Downhill.Linear.Expr

Expression

data Expr a v where

Expr a v represents a linear expression of type v, containing some free variables of type a.

Constructors

ExprVar :: Expr a a

ExprSum :: BasicVector v => [Term a v] -> Expr a v

Instances

FullVector dv => VectorSpace (Expr da dv)

Defined in Downhill.Linear.Expr

Associated Types

type Scalar (Expr da dv)

Methods

(*^) :: Scalar (Expr da dv) -> Expr da dv -> Expr da dv

FullVector v => AdditiveGroup (Expr a v)

Defined in Downhill.Linear.Expr

Methods

zeroV :: Expr a v

(^+^) :: Expr a v -> Expr a v -> Expr a v

negateV :: Expr a v -> Expr a v

(^-^) :: Expr a v -> Expr a v -> Expr a v

type Scalar (Expr da dv)

Defined in Downhill.Linear.Expr

type Scalar (Expr da dv) = Scalar dv

data Term a v where

Argument f in Term f x must be linear function. That's a law.

Constructors

Term :: (v -> VecBuilder u) -> Expr a u -> Term a v

Vectors

class Monoid (VecBuilder v) => BasicVector v where

Associated Types

type VecBuilder v :: Type

VecBuilder v is a sparse representation of vector v. Edges of a computational graph produce builders, which are then summed into vectors in nodes. Monoid operation <> means addition of vectors, but it doesn't need to compute the sum immediately - it might defer computation until sumBuilder is evaluated.

sumBuilder mempty = zeroV
sumBuilder (x <> y) = sumBuilder x ^+^ sumBuilder y

mempty must be cheap. <> must be O(1).

Methods

sumBuilder :: VecBuilder v -> v

Instances

BasicVector Double

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Double

Methods

sumBuilder :: VecBuilder Double -> Double

BasicVector Float

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Float

Methods

sumBuilder :: VecBuilder Float -> Float

BasicVector Integer

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Integer

Methods

sumBuilder :: VecBuilder Integer -> Integer

AdditiveGroup v => BasicVector (DenseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (DenseVector v)

Methods

sumBuilder :: VecBuilder (DenseVector v) -> DenseVector v

Monoid (VecBuilder v) => BasicVector (SparseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (SparseVector v)

Methods

sumBuilder :: VecBuilder (SparseVector v) -> SparseVector v

Num a => BasicVector (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type VecBuilder (AsNum a)

Methods

sumBuilder :: VecBuilder (AsNum a) -> AsNum a

(BasicVector a, BasicVector b) => BasicVector (a, b)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (a, b)

Methods

sumBuilder :: VecBuilder (a, b) -> (a, b)

(BasicVector a, BasicVector b, BasicVector c) => BasicVector (a, b, c)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (a, b, c)

Methods

sumBuilder :: VecBuilder (a, b, c) -> (a, b, c)

class (BasicVector v, VectorSpace v) => FullVector v where

Full-featured vector.

Gradients are linear functions and form a vector space. FullVector class provides functionality that is needed to make VectorSpace instances.

Methods

identityBuilder :: v -> VecBuilder v

negateBuilder :: v -> VecBuilder v

scaleBuilder :: Scalar v -> v -> VecBuilder v

Instances

FullVector Double

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: Double -> VecBuilder Double

negateBuilder :: Double -> VecBuilder Double

scaleBuilder :: Scalar Double -> Double -> VecBuilder Double

FullVector Float

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: Float -> VecBuilder Float

negateBuilder :: Float -> VecBuilder Float

scaleBuilder :: Scalar Float -> Float -> VecBuilder Float

FullVector Integer

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: Integer -> VecBuilder Integer

negateBuilder :: Integer -> VecBuilder Integer

scaleBuilder :: Scalar Integer -> Integer -> VecBuilder Integer

VectorSpace v => FullVector (DenseVector v)

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: DenseVector v -> VecBuilder (DenseVector v)

negateBuilder :: DenseVector v -> VecBuilder (DenseVector v)

scaleBuilder :: Scalar (DenseVector v) -> DenseVector v -> VecBuilder (DenseVector v)

Num a => FullVector (AsNum a)

Defined in Downhill.BVar.Num

Methods

identityBuilder :: AsNum a -> VecBuilder (AsNum a)

negateBuilder :: AsNum a -> VecBuilder (AsNum a)

scaleBuilder :: Scalar (AsNum a) -> AsNum a -> VecBuilder (AsNum a)

