The Modern Mathematics of Deep Learning

Training input indices

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.

Observations and sampling · Describe examples, targets and samples.

The selected rows supply measurements and known answers to training; held-out IDs remain separate.

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: 1.2.3 Does it work on new examples? · 2.1 A view through similarity · 4.2 Approximating with random pieces · More source sections

The indexed collection contains m inputs x⁽ⁱ⁾, one for each training position i.

The indices connect each input to its training example.

Source formula example

(x^{(i)})_{i=1}^{m}\in{\mathcal{X}}^{m}

illustration · This example contains two real vectors; the source permits other input spaces.

Symbols

$x⁽ⁱ⁾$: Input of example i.
$m$: Number of inputs.
$𝒳ᵐ$: Ordered m-tuples of inputs from 𝒳.

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

inputs = [ [1, 2], [3, 4], ]

Calculated here

Result expression: { inputs, m: inputs.length, first: inputs[0], second: inputs[1] }

Returns

Example result

inputs: array (2 items): [array (2 items): [1, 2], array (2 items): [3, 4]]
m: 2
first: array (2 items): [1, 2]
second: array (2 items): [3, 4]

JavaScript

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 contains two real vectors; the source permits other input spaces.

Source: Inline notation