Neural Network’s type of approximation math function (Cherkassky & Mulier 2007)

Abstraction and reasoning remain a challenge for artificial intelligence (AI)!

Abstraction and reasoning are elusive notions, but they may play a crucial role in artificial intelligence’ s decision making process [1]. By analogy to human brain, artificial intelligence (AI) makes decisions by “learning” from features discovered in the data (text, image, sound, sensor, video, etc.) via deep learning, which involves large artificial neural networks (ANN) with multiple layers of connected “artificial” neurons.

A biological neuron is a functional cell of the nervous system. It has dendrites that receive signals and an axon that transmits signals to another neuron
A biological neuron is a functional cell of the nervous system. It has dendrites that receive signals and an axon that transmits signals to another neuron
A biological neuron is a functional cell of the nervous system. It has dendrites that receive signals and an axon that transmits signals to another neuron - Bari (2017)
ANN — McCulloch-Pitts model neuron (i) with three inputs (dendrites) and one output (axon). The neuron receives information as the weighted sum (x=wi1x1+ wi2x2+ wi3x3) of the three inputs (x1, x2, x3), which in turn is passed through a discontinuous threshold sigmoid non-linearly to obtain a new activation (new input) value, denoted by y = f (x) = f (wi1x1+ wi2x2+ wi3x3). Golden (1996) [1] (Bari 2017)

ANN approach was conceived based on the biological structure of the human nervous system, where a neuron uses its dendrites to receive impulses/stimuli as input and an axon to transmit electric signals as output. The neuron fires when the electrical current flows to the next neurons. A typical neuron may fire 5–50 times every second and there are about 86 billion neurons in the Human brain, some articles suggested there may be even 100 billion neurons.

In recent years, remarkable gains have been made using AI that helped in processing and understanding large and different types of data sets. Data sets that have been previously dismissed as chaotic have been found to display hidden patterns. In 2017, the number of companies who mentioned “artificial intelligence” in their earnings is also skyrocketing as they are now more than 260 companies while only a few (6) of them mentioned AI in their earnings in 2013, based on Bloomberg data [2].

However, abstraction and reasoning will remain a challenge that AI has yet to overcome [3], along with other limitations. Mariya Yao [3], CTO and Head of Research & Design at Topbots wrote that “The most important problem for AI today is abstraction and reasoning”, said François Chollet, AI researcher at Google. John Launchbury, the Director of DARPA’s Information Innovation Office, explains why abstraction and reasoning remain still a challenge for AI:

Abstraction is considered since Aristotle as a reliable concept-forming and reasoning process that can be used to derive truths [5].

“Aristotelianism holds that we gain some of our knowledge from the abstraction of concepts from our experience and reflection on these very concepts”

Mares 2011 (p. 123) [5]

The reasoning process of an AI to reach conclusions or to come up with certain decisions is yet to be further elucidated. Why AI made that particular decision? In the Verge magazine, James Vincent (2016 ) [6] reported that researchers, who used an eye-tracking system for a neural network to see which pixels the computer looks at first, they noticed that the computer unexpectedly stopped looking any further when it saw a look-like object with the targeted pixels, but not the object they were aiming to. The researchers asked AI “What is covering the windows?” and the answer by AI’s “deep leaning” was that “there are curtains covering the windows”, pointing to the bed instead of the windows.

To understand better how AI comes to a decision, that may have far-reaching implications, Capital One is pursuing further research to elucidate AI’s decision with the aim to guard against bias wrote Sara Castellanos.

Recently, Facebook researchers remarked also that their AI robots (chatbots) drifted off from English language as they invented their own code to chat. The code can be interpreted well by AI chatbots as it is more pertaining to the use of logic even if it may look like opaque and may make no sense. Google’s language translator is working well although it may not necessarily “understand’ the language it is translating. Similar results were also reported by Elon Musk’s OpenAI and Google’s DeepMind leading to a vivid controversy as to the impact AI might have in the industry and our society.

AI researchers at CNRS, France, are working to factor-in in their math equations the “surprise and unexpected” in an attempt to further understand what drives AI’s decisions. The robots “surprise and unexpected” trends are neither alarming nor surprising and researchers will continue to experiment and elucidate AI’s “decisions” . There are no evidence to date to support claims of a superhuman AI intelligence arising soon or in the future. AI platforms are being used today in business and academy to improve education, improve health, enhance agriculture production and better manage financial investments.

