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Monday, January 15, 2024

Artificial neural network

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Artificial_neural_network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains.

An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold.

Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.

A network is typically called a deep neural network if it has at least 2 hidden layers.

Training

Neural networks are typically trained through empirical risk minimization. This method is based on the idea of optimizing the network's parameters to minimize the difference, or empirical risk, between the predicted output and the actual target values in a given dataset. Gradient based methods such as backpropagation are usually used to estimate the parameters of the network. During the training phase, ANNs learn from labeled training data by iteratively updating their parameters to minimize a defined loss function. This method allows the network to generalize to unseen data.

Simplified example of training a neural network in object detection: The network is trained by multiple images that are known to depict starfish and sea urchins, which are correlated with "nodes" that represent visual features. The starfish match with a ringed texture and a star outline, whereas most sea urchins match with a striped texture and oval shape. However, the instance of a ring textured sea urchin creates a weakly weighted association between them.

Subsequent run of the network on an input image (left): The network correctly detects the starfish. However, the weakly weighted association between ringed texture and sea urchin also confers a weak signal to the latter from one of two intermediate nodes. In addition, a shell that was not included in the training gives a weak signal for the oval shape, also resulting in a weak signal for the sea urchin output. These weak signals may result in a false positive result for sea urchin.
In reality, textures and outlines would not be represented by single nodes, but rather by associated weight patterns of multiple nodes.

History

The simplest kind of feedforward neural network (FNN) is a linear 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 at each node. The mean squared errors between these calculated outputs and the given target values are minimized by creating an adjustment to the weights. This technique has been known for over two centuries as the method of least squares or linear regression. It was used as a means of finding a good rough linear fit to a set of points by Legendre (1805) and Gauss (1795) for the prediction of planetary movement.

Wilhelm Lenz and Ernst Ising created and analyzed the Ising model (1925) which is essentially a non-learning artificial recurrent neural network (RNN) consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was popularised by John Hopfield in 1982.

Warren McCulloch and Walter Pitts (1943) also considered a non-learning computational model for neural networks. In the late 1940s, D. O. Hebb created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Farley and Wesley A. Clark (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. In 1958, psychologist Frank Rosenblatt invented the perceptron, the first implemented artificial neural network, funded by the United States Office of Naval Research.

The invention of the perceptron raised public excitement for research in Artificial Neural Networks, causing the US government to drastically increase funding into deep learning research. This led to "the golden age of AI" fueled by the optimistic claims made by computer scientists regarding the ability of perceptrons to emulate human intelligence. For example, in 1957 Herbert Simon famously said:

It is not my aim to surprise or shock you—but the simplest way I can summarize is to say that there are now in the world machines that think, that learn and that create. Moreover, their ability to do these things is going to increase rapidly until—in a visible future—the range of problems they can handle will be coextensive with the range to which the human mind has been applied.

However, this wasn't the case as research stagnated following the work of Minsky and Papert (1969), who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to train useful neural networks. This, along with other factors such as the 1973 Lighthill report by James Lighthill stating that research in Artificial Intelligence has not "produced the major impact that was then promised," shutting funding in research into the field of AI in all but two universities in the UK and in many major institutions across the world. This ushered an era called the AI Winter with reduced research into connectionism due to a decrease in government funding and an increased stress on symbolic artificial intelligence in the United States and other Western countries.

During the AI Winter era, however, research outside the United States continued, especially in Eastern Europe. By the time Minsky and Papert's book on Perceptrons came out, methods for training multilayer perceptrons (MLPs) were already known. The first deep learning Multi Layer Perceptron (MLP) was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, as the Group Method of Data Handling. The first deep learning MLP trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari. In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes.

Self-organizing maps (SOMs) were described by Teuvo Kohonen in 1982. SOMs are neurophysiologically inspired neural networks that learn low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using competitive learning.

The convolutional neural network (CNN) architecture with convolutional layers and downsampling layers was introduced by Kunihiko Fukushima in 1980. He called it the neocognitron. In 1969, he also introduced the ReLU (rectified linear unit) activation function. The rectifier has become the most popular activation function for CNNs and deep neural networks in general. CNNs have become an essential tool for computer vision.

The backpropagation algorithm is an efficient application of the Leibniz chain rule (1673)^[40] to networks of differentiable nodes. It is also known as the reverse mode of automatic differentiation or reverse accumulation, due to Seppo Linnainmaa (1970). The term "back-propagating errors" was introduced in 1962 by Frank Rosenblatt, but he did not have an implementation of this procedure, although Henry J. Kelley and Bryson had dynamic programming based continuous precursors of backpropagation already in 1960–61 in the context of control theory. In 1973, Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients. In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard. In 1986 Rumelhart, Hinton and Williams showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence.

The time delay neural network (TDNN) of Alex Waibel (1987) combined convolutions and weight sharing and backpropagation. In 1988, Wei Zhang et al. applied backpropagation to a CNN (a simplified Neocognitron with convolutional interconnections between the image feature layers and the last fully connected layer) for alphabet recognition. In 1989, Yann LeCun et al. trained a CNN to recognize handwritten ZIP codes on mail. In 1992, max-pooling for CNNs was introduced by Juan Weng et al. to help with least-shift invariance and tolerance to deformation to aid 3D object recognition.LeNet-5 (1998), a 7-level CNN by Yann LeCun et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32x32 pixel images.

From 1988 onward, the use of neural networks transformed the field of protein structure prediction, in particular when the first cascading networks were trained on profiles (matrices) produced by multiple sequence alignments.

In the 1980s, backpropagation did not work well for deep FNNs and RNNs. To overcome this problem, Juergen Schmidhuber (1992) proposed a hierarchy of RNNs pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales. This can substantially facilitate downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network. In 1993, a chunker solved a deep learning task whose depth exceeded 1000.

In 1992, Juergen Schmidhuber also published an alternative to RNNs which is now called a linear Transformer or a Transformer with linearized self-attention (save for a normalization operator). It learns internal spotlights of attention: a slow feedforward neural network learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns FROM and TO (which are now called key and value for self-attention). This fast weight attention mapping is applied to a query pattern.

The modern Transformer was introduced by Ashish Vaswani et al. in their 2017 paper "Attention Is All You Need." It combines this with a softmax operator and a projection matrix. Transformers have increasingly become the model of choice for natural language processing. Many modern large language models such as ChatGPT, GPT-4, and BERT use it. Transformers are also increasingly being used in computer vision.

In 1991, Juergen Schmidhuber also published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity."

In 2014, this principle was used in a generative adversarial network (GAN) by Ian Goodfellow et al. Here the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. This can be used to create realistic deepfakes. Excellent image quality is achieved by Nvidia's StyleGAN (2018) based on the Progressive GAN by Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Here the GAN generator is grown from small to large scale in a pyramidal fashion.

