<p>For a function of one variable, there are only two options for directions in the domain: left or right, so it becomes almost trivial, but you can still talk about gradient descent.</p>

<p>You would take steps to the left if the slope/derivative is positive and make steps to the right if the slope/derivative is negative--i.e. the opposite direction of the derivative (the 1d version of the "gradient" in gradient descent), which is equivalent to the higher dimensional case.</p>

CC BY-SA 4.0
2020-03-30T21:51:01.007Z
2020-03-30T21:51:01.007Z
mach
<p>"The concept of a direction of fastest descent only makes sense in more than one dimension."</p>

<p><a href="https://math.stackexchange.com/a/180573">https://math.stackexchange.com/a/180573</a></p>

CC BY-SA 4.0
2020-03-30T23:25:52.460Z
I think this answer is not correct. See the other answer: [https://ai.stackexchange.com/a/19883/2444](https://ai.stackexchange.com/a/19883/2444).
nbro
CC BY-SA 3.0
2017-07-18T14:36:10.330Z
2017-07-18T14:36:10.330Z
David Duffrin
<p>We have always known that gradient descent is a function of two or more variables. But how can we geometrically represent gradient descent if it is a function of only one variable?</p>

<gradient-descent>
How would 1D gradient descent look like?
Parul S
# How would 1D gradient descent look like?

(Asked by: username_0 on 2017-07-18)

We have always known that gradient descent is a function of two or more variables. But how can we geometrically represent gradient descent if it is a function of only one variable?

**Tags:** gradient-descent


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## 2 answers

### Answer by username_1 on 2020-03-30. Score: 2

For a function of one variable, there are only two options for directions in the domain: left or right, so it becomes almost trivial, but you can still talk about gradient descent.

You would take steps to the left if the slope/derivative is positive and make steps to the right if the slope/derivative is negative--i.e. the opposite direction of the derivative (the 1d version of the "gradient" in gradient descent), which is equivalent to the higher dimensional case.


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### Answer by username_2 on 2017-07-18. Score: 0

"The concept of a direction of fastest descent only makes sense in more than one dimension."

<https://math.stackexchange.com/a/180573>

> **Comments:**
> **username_3**: I think this answer is not correct. See the other answer: [https://ai.stackexchange.com/a/19883/2444](https://ai.stackexchange.com/a/19883/2444).  

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