# From Coal and Steam to ChatGPT: Chapters in the History of Technology

Mark Twain once famously wrote in a letter from London to a New York newspaper editor:

“I have … heard on good authority that I was dead [but] the report of my death was an exaggeration.”

The same may be true of recent reports on the grave illness and possible impending death of human culture at the hands of ChatGPT and other so-called Large Language Models (LLM).  It is argued that these algorithms have such sophisticated access to the bulk of human knowledge, and can write with apparent authority on virtually any topic, that no-one needs to learn or create anything new. It can all be recycled—the end of human culture!

While there may be a kernel of truth to these reports, they are premature.  ChatGPT is just the latest in a continuing string of advances that have disrupted human life and human culture ever since the invention of the steam engine.  We—humans, that is—weathered the steam engine in the short term and are just as likely to weather the LLM’s.

## ChatGPT: What is it?

For all the hype, ChatGPT is mainly just a very sophisticated statistical language model (SLM).

To start with a very simple example of SLM, imagine you are playing a word scramble game and have the letter “Q”. You can be pretty certain that the “Q“ will be followed by a “U” to make “QU”.  Or if you have the initial pair “TH” there is a very high probability that it will be followed by a vowel as “THA…”, “THE…”, ”THI…”, “THO..” or “THU…” and possibly with an “R” as “THR…”.  This almost exhausts the probabilities.  This is all determined by the statistical properties of English.

Statistical language models build probability distributions for the likelihood that some sequence of letters will be followed by another sequence of letters, or a sequence of words (and punctuations) will be followed by another sequence of words.  The bigger the chains of letters and words, the number of possible permutations grows exponentially.  This is why SLMs usually stop at some moderate order of statistics.  If you build sentences from such a model, it sounds OK for a sentence or two, but then it just drifts around like it’s dreaming or hallucinating in a stream of consciousness without any coherence.

ChatGPT works in much the same way.  It just extends the length of the sequences where it sounds coherent up to a paragraph or two.  In this sense, it is no more “intelligent” than the SLM that follows “Q” with “U”.  ChatGPT simply sustains the charade longer.

Now the details of how ChatGPT accomplishes this charade is nothing less than revolutionary.  The acronym GPT means Generative Pre-Trained Transformer.  Transformers were a new type of neural net architecture invented in 2017 by the Google Brain team.  Transformers removed the need to feed sentences word-by-word into a neural net, instead allowing whole sentences and even whole paragraphs to be input in parallel.  Then, by feeding the transformers on more than a Terabyte of textual data from the web, they absorbed the vast output of virtually all the crowd-sourced information from the past 20 years.  (This what transformed the model from an SLM to an LLM.)  Finally, using humans to provide scores on what good answers looked like versus bad answers, ChatGPT was supervised to provide human-like responses.  The result is a chatbot that in any practical sense passes the Turing Test—if you query it for an extended period of time, you would be hard pressed to decide if it was a computer program or a human giving you the answers.  But Turing Tests are boring and not very useful.

The true value of ChatGPT is the access it has to that vast wealth of information (note it is information and not knowledge).  Give it almost any moderately technical query, and it will provide a coherent summary for you—on amazingly esoteric topics—because almost every esoteric topic has found its way onto the net by now, and ChatGPT can find it.

As a form of search engine, this is tremendous!  Think how frustrating it has always been searching the web for something specific.  Furthermore, the lengthened coherence made possible by the transformer neural net means that a first query that leads to an unsatisfactory answer from the chatbot can be refined, and ChatGPT will find a “better” response, conditioned by the statistics of its first response that was not optimal.  In a feedback cycle, with the user in the loop, very specific information can be isolated.

Or, imagine that you are not a strong writer, or don’t know the English language as well as you would like.  But entering your own text, you can ask ChatGPT to do a copy-edit, even rephrasing your writing where necessary, because ChatGPT above all else has an unequaled command of the structure of English.

Or, for customer service, instead of the frustratingly discrete menu of 5 or 10 potted topics, ChatGPT with a voice synthesizer could respond to continuously finely graded nuances of the customer’s problem—not with any understanding or intelligence, but with probabilistic likelihoods of what the solutions are for a broad range of possible customer problems.

In the midst of all the hype surrounding ChatGPT, it is important to keep in mind two things:  First, we are witnessing the beginning of a revolution and a disruptive technology that will change how we live.  Second, it is still very early days, just like the early days of the first steam engines running on coal.