Sepp Hochreiter's diploma thesis (1991) was called "one of the most important documents in the history of machine learning" by his supervisor Juergen Schmidhuber. Hochreiter identified and analyzed the vanishing gradient problem and proposed recurrent residual connections to solve it. This led to the deep learning method called long short-term memory (LSTM), published in Neural Computation (1997). LSTM recurrent neural networks can learn "very deep learning" tasks with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. The "vanilla LSTM" with forget gate was introduced in 1999 by Felix Gers, Schmidhuber and Fred Cummins. LSTM has become the most cited neural network of the 20th century. In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used the LSTM principle to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network. This has become the most cited neural network of the 21st century.

The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), in the form of complementary MOS (CMOS) technology, enabled increasing MOS transistor counts in digital electronics. This provided more processing power for the development of practical artificial neural networks in the 1980s.

Neural networks' early successes included predicting the stock market and in 1995 a (mostly) self-driving car.

Geoffrey Hinton et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine to model each layer. In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images. Unsupervised pre-training and increased computing power from GPUs and distributed computing allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning".

Ciresan and colleagues (2010) showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks. Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in pattern recognition and handwriting recognition. For example, the bi-directional and multi-dimensional long short-term memory (LSTM) of Graves et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned.

Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance on benchmarks such as traffic sign recognition (IJCNN 2012).

Models

Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals

ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, abandoning attempts to remain true to their biological precursors. ANNs have the ability to learn and model non-linearities and complex relationships. This is achieved by neurons being connected in various patterns, allowing the output of some neurons to become the input of others. The network forms a directed, weighted graph.

An artificial neural network consists of simulated neurons. Each neuron is connected to other nodes via links like a biological axon-synapse-dendrite connection. All the nodes connected by links take in some data and use it to perform specific operations and tasks on the data. Each link has a weight, determining the strength of one node's influence on another, allowing weights to choose the signal between neurons.

Artificial neurons

ANNs are composed of artificial neurons which are conceptually derived from biological neurons. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons. The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final output neurons of the neural net accomplish the task, such as recognizing an object in an image.

To find the output of the neuron we take the weighted sum of all the inputs, weighted by the weights of the connections from the inputs to the neuron. We add a bias term to this sum. This weighted sum is sometimes called the activation. This weighted sum is then passed through a (usually nonlinear) activation function to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.

Organization

The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be pooling, where a group of neurons in one layer connects to a single neuron in the next layer, thereby reducing the number of neurons in that layer. Neurons with only such connections form a directed acyclic graph and are known as feedforward networks. Alternatively, networks that allow connections between neurons in the same or previous layers are known as recurrent networks.

Hyperparameter

A hyperparameter is a constant parameter whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size. The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.

Learning

Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of optimization theory and statistical estimation.

Learning rate

The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation. A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate. The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.

Cost function

While it is possible to define a cost function ad hoc, frequently the choice is determined by the function's desirable properties (such as convexity) or because it arises from the model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost).

Backpropagation

Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the gradient (the derivative) of the cost function associated with a given state with respect to the weights. The weight updates can be done via stochastic gradient descent or other methods, such as extreme learning machines, "no-prop" networks, training without backtracking, "weightless" networks, and non-connectionist neural networks.

Learning paradigms

Machine learning is commonly separated into three main learning paradigms, supervised learning, unsupervised learning and reinforcement learning. Each corresponds to a particular learning task.

Supervised learning

Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions. A commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for handwriting, speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.

Unsupervised learning

In unsupervised learning, input data is given along with the cost function, some function of the data $x$ and the network's output. The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model $f (x) = a$ where $a$ is a constant and the cost $C = E [(x - f (x))^{2}]$ . Minimizing this cost produces a value of $a$ that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the mutual information between $x$ and $f (x)$ , whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general estimation problems; the applications include clustering, the estimation of statistical distributions, compression and filtering.

Reinforcement learning

In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In reinforcement learning, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an instantaneous cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly.

Formally the environment is modeled as a Markov decision process (MDP) with states $s_{1}, . . ., s_{n} \in S$ and actions $a_{1}, . . ., a_{m} \in A$ . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution $P (c_{t} | s_{t})$ , the observation distribution $P (x_{t} | s_{t})$ and the transition distribution $P (s_{t + 1} | s_{t}, a_{t})$ , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the lowest-cost MC.

ANNs serve as the learning component in such applications. Dynamic programming coupled with ANNs (giving neurodynamic programming) has been applied to problems such as those involved in vehicle routing, video games, natural resource management and medicine because of ANNs ability to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

Self-learning

Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named crossbar adaptive array (CAA). It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion. Given the memory matrix, W =||w(a,s)||, the crossbar self-learning algorithm in each iteration performs the following computation:

  In situation s perform action a;
  Receive consequence situation s';
  Compute emotion of being in consequence situation v(s');
  Update crossbar memory w'(a,s) = w(a,s) + v(s').

The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.

Neuroevolution

Neuroevolution can create neural network topologies and weights using evolutionary computation. It is competitive with sophisticated gradient descent approaches. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".

Stochastic neural network

Stochastic neural networks originating from Sherrington–Kirkpatrick models are a type of artificial neural network built by introducing random variations into the network, either by giving the network's artificial neurons stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for optimization problems, since the random fluctuations help the network escape from local minima. Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks.

Other

In a Bayesian framework, a distribution over the set of allowed models is chosen to minimize the cost. Evolutionary methods, gene expression programming, simulated annealing, expectation-maximization, non-parametric methods and particle swarm optimization are other learning algorithms. Convergent recursion is a learning algorithm for cerebellar model articulation controller (CMAC) neural networks.

Modes

Two modes of learning are available: stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.

Types

ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter is much more complicated but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers.

Some of the main breakthroughs include: convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data; long short-term memory avoid the vanishing gradient problem and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition, text-to-speech synthesis, and photo-real talking heads; competitive networks such as generative adversarial networks in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game or on deceiving the opponent about the authenticity of an input.

Network design

Neural architecture search (NAS) uses machine learning to automate ANN design. 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. Available systems include AutoML and AutoKeras. scikit-learn library provides functions to help with building a deep network from scratch. We can then implement a deep network with TensorFlow or Keras.

Design issues include deciding the number, type, and connectedness of network layers, as well as the size of each and the connection type (full, pooling, etc. ).

Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc.

