Numeric.Backprop.Class

Provides the Backprop typeclass, a class for values that can be used for backpropagation.

This class replaces the old (version 0.1) API relying on Num.

Since: 0.2.0.0

Backpropagatable types

class Backprop a where

Class of values that can be backpropagated in general.

For instances of Num, these methods can be given by zeroNum, addNum, and oneNum. There are also generic options given in Numeric.Backprop.Class for functors, IsList instances, and Generic instances.

instance Backprop Double where
    zero = zeroNum
    add = addNum
    one = oneNum

If you leave the body of an instance declaration blank, GHC Generics will be used to derive instances if the type has a single constructor and each field is an instance of Backprop.

To ensure that backpropagation works in a sound way, should obey the laws:

identity

• add x (zero y) = x

• add (zero x) y = y

Also implies preservation of information, making zipWith (+) an illegal implementation for lists and vectors.

This is only expected to be true up to potential "extra zeroes" in x and y in the result.

commutativity

• add x y = add y x

associativity

• add x (add y z) = add (add x y) z

idempotence

• zero . zero = zero

• one . one = one

unital

• one = gradBP id

Note that not all values in the backpropagation process needs all of these methods: Only the "final result" needs one, for example. These are all grouped under one typeclass for convenience in defining instances, and also to talk about sensible laws. For fine-grained control, use the "explicit" versions of library functions (for example, in Numeric.Backprop.Explicit) instead of Backprop based ones.

This typeclass replaces the reliance on Num of the previous API (v0.1). Num is strictly more powerful than Backprop, and is a stronger constraint on types than is necessary for proper backpropagating. In particular, fromInteger is a problem for many types, preventing useful backpropagation for lists, variable-length vectors (like Data.Vector) and variable-size matrices from linear algebra libraries like hmatrix and accelerate.

Since: 0.2.0.0

Minimal complete definition

Nothing

Methods

zero :: a -> a

"Zero out" all components of a value. For scalar values, this should just be const 0. For vectors and matrices, this should set all components to zero, the additive identity.

Should be idempotent:

• zero . zero = zero

Should be as lazy as possible. This behavior is observed for all instances provided by this library.

See zeroNum for a pre-built definition for instances of Num and zeroFunctor for a definition for instances of Functor. If left blank, will automatically be genericZero, a pre-built definition for instances of Generic whose fields are all themselves instances of Backprop.

default zero :: (Generic a, GZero (Rep a)) => a -> a

add :: a -> a -> a

Add together two values of a type. To combine contributions of gradients, so should be information-preserving:

• add x (zero y) = x

• add (zero x) y = y

Should be as strict as possible. This behavior is observed for all instances provided by this library.

See addNum for a pre-built definition for instances of Num and addIsList for a definition for instances of IsList. If left blank, will automatically be genericAdd, a pre-built definition for instances of Generic with one constructor whose fields are all themselves instances of Backprop.

default add :: (Generic a, GAdd (Rep a)) => a -> a -> a

one :: a -> a

One all components of a value. For scalar values, this should just be const 1. For vectors and matrices, this should set all components to one, the multiplicative identity.

As the library uses it, the most important law is:

• one = gradBP id

That is, one x is the gradient of the identity function with respect to its input.

Ideally should be idempotent:

• one . one = one

Should be as lazy as possible. This behavior is observed for all instances provided by this library.

See oneNum for a pre-built definition for instances of Num and oneFunctor for a definition for instances of Functor. If left blank, will automatically be genericOne, a pre-built definition for instances of Generic whose fields are all themselves instances of Backprop.

default one :: (Generic a, GOne (Rep a)) => a -> a

Instances

Backprop Void

Defined in Numeric.Backprop.Class

Methods

zero :: Void -> Void

add :: Void -> Void -> Void

one :: Void -> Void

Backprop Word16

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Word16 -> Word16

add :: Word16 -> Word16 -> Word16

one :: Word16 -> Word16

Backprop Word32

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Word32 -> Word32

add :: Word32 -> Word32 -> Word32

one :: Word32 -> Word32

Backprop Word64

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Word64 -> Word64

add :: Word64 -> Word64 -> Word64

one :: Word64 -> Word64

Backprop Word8

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Word8 -> Word8

add :: Word8 -> Word8 -> Word8

one :: Word8 -> Word8

Backprop Integer

Defined in Numeric.Backprop.Class

Methods

zero :: Integer -> Integer

add :: Integer -> Integer -> Integer

one :: Integer -> Integer

Backprop Natural

Since: 0.2.1.0

Defined in Numeric.Backprop.Class

Methods

zero :: Natural -> Natural

add :: Natural -> Natural -> Natural

one :: Natural -> Natural

Backprop ()

add is strict, but zero and one are lazy in their arguments.

