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In deep learning, accuracy curves are crucial for evaluating a model's performance. Typically, an accuracy curve resembles a logarithmic function, although the reasons for this are beyond the scope of this question. Large spikes in the accuracy curve can indicate issues such as an inappropriate batch size. Let's examine these curves:

enter image description here

Here, I have plotted a function ($log(x)$) with different random noises of $\alpha$, using this code:

import numpy as np
import matplotlib.pyplot as plt

def f(x, alpha):
    return np.log(x) + alpha * np.random.normal(size=x.size)


def main():
    x = np.linspace(0.5, 3)
    for i in [0, 0.1, 0.3]:
        plt.plot(x, f(x, alpha=i),label=fr'$\alpha$ = {i}')
    plt.legend()
    plt.show()


if name == 'main':
    main()

My objective is to determine the smoothness of these curves in order to infer the original $\alpha$ value. I am asking this question here rather than on Stack Overflow because it is not strictly a programming question. The only thing that hints a solution to me, is the integral of squared second derivative; but I think there might be a better, more accurate solution.

Can anyone suggest a solution?

Amirhossein Rezaei
  • 191
  • The total variation of a differentiable function over an interval is the integral of the absolute value of its derivative over that interval. See also https://en.wikipedia.org/wiki/Total_variation – Gerry Myerson Jul 18 '23 at 13:11
  • @GerryMyerson Can you provide more information on how to implement this? – Amirhossein Rezaei Jul 18 '23 at 14:23
  • I'm not sure what there is to implement. You take the derivative, take its absolute value, and compute the definite integral. If the function in question is not differentiable, the Wikipedia link shows you how to set up a sum based on sampled points. – Gerry Myerson Jul 18 '23 at 22:44

0 Answers0