The Python code snippet provides an overview of the training function, which uses the training dataset, number of hidden layer units, learning rate, and number of iterations as parameters:

def train(X, y, n_hidden, learning_rate, n_iter):
    m, n_input = X.shape

    # 1. random initialize weights and biases
    w1 = np.random.randn(n_input, n_hidden)
    b1 = np.zeros((1, n_hidden))
    w2 = np.random.randn(n_hidden, 1)
    b2 = np.zeros((1, 1))

    # 2. in each iteration, feed all layers with the latest weights and biases
    for i in range(n_iter + 1):

        z2 = np.dot(X, w1) + b1

        a2 = sigmoid(z2)

        z3 = np.dot(a2, w2) + b2

        a3 = z3

        dz3 = a3 - y

        dw2 = np.dot(a2.T, dz3)

        db2 = np.sum(dz3, axis=0, keepdims=True)

        dz2 = np.dot(dz3, w2.T) * sigmoid_derivative(z2)

        dw1 = np.dot(X.T, dz2)

        db1 = np.sum(dz2, axis=0)

        # 3. update weights and biases with gradients
        w1 -= learning_rate * dw1 / m
        w2 -= learning_rate * dw2 / m
        b1 -= learning_rate * db1 / m
        b2 -= learning_rate * db2 / m

        if i % 1000 == 0:
            print("Epoch", i, "loss: ", np.mean(np.square(dz3)))

    model = {"w1": w1, "b1": b1, "w2": w2, "b2": b2}
    return model

Using artificial neural networks requires an understanding of their characteristics.

Choice of model: This depends on the data representation and the application. Overly complex models are slow learning.
Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation.
Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust.

ANN capabilities fall within the following broad categories:

Function approximation, or regression analysis, including time series prediction, fitness approximation and modeling.
Classification, including pattern and sequence recognition, novelty detection and sequential decision making.
Data processing, including filtering, clustering, blind source separation and compression.
Robotics, including directing manipulators and prostheses.

Applications

Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include system identification and control (vehicle control, trajectory prediction, process control, natural resource management), quantum chemistry, general game playing, pattern recognition (radar systems, face identification, signal classification, 3D reconstruction, object recognition and more), sensor data analysis, sequence recognition (gesture, speech, handwritten and printed text recognition), medical diagnosis, finance (e.g. ex-ante models for specific financial long-run forecasts and artificial financial markets), data mining, visualization, machine translation, social network filtering and e-mail spam filtering. ANNs have been used to diagnose several types of cancers and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.

ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters and to predict foundation settlements. It can also be useful to mitigate flood by the use of ANNs for modelling rainfall-runoff. ANNs have also been used for building black-box models in geoscience: hydrology, ocean modelling and coastal engineering, and geomorphology. ANNs have been employed in cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware, for identifying domains belonging to threat actors and for detecting URLs posing a security risk. Research is underway on ANN systems designed for penetration testing, for detecting botnets, credit cards frauds and network intrusions.

ANNs have been proposed as a tool to solve partial differential equations in physics and simulate the properties of many-body open quantum systems. In brain research ANNs have studied short-term behavior of individual neurons, the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level.

Theoretical properties

Computational power

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 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.

Capacity

A model's "capacity" property corresponds to its 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. Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book which summarizes work by Thomas Cover. The capacity of a network of standard neurons (not convolutional) can be derived by four rules that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the VC dimension. VC Dimension uses the principles of measure theory and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in, the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.

Convergence

Models may not consistently converge on a single solution, firstly because 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.

Another issue worthy to mention is that training may cross some Saddle point which may lead the convergence to the wrong direction.

The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of affine models.^[202]^[203] Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks. This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions.

Generalization and statistics

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 network capacity 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 to 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: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.

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. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of network output, 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 network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications.

The softmax activation function is:

y_{i} = \frac{e^{x_{i}}}{\sum_{j = 1}^{c} e^{x_{j}}}

Criticism

Training

A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for CMAC.

Theory

A central claim of ANNs is that they embody new and powerful general principles for processing information. These 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. In 1997, 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". One response to Dewdney is that neural networks handle many complex and diverse tasks, ranging from autonomously flying aircraft to detecting credit card fraud to mastering the game of Go.

Technology writer Roger Bridgman commented:

Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
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.

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.

Hardware

Large and effective neural networks require considerable computing resources. While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may consume vast amounts of memory and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous CPU power and time.

Schmidhuber noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before. The use of accelerators such as FPGAs and GPUs can reduce training times from months to days.

Neuromorphic engineering or a physical neural network addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a Tensor Processing Unit, or TPU.

Practical counterexamples

Analyzing what has been learned by an ANN is much easier than analyzing 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.

Hybrid approaches

Advocates of hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.

Dataset bias

Neural networks are dependent on the quality of the data they are trained on, thus low quality data with imbalanced representativeness can lead to the model learning and perpetuating societal biases. These inherited biases become especially critical when the ANNs are integrated into real-world scenarios where the training data may be imbalanced due to the scarcity of data for a specific race, gender or other attribute. This imbalance can result in the model having inadequate representation and understanding of underrepresented groups, leading to discriminatory outcomes that exasperate societal inequalities, especially in applications like facial recognition, hiring processes, and law enforcement. For example, in 2018, Amazon had to scrap a recruiting tool because the model favored men over women for jobs in software engineering due to the higher number of male workers in the field. The program would penalize any resume with the word "woman" or the name of any women's college. However, the use of synthetic data can help reduce dataset bias and increase representation in datasets.

Recent Advancements and Future Directions

Artificial Neural Networks (ANNs) are a pivotal element in the realm of machine learning, resembling the structure and function of the human brain. ANNs have undergone significant advancements, particularly in their ability to model complex systems, handle large data sets, and adapt to various types of applications. Their evolution over the past few decades has been marked by notable methodological developments and a broad range of applications in fields such as image processing, speech recognition, natural language processing, finance, and medicine.

Image Processing

In the realm of image processing, ANNs have made significant strides. They are employed in tasks such as image classification, object recognition, and image segmentation. For instance, deep convolutional neural networks (CNNs) have been instrumental in handwritten digit recognition, achieving state-of-the-art performance. This demonstrates the ability of ANNs to effectively process and interpret complex visual information, leading to advancements in fields ranging from automated surveillance to medical imaging.

Speech Recognition

ANNs have revolutionized speech recognition technology. By modeling speech signals, they are used for tasks like speaker identification and speech-to-text conversion. Deep neural network architectures have introduced significant improvements in large vocabulary continuous speech recognition, outperforming traditional techniques. These advancements have facilitated the development of more accurate and efficient voice-activated systems, enhancing user interfaces in technology products.

Natural Language Processing

In natural language processing, ANNs are vital for tasks such as text classification, sentiment analysis, and machine translation. They have enabled the development of models that can accurately translate between languages, understand the context and sentiment in textual data, and categorize text based on content. This has profound implications for automated customer service, content moderation, and language understanding technologies.

Control Systems

In the domain of control systems, ANNs are applied to model dynamic systems for tasks such as system identification, control design, and optimization. The backpropagation algorithm, for instance, has been employed for training multi-layer feedforward neural networks, which are instrumental in system identification and control applications. This highlights the versatility of ANNs in adapting to complex dynamic environments, which is crucial in automation and robotics.

