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 sample 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.defaultLogJson : System.FilePath

Default JSON log path used only when the user explicitly passes --log.

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

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

def NN.Examples.Quickstart.SimpleMLPTrain.model : TorchLean.nn.M (TorchLean.nn.Sequential (TorchLean.Shape.vec inDim) (TorchLean.Shape.vec outDim))

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

def NN.Examples.Quickstart.SimpleMLPTrain.target (x1 x2 : Float) : Float

Small piecewise-linear regression target:

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

This is a natural fit for a small ReLU MLP, which keeps the command dependable.

def NN.Examples.Quickstart.SimpleMLPTrain.buildDataset : TorchLean.Trainer.Dataset (TorchLean.Shape.vec inDim) (TorchLean.Shape.vec outDim)

Build the tutorial dataset at the runtime-selected scalar type.

Data.regression2to1Grid keeps shape-indexed tensor slicing out of the first training example. The underlying value is still a TorchLean supervised dataset with checked input/output shapes.

def NN.Examples.Quickstart.SimpleMLPTrain.usage : String

Command-line help for the simple MLP quickstart.

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