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

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

Minimal complete definition

Nothing

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

default sumBuilder :: forall b. (VecBuilder v ~ Maybe b, Generic b, Generic v, GBasicVector (Rep b) (Rep v), AdditiveGroup v) => VecBuilder v -> v

identityBuilder :: v -> VecBuilder v

default identityBuilder :: forall b. (VecBuilder v ~ Maybe b, Generic b, Generic v, GBasicVector (Rep b) (Rep v), AdditiveGroup v) => v -> VecBuilder v

Instances

BasicVector Integer

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Integer

Methods

sumBuilder :: VecBuilder Integer -> Integer

identityBuilder :: Integer -> VecBuilder Integer

BasicVector Double

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Double

Methods

sumBuilder :: VecBuilder Double -> Double

identityBuilder :: Double -> VecBuilder Double

BasicVector Float

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder Float

Methods

sumBuilder :: VecBuilder Float -> Float

identityBuilder :: Float -> VecBuilder Float

Num a => BasicVector (AsNum a)

Defined in Downhill.BVar.Num

Associated Types

type VecBuilder (AsNum a)

Methods

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

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

AdditiveGroup v => BasicVector (DenseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (DenseVector v)

Methods

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

identityBuilder :: DenseVector v -> VecBuilder (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

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

(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)

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

identityBuilder :: (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

identityBuilder :: SparseVector v -> VecBuilder (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

AdditiveGroup v => BasicVector (DenseVector v)

Defined in Downhill.Linear.Expr

Associated Types

type VecBuilder (DenseVector v)

Methods

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

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

Defined in Downhill.Linear.Expr

Associated Types

type Scalar (DenseVector v)

Methods

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

type VecBuilder (DenseVector v)

Defined in Downhill.Linear.Expr

type VecBuilder (DenseVector v) = DenseBuilder v

type Scalar (DenseVector v)

Defined in Downhill.Linear.Expr

type Scalar (DenseVector v) = Scalar v

newtype DenseBuilder v

Constructors

DenseBuilder (Maybe v)

Instances

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

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

toDenseBuilder :: v -> DenseBuilder v

Generics

genericSumBuilder :: forall b v. (Generic b, Generic v, GBasicVector (Rep b) (Rep v)) => b -> v

genericIdentityBuilder :: forall b v. (Generic b, Generic v, GBasicVector (Rep b) (Rep v)) => v -> b

genericSumMaybeBuilder :: forall b v. (Generic b, Generic v, AdditiveGroup v, GBasicVector (Rep b) (Rep v)) => Maybe b -> v

genericIdentityMaybeBuilder :: forall b v. (Generic b, Generic v, GBasicVector (Rep b) (Rep v)) => v -> Maybe b

Misc

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