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Despite showing positive results in data-rich regimes, they often fail to outperform significantly smaller supervised models in low-resource settings compared to fully supervised models. We provide a mechanistic account of this shortcoming, attributing it to a fundamental mismatch between reconstruction-based pretext tasks and the idiosyncratic spectral structure of EEG signals, which decompose into distinct high-power aperiodic and low-power oscillatory components. Using controlled, synthetically-generated EEG inputs, we demonstrate that EEG foundation model embeddings are biased to capture the aperiodic components of the EEG signal while under-representing oscillatory components, particularly at higher frequencies. 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Using controlled, synthetically-generated EEG inputs, we demonstrate that EEG foundation model embeddings are biased to capture the aperiodic components of the EEG signal while under-representing oscillatory components, particularly at higher frequencies. 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