Defined in Numeric.Backprop.Class

Methods

zero :: () -> ()

add :: () -> () -> ()

one :: () -> ()

Backprop Double

Defined in Numeric.Backprop.Class

Methods

zero :: Double -> Double

add :: Double -> Double -> Double

one :: Double -> Double

Backprop Float

Defined in Numeric.Backprop.Class

Methods

zero :: Float -> Float

add :: Float -> Float -> Float

one :: Float -> Float

Backprop Int

Defined in Numeric.Backprop.Class

Methods

zero :: Int -> Int

add :: Int -> Int -> Int

one :: Int -> Int

Backprop Word

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Word -> Word

add :: Word -> Word -> Word

one :: Word -> Word

Num a => Backprop (NumBP a)

Defined in Numeric.Backprop.Class

Methods

zero :: NumBP a -> NumBP a

add :: NumBP a -> NumBP a -> NumBP a

one :: NumBP a -> NumBP a

RealFloat a => Backprop (Complex a)

Defined in Numeric.Backprop.Class

Methods

zero :: Complex a -> Complex a

add :: Complex a -> Complex a -> Complex a

one :: Complex a -> Complex a

Backprop a => Backprop (Identity a)

Defined in Numeric.Backprop.Class

Methods

zero :: Identity a -> Identity a

add :: Identity a -> Identity a -> Identity a

one :: Identity a -> Identity a

Backprop a => Backprop (First a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: First a -> First a

add :: First a -> First a -> First a

one :: First a -> First a

Backprop a => Backprop (Last a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Last a -> Last a

add :: Last a -> Last a -> Last a

one :: Last a -> Last a

Backprop a => Backprop (First a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: First a -> First a

add :: First a -> First a -> First a

one :: First a -> First a

Backprop a => Backprop (Last a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Last a -> Last a

add :: Last a -> Last a -> Last a

one :: Last a -> Last a

Backprop a => Backprop (Dual a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Dual a -> Dual a

add :: Dual a -> Dual a -> Dual a

one :: Dual a -> Dual a

Backprop a => Backprop (Product a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Product a -> Product a

add :: Product a -> Product a -> Product a

one :: Product a -> Product a

Backprop a => Backprop (Sum a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Sum a -> Sum a

add :: Sum a -> Sum a -> Sum a

one :: Sum a -> Sum a

Integral a => Backprop (Ratio a)

Defined in Numeric.Backprop.Class

Methods

zero :: Ratio a -> Ratio a

add :: Ratio a -> Ratio a -> Ratio a

one :: Ratio a -> Ratio a

Backprop a => Backprop (IntMap a)

zero and one replace all current values, and add merges keys from both maps, adding in the case of double-occurrences.

Defined in Numeric.Backprop.Class

Methods

zero :: IntMap a -> IntMap a

add :: IntMap a -> IntMap a -> IntMap a

one :: IntMap a -> IntMap a

Backprop a => Backprop (Seq a)

add assumes the shorter sequence has trailing zeroes, and the result has the length of the longest input.

Defined in Numeric.Backprop.Class

Methods

zero :: Seq a -> Seq a

add :: Seq a -> Seq a -> Seq a

one :: Seq a -> Seq a

Backprop a => Backprop (Vector a)

Defined in Numeric.Backprop.Class

Methods

zero :: Vector a -> Vector a

add :: Vector a -> Vector a -> Vector a

one :: Vector a -> Vector a

(Prim a, Backprop a) => Backprop (Vector a)

Defined in Numeric.Backprop.Class

Methods

zero :: Vector a -> Vector a

add :: Vector a -> Vector a -> Vector a

one :: Vector a -> Vector a

(Storable a, Backprop a) => Backprop (Vector a)

Defined in Numeric.Backprop.Class

Methods

zero :: Vector a -> Vector a

add :: Vector a -> Vector a -> Vector a

one :: Vector a -> Vector a

(Unbox a, Backprop a) => Backprop (Vector a)

Defined in Numeric.Backprop.Class

Methods

zero :: Vector a -> Vector a

add :: Vector a -> Vector a -> Vector a

one :: Vector a -> Vector a

Backprop (Label field)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Label field -> Label field

add :: Label field -> Label field -> Label field

one :: Label field -> Label field

Backprop t => Backprop (ElField '(s, t))

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: ElField '(s, t) -> ElField '(s, t)

add :: ElField '(s, t) -> ElField '(s, t) -> ElField '(s, t)

one :: ElField '(s, t) -> ElField '(s, t)

Backprop a => Backprop (Identity a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Identity a -> Identity a

add :: Identity a -> Identity a -> Identity a

one :: Identity a -> Identity a

Backprop a => Backprop (Thunk a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Thunk a -> Thunk a

add :: Thunk a -> Thunk a -> Thunk a

one :: Thunk a -> Thunk a

Backprop a => Backprop (NonEmpty a)

add assumes the shorter list has trailing zeroes, and the result has the length of the longest input.

Defined in Numeric.Backprop.Class

Methods

zero :: NonEmpty a -> NonEmpty a

add :: NonEmpty a -> NonEmpty a -> NonEmpty a

one :: NonEmpty a -> NonEmpty a

Backprop a => Backprop (Maybe a)

Nothing is treated the same as Just 0. However, zero, add, and one preserve Nothing if all inputs are also Nothing.

Defined in Numeric.Backprop.Class

Methods

zero :: Maybe a -> Maybe a

add :: Maybe a -> Maybe a -> Maybe a

one :: Maybe a -> Maybe a

Backprop a => Backprop [a]

add assumes the shorter list has trailing zeroes, and the result has the length of the longest input.