## Disruptive Technology

Disruptive technologies are the coin of the high-tech realm of Silicon Valley.  But this is nothing new.  There have always been disruptive technologies—all the way back to Thomas Newcomen and James Watt and the steam engines they developed between 1712 and 1776 in England.  At first, steam engines were so crude they were used only to drain water from mines, increasing the number jobs in and around the copper and tin mines of Cornwall (viz. the popular BBC series Poldark) and the coal mines of northern England.  But over the next 50 years, steam engines improved, and they became the power source for textile factories that displaced the cottage industry of spinning and weaving that had sustained marginal farms for centuries before.

There is a pattern to a disruptive technology.  It not only disrupts an existing economic model, but it displaces human workers.  Once-plentiful jobs in an economic sector can vanish quickly after the introduction of the new technology.  The change can happen so fast, that there is not enough time for the workforce to adapt, followed by human misery in some sectors.  Yet other, newer, sectors always flourish, with new jobs, new opportunities, and new wealth.  The displaced workers often never see these benefits because they lack skills for the new jobs.

The same is likely true for the LLMs and the new market models they will launch. There will be a wealth of new jobs curating and editing LLM outputs. There will also be new jobs in the generation of annotated data and in the technical fields surrounding the support of LLMs. LLMs are incredibly hungry for high-quality annotated data in a form best provided by humans. Jobs unlikely to be at risk, despite prophesies of doom, include teachers who can use ChatGPT as an aide by providing appropriate context to its answers. Conversely, jobs that require a human to assemble information will likely disappear, such as news aggregators. The same will be true of jobs in which effort is repeated, or which follow a set of patterns, such as some computer coding jobs or data analysts. Customer service positions will continue to erode, as will library services. Media jobs are at risk, as well as technical writing. The writing of legal briefs may be taken over by LLMs, along with market and financial analysts. By some estimates, there are 300 million jobs around the world that will be impacted one way or another by the coming spectrum of LLMs.

This pattern of disruption is so set and so clear and so consistent, that forward-looking politicians or city and state planners could plan ahead, because we have been on a path of continuing waves disruption for over two hundred years.

## Waves of Disruption

In the history of technology, it is common to describe a series of revolutions as if they were distinct.  The list looks something like this:

First:          Power (The Industrial Revolution: 1760 – 1840)

Second:     Electricity and Connectivity (Technological Revolution: 1860 – 1920)

Third:        Automation, Information, Cybernetics (Digital Revolution: 1950 – )

Fourth:      Intelligence, cyber-physical (Imagination Revolution: 2010 – )

The first revolution revolved around steam power fueled by coal, radically increasing output of goods.  The second revolution shifted to electrical technologies, including communication networks through telegraph and the telephones.  The third revolution focused on automation and digital information.

Yet this discrete list belies an underlying fact:  There is, and has been, only one continuous Industrial Revolution punctuated by waves.

The Age of Industrial Revolutions began around 1760 with the invention of the spinning jenny by James Hargreaves—and that Age has continued, almost without pause, up to today and will go beyond.  Each disruptive technology has displaced the last.  Each newly trained workforce has been displaced by the last.  The waves keep coming.

Note that the fourth wave is happening now, as artificial intelligence matures. This is ironic, because this latest wave of the Industrial Revolution is referred to as the “Imagination Revolution” by the optimists who believe that we are moving into a period where human creativity is unleashed by the unlimited resources of human connectivity across the web. Yet this moment of human ascension to the heights of creativity is happening at just the moment when LLM’s are threatening to remove the need to create anything new.

So is it the end of human culture? Will all knowledge now just be recycled with nothing new added?

## A Post-Human Future?

The limitations of the generative aspects of ChatGPT might be best visualized by using an image-based generative algorithm that has also gotten a lot of attention lately. This is the ability to input a photograph, and input a Van Gogh painting, and create a new painting of the photograph in the style of Van Gogh.

In this example, the output on the right looks like a Van Gogh painting. It is even recognizable as a Van Gogh. But in fact it is a parody. Van Gogh consciously created something never before seen by humans.

