The Modern Mathematics of Deep Learningexplained for non-mathematicians

Concepts / Start here

Network hypothesis class

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.

Model classes and structure Β· Describe families of rules, their size and structural properties.

The project supplies finite observations and fitted parameters. A held-out sample does not establish population bounds or prove a theorem.

Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.

Input: 12 Γ— 2; Held-out evaluation: 102 Β· #58 Β· 40.6 mm, 193 mm. Known answer: AdΓ©lie; Prediction: AdΓ©lie Β· [β‰ˆ0.7383, β‰ˆ0.2444, β‰ˆ0.01737].

Used in these source sections: 1.2 Learning from examples Β· 2.2 Weight size and room to decide Β· 2.3 The path matters

𝓕ₐ is the class of functions realized by the architecture a using allowed parameters. f ∈ 𝓕ₐ selects one such function.

Architecture and parameter restrictions define which models are available.

Source formula example

Fa{\mathcal{F}}_{{a}}

illustration Β· This finite parameter restriction illustrates a class; the source can allow infinitely many parameters.

Symbols

aa
A network architecture.
Fa\mathcal{F}ₐ
The corresponding network function class.
ff
A function in that class.

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

  • x = 2
  • parameters = [0, 1]

Calculated here

Result expression: { x, parameters, outputs, selectedOutput: outputs[1] }

  • outputs = parameters.map((theta) => theta * x) Uses: parameters, x

Returns

Example result
x
2
parameters
array (2 items): [0, 1]
outputs
array (2 items): [0, 2]
selectedOutput
2

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 finite parameter restriction illustrates a class; the source can allow infinitely many parameters.

Source: Inline notation