Simple MLP training example (regression)

This is a focused end-to-end example of training a small MLP in TorchLean.

It mirrors the simplest PyTorch workflow:

1. build a small synthetic dataset (in-memory),
2. define an MLP (Linear -> ReLU -> Linear),
3. train with Adam,
4. report loss before/after, plus a few probe predictions.

Run:

• lake exe torchlean quickstart_mlp
• lake exe torchlean quickstart_mlp --steps 200 --dtype float --backend eager

Optional flags (tutorial-specific):

• --seed S (model init + any shuffling)
• --steps N

def NN.Examples.Quickstart.SimpleMLPTrain.inDim : ℕ

def NN.Examples.Quickstart.SimpleMLPTrain.outDim : ℕ

def NN.Examples.Quickstart.SimpleMLPTrain.mkModel : API.nn.M (API.nn.Sequential (Shape.Vec inDim) (Shape.Vec outDim))

A small 2-layer MLP 2 -> 8 -> 1.

def NN.Examples.Quickstart.SimpleMLPTrain.task (seed : ℕ) : API.TorchLean.Trainer.Task (Shape.Vec inDim) (Shape.Vec outDim)

Regression task: model + MSE loss.

def NN.Examples.Quickstart.SimpleMLPTrain.target {α : Type} [API.Semantics.Scalar α] [API.Runtime.Scalar α] (x1 x2 : α) : α

Small piecewise-linear regression target:

y = 0.8 * relu(x1 + x2) - 0.4 * relu(x2 - x1) + 0.2.

This is easy for a compact ReLU MLP to fit, which keeps the quickstart dependable.

def NN.Examples.Quickstart.SimpleMLPTrain.buildDataset {α : Type} [API.Semantics.Scalar α] [API.Runtime.Scalar α] : Runtime.Autograd.Train.Dataset (API.sample.Supervised α (Shape.Vec inDim) (Shape.Vec outDim))

Build the training dataset at the runtime-selected scalar type α.

We write the sample coordinates as Float literals first because they are convenient to read, and Data.supervisedDim0F lifts them into the chosen runtime scalar backend.

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