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Sigmoid Activation Function - Deep Learning Dictionary

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Sigmoid Activation Function - Deep Learning Dictionary

In a neural network, an activation function applies a nonlinear transformation to the output of a layer.

One activation function, called \(\text{sigmoid}\), maps its supplied inputs to a value in the interval \((0,1)\). For a given value \(x\) passed to \(\text{sigmoid}\), we define

$$\text{sigmoid}(x)=\frac{e^{x}}{e^{x}+1}$$

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The table below summarizes how sigmoid transforms its input.

Input Sigmoid Output
Most negative values A value very close to \(0\)
Most positive values A value very close to \(1\)
Values relatively close to \(0\) A value between \(0\) and \(1\)

When sigmoid is used as an activation function following a layer in a neural network, it accepts the weighted sum of outputs from the previous layer and transforms this sum to a value between \(0\) and \(1\).

Intuitively, we can think of a given node's activated output as being "more activated" the closer it is to the upper limit \(1\), and similarly "less activated" the closer it is to \(0\).

We can therefore think of \(\text{sigmoid}\)'s output as being a probability of activation for a given node.

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What is the sigmoid activation function used in artificial neural networks? πŸ‘‰ To gain early access to the full Deep Learning Dictionary course, register at: πŸ”— https://deeplizard.com/course/ddcpailzrd πŸ‘‰ For more in depth lessons, check out the Deep Learning Fundamentals course: πŸ”— https://deeplizard.com/course/dlcpailzrd πŸ•’πŸ¦Ž VIDEO SECTIONS πŸ¦ŽπŸ•’ 00:00 Welcome to DEEPLIZARD - Go to deeplizard.com for learning resources 00:10 Sigmoid Activation Function 02:21 Collective Intelligence and the DEEPLIZARD HIVEMIND πŸ’₯🦎 DEEPLIZARD COMMUNITY RESOURCES 🦎πŸ’₯ πŸ‘‹ Hey, we're Chris and Mandy, the creators of deeplizard! πŸ‘€ CHECK OUT OUR VLOG: πŸ”— https://youtube.com/deeplizardvlog πŸ‘‰ Check out the website for more learning material: πŸ”— https://deeplizard.com πŸ’» ENROLL TO GET DOWNLOAD ACCESS TO CODE FILES πŸ”— https://deeplizard.com/resources 🧠 Support collective intelligence, join the deeplizard hivemind: πŸ”— https://deeplizard.com/hivemind 🧠 Use code DEEPLIZARD at checkout to receive 15% off your first Neurohacker order πŸ‘‰ Use your receipt from Neurohacker to get a discount on deeplizard courses πŸ”— https://neurohacker.com/shop?rfsn=6488344.d171c6 ❀️🦎 Special thanks to the following polymaths of the deeplizard hivemind: Tammy Mano Prime Ling Li πŸš€ Boost collective intelligence by sharing this video on social media! πŸ‘€ Follow deeplizard: Our vlog: https://youtube.com/deeplizardvlog Facebook: https://facebook.com/deeplizard Instagram: https://instagram.com/deeplizard Twitter: https://twitter.com/deeplizard Patreon: https://patreon.com/deeplizard YouTube: https://youtube.com/deeplizard πŸŽ“ Deep Learning with deeplizard: Deep Learning Dictionary - https://deeplizard.com/course/ddcpailzrd Deep Learning Fundamentals - https://deeplizard.com/course/dlcpailzrd Learn TensorFlow - https://deeplizard.com/course/tfcpailzrd Learn PyTorch - https://deeplizard.com/course/ptcpailzrd Natural Language Processing - https://deeplizard.com/course/txtcpailzrd Reinforcement Learning - https://deeplizard.com/course/rlcpailzrd Generative Adversarial Networks - https://deeplizard.com/course/gacpailzrd πŸŽ“ Other Courses: DL Fundamentals Classic - https://deeplizard.com/learn/video/gZmobeGL0Yg Deep Learning Deployment - https://deeplizard.com/learn/video/SI1hVGvbbZ4 Data Science - https://deeplizard.com/learn/video/d11chG7Z-xk Trading - https://deeplizard.com/learn/video/ZpfCK_uHL9Y πŸ›’ Check out products deeplizard recommends on Amazon: πŸ”— https://amazon.com/shop/deeplizard 🎡 deeplizard uses music by Kevin MacLeod πŸ”— https://youtube.com/channel/UCSZXFhRIx6b0dFX3xS8L1yQ ❀️ Please use the knowledge gained from deeplizard content for good, not evil.

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