# AI applications of the Fibonacci series

I have been looking at Fibonacci series, the golden ratio and its uses in nature, like how flowers and animals grow based on the series.

I was wondering whether we could use the Fibonacci series and the golden ratio in any way in AI, especially in evolutionary algorithms. Any ideas or insights?

Is this research material? If so where can we start?

• Why cannot we grow an AI model based on physical growth patterns, just like genetic algorithms which are inspired from natural evolution. I just got the idea of using fibonacci series somehow. – Surender Harsha Jun 10 '18 at 1:46

The use of the Golden Ratio is an interesting suggestion which has intrigued many lovers of the mathematical beauty represented in nature and in AI. The problem lies in the foundations of the AI applications. For example, in designing algorithms for recognizing naturally occurring phenomena, such as face recognition or human body movements (See https://www.intechopen.com/books/machine-learning-and-biometrics/a-human-body-mathematical-model-biometric-using-golden-ratio-a-new-algorithm) it is suitable. However, for non natural occurrences, the ratio is limited since the data is usually random or chaotic. However, in order to create a master algorithm for the future which encompasses all the best of the current AI algorithms, the use of mathematical concepts such as the golden ration and fractals will be vital. Watch this space...

Face detection evaluation: A new approach based on the golden ratio Φ

Abstract:

Face detection is a fundamental research area in computer vision field. Most of the face-related applications such as face recognition and face tracking assume that the face region is perfectly detected. To adopt a certain face detection algorithm in these applications, evaluation of its performance is needed. Unfortunately, it is difficult to evaluate the performance of face detection algorithms due to the lack of universal criteria in the literature. In this paper, we propose a new evaluation measure for face detection algorithms by exploiting a biological property called Golden Ratio of the perfect human face. The new evaluation measure is more realistic and accurate compared to the existing one. Using the proposed measure, five haar-cascade classifiers provided by Intel©OpenCV have been quantitatively evaluated on three common databases to show their robustness and weakness as these classifiers have never been compared among each other on same databases under a specific evaluation measure. A thoughtful comparison between the best haar-classifier and two other face detection algorithms is presented. Moreover, we introduce a new challenging dataset, where the subjects wear the headscarf. The new dataset is used as a testbed for evaluating the current state of face detection algorithms under the headscarf occlusion

I mean you can predict these sequences quite easily(with varying levels of accuracy) just by using LSTMs in the time series forecasting context. Obviously, as the number of digits you give it increases, it will increase the prediction accuracy of the next in the sequence(with some caveats), as we can think of neural networks more generally as connectionist function approximators(nonlinear in almost all cases).

As far as direct applications in AI, I suppose not beyond mathematical modeling and economic/financial modeling as these sorts of sequences emerge from a vast majority of pure and applied mathematical concepts. This research is quite relevant and ongoing(1,2,3).

It should be a short amount of time before we start seeing exponential complexity growth as the target of AI algorithms, likely involving the golden ratio.

https://en.wikipedia.org/wiki/Golden_ratio#Relationship_to_Fibonacci_sequence

We are already using the golden ratio to perform quantum computations :

https://www.quora.com/How-are-quantum-physics-and-the-golden-ratio-connected

So, once we scale parallelization to GPU-like networks of quantum processors, we can then be sure we have entered the territory where AI and the Golden Ratio are inherently more intrinsic.

As far as accelerating the learning models/algorithms with them, we can only hope something so fantastic would be found in the future of AI as well; who knows, maybe they will come out of course through necessity much like the biological computers we all execute and replicate our code from, and it's environment :

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6047800/

Not to say it will be the only property present, as the article concludes the golden ratio is "most likely" only related by "chance". I'm sure the same random chance by which it relates to black hole entropy, and, everything else it relates to :P.