Finance

Artificial Neural Networks (ANNs) have made a significant impact on the financial sector, particularly in stock market prediction and credit scoring. These powerful AI systems can process vast amounts of financial data, recognize complex patterns, and forecast stock market trends, aiding investors and risk managers in making informed decisions. In credit scoring, ANNs offer data-driven, personalized assessments of creditworthiness, improving the accuracy of default predictions and automating the lending process. While ANNs offer numerous benefits, they also require high-quality data and careful tuning, and their "black-box" nature can pose challenges in interpretation. Nevertheless, ongoing advancements suggest that ANNs will continue to play a pivotal role in shaping the future of finance, offering valuable insights and enhancing risk management strategies.

Medicine

Artificial Neural Networks (ANNs) are revolutionizing the field of medicine with their ability to process and analyze vast medical datasets. They have become instrumental in enhancing diagnostic accuracy, especially in interpreting complex medical imaging for early disease detection, and in predicting patient outcomes for personalized treatment planning. In drug discovery, ANNs expedite the identification of potential drug candidates and predict their efficacy and safety, significantly reducing development time and costs. Additionally, their application in personalized medicine and healthcare data analysis is leading to more tailored therapies and efficient patient care management. Despite these advancements, challenges such as data privacy and model interpretability remain, with ongoing research aimed at addressing these issues and expanding the scope of ANN applications in medicine.

Content Creation

ANNs such as Generative Adversarial Networks (GAN) and transformers are also being used for content creation across numerous industries. This is because Deep Learning models are able to learn the style of an artist or musician from huge datasets and generate completely new artworks and music compositions. For instance, DALL-E is a deep neural network trained on 650 million pairs of images and texts across the internet that can create artworks based on text entered by the user. In the field of music, transformers are being used to create original music for commercials and documentaries through companies such as AIVA and Jukedeck. In the marketing industry generative models are being used to create personalized advertisements for consumers. Additionally, major film companies are partnering with technology companies to analyze the financial success of a film, such as the partnership between Warner Bros and technology company Cinelytic established in 2020. Furthermore, neural networks have found uses in video game creation, where Non Player Characters (NPCs) can make decisions based on all the characters currently in the game.

Why there is anything at all

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Why_there_is_anything_at_all

"Why is there anything at all?" or "why is there something rather than nothing?" is a question about the reason for basic existence which has been raised or commented on by a range of philosophers and physicists, including Gottfried Wilhelm Leibniz, Ludwig Wittgenstein, and Martin Heidegger, who called it "the fundamental question of metaphysics".

Introductory points

There is something

No experiment could support the hypothesis 'There is nothing' because any observation obviously implies the existence of an observer.

Defining the question

The question is usually taken as concerning practical causality (rather than a moral reason for), and posed totally and comprehensively, rather than concerning the existence of anything specific, such as the universe or multiverse, the Big Bang, God, mathematical and physical laws, time or consciousness. It can be seen as an open metaphysical question, rather than a search for an exact answer.

The circled dot was used by the Pythagoreans and later Greeks to represent the first metaphysical being and the metaphysical life, the Monad or the Absolute.

On timescales

The question does not include the timing of when anything came to exist.

Some have suggested the possibility of an infinite regress, where, if an entity can't come from nothing and this concept is mutually exclusive from something, there must have always been something that caused the previous effect, with this causal chain (either deterministic or probabilistic) extending infinitely back in time.

Arguments against attempting to answer the question

The question is outside our experience

Philosopher Stephen Law has said the question may not need answering, as it is attempting to answer a question that is outside a spatio-temporal setting, from within a spatio-temporal setting. He compares the question to asking "what is north of the North Pole?"

Causation may not apply

The ancient Greek philosopher Aristotle argued that everything in the universe must have a cause, culminating in an ultimate uncaused cause. (See Four causes)

However David Hume argued that a cause may not be necessary in the case of the formation of the universe. Whilst we demand that everything have a cause because of our experience of the necessity of causes, the formation of the universe is outside our experience and may be subject to different rules.

The brute fact approach

In philosophy the brute fact approach proposes that some facts cannot be explained in terms of a deeper, more "fundamental" fact. It is in opposition to the principle of sufficient reason approach.

On this question Bertrand Russell took a brute fact position when he said, "I should say that the universe is just there, and that's all." Sean Carroll similarly concluded that "any attempt to account for the existence of something rather than nothing must ultimately bottom out in a set of brute facts; the universe simply is, without ultimate cause or explanation."

The question may be impossible to answer

Roy Sorensen has discussed that the question may have an impossible explanatory demand, if there are no existential premises.

Explanations

Something may exist necessarily

Philosopher Brian Leftow has argued that the question cannot have a causal explanation (as any cause must itself have a cause) or a contingent explanation (as the factors giving the contingency must pre-exist), and that if there is an answer it must be something that exists necessarily (i.e., something that just exists, rather than is caused).

Natural laws may necessarily exist, and may enable the emergence of matter

Philosopher of physics Dean Rickles has argued that numbers and mathematics (or their underlying laws) may necessarily exist. If we accept that mathematics is an extension of logic, as philosophers such as Bertrand Russell and Alfred North Whitehead did, then mathematical structures like numbers and shapes must be necessarily true propositions in all possible worlds.

Physicists such as Stephen Hawking and Lawrence Krauss have offered explanations (of at least the first particle coming into existence aspect of cosmogony) that rely on quantum mechanics, saying that in a quantum vacuum state, virtual particles and spacetime bubbles will spontaneously come into existence.

A necessary being bearing the reason for its existence within itself

Gottfried Wilhelm Leibniz attributed to God as being the necessary sufficient reason for everything that exists (see: Cosmological argument). He wrote:

"Why is there something rather than nothing? The sufficient reason... is found in a substance which... is a necessary being bearing the reason for its existence within itself."

A state of nothing may be impossible

The pre-Socratic philosopher Parmenides was one of the first Western thinkers to question the possibility of nothing, and commentary on this has continued. Some have argued that by definition, nothingness is the absence of any property or possibility, thus it would be a logical contradiction for something to be created from the lack of possibility of creation.

A state of nothing may be unstable

Nobel Laureate Frank Wilczek is credited with the aphorism that "nothing is unstable." Physicist Sean Carroll argues that this accounts merely for the existence of matter, but not the existence of quantum states, space-time, or the universe as a whole.

Darwinism

From Wikipedia, the free encyclopedia

Darwinism is a theory of biological evolution developed by the English naturalist Charles Darwin (1809–1882) and others, stating that all species of organisms arise and develop through the natural selection of small, inherited variations that increase the individual's ability to compete, survive, and reproduce. Also called Darwinian theory, it originally included the broad concepts of transmutation of species or of evolution which gained general scientific acceptance after Darwin published On the Origin of Species in 1859, including concepts which predated Darwin's theories. English biologist Thomas Henry Huxley coined the term Darwinism in April 1860.

