Superintelligent Digital Brains

Source: Deep Learning on Medium

Superintelligent Digital Brains

“The human brain has about 100 billion neurons. With an estimated average of one thousand connections between each neuron and its neighbors, we have about 100 trillion connections, each capable of a simultaneous calculation … (but) only 200 calculations per second…. With 100 trillion connections, each computing at 200 calculations per second, we get 20 million billion calculations per second. This is a conservatively high estimate…. In 1997, $2,000 of neural computer chips using only modest parallel processing could perform around 2 billion calculations per second…. This capacity will double every twelve months. Thus by the year 2020, it will have doubled about twenty-three times, resulting in a speed of about 20 million billion neural connection calculations per second, which is equal to the human brain.”

Ray Kurzweil, The Age of Spiritual Machines

… the AI might … omitting lower-level neuronal processes; it might replace commonly repeated computations with calls to a lookup table; or it might put in place some arrangement whereby multiple minds would share most parts of their underlying computational machinery (their “supervenience bases” in philosophical parlance). Such tricks could greatly increase the quantity of pleasure producible with a given amount of resources.”

Nick Bostrom, Supeintelligence: Paths, Dangers, Strategies

In my last article, different types of Superintelligent AI Systems were proposed, however, in this article, the author will present a proposed theorem entitled “ Digital Brain Completeness Theorem” and why it is tremendously important to have HUGE DISTINCT varieties of Artificial Neurons in a Digital Brain just like in its counterpart Human Brain.

It is noted that currently we are dealing with the limited set of Activation Functions such as Sigmoid, Tanh, Softmax, ReLu, Leaky ReLu and others. Kindly note that these Activation Functions used in the existing Digital Brain Network are chosen ARBITRARILY with the help of the “Trial and Error” approach. Furthermore, they do not ETHICALLY and APPROPRIATELY establish any RELATIONSHIP with the REFERENCED AI DATA SET.

To establish CORRELATION between the Neural Networks’ ACTIVATION FUNCTIONS and REFERENCED AI-ML-PURIFIED DATA SET, Jamilu (2019) proposed that Advanced Optimized Activation Functions should be EMANATED from our REFERENCED AI-ML-PURIFIED DATA SET and shall satisfy “Jameel ANNAF Stochastic Criterion” and or “Jameel ANNAF Deterministic Criterion”.

Biological Neurons differ from one another structurally, functionally and genetically, as well as in how they form connections with other cells. Neurons are often described as the “fundamental units” of the brain performing internal computations. Neurons vary in shape and size and can be classified by their morphology and function. The distinction between the types of neurons in the Human Brain is much more complex. There are tens or even hundreds of different types of neurons. In fact, researchers are still trying to devise a way to neatly classify the huge variety of neurons that exist in the brain. Scientists think that neurons are the most diverse kind of cell in the body. The available literature review showed that the number of neurons in a brain differs from species to species. There are an estimated 10 to 20 billion neurons in the cerebral cortex and 55 to 70 billion neurons in the cerebellum of a Human Brain, this gives about 100 billion estimated Human Brain Distinct Biological Neurons.

Jamilu (2019) proposed that ALMIGHTY GOD has created Biological Neurons to be essentially DISTINCT containing DISTINCT BIOLOGICAL ACTIVATION FUNCTIONS to enable Human Brain capture and or sense any form of LINEAR and NON-LINEAR RELATIONSHIPS. This will basically enable it receives, process, and transmit any kind of information.

For instance, if I draw a straight line on any part of your body system and ask you to tell me the nature of what I have drawn in your body, you will affirmatively confirm to me it is a “STRAIGHT LINE”, why is it so, because there is a DISTINCT BIOLOGICAL ACTIVATION FUNCTION sitting inside a DISTINCT BIOLOGICAL NEURON designed by ALMIGHTY GOD to accommodate such action. Similarly holds for any other linear, non-linear, sounds, colors, odors among others. They indeed have Distinct Biological Activation Functions implying Distinct Biological Neurons respectively.

In my article entitled “Bye to Trial and Error Activation Functions of Neural Networks III: Proposed Jameel’s ANNAF Deterministic Criterion”, we are able to show that we can achieve up to at least TWO THOUSAND (2000) Activation Functions EMANATED from our Referenced AI-ML-Purified Data Set as shown below:

Suzana Herculano-Houzel (2019) stated that “…Count your neurons when you count your blessings”.

