Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific parameters and introduce architectural bias; or (ii) DNN-free, which rely on heuristics lacking theoretical guarantees. Neither approach explicitly constrains distributional equivalence, largely because continuous distribution matching is considered inapplicable to discrete sampling. Moreover, prevalent metrics (e.g., MSE, KL, CE, MMD) cannot accurately capture higher-order moment discrepancies, leading to suboptimal coresets. In this work, we propose FAST, the first DNN-free distribution-matching coreset selection framework that formulates the coreset selection task as a graph-constrained optimization problem grounded in spectral graph theory and employs the Characteristic Function Distance (CFD) to capture full distributional information in the frequency domain. We further discover that naive CFD suffers from a "vanishing phase gradient" issue in medium and high-frequency regions; to address this, we introduce an Attenuated Phase-Decoupled CFD. Furthermore, for better convergence, we design a Progressive Discrepancy-Aware Sampling strategy that progressively schedules frequency selection from low to high, preserving global structure before refining local details and enabling accurate matching with fewer frequencies while avoiding overfitting. Extensive experiments demonstrate that FAST significantly outperforms state-of-the-art coreset selection methods across all evaluated benchmarks, achieving an average accuracy gain of 9.12%. Compared to other baseline coreset methods, it reduces power consumption by 96.57% and achieves a 2.2x average speedup, underscoring its high performance and energy efficiency.

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