Added FFTLoss in Pytorch

[SkyeGunasekaran]

PR Description: Integration of Fourier-Domain Loss Functions

Overview

This PR introduces a suite of frequency-domain loss functions and a flexible MixedFFTLoss utility. These additions allow the model to optimize for spectral density and periodic structures, which provides a more robust loss function to trend and seasonality vs direct pointwise prediction errors.

Fourier Loss Suite

I have implemented three core frequency-domain losses based on the magnitude spectrum of the Real Discrete Fourier Transform (RFFT):

• FFTMAELoss: Mean Absolute Error in frequency space.
• FFTMSELoss: Mean Squared Error in frequency space.
• FFTRMSELoss: Root Mean Squared Error in frequency space.

These losses operate on the magnitude spectrum $|F(y)|$ which ensures the loss remains real-valued, focuses on the power distribution of seasonal and trend components rather than exact point-in-time alignment.

Hybrid Optimization (MixedFFTLoss)

To balance point-wise accuracy with structural frequency alignment, I added MixedFFTLoss. This allows for a composite objective function. This function provides the best balance for real-world use cases:

$$\mathcal{L}_{total} = \mathcal{L}_{time} + \lambda \cdot \mathcal{L}_{freq}$$

Key Features:

• Zero-Masking: Masks are applied in the time-domain prior to FFT to prevent padding or missing values from introducing high-frequency noise into the spectrum.
• Normalization: Supports magnitude normalization via the norm parameter to ensure loss stability across varying sequence lengths ($H$).
• Architectural Compatibility: The implementation respects the BasePointLoss interface to seamlessly integrate with existing loss functions in the repository.

Testing

Tests were performed locally via PyTest. The baseline formulas were computed in pure numpy and compared against the pytorch functions implemented. The loss functions are numerically stable and work within the NeuralForecast repository.

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[marcopeix]

Hi, is there a paper that details these new losses and benchmarks them on known public datasets?

Even we do decide to move forward with this, the PR is missing:

• proper tests to ensure it works with all types of models (univariate, multivariate, recurrent)
• update to the documentation