Defined in Numeric.Backprop.Class

Methods

zero :: [a] -> [a]

add :: [a] -> [a] -> [a]

one :: [a] -> [a]

(Applicative f, Backprop a) => Backprop (ABP f a)

Defined in Numeric.Backprop.Class

Methods

zero :: ABP f a -> ABP f a

add :: ABP f a -> ABP f a -> ABP f a

one :: ABP f a -> ABP f a

(Vector v a, Num a) => Backprop (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

zero :: NumVec v a -> NumVec v a

add :: NumVec v a -> NumVec v a -> NumVec v a

one :: NumVec v a -> NumVec v a

(Backprop a, Reifies s W) => Backprop (BVar s a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Internal

Methods

zero :: BVar s a -> BVar s a

add :: BVar s a -> BVar s a -> BVar s a

one :: BVar s a -> BVar s a

Backprop (Proxy a)

Defined in Numeric.Backprop.Class

Methods

zero :: Proxy a -> Proxy a

add :: Proxy a -> Proxy a -> Proxy a

one :: Proxy a -> Proxy a

(Backprop a, Backprop b) => Backprop (Arg a b)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Arg a b -> Arg a b

add :: Arg a b -> Arg a b -> Arg a b

one :: Arg a b -> Arg a b

Backprop (U1 p)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: U1 p -> U1 p

add :: U1 p -> U1 p -> U1 p

one :: U1 p -> U1 p

Backprop (V1 p)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: V1 p -> V1 p

add :: V1 p -> V1 p -> V1 p

one :: V1 p -> V1 p

(Backprop a, Ord k) => Backprop (Map k a)

zero and one replace all current values, and add merges keys from both maps, adding in the case of double-occurrences.

Defined in Numeric.Backprop.Class

Methods

zero :: Map k a -> Map k a

add :: Map k a -> Map k a -> Map k a

one :: Map k a -> Map k a

Backprop (SField field)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: SField field -> SField field

add :: SField field -> SField field -> SField field

one :: SField field -> SField field

Backprop a => Backprop (r -> a)

add adds together results; zero and one act on results.

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: (r -> a) -> r -> a

add :: (r -> a) -> (r -> a) -> r -> a

one :: (r -> a) -> r -> a

(Backprop a, Backprop b) => Backprop (a, b)

add is strict

Defined in Numeric.Backprop.Class

Methods

zero :: (a, b) -> (a, b)

add :: (a, b) -> (a, b) -> (a, b)

one :: (a, b) -> (a, b)

(Backprop a, Applicative m) => Backprop (Kleisli m r a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Kleisli m r a -> Kleisli m r a

add :: Kleisli m r a -> Kleisli m r a -> Kleisli m r a

one :: Kleisli m r a -> Kleisli m r a

Backprop w => Backprop (Const w a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Const w a -> Const w a

add :: Const w a -> Const w a -> Const w a

one :: Const w a -> Const w a

(ReifyConstraint Backprop f rs, RMap rs, RApply rs, RecApplicative rs, NatToInt (RLength rs), RPureConstrained (IndexableField rs) rs, ToARec rs) => Backprop (ARec f rs)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: ARec f rs -> ARec f rs

add :: ARec f rs -> ARec f rs -> ARec f rs

one :: ARec f rs -> ARec f rs

(ReifyConstraint Backprop f rs, RMap rs, RApply rs) => Backprop (Rec f rs)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Rec f rs -> Rec f rs

add :: Rec f rs -> Rec f rs -> Rec f rs

one :: Rec f rs -> Rec f rs

Backprop w => Backprop (Const w a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Const w a -> Const w a

add :: Const w a -> Const w a -> Const w a

one :: Const w a -> Const w a

(ReifyConstraint Backprop f rs, RMap rs, RApply rs, Storable (Rec f rs)) => Backprop (SRec f rs)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: SRec f rs -> SRec f rs

add :: SRec f rs -> SRec f rs -> SRec f rs

one :: SRec f rs -> SRec f rs

Backprop (HKD t a) => Backprop (XData t a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: XData t a -> XData t a

add :: XData t a -> XData t a -> XData t a

one :: XData t a -> XData t a

(ReifyConstraint Backprop f rs, RMap rs, RApply rs, IsoXRec f rs) => Backprop (XRec f rs)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: XRec f rs -> XRec f rs

add :: XRec f rs -> XRec f rs -> XRec f rs

one :: XRec f rs -> XRec f rs

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

add is strict

Defined in Numeric.Backprop.Class

Methods

zero :: (a, b, c) -> (a, b, c)

add :: (a, b, c) -> (a, b, c) -> (a, b, c)

one :: (a, b, c) -> (a, b, c)

(Backprop (f a), Backprop (g a)) => Backprop (Product f g a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Product f g a -> Product f g a

add :: Product f g a -> Product f g a -> Product f g a

one :: Product f g a -> Product f g a

(Backprop (f p), Backprop (g p)) => Backprop ((f :*: g) p)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: (f :*: g) p -> (f :*: g) p

add :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

one :: (f :*: g) p -> (f :*: g) p

Backprop a => Backprop (K1 i a p)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: K1 i a p -> K1 i a p

add :: K1 i a p -> K1 i a p -> K1 i a p

one :: K1 i a p -> K1 i a p

(Backprop a, Backprop b, Backprop c, Backprop d) => Backprop (a, b, c, d)

add is strict

Defined in Numeric.Backprop.Class

Methods

zero :: (a, b, c, d) -> (a, b, c, d)

add :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

one :: (a, b, c, d) -> (a, b, c, d)

Backprop (f (g a)) => Backprop (Compose f g a)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: Compose f g a -> Compose f g a

add :: Compose f g a -> Compose f g a -> Compose f g a

one :: Compose f g a -> Compose f g a

Backprop (f (g a)) => Backprop ((f :.: g) a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: (f :.: g) a -> (f :.: g) a

add :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a

one :: (f :.: g) a -> (f :.: g) a

Backprop (f p) => Backprop (M1 i c f p)

