Calculate Swish Function
Online calculator and formulas for the Swish activation function - self-gated modern activation
Swish Function Calculator
Swish (Self-gated Activation)
The f(x) = x · σ(βx) is a smooth activation function with better performance than ReLU in many neural networks. Discovered by Google, it is an important modern activation function.
Swish Graph
Swish Graph: Smooth, self-gated curve with S-shaped behavior.
Advantage: Often improves training compared to ReLU.
What Makes Swish Special?
The Swish function offers several advantages in modern neural networks:
- Self-gating: Beta parameter adjusts gating strength
- Smooth activation: Differentiable everywhere
- Better convergence: Leads to better training results
- Similar to ReLU: But with smoother transitions
- Discovered by Google: Via Neural Architecture Search
- Modern alternative: To ReLU and related functions
Swish Function Formulas
Swish Function
Product of x and sigmoid with beta scaling
Swish Derivative
Continuous and smooth derivative
Beta Parameter Influence
Beta determines the slope and behavior
Special Case: Mish
Related activation function with similar properties
Relationship to ReLU
Combines advantages of ReLU and sigmoid
Properties
Special Values (β=1)
Domain
All real numbers
Range
All real numbers (can be negative)
Smoothness
Infinitely differentiable, completely smooth curve, no jumps or kinks.
Detailed Description of the Swish Function
Mathematical Definition
The Swish function is a smooth activation function discovered in 2017 by Google researchers through automatic Neural Architecture Search (NAS). It combines the simplicity of ReLU with the smoothness of sigmoid.
Using the Calculator
Enter any real number and a beta parameter, and the calculator computes the Swish value and its derivative for backpropagation.
Discovery and Development
Swish was discovered in 2017 by Ramachandran et al. at Google. They used Neural Architecture Search to automatically find new activation functions better than hand-crafted functions like ReLU and sigmoid. Swish has since become established in many state-of-the-art models.
Properties and Variations
Deep Learning Applications
- Computer Vision (EfficientNet, etc.)
- Natural Language Processing
- State-of-the-art neural networks
- Image classification and object detection
Activation Function Variants
- Standard Swish: f(x) = x · σ(x), β=1
- Swish-β: f(x) = x · σ(βx), parametric
- Mish: x · tanh(softplus(x))
- GLU Variants: Gating Linear Units
Mathematical Properties
- Self-gating: Activation gates itself on input
- Smoothness: Infinitely differentiable (C∞)
- Gating effect: Sigmoid acts as gating mechanism
- S-shaped: Similar to sigmoid, but multiplied by x
Interesting Facts
- Automatically discovered through Neural Architecture Search
- Outperforms ReLU in many modern applications
- Used in EfficientNet and other top models
- Beta parameter allows fine-tuning
Calculation Examples (β=1)
Example 1: Standard Values
Swish(0) = 0
Swish(1) ≈ 0.731
Swish(-1) ≈ -0.269
Example 2: Positive Values
Swish(5) ≈ 4.967
Swish(10) ≈ 10.000
Swish(100) ≈ 100.000
Example 3: Negative Values
Swish(-5) ≈ -0.034
Swish(-10) ≈ -0.00005
Swish(-100) ≈ 0
Comparison: Swish vs. ReLU vs. Softplus
Swish Advantages
- Self-gating through sigmoid
- Better than ReLU in many tests
- Smooth, differentiable function
- Discovered and validated by Google
- Parametrically tunable via β
Swish Disadvantages
- Computationally more expensive than ReLU
- Slower than ReLU during training
- Less intuitive than ReLU
- Beta parameter needs optimization
- Newer functions may be better
Role in Neural Networks
Activation Function
In neural networks, Swish acts as an intelligent gating mechanism:
Sigmoid acts as dynamic gating for input x.
Backpropagation
Smooth derivative enables stable gradient propagation:
Gentle gradients promote stable training.
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