Table of Contents

Class SquaredHingeLoss<T>

Namespace
AiDotNet.LossFunctions
Assembly
AiDotNet.dll

Implements the Squared Hinge Loss function for binary classification problems.

public class SquaredHingeLoss<T> : LossFunctionBase<T>, ILossFunction<T>

Type Parameters

T

The numeric type used for calculations (e.g., float, double).

Inheritance
SquaredHingeLoss<T>
Implements
Inherited Members
Extension Methods

Remarks

For Beginners: Squared Hinge Loss is a variation of the Hinge Loss used in Support Vector Machines (SVMs) that applies a squared penalty to incorrectly classified examples.

The formula is: max(0, 1 - y*f(x))² Where:

  • y is the true label (usually -1 or 1)
  • f(x) is the model's prediction

Key properties:

  • It heavily penalizes predictions that are incorrect or not confident enough
  • The quadratic nature creates a smoother loss surface compared to regular Hinge Loss
  • It has a continuous derivative everywhere, which can make optimization easier
  • It's zero when predictions are correct and confident (y*f(x) = 1)

Squared Hinge Loss is particularly useful for:

  • Binary classification problems
  • Support Vector Machines
  • Any situation where smoother gradients are beneficial for optimization

Compared to regular Hinge Loss, it penalizes violations more severely due to the squaring operation.

Methods

CalculateDerivative(Vector<T>, Vector<T>)

Calculates the derivative of the Squared Hinge Loss function.

public override Vector<T> CalculateDerivative(Vector<T> predicted, Vector<T> actual)

Parameters

predicted Vector<T>

The predicted values vector.

actual Vector<T>

The actual (ground truth) values vector, typically -1 or 1.

Returns

Vector<T>

A vector containing the derivatives of the squared hinge loss with respect to each predicted value.

CalculateLoss(Vector<T>, Vector<T>)

Calculates the Squared Hinge Loss between predicted and actual values.

public override T CalculateLoss(Vector<T> predicted, Vector<T> actual)

Parameters

predicted Vector<T>

The predicted values vector.

actual Vector<T>

The actual (ground truth) values vector, typically -1 or 1.

Returns

T

The squared hinge loss value.

CalculateLossAndGradientGpu(IGpuTensor<T>, IGpuTensor<T>)

Calculates both Squared Hinge loss and gradient on GPU in a single efficient pass.

public override (T Loss, IGpuTensor<T> Gradient) CalculateLossAndGradientGpu(IGpuTensor<T> predicted, IGpuTensor<T> actual)

Parameters

predicted IGpuTensor<T>

The predicted GPU tensor from the model.

actual IGpuTensor<T>

The actual (target) GPU tensor.

Returns

(T Loss, IGpuTensor<T> Gradient)

A tuple containing the loss value and gradient tensor.

Edit this page