Since: 0.2.2.0

Defined in Numeric.Backprop.Class

Methods

zero :: M1 i c f p -> M1 i c f p

add :: M1 i c f p -> M1 i c f p -> M1 i c f p

one :: M1 i c f p -> M1 i c f p

Backprop (f (g a)) => Backprop (Compose f g a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Compose f g a -> Compose f g a

add :: Compose f g a -> Compose f g a -> Compose f g a

one :: Compose f g a -> Compose f g a

(Backprop a, Backprop b, Backprop c, Backprop d, Backprop e) => Backprop (a, b, c, d, e)

add is strict

Defined in Numeric.Backprop.Class

Methods

zero :: (a, b, c, d, e) -> (a, b, c, d, e)

add :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

one :: (a, b, c, d, e) -> (a, b, c, d, e)

Backprop (op (f a) (g a)) => Backprop (Lift op f g a)

Since: 0.2.6.3

Defined in Numeric.Backprop.Class

Methods

zero :: Lift op f g a -> Lift op f g a

add :: Lift op f g a -> Lift op f g a -> Lift op f g a

one :: Lift op f g a -> Lift op f g a

Derived methods

zeroNum :: Num a => a -> a

zero for instances of Num.

Is lazy in its argument.

addNum :: Num a => a -> a -> a

add for instances of Num.

oneNum :: Num a => a -> a

one for instances of Num.

Is lazy in its argument.

zeroVec :: (Vector v a, Backprop a) => v a -> v a

zero for instances of Vector.

addVec :: (Vector v a, Backprop a) => v a -> v a -> v a

add for instances of Vector. Automatically pads the end of the shorter vector with zeroes.

oneVec :: (Vector v a, Backprop a) => v a -> v a

one for instances of Vector.

zeroVecNum :: (Vector v a, Num a) => v a -> v a

zero for instances of Vector when the contained type is an instance of Num. Is potentially more performant than zeroVec when the vectors are larger.

See NumVec for a Backprop instance for Vector instances that uses this for zero.

Since: 0.2.4.0

oneVecNum :: (Vector v a, Num a) => v a -> v a

one for instances of Vector when the contained type is an instance of Num. Is potentially more performant than oneVec when the vectors are larger.

See NumVec for a Backprop instance for Vector instances that uses this for one.

Since: 0.2.4.0

zeroFunctor :: (Functor f, Backprop a) => f a -> f a

zero for Functor instances.

addIsList :: (IsList a, Backprop (Item a)) => a -> a -> a

add for instances of IsList. Automatically pads the end of the "shorter" value with zeroes.

addAsList

Arguments

:: Backprop b

=> (a -> [b])

convert to list (should form isomorphism)

-> ([b] -> a)

convert from list (should form isomorphism)

-> a

-> a

-> a

add for types that are isomorphic to a list. Automatically pads the end of the "shorter" value with zeroes.

oneFunctor :: (Functor f, Backprop a) => f a -> f a

one for instances of Functor.

genericZero :: (Generic a, GZero (Rep a)) => a -> a

zero using GHC Generics; works if all fields are instances of Backprop.

genericAdd :: (Generic a, GAdd (Rep a)) => a -> a -> a

add using GHC Generics; works if all fields are instances of Backprop, but only for values with single constructors.

genericOne :: (Generic a, GOne (Rep a)) => a -> a

one using GHC Generics; works if all fields are instaces of Backprop.

Newtype

newtype ABP f a

A newtype wrapper over an f a for Applicative f that gives a free Backprop instance (as well as Num etc. instances).

Useful for performing backpropagation over functions that require some monadic context (like IO) to perform.

Since: 0.2.1.0

Constructors

ABP

Fields

• runABP :: f a

Instances

Foldable f => Foldable (ABP f)

Defined in Numeric.Backprop.Class

Methods

fold :: Monoid m => ABP f m -> m

foldMap :: Monoid m => (a -> m) -> ABP f a -> m

foldMap' :: Monoid m => (a -> m) -> ABP f a -> m

foldr :: (a -> b -> b) -> b -> ABP f a -> b

foldr' :: (a -> b -> b) -> b -> ABP f a -> b

foldl :: (b -> a -> b) -> b -> ABP f a -> b

foldl' :: (b -> a -> b) -> b -> ABP f a -> b

foldr1 :: (a -> a -> a) -> ABP f a -> a

foldl1 :: (a -> a -> a) -> ABP f a -> a

toList :: ABP f a -> [a]

null :: ABP f a -> Bool

length :: ABP f a -> Int

elem :: Eq a => a -> ABP f a -> Bool

maximum :: Ord a => ABP f a -> a

minimum :: Ord a => ABP f a -> a

sum :: Num a => ABP f a -> a

product :: Num a => ABP f a -> a

Traversable f => Traversable (ABP f)

Defined in Numeric.Backprop.Class

Methods

traverse :: Applicative f0 => (a -> f0 b) -> ABP f a -> f0 (ABP f b)

sequenceA :: Applicative f0 => ABP f (f0 a) -> f0 (ABP f a)

mapM :: Monad m => (a -> m b) -> ABP f a -> m (ABP f b)

sequence :: Monad m => ABP f (m a) -> m (ABP f a)

Alternative f => Alternative (ABP f)

Defined in Numeric.Backprop.Class

Methods

empty :: ABP f a

(<|>) :: ABP f a -> ABP f a -> ABP f a

some :: ABP f a -> ABP f [a]

many :: ABP f a -> ABP f [a]

Applicative f => Applicative (ABP f)