Terminology

Darwinism subsequently referred to the specific concepts of natural selection, the Weismann barrier, or the central dogma of molecular biology. Though the term usually refers strictly to biological evolution, creationists have appropriated it to refer to the origin of life or to cosmic evolution, that are distinct to biological evolution. It is therefore considered the belief and acceptance of Darwin's and of his predecessors' work, in place of other concepts, including divine design and extraterrestrial origins.

English biologist Thomas Henry Huxley coined the term Darwinism in April 1860. It was used to describe evolutionary concepts in general, including earlier concepts published by English philosopher Herbert Spencer. Many of the proponents of Darwinism at that time, including Huxley, had reservations about the significance of natural selection, and Darwin himself gave credence to what was later called Lamarckism. The strict neo-Darwinism of German evolutionary biologist August Weismann gained few supporters in the late 19th century. During the approximate period of the 1880s to about 1920, sometimes called "the eclipse of Darwinism", scientists proposed various alternative evolutionary mechanisms which eventually proved untenable. The development of the modern synthesis in the early 20th century, incorporating natural selection with population genetics and Mendelian genetics, revived Darwinism in an updated form.

While the term Darwinism has remained in use amongst the public when referring to modern evolutionary theory, it has increasingly been argued by science writers such as Olivia Judson, Eugenie Scott, and Carl Safina that it is an inappropriate term for modern evolutionary theory. For example, Darwin was unfamiliar with the work of the Moravian scientist and Augustinian friar Gregor Mendel, and as a result had only a vague and inaccurate understanding of heredity. He naturally had no inkling of later theoretical developments and, like Mendel himself, knew nothing of genetic drift, for example.

In the United States, creationists often use the term "Darwinism" as a pejorative term in reference to beliefs such as scientific materialism. This is now also the case even in the United Kingdom.

Huxley and Kropotkin

Huxley, upon first reading Darwin's theory in 1858, responded, "How extremely stupid not to have thought of that!"

While the term Darwinism had been used previously to refer to the work of Erasmus Darwin in the late 18th century, the term as understood today was introduced when Charles Darwin's 1859 book On the Origin of Species was reviewed by Thomas Henry Huxley in the April 1860 issue of the Westminster Review. Having hailed the book as "a veritable Whitworth gun in the armoury of liberalism" promoting scientific naturalism over theology, and praising the usefulness of Darwin's ideas while expressing professional reservations about Darwin's gradualism and doubting if it could be proved that natural selection could form new species, Huxley compared Darwin's achievement to that of Nicolaus Copernicus in explaining planetary motion:

What if the orbit of Darwinism should be a little too circular? What if species should offer residual phenomena, here and there, not explicable by natural selection? Twenty years hence naturalists may be in a position to say whether this is, or is not, the case; but in either event they will owe the author of "The Origin of Species" an immense debt of gratitude.... And viewed as a whole, we do not believe that, since the publication of Von Baer's "Researches on Development," thirty years ago, any work has appeared calculated to exert so large an influence, not only on the future of Biology, but in extending the domination of Science over regions of thought into which she has, as yet, hardly penetrated.

These are the basic tenets of evolution by natural selection as defined by Darwin:

More individuals are produced each generation than can survive.
Phenotypic variation exists among individuals and the variation is heritable.
Those individuals with heritable traits better suited to the environment will survive.
When reproductive isolation occurs new species will form.

Another important evolutionary theorist of the same period was the Russian geographer and prominent anarchist Pyotr Kropotkin who, in his book Mutual Aid: A Factor of Evolution (1902), advocated a conception of Darwinism counter to that of Huxley. His conception was centred around what he saw as the widespread use of co-operation as a survival mechanism in human societies and animals. He used biological and sociological arguments in an attempt to show that the main factor in facilitating evolution is cooperation between individuals in free-associated societies and groups. This was in order to counteract the conception of fierce competition as the core of evolution, which provided a rationalization for the dominant political, economic and social theories of the time; and the prevalent interpretations of Darwinism, such as those by Huxley, who is targeted as an opponent by Kropotkin. Kropotkin's conception of Darwinism could be summed up by the following quote:

In the animal world we have seen that the vast majority of species live in societies, and that they find in association the best arms for the struggle for life: understood, of course, in its wide Darwinian sense—not as a struggle for the sheer means of existence, but as a struggle against all natural conditions unfavourable to the species. The animal species, in which individual struggle has been reduced to its narrowest limits, and the practice of mutual aid has attained the greatest development, are invariably the most numerous, the most prosperous, and the most open to further progress. The mutual protection which is obtained in this case, the possibility of attaining old age and of accumulating experience, the higher intellectual development, and the further growth of sociable habits, secure the maintenance of the species, its extension, and its further progressive evolution. The unsociable species, on the contrary, are doomed to decay.
— Peter Kropotkin, Mutual Aid: A Factor of Evolution (1902), Conclusion

Other 19th-century usage

"Darwinism" soon came to stand for an entire range of evolutionary (and often revolutionary) philosophies about both biology and society. One of the more prominent approaches, summed in the 1864 phrase "survival of the fittest" by Herbert Spencer, later became emblematic of Darwinism even though Spencer's own understanding of evolution (as expressed in 1857) was more similar to that of Jean-Baptiste Lamarck than to that of Darwin, and predated the publication of Darwin's theory in 1859. What is now called "Social Darwinism" was, in its day, synonymous with "Darwinism"—the application of Darwinian principles of "struggle" to society, usually in support of anti-philanthropic political agenda. Another interpretation, one notably favoured by Darwin's half-cousin Francis Galton, was that "Darwinism" implied that because natural selection was apparently no longer working on "civilized" people, it was possible for "inferior" strains of people (who would normally be filtered out of the gene pool) to overwhelm the "superior" strains, and voluntary corrective measures would be desirable—the foundation of eugenics.

In Darwin's day there was no rigid definition of the term "Darwinism", and it was used by opponents and proponents of Darwin's biological theory alike to mean whatever they wanted it to in a larger context. The ideas had international influence, and Ernst Haeckel developed what was known as Darwinismus in Germany, although, like Spencer's "evolution", Haeckel's "Darwinism" had only a rough resemblance to the theory of Charles Darwin, and was not centred on natural selection. In 1886, Alfred Russel Wallace went on a lecture tour across the United States, starting in New York and going via Boston, Washington, Kansas, Iowa and Nebraska to California, lecturing on what he called "Darwinism" without any problems.

