Spaces:
Running
Running
File size: 5,203 Bytes
e3bf489 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 |
## **1. Sigmoid (Logistic)**
**Formula:** σ(x) = 1 / (1 + exp(-x))
**Strengths:** Maps any real-valued number to a value between 0 and 1, making it suitable for binary classification problems.
**Weaknesses:** Saturates (i.e., output values approach 0 or 1) for large inputs, leading to vanishing gradients during backpropagation.
**Usage:** Binary classification, logistic regression.
## **2. Hyperbolic Tangent (Tanh)**
**Formula:** tanh(x) = 2 / (1 + exp(-2x)) - 1
**Strengths:** Similar to sigmoid, but maps to (-1, 1), which can be beneficial for some models.
**Weaknesses:** Also saturates, leading to vanishing gradients.
**Usage:** Similar to sigmoid, but with a larger output range.
## **3. Rectified Linear Unit (ReLU)**
**Formula:** f(x) = max(0, x)
**Strengths:** Computationally efficient, non-saturating, and easy to compute.
**Weaknesses:** Not differentiable at x=0, which can cause issues during optimization.
**Usage:** Default activation function in many deep learning frameworks, suitable for most neural networks.
## **4. Leaky ReLU**
**Formula:** f(x) = max(αx, x), where α is a small constant (e.g., 0.01)
**Strengths:** Similar to ReLU, but allows a small fraction of the input to pass through, helping with dying neurons.
**Weaknesses:** Still non-differentiable at x=0.
**Usage:** Alternative to ReLU, especially when dealing with dying neurons.
## **5. Swish**
**Formula:** f(x) = x \* g(x), where g(x) is a learned function (e.g., sigmoid or ReLU)
**Strengths:** Self-gated, adaptive, and non-saturating.
**Weaknesses:** Computationally expensive, requires additional learnable parameters.
**Usage:** Can be used in place of ReLU or other activations, but may not always outperform them.
## **6. Softmax**
**Formula:** softmax(x) = exp(x) / Σ exp(x)
**Strengths:** Normalizes output to ensure probabilities sum to 1, making it suitable for multi-class classification.
**Weaknesses:** Only suitable for output layers with multiple classes.
**Usage:** Output layer activation for multi-class classification problems.
## **7. Softsign**
**Formula:** f(x) = x / (1 + |x|)
**Strengths:** Similar to sigmoid, but with a more gradual slope.
**Weaknesses:** Not commonly used, may not provide significant benefits over sigmoid or tanh.
**Usage:** Alternative to sigmoid or tanh in certain situations.
## **8. ArcTan**
**Formula:** f(x) = arctan(x)
**Strengths:** Non-saturating, smooth, and continuous.
**Weaknesses:** Not commonly used, may not outperform other activations.
**Usage:** Experimental or niche applications.
## **9. SoftPlus**
**Formula:** f(x) = log(1 + exp(x))
**Strengths:** Smooth, continuous, and non-saturating.
**Weaknesses:** Not commonly used, may not outperform other activations.
**Usage:** Experimental or niche applications.
## **10. Gaussian Error Linear Unit (GELU)**
**Formula:** f(x) = x \* Φ(x), where Φ is the cumulative distribution function of the standard normal distribution
**Strengths:** Non-saturating, smooth, and computationally efficient.
**Weaknesses:** Not as well-studied as ReLU or other activations.
**Usage:** Alternative to ReLU, especially in Bayesian neural networks.
## **11. Mish**
**Formula:** f(x) = x \* tanh(softplus(x))
**Strengths:** Non-saturating, smooth, and computationally efficient.
**Weaknesses:** Not as well-studied as ReLU or other activations.
**Usage:** Alternative to ReLU, especially in computer vision tasks.
## **12. Silu (SiLU)**
**Formula:** f(x) = x \* sigmoid(x)
**Strengths:** Non-saturating, smooth, and computationally efficient.
**Weaknesses:** Not as well-studied as ReLU or other activations.
**Usage:** Alternative to ReLU, especially in computer vision tasks.
## **13. GELU Approximation (GELU Approx.)**
**Formula:** f(x) ≈ 0.5 \* x \* (1 + tanh(√(2/π) \* (x + 0.044715 \* x^3)))
**Strengths:** Fast, non-saturating, and smooth.
**Weaknesses:** Approximation, not exactly equal to GELU.
**Usage:** Alternative to GELU, especially when computational efficiency is crucial.
## **14. SELU (Scaled Exponential Linear Unit)**
**Formula:** f(x) = λ { x if x > 0, α(e^x - 1) if x ≤ 0 }
**Strengths:** Self-normalizing, non-saturating, and computationally efficient.
**Weaknesses:** Requires careful initialization and α tuning.
**Usage:** Alternative to ReLU, especially in deep neural networks.
When choosing an activation function, consider the following:
* **Non-saturation:** Avoid activations that saturate (e.g., sigmoid, tanh) to prevent vanishing gradients.
* **Computational efficiency:** Choose activations that are computationally efficient (e.g., ReLU, Swish) for large models or real-time applications.
* **Smoothness:** Smooth activations (e.g., GELU, Mish) can help with optimization and convergence.
* **Domain knowledge:** Select activations based on the problem domain and desired output (e.g., softmax for multi-class classification).
* **Experimentation:** Try different activations and evaluate their performance on your specific task.
|