Defined in Numeric.Backprop.Class

Methods

pure :: a -> ABP f a

(<*>) :: ABP f (a -> b) -> ABP f a -> ABP f b

liftA2 :: (a -> b -> c) -> ABP f a -> ABP f b -> ABP f c

(*>) :: ABP f a -> ABP f b -> ABP f b

(<*) :: ABP f a -> ABP f b -> ABP f a

Functor f => Functor (ABP f)

Defined in Numeric.Backprop.Class

Methods

fmap :: (a -> b) -> ABP f a -> ABP f b

(<$) :: a -> ABP f b -> ABP f a

Monad f => Monad (ABP f)

Defined in Numeric.Backprop.Class

Methods

(>>=) :: ABP f a -> (a -> ABP f b) -> ABP f b

(>>) :: ABP f a -> ABP f b -> ABP f b

return :: a -> ABP f a

MonadPlus f => MonadPlus (ABP f)

Defined in Numeric.Backprop.Class

Methods

mzero :: ABP f a

mplus :: ABP f a -> ABP f a -> ABP f a

(Applicative f, Backprop a) => Backprop (ABP f a)

Defined in Numeric.Backprop.Class

Methods

zero :: ABP f a -> ABP f a

add :: ABP f a -> ABP f a -> ABP f a

one :: ABP f a -> ABP f a

(Typeable f, Typeable a, Data (f a)) => Data (ABP f a)

Defined in Numeric.Backprop.Class

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ABP f a -> c (ABP f a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ABP f a)

toConstr :: ABP f a -> Constr

dataTypeOf :: ABP f a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ABP f a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ABP f a))

gmapT :: (forall b. Data b => b -> b) -> ABP f a -> ABP f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ABP f a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ABP f a -> r

gmapQ :: (forall d. Data d => d -> u) -> ABP f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> ABP f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> ABP f a -> m (ABP f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ABP f a -> m (ABP f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ABP f a -> m (ABP f a)

(Applicative f, Floating a) => Floating (ABP f a)

Defined in Numeric.Backprop.Class

Methods

pi :: ABP f a

exp :: ABP f a -> ABP f a

log :: ABP f a -> ABP f a

sqrt :: ABP f a -> ABP f a

(**) :: ABP f a -> ABP f a -> ABP f a

logBase :: ABP f a -> ABP f a -> ABP f a

sin :: ABP f a -> ABP f a

cos :: ABP f a -> ABP f a

tan :: ABP f a -> ABP f a

asin :: ABP f a -> ABP f a

acos :: ABP f a -> ABP f a

atan :: ABP f a -> ABP f a

sinh :: ABP f a -> ABP f a

cosh :: ABP f a -> ABP f a

tanh :: ABP f a -> ABP f a

asinh :: ABP f a -> ABP f a

acosh :: ABP f a -> ABP f a

atanh :: ABP f a -> ABP f a

log1p :: ABP f a -> ABP f a

expm1 :: ABP f a -> ABP f a

log1pexp :: ABP f a -> ABP f a

log1mexp :: ABP f a -> ABP f a

Generic (ABP f a)

Defined in Numeric.Backprop.Class

Associated Types

type Rep (ABP f a) :: Type -> Type

Methods

from :: ABP f a -> Rep (ABP f a) x

to :: Rep (ABP f a) x -> ABP f a

(Applicative f, Num a) => Num (ABP f a)

Defined in Numeric.Backprop.Class

Methods

(+) :: ABP f a -> ABP f a -> ABP f a

(-) :: ABP f a -> ABP f a -> ABP f a

(*) :: ABP f a -> ABP f a -> ABP f a

negate :: ABP f a -> ABP f a

abs :: ABP f a -> ABP f a

signum :: ABP f a -> ABP f a

fromInteger :: Integer -> ABP f a

Read (f a) => Read (ABP f a)

Defined in Numeric.Backprop.Class

Methods

readsPrec :: Int -> ReadS (ABP f a)

readList :: ReadS [ABP f a]

readPrec :: ReadPrec (ABP f a)

readListPrec :: ReadPrec [ABP f a]

(Applicative f, Fractional a) => Fractional (ABP f a)

Defined in Numeric.Backprop.Class

Methods

(/) :: ABP f a -> ABP f a -> ABP f a

recip :: ABP f a -> ABP f a

fromRational :: Rational -> ABP f a

Show (f a) => Show (ABP f a)

Defined in Numeric.Backprop.Class

Methods

showsPrec :: Int -> ABP f a -> ShowS

show :: ABP f a -> String

showList :: [ABP f a] -> ShowS

NFData (f a) => NFData (ABP f a)

Defined in Numeric.Backprop.Class

Methods

rnf :: ABP f a -> ()

Eq (f a) => Eq (ABP f a)

Defined in Numeric.Backprop.Class

Methods

(==) :: ABP f a -> ABP f a -> Bool

(/=) :: ABP f a -> ABP f a -> Bool

Ord (f a) => Ord (ABP f a)

Defined in Numeric.Backprop.Class

Methods

compare :: ABP f a -> ABP f a -> Ordering

(<) :: ABP f a -> ABP f a -> Bool

(<=) :: ABP f a -> ABP f a -> Bool

(>) :: ABP f a -> ABP f a -> Bool

(>=) :: ABP f a -> ABP f a -> Bool

max :: ABP f a -> ABP f a -> ABP f a

min :: ABP f a -> ABP f a -> ABP f a

type Rep (ABP f a)

Defined in Numeric.Backprop.Class

type Rep (ABP f a) = D1 ('MetaData "ABP" "Numeric.Backprop.Class" "backprop-0.2.6.5-9EG5Bvd6XS08wzziHCnTrt" 'True) (C1 ('MetaCons "ABP" 'PrefixI 'True) (S1 ('MetaSel ('Just "runABP") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

newtype NumBP a

A newtype wrapper over an instance of Num that gives a free Backprop instance.

