Model Regresi Non-Linear
Model: $y = \sigma(m \cdot x + c)$ (dengan
fungsi aktivasi)
Loss Function: $L = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$ (Mean Squared Error)
Fungsi Aktivasi: $\sigma(z)$ mentransformasi output linear menjadi non-linear
Loss Function: $L = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$ (Mean Squared Error)
Fungsi Aktivasi: $\sigma(z)$ mentransformasi output linear menjadi non-linear
Non-Linear Gradient Descent with Activation Functions
Watch as the algorithm learns non-linear relationships using activation functions:
0.10
0.50
0.00
0.50
0.00
Current Loss (MSE):
0.000
Ready to start gradient descent algorithm
Data Points & Non-Linear Model
3D Loss Surface & Non-Linear Path
Informasi Model Non-Linear
Non-Linear Model Equation:
$y = \sigma(m \cdot x + c)$ where $\sigma$ is the activation function
Chain Rule Derivatives:
$\frac{\partial L}{\partial m} = \frac{2}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i) \cdot \sigma'(z_i) \cdot x_i$
$\frac{\partial L}{\partial c} = \frac{2}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i) \cdot \sigma'(z_i)$
where $z_i = m \cdot x_i + c$ and $\sigma'$ is the activation derivative
Current Iteration: 0
Current Parameters: m = 0.500, c = 0.000
Current Gradients: ∂L/∂m = 0.000, ∂L/∂c = 0.000
$y = \sigma(m \cdot x + c)$ where $\sigma$ is the activation function
Chain Rule Derivatives:
$\frac{\partial L}{\partial m} = \frac{2}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i) \cdot \sigma'(z_i) \cdot x_i$
$\frac{\partial L}{\partial c} = \frac{2}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i) \cdot \sigma'(z_i)$
where $z_i = m \cdot x_i + c$ and $\sigma'$ is the activation derivative
Current Iteration: 0
Current Parameters: m = 0.500, c = 0.000
Current Gradients: ∂L/∂m = 0.000, ∂L/∂c = 0.000
| # | X Value | Y Value (True) | Y Predicted | Loss (Squared Error) |
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