Goal.Geometry.Map.NeuralNetwork

Multilayer perceptrons which instantiate backpropagation through laziness. Right now the structure is simplier than it could be, but it leads to nice types. If anyone ever wants to use a DNN with super-Affine biases, the code is willing.

Neural Networks

data NeuralNetwork (gys :: [(Type -> Type -> Type, Type)]) (f :: Type -> Type -> Type) z x

A multilayer, artificial neural network.

Instances

Map c f z x => Map c (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

(>.>) :: (c # NeuralNetwork '[] f z x) -> (c #* x) -> c # z

(>$>) :: (c # NeuralNetwork '[] f z x) -> [c #* x] -> [c # z]

(Map c f z y, Map c (NeuralNetwork gys g) y x, Transition c (Dual c) y) => Map c (NeuralNetwork ('(g, y) ': gys) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

(>.>) :: (c # NeuralNetwork ('(g, y) ': gys) f z x) -> (c #* x) -> c # z

(>$>) :: (c # NeuralNetwork ('(g, y) ': gys) f z x) -> [c #* x] -> [c # z]

(Propagate c f z y, Propagate c (NeuralNetwork gys g) y x, Map c f y z, Transition c (Dual c) y, Legendre y, Riemannian c y, Bilinear f z y) => Propagate c (NeuralNetwork ('(g, y) ': gys) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

propagate :: [c #* z] -> [c #* x] -> (c # NeuralNetwork ('(g, y) ': gys) f z x) -> (c #* NeuralNetwork ('(g, y) ': gys) f z x, [c # z])

Propagate c f z x => Propagate c (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f) z x

Defined in Goal.Geometry.Map.NeuralNetwork

Methods

propagate :: [c #* z] -> [c #* x] -> (c # NeuralNetwork '[] f z x) -> (c #* NeuralNetwork '[] f z x, [c # z])

(Manifold (Affine f z z y), Manifold (NeuralNetwork gys g y x)) => Product (NeuralNetwork ('(g, y) ': gys) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

Associated Types

type First (NeuralNetwork ('(g, y) ': gys) f z x)

type Second (NeuralNetwork ('(g, y) ': gys) f z x)

Methods

join :: (c # First (NeuralNetwork ('(g, y) ': gys) f z x)) -> (c # Second (NeuralNetwork ('(g, y) ': gys) f z x)) -> c # NeuralNetwork ('(g, y) ': gys) f z x

split :: (c # NeuralNetwork ('(g, y) ': gys) f z x) -> (c # First (NeuralNetwork ('(g, y) ': gys) f z x), c # Second (NeuralNetwork ('(g, y) ': gys) f z x))

(Manifold (Affine f z z y), Manifold (NeuralNetwork gys g y x)) => Manifold (NeuralNetwork ('(g, y) ': gys) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

Associated Types

type Dimension (NeuralNetwork ('(g, y) ': gys) f z x) :: Nat

Manifold (Affine f z z x) => Manifold (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

Associated Types

type Dimension (NeuralNetwork '[] f z x) :: Nat

type First (NeuralNetwork ('(g, y) ': gys) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

type First (NeuralNetwork ('(g, y) ': gys) f z x) = Affine f z z y

type Second (NeuralNetwork ('(g, y) ': gys) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

type Second (NeuralNetwork ('(g, y) ': gys) f z x) = NeuralNetwork gys g y x

type Dimension (NeuralNetwork ('(g, y) ': gys) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

type Dimension (NeuralNetwork ('(g, y) ': gys) f z x) = Dimension (Affine f z z y) + Dimension (NeuralNetwork gys g y x)

type Dimension (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f z x)

Defined in Goal.Geometry.Map.NeuralNetwork

type Dimension (NeuralNetwork ('[] :: [(Type -> Type -> Type, Type)]) f z x) = Dimension (Affine f z z x)