The Modern Mathematics of Deep Learning

A learned model

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: 1.2 Learning from examples

A learning algorithm can return a network with a fitted parameter.

This example makes the source statement computable on a finite model.

Source formula example

f_{s}={\mathcal{A}}({s})=\Phi_{{a}}(\cdot,\bar{\theta}),

illustration · This single fitting rule does not imply good risk or optimality.

Symbols

$f_{s}$: Model learned from training sample s.
$A$: Learning algorithm.
$Φₐ$: Network of architecture a.
$θ̄$: Fitted network parameters.

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

Initial values in code

sample = [1, 2, 3]

Calculated here

Result expression: { sample, theta, prediction: theta * input.x }

theta = sample.reduce((a, b) => a + b, 0) / sample.length Uses: sample

Returns

Example result

sample: array (3 items): [1, 2, 3]
theta: 2
prediction: 4

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The invented rule returns θ as the mean of three targets and Φ(x,θ)=θx.

Source: Source expression