Even if an algorithm can create “new” art, it is a type of “found” art, like a picturesque stone formation or a sunset. The beauty becomes real only in the response it elicits in the human viewer. Art and beauty do not exist by themselves; they only exist in relationship to the internal state of the conscious observer, like a text or symbol signifying to an interpreter. The interpreter is human, even if the artist is not.

ChatGPT, or any LLM like Google’s Bard, can generate original text, but its value only resides in the human response to it. The human interpreter can actually add value to the LLM text by “finding” sections that are interesting or new, or that inspire new thoughts in the interpreter. The interpreter can also “edit” the text, to bring it in line with their aesthetic values. This way, the LLM becomes a tool for discovery. It cannot “discover” anything on its own, but it can present information to a human interpreter who can mold it into something that they recognize as new. From a semiotic perspective, the LLM can create the signifier, but the signified is only made real by the Human interpreter—emphasize Human.

Therefore, ChatGPT and the LLMs become part of the Fourth Wave of the human Industrial Revolution rather than replacing it.

We are moving into an exciting time in the history of technology, giving us a rare opportunity to watch as the newest wave of revolution takes shape before our very eyes. That said … just as the long-term consequences of the steam engine are only now coming home to roost two hundred years later in the form of threats to our global climate, the effect of ChatGPT in the long run may be hard to divine until far in the future—and then, maybe after it’s too late, so a little caution now would be prudent.

## Resources

OpenAI ChatGPT: https://openai.com/blog/chatgpt/

Training GPT with human input: https://arxiv.org/pdf/2203.02155.pdf

Status of Large Language Models: https://www.tasq.ai/blog/large-language-models/

The start of the Transformer: https://arxiv.org/abs/1706.03762

# Post-Modern Machine Learning: The Deep Revolution

The mysteries of human intelligence are among the final frontiers of science. Despite our pride in what science has achieved across the past century, we have stalled when it comes to understanding intelligence or emulating it. The best we have done so far is through machine learning — harnessing the computational power of computers to begin to mimic the mind, attempting to answer the essential question:

How do we get machines to Know what we Know?

In modern machine learning, the answer is algorithmic.

In post-modern machine learning, the answer is manifestation.

The algorithms of modern machine learning are cause and effect, rules to follow, producing only what the programmer can imagine. But post-modern machine learning has blown past explicit algorithms to embrace deep networks. Deep networks today are defined by neural networks with thousands, or tens of thousands, or even hundreds of thousands, of neurons arrayed in multiple layers of dense connections. The interactivity of so many crossing streams of information defies direct deconstruction of what the networks are doing — they are post-modern. Their outputs manifest themselves, self-assembling into simplified structures and patterns and dependencies that are otherwise buried unseen in complicated data.

Deep learning emerged as recently as 2006 and has opened wide new avenues of artificial intelligence that move beyond human capabilities for some tasks.  But deep learning also has pitfalls, some of which are inherited from the legacy approaches of traditional machine learning, and some of which are inherent in the massively high-dimensional spaces in which deep learning takes place.  Nonetheless, deep learning has revolutionized many aspects of science, and there is reason for optimism that the revolution will continue. Fifty years from now, looking back, we may recognize this as the fifth derivative of the industrial revolution (Phase I: Steam. Phase II: Electricity. Phase III: Automation. Phase IV: Information. Phase V: Intelligence).

## From Multivariate Analysis to Deep Learning

Conventional machine learning, as we know it today, has had many names.  It began with Multivariate Analysis of mathematical population dynamics around the turn of the last century, pioneered by Francis Galton (1874), Karl Pearson (1901), Charles Spearman (1904) and Ronald Fisher (1922) among others.

The first on-line computers during World War II were developed to quickly calculate the trajectories of enemy aircraft for gunnery control, introducing the idea of feedback control of machines. This was named Cybernetics by Norbert Wiener, who had participated in the development of automated control of antiaircraft guns.

Table I. Evolution of Names for Machine Learning

A decade later, during the Cold War, it became necessary to find hidden objects in large numbers of photographs.  The embryonic electronic digital computers of the day were far too slow with far too little memory to do the task, so the Navy contracted with the Cornell Aeronautical Laboratory in Cheektowaga, New York, a suburb of Buffalo, to create an analog computer capable of real-time image analysis.  This led to the invention of the Perceptron by Frank Rosenblatt as the first neural network-inspired computer [1], building on ideas of neural logic developed by Warren McColloch and Walter Pitts.

