<p>I want a neural network to learn the representation of a periodic function whose period is known to be <span class="math-container">$T$</span>.</p>
<p>What is the correct way to achieve that? From my reading, I could infer two things:</p>
<ol>
<li>This <a href="https://arxiv.org/abs/2006.08195" rel="nofollow noreferrer">paper</a> proposes using an activation function of form <span class="math-container">$x + sin^2(x)$</span>.</li>
<li>The above paper mentions that we can use <em>fourier features</em> when the period is known. However, I could not find any good reference of what does <em>fourier features</em> exactly mean.</li>
</ol>
<p>Can someone please explain or point to a resource that can explain how to incorporate fourier features into a NN?</p>

CC BY-SA 4.0
2024-02-02T08:18:54.043Z
Is there only one input variable? Or multiple variables, only one of which defines the space that the output repeats over? Do you have a strong requirement of continuity over the $T \rightarrow 0$ boundary?
Neil Slater
CC BY-SA 4.0
2024-02-02T08:58:51.650Z
Multiple variables, only one of which defines the space that the boundary repeats over. No requirement of continuity over the mentioned boundary
user185887
<neural-networks><machine-learning><deep-learning>
What is the right way to make a neural network learn a period function with known period
user185887
# What is the right way to make a neural network learn a period function with known period

(Asked by: username_0 on 2024-02-02)

I want a neural network to learn the representation of a periodic function whose period is known to be $T$.

What is the correct way to achieve that? From my reading, I could infer two things:

1. This [paper](https://arxiv.org/abs/2006.08195) proposes using an activation function of form $x + sin^2(x)$.
2. The above paper mentions that we can use *fourier features* when the period is known. However, I could not find any good reference of what does *fourier features* exactly mean.

Can someone please explain or point to a resource that can explain how to incorporate fourier features into a NN?

**Tags:** neural-networks, machine-learning, deep-learning

> **Comments:**
> **username_1**: Is there only one input variable? Or multiple variables, only one of which defines the space that the output repeats over? Do you have a strong requirement of continuity over the $T \rightarrow 0$ boundary?  
> **username_0**: Multiple variables, only one of which defines the space that the boundary repeats over. No requirement of continuity over the mentioned boundary  

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## 0 answers