Limitations of the existing Digital Brain Network

(1) Biological Neurons differs just from looking down a microscope, it is crystal clear that not all neurons are the same. The existing Artificial Neural Network perceived the Activation Functions of Artificial Neurons as very few sets and can just be represented by Sigmoid, Tanh, Softmax, ReLu, Leaky ReLu among others;

(2) The existing Sigmoid, Tanh, Softmax, ReLu, Leaky ReLu among others neither EMANTED from the Referenced AI-ML-Purified Data, Training Data nor Testing Data, so they do not have any correlation with the Referenced AI-ML-Purified Data;

3 Available Literature Reviewed showed that Human Brain contains about an estimated 100 billion Biological Neurons. While the existing Digital Brain Network contains a few number of Activation Functions;

4– Biological Neurons do give Birth and Die while the Artificial Neurons do not;

5– Scientists used to believe that the brain has ultra-specialized neurons for vision that become even more and more complex to be able to detect more complex shapes and objects while Digital Brain did not favor that.

Proposed Digital Brain Completeness Theorem

Let {AN1, AN2,…, ANn} and {AF1, AF2,…, AFn} be respectively number of Distinct Artificial Neurons and Distinct Activation Functions that satisfies Jameel’s ANNAF Stochastic and or Deterministic Criterion, then since Human Brain is made up of FINITE NUMBER of Distinct Biological Neurons (for instance up to 100 billion) then the corresponding Digital Brain should be appropriately made up of VERY HUGE and FINITE NUMBER of Distinct Artificial Neurons, otherwise, the Deep Learning Neural Network System that made up of the Digital Brain is INCOMPLETE.

Then in any Artificial Digital Brain System, there are exists set Very Huge and Finite Number of Distinct Artificial Activation Functions {AF1, AF2,…, AFn}, implying Distinct Artificial Neurons {AN1, AN2,…, ANn} such that for each ANi there exists UNIQUE AFi, i=1,2,…,n satisfies “Jameel’s ANNAF Stochastic Criterion” and or “Jameel’s ANNAF Deterministic Criterion” such that:

Even though it is very hard to have 100 billion Artificial Neurons in a Digital Brain as in the case of Human Brain nowadays, but our AI Data tells us how many Artificial Neurons and Activation Functions are suppose to be in a Neural Network of a given Task (for a simple project).

Given our AI Data D generated from a given Task Ṫ then the set of Distinct Activation Functions EMANATED from our AI Data satisfies Jameel’s ANNAF Stochastic and or Deterministic Criterion GIVES the TOTAL NUMBER of the Distinct Activation Functions implying TOTAL NUMBER of Distinct Artificial Neurons sitting in the Deep Learning Artificial Neural Network System of a Digital Brain of a given Task (for a simple project).

Proposed Normal Digital Brain

An artificial Digital Brain is said to be Normal Digital Brain if it is essentially made up of combination of 2000<f(x)<100 billion Distinct Deterministic and Stochastic Activation Functions (implying 2000<f(x)<100 billion Artificial Neurons, x is the number of Artificial Neurons) satisfies Jameel’s ANNAF Deterministic and Stochastic Criterion. This will enable the Deep Learning Neural Network to essentially CAPTURE and SENSE a tremendous number of LINEAR and NON-LINEAR RELATIONSHIPS exists just like Human Brain as shown in the following diagram:

Proposed Deterministic Superintelligent Digital Brain

An artificial Digital Brain is said to be a Deterministic Superintelligent Digital Brain if it is essentially made up of at least 100 billion Distinct Deterministic Activation Functions (implying 100 billion Artificial Neurons) satisfies Jameel’s ANNAF Deterministic Criterion. This will enable the Deep Learning Neural Network to essentially CAPTURE and SENSE almost ALL of the LINEAR and NON-LINEAR RELATIONSHIPS exists just like Human Brain as shown in the following diagram:

Proposed Stochastic Superintelligent Digital Brain

An Artificial Digital Brain is said to be Stochastic Superintelligent Digital Brain if it is essentially made up of at least 100 billion Distinct Stochastic Activation Functions (implying 100 billion Artificial Neurons) satisfies Jameel’s ANNAF Stochastic Criterion. This will enable the Deep Learning Neural Network to essentially CAPTURE and SENSE almost ALL of the LINEAR and NON-LINEAR RELATIONSHIPS exists just like Human Brain as shown in the following diagram:

