Gaussian weight and bias initialization
Penguin learning project
The project uses 342 complete Palmer penguin records: 240 training-pool and 102 held-out rows. The selected training rows determine feature scaling and model parameters. Source CSV
This project trains weights with softmax, unlike the homepage lab, which uses nearest species averages. Same penguin measurements; different classification methods. Predictions can differ.
Initialization · Describe initial parameters and their distributions.
The current objective supplies a gradient; training updates the model parameters.
Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.
Input: 12 × 2; Held-out evaluation: 102 · #58 · 40.6 mm, 193 mm. Known answer: Adélie; Prediction: Adélie · [≈0.7383, ≈0.2444, ≈0.01737].
Used in these source sections: 2.1 A view through similarity
For the ℓ-th layer, initial weights have mean zero and variance σw²/Nℓ; biases have mean zero and variance σb².
These values specify the normal initialization laws.
Source formula example
illustration · This gives the moments of the source normal laws; it does not draw values or establish convergence.
Symbols
- Layer index.
- Layer width.
- Positive initialization scales.
Source formula example
This source example uses its own inputs and assumptions. Editing it does not change the project.
Edit a value or the code, then run the example. This is a finite demonstration, not a proof of the paper’s theorem.
This example’s data flow
Code changed. Reset to restore this example’s data flow.
Initial values in code
layer=1width=4sigmaW=2sigmaB=1
Calculated here
Result expression: {
layer,
width,
weightMean: 0,
weightVariance: (sigmaW * sigmaW) / width,
biasMean: 0,
biasVariance: sigmaB * sigmaB,
}
Returns
layer- 1
width- 4
weightMean- 0
weightVariance- 1
biasMean- 0
biasVariance- 1
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. This gives the moments of the source normal laws; it does not draw values or establish convergence.
Source: Inline notation