The Modern Mathematics of Deep Learning

Composing ReLU layers

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.

Prediction rules and layers · Describe or apply prediction rules, layers and parameters.

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: 3.2 Simple pieces, many layers

Apply one operation, then use its output as the input to the next operation.

Composition is how layers build a network function.

Source formula example

x\mapsto\varrho_R(2\varrho_R(x)-1)

illustration · This is an invented two-layer example, not a proof of a source theorem.

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.

Input

This example’s data flow

You choose

input.x = 2

Calculated here

Result expression: { first, second }

first = Math.max(0, input.x) Uses: input.x
second = Math.max(0, 2 * first - 1) Uses: first

Returns

Example result

first: 2
second: 3

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

Change the input and run the same code again. The displayed result uses the values shown above.

Source: Teaching example