Useful for things like DerivingVia, or for avoiding orphan instances.

Since: 0.2.1.0

Constructors

NumBP

Fields

• runNumBP :: a

Instances

Foldable NumBP

Defined in Numeric.Backprop.Class

Methods

fold :: Monoid m => NumBP m -> m

foldMap :: Monoid m => (a -> m) -> NumBP a -> m

foldMap' :: Monoid m => (a -> m) -> NumBP a -> m

foldr :: (a -> b -> b) -> b -> NumBP a -> b

foldr' :: (a -> b -> b) -> b -> NumBP a -> b

foldl :: (b -> a -> b) -> b -> NumBP a -> b

foldl' :: (b -> a -> b) -> b -> NumBP a -> b

foldr1 :: (a -> a -> a) -> NumBP a -> a

foldl1 :: (a -> a -> a) -> NumBP a -> a

toList :: NumBP a -> [a]

null :: NumBP a -> Bool

length :: NumBP a -> Int

elem :: Eq a => a -> NumBP a -> Bool

maximum :: Ord a => NumBP a -> a

minimum :: Ord a => NumBP a -> a

sum :: Num a => NumBP a -> a

product :: Num a => NumBP a -> a

Traversable NumBP

Defined in Numeric.Backprop.Class

Methods

traverse :: Applicative f => (a -> f b) -> NumBP a -> f (NumBP b)

sequenceA :: Applicative f => NumBP (f a) -> f (NumBP a)

mapM :: Monad m => (a -> m b) -> NumBP a -> m (NumBP b)

sequence :: Monad m => NumBP (m a) -> m (NumBP a)

Applicative NumBP

Defined in Numeric.Backprop.Class

Methods

pure :: a -> NumBP a

(<*>) :: NumBP (a -> b) -> NumBP a -> NumBP b

liftA2 :: (a -> b -> c) -> NumBP a -> NumBP b -> NumBP c

(*>) :: NumBP a -> NumBP b -> NumBP b

(<*) :: NumBP a -> NumBP b -> NumBP a

Functor NumBP

Defined in Numeric.Backprop.Class

Methods

fmap :: (a -> b) -> NumBP a -> NumBP b

(<$) :: a -> NumBP b -> NumBP a

Monad NumBP

Defined in Numeric.Backprop.Class

Methods

(>>=) :: NumBP a -> (a -> NumBP b) -> NumBP b

(>>) :: NumBP a -> NumBP b -> NumBP b

return :: a -> NumBP a

Num a => Backprop (NumBP a)

Defined in Numeric.Backprop.Class

Methods

zero :: NumBP a -> NumBP a

add :: NumBP a -> NumBP a -> NumBP a

one :: NumBP a -> NumBP a

Data a => Data (NumBP a)

Defined in Numeric.Backprop.Class

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NumBP a -> c (NumBP a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NumBP a)

toConstr :: NumBP a -> Constr

dataTypeOf :: NumBP a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NumBP a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NumBP a))

gmapT :: (forall b. Data b => b -> b) -> NumBP a -> NumBP a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NumBP a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NumBP a -> r

gmapQ :: (forall d. Data d => d -> u) -> NumBP a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> NumBP a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> NumBP a -> m (NumBP a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NumBP a -> m (NumBP a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NumBP a -> m (NumBP a)

Floating a => Floating (NumBP a)

Defined in Numeric.Backprop.Class

Methods

pi :: NumBP a

exp :: NumBP a -> NumBP a

log :: NumBP a -> NumBP a

sqrt :: NumBP a -> NumBP a

(**) :: NumBP a -> NumBP a -> NumBP a

logBase :: NumBP a -> NumBP a -> NumBP a

sin :: NumBP a -> NumBP a

cos :: NumBP a -> NumBP a

tan :: NumBP a -> NumBP a

asin :: NumBP a -> NumBP a

acos :: NumBP a -> NumBP a

atan :: NumBP a -> NumBP a

sinh :: NumBP a -> NumBP a

cosh :: NumBP a -> NumBP a

tanh :: NumBP a -> NumBP a

asinh :: NumBP a -> NumBP a

acosh :: NumBP a -> NumBP a

atanh :: NumBP a -> NumBP a

log1p :: NumBP a -> NumBP a

expm1 :: NumBP a -> NumBP a

log1pexp :: NumBP a -> NumBP a

log1mexp :: NumBP a -> NumBP a

Generic (NumBP a)

Defined in Numeric.Backprop.Class

Associated Types

type Rep (NumBP a) :: Type -> Type

Methods

from :: NumBP a -> Rep (NumBP a) x

to :: Rep (NumBP a) x -> NumBP a

Num a => Num (NumBP a)

Defined in Numeric.Backprop.Class

Methods

(+) :: NumBP a -> NumBP a -> NumBP a

(-) :: NumBP a -> NumBP a -> NumBP a

(*) :: NumBP a -> NumBP a -> NumBP a

negate :: NumBP a -> NumBP a

abs :: NumBP a -> NumBP a

signum :: NumBP a -> NumBP a

fromInteger :: Integer -> NumBP a

Read a => Read (NumBP a)

Defined in Numeric.Backprop.Class

Methods

readsPrec :: Int -> ReadS (NumBP a)

readList :: ReadS [NumBP a]

readPrec :: ReadPrec (NumBP a)

readListPrec :: ReadPrec [NumBP a]