In his book Darwinism (1889), Wallace had used the term pure-Darwinism which proposed a "greater efficacy" for natural selection. George Romanes dubbed this view as "Wallaceism", noting that in contrast to Darwin, this position was advocating a "pure theory of natural selection to the exclusion of any supplementary theory." Taking influence from Darwin, Romanes was a proponent of both natural selection and the inheritance of acquired characteristics. The latter was denied by Wallace who was a strict selectionist. Romanes' definition of Darwinism conformed directly with Darwin's views and was contrasted with Wallace's definition of the term.

Contemporary usage

The term Darwinism is often used in the United States by promoters of creationism, notably by leading members of the intelligent design movement, as an epithet to attack evolution as though it were an ideology (an "ism") based on philosophical naturalism, atheism, or both. For example, in 1993, UC Berkeley law professor and author Phillip E. Johnson made this accusation of atheism with reference to Charles Hodge's 1874 book What Is Darwinism?. However, unlike Johnson, Hodge confined the term to exclude those like American botanist Asa Gray who combined Christian faith with support for Darwin's natural selection theory, before answering the question posed in the book's title by concluding: "It is Atheism."

Creationists use pejoratively the term Darwinism to imply that the theory has been held as true only by Darwin and a core group of his followers, whom they cast as dogmatic and inflexible in their belief. In the 2008 documentary film Expelled: No Intelligence Allowed, which promotes intelligent design (ID), American writer and actor Ben Stein refers to scientists as Darwinists. Reviewing the film for Scientific American, John Rennie says "The term is a curious throwback, because in modern biology almost no one relies solely on Darwin's original ideas... Yet the choice of terminology isn't random: Ben Stein wants you to stop thinking of evolution as an actual science supported by verifiable facts and logical arguments and to start thinking of it as a dogmatic, atheistic ideology akin to Marxism."

However, Darwinism is also used neutrally within the scientific community to distinguish the modern evolutionary synthesis, which is sometimes called "neo-Darwinism", from those first proposed by Darwin. Darwinism also is used neutrally by historians to differentiate his theory from other evolutionary theories current around the same period. For example, Darwinism may refer to Darwin's proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow. It may also refer specifically to the role of Charles Darwin as opposed to others in the history of evolutionary thought—particularly contrasting Darwin's results with those of earlier theories such as Lamarckism or later ones such as the modern evolutionary synthesis.

In political discussions in the United States, the term is mostly used by its enemies. "It's a rhetorical device to make evolution seem like a kind of faith, like 'Maoism,'" says Harvard University biologist E. O. Wilson. He adds, "Scientists don't call it 'Darwinism'." In the United Kingdom, the term often retains its positive sense as a reference to natural selection, and for example British ethologist and evolutionary biologist Richard Dawkins wrote in his collection of essays A Devil's Chaplain, published in 2003, that as a scientist he is a Darwinist.

In his 1995 book Darwinian Fairytales, Australian philosopher David Stove used the term "Darwinism" in a different sense than the above examples. Describing himself as non-religious and as accepting the concept of natural selection as a well-established fact, Stove nonetheless attacked what he described as flawed concepts proposed by some "Ultra-Darwinists." Stove alleged that by using weak or false ad hoc reasoning, these Ultra-Darwinists used evolutionary concepts to offer explanations that were not valid: for example, Stove suggested that the sociobiological explanation of altruism as an evolutionary feature was presented in such a way that the argument was effectively immune to any criticism. English philosopher Simon Blackburn wrote a rejoinder to Stove, though a subsequent essay by Stove's protégé James Franklin suggested that Blackburn's response actually "confirms Stove's central thesis that Darwinism can 'explain' anything."

In more recent times, the Australian moral philosopher and professor Peter Singer, who serves as the Ira W. DeCamp Professor of Bioethics at Princeton University, has proposed the development of a "Darwinian left" based on the contemporary scientific understanding of biological anthropology, human evolution, and applied ethics in order to achieve the establishment of a more equal and cooperative human society in accordance with the sociobiological explanation of altruism.

Esoteric usage

In evolutionary aesthetics theory, there is evidence that perceptions of beauty are determined by natural selection and therefore Darwinian; that things, aspects of people and landscapes considered beautiful are typically found in situations likely to give enhanced survival of the perceiving human's genes.

Limbic resonance

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Limbic_resonance

Limbic resonance is the idea that the capacity for sharing deep emotional states arises from the limbic system of the brain. These states include the dopamine circuit-promoted feelings of empathic harmony, and the norepinephrine circuit-originated emotional states of fear, anxiety and anger.

The concept was advanced in the book A General Theory of Love (2000), and is one of three interrelated concepts central to the book's premise: that our brain chemistry and nervous systems are measurably affected by those closest to us (limbic resonance); that our systems synchronize with one another in a way that has profound implications for personality and lifelong emotional health (limbic regulation); and that these set patterns can be modified through therapeutic practice (limbic revision).

In other words, it refers to the capacity for empathy and non-verbal connection that is present in mammals, and that forms the basis of our social connections as well as the foundation for various modes of therapy and healing. According to the authors (Thomas Lewis, M.D, Fari Amini, M.D. and Richard Lannon, M.D.), our nervous systems are not self-contained, but rather demonstrably attuned to those around us with whom we share a close connection. "Within the effulgence of their new brain, mammals developed a capacity we call 'limbic resonance' — a symphony of mutual exchange and internal adaptation whereby two mammals become attuned to each other's inner states."

This notion of limbic resonance builds on previous formulations and similar ideas. For example, the authors retell at length the notorious experiments of Harry Harlow establishing the importance of physical contact and affection in social and cognitive development of rhesus monkeys. They also make extensive use of subsequent research by Tiffany Field in mother/infant contact, Paul D. MacLean on the triune brain (reptilian, limbic, and neocortex), and the work of G.W. Kraemer.

Importance and history

Lewis, Amini and Lannon first make their case by examining a story from the dawn of scientific experimentation in human development when in the thirteenth century Frederick II raised a group of infants to be completely cut off from human interaction, other than the most basic care and feeding, so as to discover what language would spontaneously arise in the absence of any communication prompts. The result of this notorious experiment was that the infants, deprived of any human discourse or affection, all died.

The authors find the hegemony of Freudian theory in the early days of psychology and psychiatry to be almost as harmful as the ideas of Frederick II. They condemn the focus on cerebral insight, and the ideal of a cold, emotionless analyst, as negating the very benefit that psychotherapy can confer by virtue of the empathetic bond and neurological reconditioning that can occur in the course of sustained therapeutic sessions. "Freud's enviable advantage is that he never seriously undertook to follow his own advice. Many promising young therapists have their responsiveness expunged, as they are taught to be dutifully neutral observers, avoiding emotional contact....But since therapy is limbic relatedness, emotional neutrality drains life out of the process..."