Proposed Deterministic/Stochastic Superintelligent Digital Brain

An artificial Digital Brain is said to be a Deterministic/Stochastic Superintelligent Digital Brain if it is essentially made up of at least a combination of 100 billion Distinct Stochastic and Deterministic Activation Functions (implying 100 billion Artificial Neurons) satisfies Jameel’s ANNAF Deterministic and Stochastic Criterion. This will enable the Deep Learning Artificial Neural Network to essentially CAPTURE and SENSE almost ALL of the LINEAR and NON-LINEAR RELATIONSHIPS exists just like Human Brain as shown in the following diagram:

Life and Death of Artificial Neurons

1- A new set of Artificial Neurons are said to birth when there is an advancement in our AI Data with respect to TIME and AREA OF APPLICATION of a Deep Learning Artificial Neural Network

2- Also, a new set of Artificial Neurons are said to die when there is advancement in our AI Data with respect to TIME and AREA OF APPLICATION of a Deep Learning Artificial Neural Network.

In conclusion:

(a) The existing set of Activation Functions used in the Digital Brain Network are Trial and Error, not emanated from the AI-ML-Purified Data Set

(b) The existing Digital Brain Network Structure was made up of a very little number of DISTINCT Artificial Neurons as compared to the number of Biological Neurons in the Human Brain.

To address these, we need to increase the “Probability of mimicking Human Brain” by introducing additional Artificial Neurons emanated from AI Data to the Artificial Digital Brain System. For instance, increasing from 50 neurons to 100 neurons will increase the Probability of mimicking Human Brain from:

This implies we can only build a TRUE Sophisticated and complicated digital brain by means of increasing Probability of mimicking the Human Brain through increasing Distinct Activation Functions (implying increasing Distinct Artificial Neurons) emanated from our AI Data satisfied Jameel’s ANNAF Stochastic and or Deterministic Criterion.

This paper showed an example where we can build a digital system that could have up to 2224 neurons. This tremendously increased the Probability of mimicking Human Brain from for instance says:

This also implies the more we ethically increased the number of Activation Functions (implying increased in Artificial Neurons) emanated from our AI Data, the more we ethically increased Probability of mimicking Human Brain, the MORE DIGITAL BRAIN APPROXIMATE HUMAN BRAIN with Certainty.

Indeed, this is quite compatible, I strongly hold a positive view that the Almighty God has created Human Brain so sophisticated and complicated, scientifically proven contained approximately 100 billion Biological Neurons. These Biological Neurons are essentially DISTINCT containing DISTINCT BIOLOGICAL ACTIVATION FUNCTIONS to enable Human Brain to capture any LINEAR and NON-LINEAR RELATIONSHIPS received.

Therefore, in order to build a sophisticated Digital Brain that may approximate Human Brain, we need to think of building a Digital System that will contain 2000<x<100 billion DISTINCT ARTIFICIAL NEURONS, x is the number of Artificial Neurons.

The direction of the future research will tremendously focus on how we can build extremely high computing Technology that will enable us to come up with the FIRST SET OF 1 BILLION DISTINCT ARTIFICIAL ACTIVATION FUNCTIONS emanated from our REFERENCED AI-ML-PURIFIED DATA SET satisfies Jameel’s ANNAF Stochastic and or Deterministic Criterion in our QUEST to achieve FIRST 1 BILLION DISTINCT ARTIFICIAL NEURONS in an attempt to build FIRST 1 BILLION NEURONS DIGITAL BRAIN.

I strongly believed that this can be achieved using QUANTUM SUPER-COMPUTING (QUANTUM SUPREMACY).

The article’s fundamental Ideas were SUMMARIZED in the following FIVE (5) Youtube Videos:

(1) https://www.youtube.com/watch?v=nth3cJqgFts&t=5s

(2) https://www.youtube.com/watch?v=lcyR4TCOBFw

(3) https://www.youtube.com/watch?v=15NgJh71KRQ&t=3s

(4) https://www.youtube.com/watch?v=6emMNluHMZg

(5) https://www.youtube.com/watch?v=IlDTNWc7C-8

AUTHOR

Jamilu Auwalu Adamu, FIMC, CMC, FIMS (UK), FICA (in view)

Associate Editor, Risk and Financial Management Journal, USA

Editor, Journal of Economics and Management Sciences, USA

Former Associate Editor, Journal of Risk Model Validation, UK

PEER-REVIEWER, RISK.NET Journals, London

Former, Steering Committee Member, PRMIA Nigeria Chapter

Books Author

Correspondence: Mathematics Programme Building, 118 National Mathematical Centre, Small Sheda, Kwali, 904105, FCT-Abuja, Nigeria. Tel: +2348038679094. E-mail: whitehorseconsult@yahoo.com

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