Loss Functions

NeuralFieldManifold.utils.loss_p(p_logits, p_true)

Cross-entropy loss for AR-order classification.

Parameters:

• p_logits (torch.Tensor) – Raw logits of shape (N, n_classes).

• p_true (torch.Tensor) – Ground-truth class indices of shape (N,).

Returns:

Scalar cross-entropy loss.

Return type:

torch.Tensor

NeuralFieldManifold.utils.loss_ar(x, x_hat, p_max)

Mean squared error between the true and reconstructed signal.

Only the portion after the first p_max time steps is considered to avoid the zero-padded region where lagged values are unavailable.

Parameters:

• x (torch.Tensor) – True input signal of shape (N, T).

• x_hat (torch.Tensor) – Reconstructed signal of shape (N, T).

• p_max (int) – Maximum AR order; the first p_max steps are excluded.

Returns:

Scalar MSE loss.

Return type:

torch.Tensor

NeuralFieldManifold.utils.loss_energy(x_hat, P0=0.5, W=40)

Sliding-window power constraint loss.

Penalises deviations of the local mean-squared power from the target level P0 by computing the MSE between windowed power and P0 across all positions.

Parameters:

• x_hat (torch.Tensor) – Reconstructed signal of shape (N, T).

• P0 (float, optional) – Target power level. Default is 0.5.

• W (int, optional) – Sliding-window size. Default is 40.

Returns:

Scalar energy loss.

Return type:

torch.Tensor

NeuralFieldManifold.utils.loss_smooth(coeffs)

Temporal smoothness penalty on AR coefficients.

Computes the mean squared first-order difference of the coefficient trajectories along the time axis.

Parameters:

coeffs (torch.Tensor) – Predicted AR coefficients of shape (N, T, max_ar_order).

Returns:

Scalar smoothness loss.

Return type:

torch.Tensor

NeuralFieldManifold.utils.loss_order(p_logits)

Regularizer. Computes expected order index from softmax probabilities and penalizes higher values.