# What if the y\_hat is not a linear combination of features x1,x2,x3...?

**URL:** <https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847>\
**Category:** Improving Deep Neural Networks: Hyperparameter tun\
**Tags:** coursera-platform\
**Created:** [December 2, 2023, 6:01am UTC](https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847 "2023-12-02T06:01:06Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![zway\_woo](https://avatars.discourse-cdn.com/v4/letter/z/b77776/32.png) [@zway\_woo](https://community.deeplearning.ai/u/zway_woo)\
**Post date:** [December 2, 2023, 6:01am UTC](https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847/1 "2023-12-02T06:01:07Z")

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I was wondering what if the y\_hat is not a linear combination of all the input features, say x has got four features x1,x2,x3,x4, just for the sake of argument, I’ve already known that y = 1/x1 + x2\*\*2 + c3x3 + c4x4, can the neural network still function well if it’s of both low bias and low variance in the end of training done?

I mean, can the neural network, (say with two hidden layers of 4, 5 for example) be able to find a somewhat approximating formula for the original theoretical one somehow? In a sense that even though the y is not a linear combination of x1,x2,x3,x4, but it still can give us some formula for predicting y\_hat? Please give some insightful opinions on that, many thanks!

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**Author:** ![TMosh](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/tmosh/32/9321_2.png) [@TMosh](https://community.deeplearning.ai/u/TMosh)\
**Post date:** [December 2, 2023, 6:19am UTC](https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847/2 "2023-12-02T06:19:28Z")

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The neural network hidden layers always use a non-linear function as their activation.

This creates non-linear combinations of the input features.

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<div class="post-metadata">

**Author:** ![zway\_woo](https://avatars.discourse-cdn.com/v4/letter/z/b77776/32.png) [@zway\_woo](https://community.deeplearning.ai/u/zway_woo)\
**Post date:** [December 2, 2023, 7:34am UTC](https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847/3 "2023-12-02T07:34:01Z")

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So you’re basically saying that it doesn’t matter right? I see, thanks.

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<div class="post-metadata">

**Author:** ![TMosh](https://sea1.discourse-cdn.com/dlai/user_avatar/community.deeplearning.ai/tmosh/32/9321_2.png) [@TMosh](https://community.deeplearning.ai/u/TMosh)\
**Post date:** [December 2, 2023, 1:55pm UTC](https://community.deeplearning.ai/t/what-if-the-y-hat-is-not-a-linear-combination-of-features-x1-x2-x3/508847/4 "2023-12-02T13:55:11Z")

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> [@zway\_woo](#):
>
> can the neural network, (say with two hidden layers of 4, 5 for example) be able to find a somewhat approximating formula for the original theoretical one somehow

Yes.