Goal.Geometry.Map.Linear.Convolutional

Manifolds of Convolutional operators. This is hardly used, but could in theory power conv nets. One day.

Convolutional Manifolds

data Convolutional (rd :: Nat) (r :: Nat) (c :: Nat) :: Type -> Type -> Type

A Manifold of correlational/convolutional transformations, defined by the number of kernels, their radius, the depth of the input, and its number of rows and columns.

Instances

KnownConvolutional rd r c z x => Map a (Convolutional rd r c) z x

Defined in Goal.Geometry.Map.Linear.Convolutional

Methods

(>.>) :: (a # Convolutional rd r c z x) -> (a #* x) -> a # z

(>$>) :: (a # Convolutional rd r c z x) -> [a #* x] -> [a # z]

KnownConvolutional rd r c z x => Propagate a (Convolutional rd r c) z x

Defined in Goal.Geometry.Map.Linear.Convolutional

Methods

propagate :: [a #* z] -> [a #* x] -> (a # Convolutional rd r c z x) -> (a #* Convolutional rd r c z x, [a # z])

KnownConvolutional rd r c z x => Bilinear (Convolutional rd r c) z x

Defined in Goal.Geometry.Map.Linear.Convolutional

Methods

(>.<) :: (c0 # z) -> (c0 # x) -> c0 # Convolutional rd r c z x

(>$<) :: [c0 # z] -> [c0 # x] -> c0 # Convolutional rd r c z x

transpose :: (c0 # Convolutional rd r c z x) -> c0 # Convolutional rd r c x z

(1 <= (r * c), Manifold x, Manifold y, KnownNat r, KnownNat c, KnownNat rd, KnownNat (Div (Dimension x) (r * c)), KnownNat (Div (Dimension y) (r * c))) => Manifold (Convolutional rd r c y x)

Defined in Goal.Geometry.Map.Linear.Convolutional

Associated Types

type Dimension (Convolutional rd r c y x) :: Nat

type Dimension (Convolutional rd r c y x)

Defined in Goal.Geometry.Map.Linear.Convolutional

type Dimension (Convolutional rd r c y x) = Div (Dimension y) (r * c) * ((Div (Dimension x) (r * c) * ((2 * rd) + 1)) * ((2 * rd) + 1))

type KnownConvolutional rd r c z x = (KnownNat rd, KnownNat r, KnownNat c, 1 <= (r * c), Dimension x ~ ((Div (Dimension x) (r * c) * r) * c), Dimension z ~ ((Div (Dimension z) (r * c) * r) * c), Manifold (Convolutional rd r c z x), Manifold x, Manifold z, KnownNat (Div (Dimension x) (r * c)), KnownNat (Div (Dimension z) (r * c)))

A convenience type for ensuring that all the type-level Nats of a Convolutional Manifolds are KnownNats.