Several decades passed with fits and starts as neural networks remained too simple to accomplish anything profound.  Then in 1986, David Rumelhart and Ronald Williams at UC San Diego with Geoff Hinton at Carnegie-Mellon discovered a way to train multiple layers of neurons, in a process called error back propagation [2].  This publication opened the floodgates of Connectionism — also known as Parallel Distributed Processing.  The late 80’s and much of the 90’s saw an expansion of interest in neural networks, until the increasing size of the networks ran into limits caused by the processing speed and capacity of conventional computers towards the end of the decade.  During this time it had become clear that the most interesting computations required many layers of many neurons, and the number of neurons expanded into the thousands, but it was difficult to train such systems that had tens of thousands of adjustable parameters, and research in neural networks once again went into a lull.

The beginnings of deep learning started with two breakthroughs.  The first was by Yann Lecun at Bell Labs in 1998 who developed, with Leon Bottou, Yoshua Bengio and Patrick Haffner, a Convolutional Neural Network that had seven layers of neurons that classified hand-written digits [3]. The second was from Geoff Hinton in 2006, by then at the University of Toronto, who discovered a fast learning algorithm for training deep layers of neurons [4].  By the mid 2010’s, research on neural networks was hotter than ever, propelled in part by several very public successes, such as Deep Mind’s machine that beat the best player in the world at Go in 2017, self-driving cars, personal assistants like Siri and Alexa, and YouTube recommendations.

## The Challenges of Deep Learning

Deep learning today is characterized by neural network architectures composed of many layers of many neurons.  The nature of deep learning brings with it two main challenges:  1) efficient training of the neural weights, and 2) generalization of trained networks to perform accurately on previously unseen data inputs.

Solutions to the first challenge, efficient training, are what allowed the deep revolution in the first place—the result of a combination of increasing computer power with improvements in numerical optimization. This included faster personal computers that allowed nonspecialists to work with deep network programming environments like Matlab’s Deep Learning toolbox and Python’s TensorFlow.

Solutions to the second challenge, generalization, rely heavily on a process known as “regularization”. The term “regularization” has a slippery definition, an obscure history, and an awkward sound to it. Regularization is the noun form of the verb “to regularize” or “to make regular”. Originally, regularization was used to keep certain inverse algorithms from blowing up, like inverse convolutions, also known as deconvolution. Direct convolution is a simple mathematical procedure that “blurs” ideal data based on the natural response of a measuring system. However, if one has experimental data, one might want to deconvolve the system response from the data to recover the ideal data. But this procedure is numerically unstable and can “blow up”, often because of the divide-by-zero problem. Regularization was a simple technique that kept denominators from going to zero.

Regularization became a common method for inverse problems that are notorious to solve because of the many-to-one mapping that can occur in measurement systems. There can be a number of possible causes that produce a single response. Regularization was a way of winnowing out “unphysical” solutions so that the physical inverse solution remained.

During the same time, regularization became a common tool used by quantum field theorists to prevent certain calculated quantities from diverging to infinity. The solution was again to keep denominators from going to zero by setting physical cut-off lengths on the calculations. These cut-offs were initially ad hoc, but the development of renormalization group theory by Kenneth Wilson at Cornell (Nobel Prize in 1982) provided a systematic approach to solving the infinities of quantum field theory.

With the advent of neural networks, having hundreds to thousands to millions of adjustable parameters, regularization became the catch-all term for fighting the problem of over-fitting. Over-fitting occurs when there are so many adjustable parameters that any training data can be fit, and the neural network becomes just a look-up table. Look-up tables are the ultimate hash code, but they have no predictive capability. If a slightly different set of data are fed into the network, the output can be anything. In over-fitting, there is no generalization, the network simply learns the idiosyncrasies of the training data without “learning” the deeper trends or patterns that would allow it to generalize to handle different inputs.

Over the past decades a wide collection of techniques have been developed to reduce over-fitting of neural networks. These techniques include early stopping, k-fold holdout, drop-out, L1 and L2 weight-constraint regularization, as well as physics-based constraints. The goal of all of these techniques is to keep neural nets from creating look-up tables and instead learning the deep codependencies that exist within complicated data.

Table II. Regularization Techniques in Machine Learning

By judicious application of these techniques, combined with appropriate choices of network design, amazingly complex problems can be solved by deep networks and they can generalized too (to some degree). As the field moves forward, we may expect additional regularization tricks to improve generalization, and design principles will emerge so that the networks no longer need to be constructed by trial and error.

