Loss Functions

EikonalLoss()

The Eikonal loss regularizes the gradient of a neural implicit to have unit norm everywhere:

\[\mathcal{L}_{\text{eik}}(x) = (||\nabla f_\theta(x)|| -1)^2\]

The gradient is computed from the input \(X\) and the output \(Y\) of the neural model.

__call__(X, Y)

Parameters:

Name	Type	Description	Default
X	Tensor	input batch of the model	required
Y	Tensor	output of the model.	required

Returns:

Type	Description
	torch.Tensor: Eikonal loss

HKRLoss(margin=0.01, lmbd=10.0)

Hinge Kantorovitch-Rubinstein loss

\[\text{hKR}(x) = \max(0, m-x) - \frac{x}{\lambda}\]

Parameters:

Name	Type	Description	Default
margin	float	hinge margin. Must be small but not too small. Defaults to 1e-2.	0.01
lmbd	float	weight balance between the two terms.. Defaults to 10.	10.0

References

• Achieving robustness in classification using optimal transport with hinge regularization, Serrurier et al., 2021
• 1-Lipschitz neural distance fields, Coiffier and Béthune, 2024

__call__(y)

Parameters:

Name	Type	Description	Default
y	Tensor	vector of predicted values	required

HotspotLoss(lmbd)

\[\mathcal{L}_{\text{heat}}(f) = \mathbb{E}_x \left[ e^{-2 \lambda |f(x)|} \left( || \nabla f||^2 + 1 \right) \right].\]

References

• HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition, Wang et al., 2025

SALDLoss()

Sign agnostic learning loss with derivatives

References

SALD: Sign Agnostic Learning with Derivatives, Atzmon and Lipman, 2020

__call__(y_pred, y_target)

Parameters:

Name	Type	Description	Default
y_pred	Tensor	predicted values by the model	required
y_target	Tensor	target values	required

SALLoss(l=1.0, metric='l2')

Signed agnostic learning loss.

Parameters:

Name	Type	Description	Default
l	float	Power value for the distance. Defaults to 1.	1.0
metric	str	which metric to use. Choices are "l2" and "l0". Defaults to "l2".	'l2'

References

SAL: Sign Agnostic Learning of Shapes From Raw Data, Atzmon and Lipman, 2020

__call__(y_pred, y_target)

Parameters:

Name	Type	Description	Default
y_pred	Tensor	predicted values by the model	required
y_target	Tensor	target values	required

SingularHessianLoss

TODO

ThinPlateLoss

References

• NeuVAS: Neural Implicit Surfaces for Variational Shape Modeling, Wang et al., 2025
• https://github.com/GeometryArt/NeuVAS/tree/main/code

VectorAlignmentLoss()

Cosine similarity loss between two vectors.

__call__(y, target)

Parameters:

Name	Type	Description	Default
y	Tensor	input tensor	required
target	Tensor	target tensor	required

Returns:

Type	Description
	torch.Tensor: Cosine similarity