Getting some sort of Math Formula from a Machine Learning trained model

Question

I already asked this question here: Can Convolutional Neural Networks (CNN) be represented by a Mathematical formula? but I feel that I was not clear enough and also the proposed idea did not work for me.

Let's say that using my computer, I train a certain machine learning algorithm (i.e. naive bayes, decision tree, linear regression, and others). So I already have a trained model which I can give a input value and it returns the result of the prediction (i.e. 1 or 0).

Now, let's say that I still want to give an input and get a predicted output. However, at this time I would like that my input value to be, for example, multiplied by some sort of mathematical formula, weights, or matrix that represents my "trained model".

In other words, I would like that my trained model "transformed" in some sort of formula which I can give an input and get the predicted number.

The reason why I want to do this is because I wanna train a big dataset and use complex prediction model. And use this trained prediciton model in simpler hardwares such as a PIC32 microcontroler. The PIC32 Microntroler would not train the machine learning or store all inputs. Instead, the microcontroler would simple read from the system certain numbers, apply a math formula or some sort of matrix multiplication and give me the predicted output. With that, I can use "fancy" neural networks in much simpler devices that can easily operate math formulas.

Answer 1

You can use my work as an example, from my GitHub

Skyline v1.1 Equation by rainmanp7.
Date of Completion 08/08/2023 1:20pm
QuantumAI for Reinforced Machine Learning.

The concept of memoization, which involves caching and reusing previously computed results, can be expressed explicitly in the equation like this:

wi = (wi0 / (1 + (vector_dij / τ))) * (1 + α * Ps + β * T + γ * M + δ

• V + ε * MA + ζ * C + η * S + θ * Si + φ * Td_i + _cache[(wi0, dij, τ, learning_method_coefficients, complexity_factor, object_properties, position_relative_to_center)] + complexity_factor * (multithreaded_vector_pipeline(vector_data, T1, T2, ...) | pipeline |

• multithreaded_pipeline(vector_calculations, T1, T2, ...)))

Where: - _cache[(wi0, dij, τ, learning_method_coefficients, complexity_factor, object_properties, position_relative_to_center)]:

This represents the cached weight update value for specific input parameters. If the calculation has been done before with the same input parameters, this cached value is used directly, avoiding redundant calculations.

You take this equation and formulate a high level construct skeleton for machine learning. The basis and operational situation is already present.

This model I made is based on Reinforced Machine Training. I hope this can help you. Put that equation into a Artificial intelligence Chat bot and ask it questions about it.

Answer 2

Essentially, every machine learning algorithm is a parameterized formula, with your trained model being the learned parameters that are applied to the input.

So what you're actually asking is to simplify arbitrary computations to, more or less, a matrix multiplication. I'm afraid that's mathematically impossible. If you ever do come up with a solution to this, make sure to share it - you'd instantly become famous, most likely rich, and put a hell of a lot of researchers out of business. If you can't train a matrix multiplication to get the accuracy you want from the start, what makes you think you can boil down arbitrary "complex prediction models" to such simple computations?

Answer 3

If I read this properly, you want a generally continuous function in many variables to replace a CNN. The central point of a CNN existing in a world with ANNs ("normal" neural networks) is that in includes irruptive transformations: non-linearities, discontinuities, etc. that enable the CNN to develop recognitions and relationships that simple linear combinations -- such as matrix multiplication -- cannot handle.

If you want to understand this better, I recommend that you choose an introduction to Deep Learning and CNNs in whatever presentation mode fits your learning styles.