I am looking on very specific papers or presentations in which
machine learning (let say TensorFlow) is used to model simple operations like summation, division, multiplication, square root?
It is possible and actually trivial to solve math operations with neural networks. People have actually tried more complex stuff:
1. http://www.aclweb.org/anthology/I17-3017
2. https://arxiv.org/pdf/physics/9705023.pdf
yes you can use either Python or R to perform arthimatic operations
Radu,
I will look at paper more carefully. What I need is the following - input data let say
a output data 1/a - I teach TensorFlow on 1000 examples and what we observe that results are very inaccurate when a
You need a network with at least two hidden layers to model 1/a, since the function is nonlinear. If a is in [-1, 1] interval, the function is a bit hard to model since it jumps from -infinity (for negative values) to +infinity (for positive values), i.e. it is not continuous. In the first hidden layer, I would put 2 neurons (with ReLU activations) to model the cases a < 0 and a > 0 independently. In the second hidden layer you need more neurons (try 10 neurons with logistic or tanh activations) to model the nonlinear 1/a function. Maybe this blog post can provide some additional insight: https://towardsdatascience.com/can-neural-networks-really-learn-any-function-65e106617fc6
Thanks again, I was assuming that range for a is from some small positive number to infinity, that is 1/a is continuous. Thanks for your suggestions.
If a is in (0, +infinity), the function is indeed continuous. In this case, you just need to use enough neurons to model the function with the desired accuracy (below a certain epsilon).
We have used a lot of neurons and still getting very low accuracy for
a < 1
The attached code works just fine for me. The MSE is around 0.002249 and the plots overlap.
When switching to machine learning powered by Clifford/geometric algebra, simple operations like summation, division, multiplication and square root are well-defined geometric operations.
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