Quickstart: Autograd Basics

Tour of the public autograd APIs beyond .backward():

• API.autograd.model.* for model-level VJP / jacobian / loss gradients.
• API.autograd.model.OutputLoss.* for reusable scalar losses on model outputs.
• API.autograd.fn1.* for Jacobian / Hessian helpers on single-input tensor functions.
• API.nn.functional.detach for stop-gradient behavior.

Run: lake exe torchlean quickstart_autograd --dtype float --backend eager lake exe torchlean quickstart_autograd --dtype float32 --backend compiled

This file is a curated "autodiff API tour". It intentionally avoids:

• low-level runtime tape/session code,
• hand-written parameter-shape bookkeeping,
• noisy castTensor helpers.

Instead, it uses the public API.autograd.* facade and tensorF! cast ... to build deterministic constants for any runtime scalar α.

def NN.Examples.Quickstart.AutogradBasics.model : API.nn.Sequential (Shape.Vec 2) (Shape.Vec 3)

def NN.Examples.Quickstart.AutogradBasics.mseLoss : API.autograd.model.OutputLoss (Shape.Vec 3) (Shape.Vec 3)

def NN.Examples.Quickstart.AutogradBasics.detachedMSELoss : API.autograd.model.OutputLoss (Shape.Vec 3) (Shape.Vec 3)

def NN.Examples.Quickstart.AutogradBasics.squareFn : API.autograd.fn1.Fn (Shape.Vec 2) (Shape.Vec 2)

def NN.Examples.Quickstart.AutogradBasics.sumsqFn : API.autograd.fn1.Fn (Shape.Vec 2) Spec.Shape.scalar

def NN.Examples.Quickstart.AutogradBasics.runOnce {α : Type} [API.Semantics.Scalar α] [DecidableEq Spec.Shape] [ToString α] (cast : Float → α) : IO Unit

def NN.Examples.Quickstart.AutogradBasics.main (args : List String) : IO Unit