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This paper develops a Fourier analysis framework to study data augmentation under group invariances, showing that partial augmentation can achieve the same minimax rates as full augmentation up to a vanishing approximation error, while also proving that exact invariance requires full group averaging.
Introduces SpikF-GO, a spiking neural network model for multivariate time series forecasting that combines graph-based inter-variable dependency modeling with spike-driven spectral processing, achieving state-of-the-art results among SNN methods with reduced energy consumption.
This paper provides a theoretical analysis of how neural networks learn structured representations during group composition tasks, proving that training dynamics drive neurons to converge to irreducible group representations with exponential convergence rates. The work establishes a representation-theoretic account of feature learning and characterizes a low-rank compression phenomenon for matrix-valued group representations.