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Rectified linear unit

Rectified linear unit is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Rectified linear unit rather than just read about it. In short: In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU ⁡ ( x ) = x + = max ( 0 , x ) = x + | x | 2 = { x if x > 0 , 0 x ≤ 0 {\displaystyle \operatorname {ReLU} (x)=x^{+}=\max(0,x)={\frac {x+|x|}{2}}={\begin{cases}x&{\text{if }}x>0,\\0&x\leq 0\end{cases}}}…

Rectified linear unit — main illustration
Rectified linear unit — illustration

Key takeaways

  • Rectified linear unit belongs to computer science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Rectified linear unit to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Rectified linear unit from memory before moving on to harder problems.

Reference excerpt

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function:

ReLU ⁡ ( x ) = x + = max ( 0 , x ) = x + | x | 2 = { x if x > 0 , 0 x ≤ 0 {\displaystyle \operatorname {ReLU} (x)=x^{+}=\max(0,x)={\frac {x+|x|}{2}}={\begin{cases}x&{\text{if }}x>0,\\0&x\leq 0\end{cases}}}

where x {\displaystyle x} is the input to a neuron. This is analogous to half-wave rectification in electrical engineering. ReLU is one of the most popular activation functions for artificial neural networks, and finds application in computer vision and speech recognition using deep neural nets and computational neuroscience.

… excerpt ends here. Continue reading the full article.

Illustrations

Rectified linear unit: Plot of the ReLU (blue) and GELU (green) functions near x = 0
Plot of the ReLU (blue) and GELU (green) functions near x = 0
Rectified linear unit: Plot of the softplus function and the ramp function
Plot of the softplus function and the ramp function
Rectified linear unit: The swish function
The swish function

Worked examples

Example 1 — a first encounter with Rectified linear unit

Start with the simplest possible case. Write down what Rectified linear unit claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Rectified linear unit before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Rectified linear unit ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Rectified linear unit

In research
Rectified linear unit appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Rectified linear unit in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Rectified linear unit is common in secondary-school and first-year university syllabi. It links to neighbouring topics Artificial neural networks, so understanding it makes those chapters shorter.
In everyday life
Look for Rectified linear unit outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Rectified linear unit in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Rectified linear unit means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Rectified linear unit out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Rectified linear unit in simple terms?

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU ⁡ ( x ) = x + = max ( 0 , x ) = x + | x | 2 = { x if x > 0 , 0 x ≤ 0 {\displaysty…

Why does Rectified linear unit matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Rectified linear unit?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Rectified linear unit.

Tags

  • Artificial neural networks

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