A General Theory of Love is scarcely more sympathetic to Dr. Benjamin Spock and his "monumentally influential volume" Baby and Child Care, especially given Spock's role in promoting the movement against co-sleeping, or allowing infants to sleep in the same bed as their parents. Lewis, Amini and Lannon cite the research of sleep scientist James McKenna, which seems to suggest that the limbic regulation between sleeping parents and infants is essential to the neurological development of the latter and a major factor in preventing Sudden Infant Death Syndrome (SIDS). "The temporal unfolding of particular sleep stages and awake periods of the mother and infant become entwined....on a minute to minute basis, throughout the night, much sensory communication is occurring between them."

Subsequent use of the term

Since the first publication of A General Theory of Love in 2000, the term limbic resonance has gained popularity with subsequent writers and researchers. The term brings a higher degree of specificity to the ongoing discourse in psychological literature concerning the importance of empathy and relatedness. In "A handbook of Psychology" (2003) a clear path is traced from Winnicott 1965 identifying the concept of mother and child as a relational organism or dyad and goes on to examine the interrelation of social and emotional responding with neurological development and the role of the limbic system in regulating response to stress.

Limbic resonance is also referred to as "empathic resonance", as in the book Empathy in Mental Illness (2007), which establishes the centrality of empathy or lack thereof in a range of individual and social pathologies. The authors Farrow and Woodruff cite the work of Maclean, 1985, as establishing that "Empathy is perhaps the heart of mammalian development, limbic regulation and social organization", as well as research by Carr et al., 2003, who used fMRI to map brain activity during the observation and imitation of emotional facial expressions, concluding that "we understand the feelings of others via a mechanism of action representation that shapes emotional content and that our empathic resonance is grounded in the experience of our bodies in action and the emotions associated with specific bodily movements". Other studies cited examine the link between mirror neurons (activated during such mimicking activity) and the limbic system, such as Chartrand & Bargh, 1999: "Mirror neurone areas seem to monitor this interdependence, this intimacy, this sense of collective agency that comes out of social interactions and that is tightly linked to the ability to form empathic resonance."

Limbic resonance and limbic regulation are also referred to as "mood contagion" or "emotional contagion" as in the work of Sigal Barsade and colleagues at the Yale School of Management. In The Wise Heart, Buddhist teacher Jack Kornfield echoes the musical metaphor of the original definition of "limbic resonance" offered by authors Lewis, Amini and Lannon of A General Theory of Love, and correlates these findings of Western psychology with the tenets of Buddhism: "Each time we meet another human being and honor their dignity, we help those around us. Their hearts resonate with ours in exactly the same way the strings of an unplucked violin vibrate with the sounds of a violin played nearby. Western psychology has documented this phenomenon of 'mood contagion' or limbic resonance. If a person filled with panic or hatred walks into a room, we feel it immediately, and unless we are very mindful, that person's negative state will begin to overtake our own. When a joyfully expressive person walks into a room, we can feel that state as well."

In March 2010, citing A General Theory of Love, Kevin Slavin referred to limbic resonance in considering the dynamics of Social television. Slavin suggests that the laugh track evolved to provide the audience—alone at home—with a sense that others around them were laughing, and that limbic resonance explains the need for that laughing audience.

Limbic regulation

Limbic regulation, mood contagion or emotional contagion is the effect of contact with other people upon the development and stability of personality and mood.

Subsequent use and definitions of the term

In Living a connected life (2003), Dr. Kathleen Brehony looks at recent brain research which shows the importance of proximity of others in our development. "Especially in infancy, but throughout our lives, our physical bodies are influencing and being influenced by others with whom we feel a connection. Scientists call this limbic regulation."

Brehony goes on to describe the parallels between the "protest/despair" cycles of an abandoned puppy and human development. Mammals have developed a tendency to experience distraction, anxiety and measurable levels of stress in response to separation from their care-givers and companions, precisely because such separation has historically constituted a threat to their survival. As anyone who has owned a puppy can attest, when left alone it will cry, bark, howl, and seek to rejoin its human or canine companions. If these efforts are unsuccessful and the isolation is prolonged, it will sink into a state of dejection and despair. The marginal effectiveness of placing a ticking clock in the puppy's bed is based on a universal need in mammals to synchronize to the rhythms of their fellow creatures.

Limbic resonance and limbic regulation are also referred to as "mood contagion" or "emotional contagion" as in the work of Sigal Barsade. Barsade and colleagues at the Yale School of Management build on research in social cognition, and find that some emotions, especially positive ones, are spread more easily than others through such "interpersonal limbic regulation".

Author Daniel Goleman has explored similar terrain across several works: in Emotional Intelligence (1995), an international best seller, The Joy Of Living, coauthored with Yongey Mingyur Rinpoche, and the Harvard Business Review on Breakthrough Leadership. In the latter book, Goleman considers the "open loop nature of the brain's limbic system" which depends on external sources to manage itself, and examines the implications of interpersonal limbic regulation and the science of moods on leadership.

In Mindfully Green: A Personal and Spiritual Guide to Whole Earth Thinking (2003) author Staphine Kaza defines the term as follows: "Limbic regulation is a mutual simultaneous exchange of body signals that unfolds between people who are deeply involved with each other, especially parents and children." She goes on to correlate love with limbic engagement and asserts that children raised with love learn and remember better than those who are abused. Kaza then proposes to "take this work a step further from a systems perspective, and imagine that a child learns through some sort of limbic regulation with nature".

Limbic revision

Limbic revision is the therapeutic alteration of personality residing in the human limbic system of the brain.

Relation to affect regulation and limbic resonance

Dr. Allan Schore, of the UCLA David Geffen School of Medicine, has explored related ideas beginning with his book Affect Regulation and the Origin of the Self published in 1994. Dr. Shore looks at the contribution of the limbic system to the preservation of the species, its role in forming social bonds with other members of the species and intimate relations leading to reproduction. "It is said that natural selection favors characteristics that maximize an individual's contribution of the gene pool of succeeding generations. In humans this may entail not so much competitive and aggressive traits as an ability to enter into a positive affective relationship with a member of the opposite sex." In his subsequent book Affect regulation & the repair of the self, Schor correlates the "interactive transfer of affect" between mother and infant, on the one hand, and in a therapeutic context on the other, and describes it as "intersubjectivity". He then goes on to explore what developmental neuropsychology can reveal about both types of interrelatedness.

In Integrative Medicine: Principles for Practice, authors Kligler and Lee state "The empathic therapist offers a form of affect regulation. The roots of empathy — Limbic resonance — are found in the early caregiver experiences, which shape the ways the child learns to experience, share, and communicate affects."

In popular culture

Limbic Resonance is the title of the first episode of the Netflix series Sense8, the episode describes how eight uniquely different people from across the globe start seeing and hearing things after inexplicably seeing a vision of a woman they've never met before.

Quantum neural network

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_neural_network

Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models (which are widely used in machine learning for the important task of pattern recognition) with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments.