(Scalar a ~ Scalar b, FullVector a, FullVector b) => FullVector (a, b)

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: (a, b) -> VecBuilder (a, b)

negateBuilder :: (a, b) -> VecBuilder (a, b)

scaleBuilder :: Scalar (a, b) -> (a, b) -> VecBuilder (a, b)

(s ~ Scalar a, s ~ Scalar b, s ~ Scalar c, FullVector a, FullVector b, FullVector c) => FullVector (a, b, c)

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: (a, b, c) -> VecBuilder (a, b, c)

negateBuilder :: (a, b, c) -> VecBuilder (a, b, c)

scaleBuilder :: Scalar (a, b, c) -> (a, b, c) -> VecBuilder (a, b, c)

newtype SparseVector v

Normally graph node would compute the sum of gradients and then propagate it to ancestor nodes. That's the best strategy when some computation needs to be performed for backpropagation. Some operations, like constructing/deconstructing tuples or wrapping/unwrapping, don't need to compute the sum. Doing so only destroys sparsity. A node of type SparseVector v won't sum the gradients, it will simply forward builders to its parents.

Constructors

SparseVector

Fields

• unSparseVector :: VecBuilder v

Instances

Semigroup (VecBuilder v) => Semigroup (SparseVector v)

Defined in Downhill.Linear.Expr

Methods

(<>) :: SparseVector v -> SparseVector v -> SparseVector v

sconcat :: NonEmpty (SparseVector v) -> SparseVector v

stimes :: Integral b => b -> SparseVector v -> SparseVector v

Monoid (VecBuilder v) => BasicVector (SparseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (SparseVector v)

Methods

sumBuilder :: VecBuilder (SparseVector v) -> SparseVector v

type VecBuilder (SparseVector v)

Defined in Downhill.Linear.Expr

type VecBuilder (SparseVector v) = VecBuilder v

newtype DenseVector v

When sparsity is not needed, we can use vector v as a builder of itself. DenseVector takes care of that.

Constructors

DenseVector v

Instances

VectorSpace v => VectorSpace (DenseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type Scalar (DenseVector v)

Methods

(*^) :: Scalar (DenseVector v) -> DenseVector v -> DenseVector v

AdditiveGroup v => AdditiveGroup (DenseVector v)

Defined in Downhill.Linear.Expr

Methods

zeroV :: DenseVector v

(^+^) :: DenseVector v -> DenseVector v -> DenseVector v

negateV :: DenseVector v -> DenseVector v

(^-^) :: DenseVector v -> DenseVector v -> DenseVector v

VectorSpace v => FullVector (DenseVector v)

Defined in Downhill.Linear.Expr

Methods

identityBuilder :: DenseVector v -> VecBuilder (DenseVector v)

negateBuilder :: DenseVector v -> VecBuilder (DenseVector v)

scaleBuilder :: Scalar (DenseVector v) -> DenseVector v -> VecBuilder (DenseVector v)

AdditiveGroup v => BasicVector (DenseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (DenseVector v)

Methods

sumBuilder :: VecBuilder (DenseVector v) -> DenseVector v

type Scalar (DenseVector v)

Defined in Downhill.Linear.Expr

type Scalar (DenseVector v) = Scalar v

type VecBuilder (DenseVector v)

Defined in Downhill.Linear.Expr

type VecBuilder (DenseVector v) = DenseBuilder v

newtype DenseBuilder v

Constructors

DenseBuilder (Maybe v)

Instances

AdditiveGroup v => Semigroup (DenseBuilder v)

Defined in Downhill.Linear.Expr

Methods

(<>) :: DenseBuilder v -> DenseBuilder v -> DenseBuilder v

sconcat :: NonEmpty (DenseBuilder v) -> DenseBuilder v

stimes :: Integral b => b -> DenseBuilder v -> DenseBuilder v

AdditiveGroup v => Monoid (DenseBuilder v)

Defined in Downhill.Linear.Expr

Methods

mempty :: DenseBuilder v

mappend :: DenseBuilder v -> DenseBuilder v -> DenseBuilder v

mconcat :: [DenseBuilder v] -> DenseBuilder v

toDenseBuilder :: v -> DenseBuilder v

Misc

maybeToMonoid :: Monoid m => Maybe m -> m