The Modern Mathematics of Deep Learning

Learning as a map

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.

Learning and parameter updates · Select a rule or update parameters using a learning rule.

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: 1.2 Learning from examples

A learning rule takes a finite training sample and returns a prediction function.

This separates a learning algorithm from the model it returns.

Source formula example

{\mathcal{A}}\colon\bigcup_{m\in{\mathbb{N}}}{\mathcal{Z}}^{m}\to{\mathcal{F}},

illustration · This is one invented learning algorithm, not a general learning guarantee.

Symbols

$A$: Learning algorithm mapping finite samples to prediction functions.
$Z$: Space of individual training examples.
$F$: Set of possible prediction functions.
$m$: Positive sample size.

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.

Second target

This example’s data flow

You choose

input.target = 2

Calculated here

Result expression: { sample, fittedConstant, predictionAtTwo: predict(2) }

sample = [1, input.target, 3] Uses: input.target
fittedConstant = sample.reduce((a, b) => a + b, 0) / sample.length Uses: sample

Returns

Example result

sample: array (3 items): [1, 2, 3]
fittedConstant: 2
predictionAtTwo: 2

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

The toy algorithm returns the constant function equal to the mean of three targets.

Source: Source expression