## The Potential of Deep Learning

In conventional machine learning, one of the most critical first steps performed on a dataset has been feature extraction. This step is complicated and difficult, especially when the signal is buried either in noise or in confounding factors (also known as distractors). The analysis is often highly sensitive to the choice of features, and the selected features may not even be the right ones, leading to bad generalization. In deep learning, feature extraction disappears into the net itself. Optimizing the neural weights subject to appropriate constraints forces the network to find where the relevant information lies and what to do with it.

The key to finding the right information was not just having many neurons, but having many layers, which is where the potential of deep learning emerges. It is as if each successive layer is learning a more abstract or more generalized form of the information than the last. This hierarchical layering is most evident in the construction of convolutional deep networks, where the layers are receiving a telescoping succession of information fields from lower levels. Geoff Hinton‘s Deep Belief Network, which launched the deep revolution in 2006, worked explicitly with this hierarchy in mind through direct design of the network architecture. Since then, network architecture has become more generalized, with less up-front design while relying on the increasingly sophisticated optimization techniques of training to set the neural weights. For instance, a simplified instance of a deep network is shown in Fig. 4 with three hidden layers of neurons.

The mathematical structure of a deep network is surprisingly simple. The equations for the network in Fig. 4, that convert an input xa to an output ye, are

These equations use index notation to denote vectors (single superscript) and matrices (double indexes). The repeated index (one up and one down) denotes an implicit “Einstein” summation. The function φ(.) is known as the activation function, which is nonlinear. One of the simplest activation functions to use and analyze, and the current favorite, is known as the ReLU (for rectifying linear unit). Note that these equations represent a simple neural cascade, as the output of one layer becomes the input for the next.

The training of all the matrix elements assumes a surprisingly simply optimization function, known as an objective function or a loss function, that can look like

where the first term is the mean squared error of the network output ye relative to the desired output y0 for the training set, and the second term, known as a regularization term (see section above) is a quadratic form that keeps the weights from blowing up. This loss function is minimized over the set of adjustable matrix weights.

The network in Fig. 4 is just a toy, with only 5 inputs and 5 outputs and only 23 neurons. But it has 30+36+36+30+23 = 155 adjustable weights. If this seems like overkill, but it is nothing compared to neural networks with thousands of neurons per layer and tens of layers. That massive overkill is exactly the power of deep learning — as well as its pitfall.

## The Pitfalls of Deep Learning

Despite the impressive advances in deep learning, serious pitfalls remain for practitioners. One of the most challenging problems in deep learning is the saddle-point problem. A saddle-point in an objective function is like a mountain pass through the mountains: at the top of the pass it slopes downward in two opposite directions into the valleys but slopes upward in the two orthogonal directions to mountain peaks. A saddle point is an unstable equilibrium where a slight push this way or that can lead the traveller to two very different valleys separated by high mountain ridges. In our familiar three-dimensional space, saddle points are relatively rare and landscapes are dominated by valleys and mountaintops. But this intuition about landscapes fails in high dimensions.

Landscapes in high dimensions are dominated by neutral ridges that span the domain of the landscape. This key understanding about high-dimensional space actually came from the theory of evolutionary dynamics for the evolution of species. In the early days of evolutionary dynamics, there was a serious challenge to understand how genetic mutations could allow such diverse speciation to occur. If the fitness of a species were viewed as a fitness landscape, and if a highly-adapted species were viewed as a mountain peak in this landscape, then genetic mutations would need to drive the population state point into “valleys of death” that would need to be crossed to arrive at a neighboring fitness peak. It would seem that genetic mutations would likely kill off the species in the valleys before they could rise to the next equilibrium.

However, the geometry of high dimensions does not follow this simple low-dimensional intuition. As more dimensions come available, landscapes have more and more ridges of relatively constant height that span the full space (See my recent blog on random walks in 10-dimensions and my short YouTube video). For a species to move from one fitness peak to another fitness peak in a fitness landscape (in ultra-high-dimensional mutation space), all that is needed is for a genetic mutation to step the species off of the fitness peak onto a neutral ridge where many mutations can keep the species on that ridge as it moves ever farther away from the last fitness peak. Eventually, the neutral ridge brings the species near a new fitness peak where it can climb to the top, creating a new stable species. The point is that most genetic mutations are neutral — they do not impact the survivability of an individual. This is known as the neutral network theory of evolution proposed by Motoo Kimura (1924 – 1994) [5]. As these mutation accumulate, the offspring can get genetically far from the progenitor. And when a new fitness peak comes near, many of the previously neutral mutations can come together and become a positive contribution to fitness as the species climbs the new fitness peak.