“AI can only help us to make our daily activities easier and in this process open up new ventures that can be explored” according to Yoshua Bengio, one of the pioneers in the field of artificial intelligence. Microsoft has launched a new initiative where Humans and AI will complement each other more effectively. The company has shifted from mobile-first to AI-first and considers AI as as one of its top priorities, according to CNCB News.

To address AI challenges of abstraction and reasoning researchers are also using mathematical proofs (inferential arguments) in the process simulating a mathematician’s intuition [4]. There are some analogies with early Greek mathematics to address early mathematical geometry artifacts, such as Müller-Lyer illusion.

Contemporary mathematics are considered as a model of Aristotle’s work using mathematical arguments across disciplines (sciences) including mathematical science. The first mathematical proof dates back to Pythagoras’ time, before Aristotle, to prove that the square root of 2 is not rational.

“It is through science that we prove, but through intuition that we discover…to invent is to discern.” Henri Poincaré (a polymath and early proponent of chaos theory)

While science is based on collecting data to validate the hypotheses and elaborate theories in support of data’s outcome, mathematics deal with proofs in support of axioms (statements). Mathematician‘s “intuition” is supported by proofs but not totally by observations or data’s outcome alone, but combined (Henri Poincaré).

Math has helped to show how neurons fire in the brain based on an ANN math model involving over 31,000 neurons. The data of the model consists of physiological data that has been collected to be close as possible to the reality, wrote Brenda Kelley Kim (2017 — Labroot).

Sources: Brenda Kelley Kim (2017 — Labroot) / EPFL, Frontiers in Computational Neuroscience, Blue Brain

To further explore the immense mathematics’ potential, researchers at Cornell University in Ithaca, New York developed a software that generates mathematical equations in physics, leading the software to propose an equation that described conservation of angular momentum in physics (kg m 2/s). In business, ThoughtSpot company has developed its new AI (SpotIQ) that asks questions which generate information that can in turn be used to develop further decisions rules. In biology, robot scientists, although not yet close to the goal of an artificially intelligent machine, were able to make discoveries by finding genes.

Our multi-disciplinary team of researchers, academicians, and mathematicians from different countries, across the 5 continents, used a combination of ANN with elaborated mathematical theoretical frameworks, that helped us in the identification of rare and adaptive genes in plants, some of them have been long sought-for in vain by researchers. This helped in shortening the time of screening and in reducing the cost of evaluation of thousands of samples as the evaluation of a sample that is unlikely to yield the sought after genes or traits incurs higher costs.

Mathematics are helping to develop climate proof crops and to speed up the process of genetic improvement of new crop varieties. Mathematics are also helping to address the limitation of computing space. Google has used recently advanced mathematics to cope with its infrastructure’ s limitation that helped to expand its range of services.The Wired magazine reported that Google has built its own AI chips because of the limitation of the company’s existing infrastructure [7].

The object of mathematical rigor is to sanction and legitimize the conquests of intuition, and there was never any other object for it. Jacques Hadamard

The new book on “Subtle Challenges of Big Data”, which refers to Aristotle and Euclid’s work on abstraction and reasoning, refers also to Gaston Bachelard ‘s work (interplay between data and mathematical theoretical frameworks), Henri Poincaré’s work (intuition and convention in mathematics), Thomas Kuhn’s work (paradigm shifts), John von Neumann’s contemporary work (self-replicating machines), and many others, including Nils J. Nilsson, Professor at Stanford University and one of the founding researchers of Artificial Intelligence, whom I would like to thank once more for his permission to quote some of his work in this new book.

This second book on scaling Big Data Discovery relates to the first book, while the first book on Big Data challenges addresses conceptual frameworks, this second book focuses more on practical aspects to search for novelty in Big Data. This book has been highly rated and also recommended by readers.

[1] Jean-Daniel Zucker — 2003. A grounded theory of abstraction in artificial intelligence

[2] Alex Kantrowitz, BuzzFeed News Reporter

[3] David Tucker (2017) With AI and machine learning, new technology enables scientists to understand more research and data than ever before. Elsevier’s Research.

[4] Mariya Yao (2017). Understanding the limits of deep learning.

[5] Mares (2011 p 136–137, p124).

[6] James Vincent (2016) These are three of the biggest problems facing today’s AI. The Verge.

[7] Klint Finley (06.07.17). How Google copes when even it can’t afford enough gear. Wired Business Conference 2017.

OperAI develops IoTs with Math and AI Embedded Solutions to speed up and streamline operational processes at the edges of the cloud.