recognition. Alexander Dewdney commented that, as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are.

No human hand or mind intervenes; solutions are found as if by magic; and no one, it seems, has learned anything". Biological brains use both shallow and deep circuits as reported by brain anatomy, [] displaying a wide variety of invariance. Weng [] argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.

Large and effective neural networks require considerable computing resources. Schmidhuber notes that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: Neuromorphic engineering addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Arguments against Dewdney's position are that neural networks have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft [] to detecting credit card fraud to mastering the game of Go.

Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, what hasn't?

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In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having. Although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network.

Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs non-local learning and shallow vs deep architecture. Advocates of hybrid models combining neural networks and symbolic approaches , claim that such a mixture can better capture the mechanisms of the human mind. Artificial neural networks have many variations. The simplest, static types have one or more static components, including number of units, number of layers, unit weights and topology.

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Dynamic types allow one or more of these to change during the learning process. The latter are much more complicated, but can shorten learning periods and produce better results. Some types operate purely in hardware, while others are purely software and run on general purpose computers. A single-layer feedforward artificial neural network.