Initialization Results
Formula substitution
Recommendation
Sample Weights and Statistics
Initialization Comparison
| Method | Variance | Std. deviation | Bounds | Best fit | Notes |
|---|---|---|---|---|---|
| Calculate or build a comparison. | |||||
Framework Code Generator
Calculate first, then generate matching framework code.
Formula Used
Xavier initialization balances forward and backward signal variance. It uses both fan values. This often suits sigmoid and tanh activations.
He initialization preserves variance through ReLU-family layers. It usually uses fan-in. Fan-out can support backward signal preservation.
LeCun initialization commonly pairs with SELU networks. Its variance equals one divided by fan-in. Proper normalization assumptions still matter.
How to Use This Calculator
- Select the neural network layer type.
- Enter its input, output, kernel, and group dimensions.
- Choose the activation and initialization method.
- Review or adjust advanced distribution settings.
- Set the preview size and numerical precision.
- Press Calculate Initialization.
- Review fan values, variance, bounds, samples, and warnings.
- Compare methods or generate framework code.
- Copy, print, or export the results.
Example Data
| Layer | Shape | Activation | Common initializer | Reason |
|---|---|---|---|---|
| Dense | 784 × 256 | ReLU | He normal | Supports ReLU variance flow. |
| Dense | 128 × 64 | Tanh | Xavier uniform | Balances fan-in and fan-out. |
| Conv2D | 128 × 64 × 3 × 3 | ReLU | He uniform | Accounts for the receptive field. |
| Dense | 256 × 128 | SELU | LeCun normal | Supports self-normalizing assumptions. |
| Recurrent matrix | 128 × 128 | Tanh | Orthogonal | Can preserve vector norms. |
Initialization Guidance
Fan-in and fan-out
Fan-in counts incoming connections per output unit. Fan-out counts outgoing connections per input unit. Convolutions also include kernel positions.
Vanishing gradients
Very small weights can shrink activations and gradients. Deep saturated networks are especially vulnerable. Matching variance helps preserve useful signals.
Exploding gradients
Very large weights can amplify signals repeatedly. Training may become unstable or produce invalid numbers. Initialization and normalization can reduce this risk.
Important limitation
Calculated values are theoretical starting points. Architecture, normalization, residual paths, and optimizer choices matter. Always verify behavior during real training.
Frequently Asked Questions
Why should weights not all start at zero?
Equal hidden-unit weights receive equal gradient updates. Their learned features remain identical. Random initialization breaks this symmetry.
When should Xavier initialization be used?
Xavier commonly suits tanh, sigmoid, or linear layers. It balances incoming and outgoing variance. Saturating activations still need careful monitoring.
When should He initialization be used?
He initialization commonly suits ReLU-family activations. It compensates for inactive negative responses. The correct gain depends on nonlinearity.
What is the difference between fan-in and fan-out?
Fan-in represents inputs reaching each output. Fan-out represents outputs reached by each input. Their choice affects forward or backward variance.
Does the random seed affect the formula?
The seed does not change theoretical variance. It changes the generated random sequence. Reusing it improves experiment reproducibility.
Why use truncated normal initialization?
Truncation removes extreme random draws. This can reduce unusually large starting values. The resulting variance may differ from untruncated normal.
What does orthogonal initialization do?
Orthogonal matrices preserve lengths in ideal linear transformations. They are useful for some recurrent layers. Rectangular tensors require careful reshaping.
How are grouped convolutions handled?
Input channels per filter are divided by groups. Output connectivity is adjusted similarly. Invalid divisibility produces a warning.
Should biases use the same initializer?
Biases commonly start at zero. Some architectures use small constants or priors. The calculator lets you compare choices.
Are generated samples identical to framework output?
The formulas target equivalent distributions. Random algorithms and truncation details can differ. Framework-specific results may therefore vary.