HMath.DeepLearning.Core¶

Description

Checked Double activations, losses, and real-coordinate reverse rules. Probabilities must be in [0,1]; impossible events return a domain failure instead of silently clipping probabilities. Logit losses avoid exp overflow. Nondifferentiable hinges use zero at equality; MAE uses signum(0)=0.

On this page¶

API	Purpose
Activation	Scalar activation selector.
Sigmoid	Declaration and type contract below.
Tanh	Declaration and type contract below.
ReLU	Declaration and type contract below.
LeakyReLU	Declaration and type contract below.
PReLU	Declaration and type contract below.
ELU	Declaration and type contract below.
SELU	Declaration and type contract below.
GELU	Declaration and type contract below.
SiLU	Declaration and type contract below.
Mish	Declaration and type contract below.
Softplus	Declaration and type contract below.
Softsign	Declaration and type contract below.
HardSigmoid	Declaration and type contract below.
HardSwish	Declaration and type contract below.
activation	Given Activation selector then finite scalar, evaluate the selected activation.
activationDerivative	Evaluate the analytic first derivative with documented kink conventions and stable saturated sigmoid/tanh behavior.
activationExpr	Embed the checked activation and analytic custom reverse rule in an automatic differentiation graph.
softmax	Exponentiate stable log-softmax values; the output sums to one within floating error.
logSoftmax	Normalize a nonempty finite vector in log space after subtracting its maximum.
sparsemax	Project a finite vector onto the probability simplex using sorted active-support thresholds.
gatedLinearUnit	Multiply values by sigmoid(gates), requiring equal vector lengths.
softmaxExpr	First-order softmax reverse rule, including cross-coordinate coupling.
logSoftmaxExpr	First-order stable log-softmax rule; gradient rows sum to zero.
sparsemaxExpr	Sparsemax's piecewise-linear Jacobian.
ctcLossExpr	CTC graph operation on rectangular time-major log probabilities.
Reduction	Loss aggregation: Sum adds elementwise losses and Mean divides by their count; vector-level loss exceptions are documented by loss.
Sum	Declaration and type contract below.
Mean	Declaration and type contract below.
Loss	Checked loss selector,including squared/absolute error,cross entropy,KL,hinge,cosine,and parameterized Hubersmooth losses.
MeanSquaredError	Declaration and type contract below.
MeanAbsoluteError	Declaration and type contract below.
Huber	Declaration and type contract below.
SmoothL1	Declaration and type contract below.
BinaryCrossEntropy	Declaration and type contract below.
CategoricalCrossEntropy	Declaration and type contract below.
NegativeLogLikelihood	Declaration and type contract below.
KLDivergence	Declaration and type contract below.
CosineLoss	Declaration and type contract below.
Hinge	Declaration and type contract below.
loss	Evaluate the selected checked loss.
lossGradient	Analytic derivatives with respect to predictions under the exact loss/reduction convention.
lossExpr	Use a constant target with symbolic prediction inputs and the matching analytic reverse rule.
binaryCrossEntropyLogits	Stable binary cross entropy from logits and [0,1] targets, including extreme finite logits.
categoricalCrossEntropyLogits	Cross entropy from one class-logit vector; nonnegative targets must sum to one.
regularization	Return l1sum(abs(w)) + l2/2sum(w*w); both coefficients must be finite and nonnegative.
contrastiveLoss	Pairwise Euclidean contrastive loss; similar=True penalizes squared distance and dissimilar pairs use the positive margin.
tripletLoss	Return max(0,positiveDistance-negativeDistance+margin) for equal nonempty vector dimensions.
focalLoss	Mean binary focal loss with alpha in [0,1], gamma>=0, and exact zero/one targets.
diceLoss	Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.
iouLoss	Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.
ctcLoss	Single sequence, time-major log-probabilities [time,class].
ctcLossGradient	Given blank class index, target labels, then rectangular time-by-class log probabilities, return CTC negative log likelihood and gradient rows.

Documentation

Activation

data Activation Source #

Scalar activation selector. LeakyReLU/PReLU carry negative-side slope and ELU carries positive alpha; other constructors select the named standard activation.

Constructors

Sigmoid
Tanh
ReLU
LeakyReLU Double
PReLU Double
ELU Double
SELU
GELU
SiLU
Mish
Softplus
Softsign
HardSigmoid
HardSwish

Instances

Instances details

Show Activation Source #
Instance details Defined in HMath.DeepLearning.Core Methods showsPrec :: Int -> Activation -> ShowS # show :: Activation -> String # showList :: [Activation] -> ShowS #
Eq Activation Source #
Instance details Defined in HMath.DeepLearning.Core Methods (==) :: Activation -> Activation -> Bool # (/=) :: Activation -> Activation -> Bool #

activation

activation :: Activation -> Double -> Either MathError Double Source #

Given Activation selector then finite scalar, evaluate the selected activation. Parameterized LeakyReLU/PReLU slopes must be finite and ELU alpha positive. Invalid input/parameters or non-finite output returns Left MathError.

activationDerivative

activationDerivative :: Activation -> Double -> Either MathError Double Source #

Evaluate the analytic first derivative with documented kink conventions and stable saturated sigmoid/tanh behavior.

activationExpr

activationExpr :: Activation -> Expr -> Expr Source #

Embed the checked activation and analytic custom reverse rule in an automatic differentiation graph.

softmax

softmax :: [Double] -> Either MathError [Double] Source #

Exponentiate stable log-softmax values; the output sums to one within floating error.

