The Modern Mathematics of Deep Learningexplained for non-mathematicians

Random initial parameters

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

Θ₀ is the random parameter vector at initialization. A realization fixes one concrete parameter vector and thereby one network function.

Initialization determines the network before training.

Source formula example

Θ0\Theta_{0}

illustration · The example fixes one realization; the source specifies independent normal initial entries.

Symbols

Θ0Θ₀
A random initial parameter vector.
Φ(⋅,Θ0)Φ(·,Θ₀)
The corresponding network function.

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

Initial values in code

  • theta0 = [1, -1]

Calculated here

Result expression: { theta0, input: 2, output: f(2) }

Returns

Example result
theta0
array (2 items): [1, -1]
input
2
output
1

Read numbers from input and return the result. JavaScript basics.

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented. The example fixes one realization; the source specifies independent normal initial entries.

Source: Inline notation