Fractional a => Fractional (NumBP a)

Defined in Numeric.Backprop.Class

Methods

(/) :: NumBP a -> NumBP a -> NumBP a

recip :: NumBP a -> NumBP a

fromRational :: Rational -> NumBP a

Show a => Show (NumBP a)

Defined in Numeric.Backprop.Class

Methods

showsPrec :: Int -> NumBP a -> ShowS

show :: NumBP a -> String

showList :: [NumBP a] -> ShowS

NFData a => NFData (NumBP a)

Defined in Numeric.Backprop.Class

Methods

rnf :: NumBP a -> ()

Eq a => Eq (NumBP a)

Defined in Numeric.Backprop.Class

Methods

(==) :: NumBP a -> NumBP a -> Bool

(/=) :: NumBP a -> NumBP a -> Bool

Ord a => Ord (NumBP a)

Defined in Numeric.Backprop.Class

Methods

compare :: NumBP a -> NumBP a -> Ordering

(<) :: NumBP a -> NumBP a -> Bool

(<=) :: NumBP a -> NumBP a -> Bool

(>) :: NumBP a -> NumBP a -> Bool

(>=) :: NumBP a -> NumBP a -> Bool

max :: NumBP a -> NumBP a -> NumBP a

min :: NumBP a -> NumBP a -> NumBP a

type Rep (NumBP a)

Defined in Numeric.Backprop.Class

type Rep (NumBP a) = D1 ('MetaData "NumBP" "Numeric.Backprop.Class" "backprop-0.2.6.5-9EG5Bvd6XS08wzziHCnTrt" 'True) (C1 ('MetaCons "NumBP" 'PrefixI 'True) (S1 ('MetaSel ('Just "runNumBP") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype NumVec v a

Newtype wrapper around a v a for Vector v a, that gives a more efficient Backprop instance for long vectors when a is an instance of Num. The normal Backprop instance for vectors will map zero or one over all items; this instance will completely ignore the contents of the original vector and instead produce a new vector of the same length, with all 0 or 1 using the Num instance of a (essentially using zeroVecNum and oneVecNum instead of zeroVec and oneVec).

add is essentially the same as normal, but using + instead of the type's add.

Since: 0.2.4.0

Constructors

NumVec

Fields

• runNumVec :: v a

Instances

Foldable v => Foldable (NumVec v)

Defined in Numeric.Backprop.Class

Methods

fold :: Monoid m => NumVec v m -> m

foldMap :: Monoid m => (a -> m) -> NumVec v a -> m

foldMap' :: Monoid m => (a -> m) -> NumVec v a -> m

foldr :: (a -> b -> b) -> b -> NumVec v a -> b

foldr' :: (a -> b -> b) -> b -> NumVec v a -> b

foldl :: (b -> a -> b) -> b -> NumVec v a -> b

foldl' :: (b -> a -> b) -> b -> NumVec v a -> b

foldr1 :: (a -> a -> a) -> NumVec v a -> a

foldl1 :: (a -> a -> a) -> NumVec v a -> a

toList :: NumVec v a -> [a]

null :: NumVec v a -> Bool

length :: NumVec v a -> Int

elem :: Eq a => a -> NumVec v a -> Bool

maximum :: Ord a => NumVec v a -> a

minimum :: Ord a => NumVec v a -> a

sum :: Num a => NumVec v a -> a

product :: Num a => NumVec v a -> a

Traversable v => Traversable (NumVec v)

Defined in Numeric.Backprop.Class

Methods

traverse :: Applicative f => (a -> f b) -> NumVec v a -> f (NumVec v b)

sequenceA :: Applicative f => NumVec v (f a) -> f (NumVec v a)

mapM :: Monad m => (a -> m b) -> NumVec v a -> m (NumVec v b)

sequence :: Monad m => NumVec v (m a) -> m (NumVec v a)

Alternative v => Alternative (NumVec v)

Defined in Numeric.Backprop.Class

Methods

empty :: NumVec v a

(<|>) :: NumVec v a -> NumVec v a -> NumVec v a

some :: NumVec v a -> NumVec v [a]

many :: NumVec v a -> NumVec v [a]

Applicative v => Applicative (NumVec v)

Defined in Numeric.Backprop.Class

Methods

pure :: a -> NumVec v a

(<*>) :: NumVec v (a -> b) -> NumVec v a -> NumVec v b

liftA2 :: (a -> b -> c) -> NumVec v a -> NumVec v b -> NumVec v c

(*>) :: NumVec v a -> NumVec v b -> NumVec v b

(<*) :: NumVec v a -> NumVec v b -> NumVec v a

Functor v => Functor (NumVec v)

Defined in Numeric.Backprop.Class

Methods

fmap :: (a -> b) -> NumVec v a -> NumVec v b

(<$) :: a -> NumVec v b -> NumVec v a

Monad v => Monad (NumVec v)

Defined in Numeric.Backprop.Class

Methods

(>>=) :: NumVec v a -> (a -> NumVec v b) -> NumVec v b

(>>) :: NumVec v a -> NumVec v b -> NumVec v b

return :: a -> NumVec v a

MonadPlus v => MonadPlus (NumVec v)