The neutral network of genetic mutation was a paradigm shift in the field of evolutionary dynamics, and it also taught everyone how different random walks in high-dimensional spaces are from random walks in 3D. But although neutral networks solved the evolution problem, they become a two-edged sword in machine learning. On the positive side, fitness peaks are just like the minima of objective functions, and the ability for partial solutions to perform random walks along neutral ridges in the objective-function space allows optimal solutions to be found across a broad range of the configuration space of the neural weights. However, on the negative side, ridges are loci of unstable equilibrium. Hence there are always multiple directions that a solution state can go to minimize the objective function. Each successive run of a deep-network neural weight optimizer can find equivalent optimal solutions — but they each can be radically different. There is no hope of averaging the weights of an ensemble of networks to arrive at an “average” deep network. The averaging would simply drive all weights to zero. Certainly, the predictions of an ensemble of equivalently trained networks can be averaged—but this does not illuminate what is happening “under the hood” of the machine, which is where our own “understanding” of what the network is doing would come from.

## Post-Modern Machine Learning

Post-modernism is admittedly kind of a joke — it works so hard to pull down every aspect of human endeavor that it falls victim to its own methods. The convoluted arguments made by its proponents sound like ultimate slacker talk — circuitous logic circling itself in an endless loop of denial.

But post-modernism does have its merits. It surfs on the moving crest of what passes as modernism, as modernism passes onward to its next phase. The philosophy of post-modernism moves beyond rationality in favor of a subjectivism in which cause and effect are blurred.  For instance, in post-modern semiotic theory, a text or a picture is no longer an objective element of reality, but fragments into multiple semiotic versions, each one different for each different reader or watcher — a spectrum of collaborative efforts between each consumer and the artist. The reader brings with them a unique set of life experiences that interact with the text to create an entirely new experience in each reader’s mind.

Deep learning is post-modern in the sense that deterministic algorithms have disappeared. Instead of a traceable path of sequential operations, neural nets scramble information into massively-parallel strings of partial information that cross and interact nonlinearly with other massively-parallel strings. It is difficult to impossible to trace any definable part of the information from input to output. The output simply manifests some aspect of the data that was hidden from human view.

But the Age of Artificial Intelligence is not here yet. The vast multiplicity of saddle ridges in high dimensions is one of the drivers for one of the biggest pitfalls of deep learning — the need for massive amounts of training data. Because there are so many adjustable parameters in a neural network, and hence so many dimensions, a tremendous amount of training data is required to train a network to convergence. This aspect of deep learning stands in strong contrast to human children who can be shown a single picture of a bicycle next to a tricycle, and then they can achieve almost perfect classification accuracy when shown any number of photographs of different bicycles and tricycles. Humans can generalize with an amazingly small amount of data, while deep networks often need thousands of examples. This example alone points to the marked difference between human intelligence and the current state of deep learning. There is still a long road ahead.

By David D. Nolte, April 18, 2022

[1] F. Rosenblatt, “THE PERCEPTRON – A PROBABILISTIC MODEL FOR INFORMATION-STORAGE AND ORGANIZATION IN THE BRAIN,” Psychological Review, vol. 65, no. 6, pp. 386-408, (1958)

[2] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “LEARNING REPRESENTATIONS BY BACK-PROPAGATING ERRORS,” Nature, vol. 323, no. 6088, pp. 533-536, Oct (1986)

[3] LeCun, Yann; Léon Bottou; Yoshua Bengio; Patrick Haffner (1998). “Gradient-based learning applied to document recognition”. Proceedings of the IEEE. 86 (11): 2278–2324.

[4] G. E. Hinton, S. Osindero, and Y. W. Teh, “A fast learning algorithm for deep belief nets,” Neural Computation, vol. 18, no. 7, pp. 1527-1554, Jul (2006)

[5] M. Kimura, The Neutral Theory of Molecular Evolution. Cambridge University Press, 1968.