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Supplementary Materials for " Deep Fractional Fourier Transform " Hu Y u
This supplementary document is organized as follows: Section 1 shows the proof that the formula of FRFT degrades to that of FT when α = π/ 2. Section 2 shows the discrete implementation of 2D FRFT. Section 4 shows the experimental results with single branch. Section 5 shows the architecture design of SFC and example usage of SFC and MFRFC. Section 6 introduces the periodicity of FRFT. Section 7 introduces the energy distribution of FRFT.
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DataPerf: Benchmarks for Data-Centric AI Development Mark Mazumder
Machine learning research has long focused on models rather than datasets, and prominent datasets are used for common ML tasks without regard to the breadth, difficulty, and faithfulness of the underlying problems. Neglecting the fundamental importance of data has given rise to inaccuracy, bias, and fragility in real-world applications, and research is hindered by saturation across existing dataset benchmarks.
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A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting
Caldas, Francisco, Kumar, Sahil, Soares, Cláudia
We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains high signal-to-noise ratios for dominant frequencies throughout the diffusion trajectory, thereby improving the recoverability of long-term patterns. This strategy enables the model to maintain the signal structure for a longer period in the forward process, leading to improved forecast quality. Across standard forecasting benchmarks, we show that applying spectral decomposition strategies, such as the Fourier or Wavelet transform, consistently improves upon diffusion models using the baseline forward process, with negligible computational overhead. The code for this paper is available at https://anonymous.4open.science/r/D-FDP-4A29.
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