logSoftmax

logSoftmax :: [Double] -> Either MathError [Double] Source #

Normalize a nonempty finite vector in log space after subtracting its maximum.

sparsemax

sparsemax :: [Double] -> Either MathError [Double] Source #

Project a finite vector onto the probability simplex using sorted active-support thresholds.

gatedLinearUnit

gatedLinearUnit :: [Double] -> [Double] -> Either MathError [Double] Source #

Multiply values by sigmoid(gates), requiring equal vector lengths.

softmaxExpr

softmaxExpr :: [Expr] -> [Expr] Source #

First-order softmax reverse rule, including cross-coordinate coupling.

logSoftmaxExpr

logSoftmaxExpr :: [Expr] -> [Expr] Source #

First-order stable log-softmax rule; gradient rows sum to zero.

sparsemaxExpr

sparsemaxExpr :: [Expr] -> [Expr] Source #

Sparsemax's piecewise-linear Jacobian. At a support boundary its inactive coordinate convention chooses zero, giving a defined subgradient.

ctcLossExpr

ctcLossExpr :: Int -> [Int] -> [[Expr]] -> Either MathError Expr Source #

CTC graph operation on rectangular time-major log probabilities. Its custom backward uses forward/backward occupancies, rather than numerical differences.

Reduction

data Reduction Source #

Loss aggregation: Sum adds elementwise losses and Mean divides by their count; vector-level loss exceptions are documented by loss.

Constructors

Sum
Mean

Instances

Instances details

Show Reduction Source #
Instance details Defined in HMath.DeepLearning.Core Methods showsPrec :: Int -> Reduction -> ShowS # show :: Reduction -> String # showList :: [Reduction] -> ShowS #
Eq Reduction Source #
Instance details Defined in HMath.DeepLearning.Core Methods (==) :: Reduction -> Reduction -> Bool # (/=) :: Reduction -> Reduction -> Bool #

Loss

data Loss Source #

Checked loss selector,including squared/absolute error,cross entropy,KL,hinge,cosine,and parameterized Hubersmooth losses. Targetprediction domain rules belong to loss.

Constructors

MeanSquaredError
MeanAbsoluteError
Huber Double
SmoothL1 Double
BinaryCrossEntropy
CategoricalCrossEntropy
NegativeLogLikelihood
KLDivergence
CosineLoss
Hinge Double

Instances

Instances details

Show Loss Source #
Instance details Defined in HMath.DeepLearning.Core Methods showsPrec :: Int -> Loss -> ShowS # show :: Loss -> String # showList :: [Loss] -> ShowS #
Eq Loss Source #
Instance details Defined in HMath.DeepLearning.Core Methods (==) :: Loss -> Loss -> Bool # (/=) :: Loss -> Loss -> Bool #

loss

loss :: Loss -> Reduction -> [Double] -> [Double] -> Either MathError Double Source #

Evaluate the selected checked loss. Mean divides elementwise losses by count; CosineLoss is one vector loss.

lossGradient

lossGradient :: Loss -> Reduction -> [Double] -> [Double] -> Either MathError [Double] Source #

Analytic derivatives with respect to predictions under the exact loss/reduction convention.

lossExpr

lossExpr :: Loss -> Reduction -> [Double] -> [Expr] -> Expr Source #

Use a constant target with symbolic prediction inputs and the matching analytic reverse rule.

binaryCrossEntropyLogits

binaryCrossEntropyLogits :: Reduction -> [Double] -> [Double] -> Either MathError Double Source #

Stable binary cross entropy from logits and [0,1] targets, including extreme finite logits.

categoricalCrossEntropyLogits

categoricalCrossEntropyLogits :: [Double] -> [Double] -> Either MathError Double Source #

Cross entropy from one class-logit vector; nonnegative targets must sum to one.

regularization

regularization :: Double -> Double -> [Double] -> Either MathError Double Source #

Return l1*sum(abs(w)) + l2/2*sum(w*w); both coefficients must be finite and nonnegative.

contrastiveLoss

contrastiveLoss :: Double -> Bool -> [Double] -> [Double] -> Either MathError Double Source #

Pairwise Euclidean contrastive loss; similar=True penalizes squared distance and dissimilar pairs use the positive margin.

tripletLoss

tripletLoss :: Double -> [Double] -> [Double] -> [Double] -> Either MathError Double Source #

Return max(0,positiveDistance-negativeDistance+margin) for equal nonempty vector dimensions.

focalLoss

focalLoss :: Double -> Double -> [Double] -> [Double] -> Either MathError Double Source #

Mean binary focal loss with alpha in [0,1], gamma>=0, and exact zero/one targets.

diceLoss

diceLoss :: Double -> [Double] -> [Double] -> Either MathError Double Source #

Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.

iouLoss

iouLoss :: Double -> [Double] -> [Double] -> Either MathError Double Source #

Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.

ctcLoss

ctcLoss :: Int -> [Int] -> [[Double]] -> Either MathError Double Source #

Single sequence, time-major log-probabilities [time,class]. Blank index is explicit; labels exclude blank. The forward/backward dynamic program sums alignments in log space, including adjacent repeated-label restrictions. Gradients are with respect to independent log probabilities, before a log-softmax chain rule. Impossible alignments return DomainError.

ctcLossGradient

ctcLossGradient :: Int -> [Int] -> [[Double]] -> Either MathError (Double, [[Double]]) Source #

Given blank class index, target labels, then rectangular time-by-class log probabilities, return CTC negative log likelihood and gradient rows. Validate class indices, finite/log-probability constraints and alignment feasibility. Empty time permits only empty labels; invalid/impossible inputs return Left MathError.