The Modern Mathematics of Deep Learningexplained for non-mathematicians

Zero output weights

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.

Pruning · Describe removal of network weights and related error bounds.

The project uses a linear rule with two features. The fitted weights produce scores or normalized mass.

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: 6.5 Removing connections

When the second-layer output weights are all zero, their weighted contribution is zero.

This is the trivial zero-output-weight case in the pruning argument.

Source formula example

w(2)=0w^{(2)}=0

illustration · This example covers the contribution of these weights; an additional output bias would need to be included separately.

Symbols

w(2)w⁽²⁾
The output weight vector.

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

  • weights = [0, 0]
  • features = [2, 3]

Calculated here

Result expression: { weights, features, output: weights.reduce((s, w, i) => s + w * features[i], 0), }

Returns

Example result
weights
array (2 items): [0, 0]
features
array (2 items): [2, 3]
output
0

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

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented. This example covers the contribution of these weights; an additional output bias would need to be included separately.

Source: Inline notation