Defined in Numeric.Backprop.Class

Methods

mzero :: NumVec v a

mplus :: NumVec v a -> NumVec v a -> NumVec v a

(Vector v a, Num a) => Backprop (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

zero :: NumVec v a -> NumVec v a

add :: NumVec v a -> NumVec v a -> NumVec v a

one :: NumVec v a -> NumVec v a

(Typeable v, Typeable a, Data (v a)) => Data (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NumVec v a -> c (NumVec v a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NumVec v a)

toConstr :: NumVec v a -> Constr

dataTypeOf :: NumVec v a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NumVec v a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NumVec v a))

gmapT :: (forall b. Data b => b -> b) -> NumVec v a -> NumVec v a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NumVec v a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NumVec v a -> r

gmapQ :: (forall d. Data d => d -> u) -> NumVec v a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> NumVec v a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> NumVec v a -> m (NumVec v a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NumVec v a -> m (NumVec v a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NumVec v a -> m (NumVec v a)

Generic (NumVec v a)

Defined in Numeric.Backprop.Class

Associated Types

type Rep (NumVec v a) :: Type -> Type

Methods

from :: NumVec v a -> Rep (NumVec v a) x

to :: Rep (NumVec v a) x -> NumVec v a

Read (v a) => Read (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

readsPrec :: Int -> ReadS (NumVec v a)

readList :: ReadS [NumVec v a]

readPrec :: ReadPrec (NumVec v a)

readListPrec :: ReadPrec [NumVec v a]

Show (v a) => Show (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

showsPrec :: Int -> NumVec v a -> ShowS

show :: NumVec v a -> String

showList :: [NumVec v a] -> ShowS

NFData (v a) => NFData (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

rnf :: NumVec v a -> ()

Eq (v a) => Eq (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

(==) :: NumVec v a -> NumVec v a -> Bool

(/=) :: NumVec v a -> NumVec v a -> Bool

Ord (v a) => Ord (NumVec v a)

Defined in Numeric.Backprop.Class

Methods

compare :: NumVec v a -> NumVec v a -> Ordering

(<) :: NumVec v a -> NumVec v a -> Bool

(<=) :: NumVec v a -> NumVec v a -> Bool

(>) :: NumVec v a -> NumVec v a -> Bool

(>=) :: NumVec v a -> NumVec v a -> Bool

max :: NumVec v a -> NumVec v a -> NumVec v a

min :: NumVec v a -> NumVec v a -> NumVec v a

type Rep (NumVec v a)

Defined in Numeric.Backprop.Class

type Rep (NumVec v a) = D1 ('MetaData "NumVec" "Numeric.Backprop.Class" "backprop-0.2.6.5-9EG5Bvd6XS08wzziHCnTrt" 'True) (C1 ('MetaCons "NumVec" 'PrefixI 'True) (S1 ('MetaSel ('Just "runNumVec") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (v a))))

Generics

class GZero f

Helper class for automatically deriving zero using GHC Generics.

Minimal complete definition

gzero

Instances

GZero (U1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gzero :: U1 t -> U1 t

GZero (V1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gzero :: V1 t -> V1 t

(GZero f, GZero g) => GZero (f :*: g)

Defined in Numeric.Backprop.Class

Methods

gzero :: (f :*: g) t -> (f :*: g) t

(GZero f, GZero g) => GZero (f :+: g)

Defined in Numeric.Backprop.Class

Methods

gzero :: (f :+: g) t -> (f :+: g) t

Backprop a => GZero (K1 i a :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gzero :: K1 i a t -> K1 i a t

GZero f => GZero (f :.: g)

Defined in Numeric.Backprop.Class

Methods

gzero :: (f :.: g) t -> (f :.: g) t

GZero f => GZero (M1 i c f)

Defined in Numeric.Backprop.Class

Methods

gzero :: M1 i c f t -> M1 i c f t

class GAdd f

Helper class for automatically deriving add using GHC Generics.

Minimal complete definition

gadd

Instances

GAdd (U1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gadd :: U1 t -> U1 t -> U1 t

GAdd (V1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gadd :: V1 t -> V1 t -> V1 t

(GAdd f, GAdd g) => GAdd (f :*: g)

Defined in Numeric.Backprop.Class

Methods

gadd :: (f :*: g) t -> (f :*: g) t -> (f :*: g) t

Backprop a => GAdd (K1 i a :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gadd :: K1 i a t -> K1 i a t -> K1 i a t

GAdd f => GAdd (f :.: g)

Defined in Numeric.Backprop.Class

Methods

gadd :: (f :.: g) t -> (f :.: g) t -> (f :.: g) t

GAdd f => GAdd (M1 i c f)

Defined in Numeric.Backprop.Class

Methods

gadd :: M1 i c f t -> M1 i c f t -> M1 i c f t

class GOne f

Helper class for automatically deriving one using GHC Generics.

Minimal complete definition

gone

Instances

GOne (U1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gone :: U1 t -> U1 t

GOne (V1 :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gone :: V1 t -> V1 t

(GOne f, GOne g) => GOne (f :*: g)

Defined in Numeric.Backprop.Class

Methods

gone :: (f :*: g) t -> (f :*: g) t

(GOne f, GOne g) => GOne (f :+: g)

Defined in Numeric.Backprop.Class

Methods

gone :: (f :+: g) t -> (f :+: g) t

Backprop a => GOne (K1 i a :: Type -> Type)

Defined in Numeric.Backprop.Class

Methods

gone :: K1 i a t -> K1 i a t

GOne f => GOne (f :.: g)

Defined in Numeric.Backprop.Class

Methods

gone :: (f :.: g) t -> (f :.: g) t

GOne f => GOne (M1 i c f)

Defined in Numeric.Backprop.Class

Methods

gone :: M1 i c f t -> M1 i c f t