Most Quantum neural networks are developed as feed-forward networks. Similar to their classical counterparts, this structure intakes input from one layer of qubits, and passes that input onto another layer of qubits. This layer of qubits evaluates this information and passes on the output to the next layer. Eventually the path leads to the final layer of qubits. The layers do not have to be of the same width, meaning they don't have to have the same number of qubits as the layer before or after it. This structure is trained on which path to take similar to classical artificial neural networks. This is discussed in a lower section. Quantum neural networks refer to three different categories: Quantum computer with classical data, classical computer with quantum data, and quantum computer with quantum data.

Examples

Quantum neural network research is still in its infancy, and a conglomeration of proposals and ideas of varying scope and mathematical rigor have been put forward. Most of them are based on the idea of replacing classical binary or McCulloch-Pitts neurons with a qubit (which can be called a “quron”), resulting in neural units that can be in a superposition of the state ‘firing’ and ‘resting’.

Quantum perceptrons

A lot of proposals attempt to find a quantum equivalent for the perceptron unit from which neural nets are constructed. A problem is that nonlinear activation functions do not immediately correspond to the mathematical structure of quantum theory, since a quantum evolution is described by linear operations and leads to probabilistic observation. Ideas to imitate the perceptron activation function with a quantum mechanical formalism reach from special measurements to postulating non-linear quantum operators (a mathematical framework that is disputed). A direct implementation of the activation function using the circuit-based model of quantum computation has recently been proposed by Schuld, Sinayskiy and Petruccione based on the quantum phase estimation algorithm.

Quantum networks

At a larger scale, researchers have attempted to generalize neural networks to the quantum setting. One way of constructing a quantum neuron is to first generalise classical neurons and then generalising them further to make unitary gates. Interactions between neurons can be controlled quantumly, with unitary gates, or classically, via measurement of the network states. This high-level theoretical technique can be applied broadly, by taking different types of networks and different implementations of quantum neurons, such as photonically implemented neuronsand quantum reservoir processor (quantum version of reservoir computing). Most learning algorithms follow the classical model of training an artificial neural network to learn the input-output function of a given training set and use classical feedback loops to update parameters of the quantum system until they converge to an optimal configuration. Learning as a parameter optimisation problem has also been approached by adiabatic models of quantum computing.

Quantum neural networks can be applied to algorithmic design: given qubits with tunable mutual interactions, one can attempt to learn interactions following the classical backpropagation rule from a training set of desired input-output relations, taken to be the desired output algorithm's behavior.The quantum network thus ‘learns’ an algorithm.

Quantum associative memory

The first quantum associative memory algorithm was introduced by Dan Ventura and Tony Martinez in 1999. The authors do not attempt to translate the structure of artificial neural network models into quantum theory, but propose an algorithm for a circuit-based quantum computer that simulates associative memory. The memory states (in Hopfield neural networks saved in the weights of the neural connections) are written into a superposition, and a Grover-like quantum search algorithm retrieves the memory state closest to a given input. As such, this is not a fully content-addressable memory, since only incomplete patterns can be retrieved.

The first truly content-addressable quantum memory, which can retrieve patterns also from corrupted inputs, was proposed by Carlo A. Trugenberger. Both memories can store an exponential (in terms of n qubits) number of patterns but can be used only once due to the no-cloning theorem and their destruction upon measurement.

Trugenberger, however, has shown that his proababilistic model of quantum associative memory can be efficiently implemented and re-used multiples times for any polynomial number of stored patterns, a large advantage with respect to classical associative memories.

Classical neural networks inspired by quantum theory

A substantial amount of interest has been given to a “quantum-inspired” model that uses ideas from quantum theory to implement a neural network based on fuzzy logic.

Training

Quantum Neural Networks can be theoretically trained similarly to training classical/artificial neural networks. A key difference lies in communication between the layers of a neural networks. For classical neural networks, at the end of a given operation, the current perceptron copies its output to the next layer of perceptron(s) in the network. However, in a quantum neural network, where each perceptron is a qubit, this would violate the no-cloning theorem. A proposed generalized solution to this is to replace the classical fan-out method with an arbitrary unitary that spreads out, but does not copy, the output of one qubit to the next layer of qubits. Using this fan-out Unitary ( $U_{f}$ ) with a dummy state qubit in a known state (Ex. $| 0 ⟩$ in the computational basis), also known as an Ancilla bit, the information from the qubit can be transferred to the next layer of qubits. This process adheres to the quantum operation requirement of reversibility.

Using this quantum feed-forward network, deep neural networks can be executed and trained efficiently. A deep neural network is essentially a network with many hidden-layers, as seen in the sample model neural network above. Since the Quantum neural network being discussed uses fan-out Unitary operators, and each operator only acts on its respective input, only two layers are used at any given time. In other words, no Unitary operator is acting on the entire network at any given time, meaning the number of qubits required for a given step depends on the number of inputs in a given layer. Since Quantum Computers are notorious for their ability to run multiple iterations in a short period of time, the efficiency of a quantum neural network is solely dependent on the number of qubits in any given layer, and not on the depth of the network.

Cost functions

To determine the effectiveness of a neural network, a cost function is used, which essentially measures the proximity of the network's output to the expected or desired output. In a Classical Neural Network, the weights ( $w$ ) and biases ( $b$ ) at each step determine the outcome of the cost function $C (w, b)$ . When training a Classical Neural network, the weights and biases are adjusted after each iteration, and given equation 1 below, where $y (x)$ is the desired output and $a^{out} (x)$ is the actual output, the cost function is optimized when $C (w, b)$ = 0. For a quantum neural network, the cost function is determined by measuring the fidelity of the outcome state ( $ρ^{out}$ ) with the desired outcome state ( $ϕ^{out}$ ), seen in Equation 2 below. In this case, the Unitary operators are adjusted after each iteration, and the cost function is optimized when C = 1.

Equation 1  $C (w, b) = \frac{1}{N} \sum_{x} \frac{| | y (x) - a^{out} (x) | |}{2}$

Equation 2  $C = \frac{1}{N} \sum_{x}^{N} ⟨ ϕ^{out} | ρ^{out} | ϕ^{out} ⟩$

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Monday, January 15, 2024

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There is something

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The question is outside our experience

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The question may be impossible to answer

Explanations

Something may exist necessarily

Natural laws may necessarily exist, and may enable the emergence of matter

A necessary being bearing the reason for its existence within itself

A state of nothing may be impossible

A state of nothing may be unstable

Terminology

Huxley and Kropotkin

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Contemporary usage

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Subsequent use of the term

Limbic regulation

Subsequent use and definitions of the term

Limbic revision

Relation to affect regulation and limbic resonance

In popular culture

Examples

Quantum perceptrons

Quantum networks

Quantum associative memory

Classical neural networks inspired by quantum theory

Training

Cost functions