We introduce Adaptive Spectral Shaping, a data-driven framework for graph filtering that learns a reusable baseline spectral kernel and modulates it with a small set of Gaussian factors. The resulting multi-peak, multi-scale responses allocate energy to heterogeneous regions of the Laplacian spectrum while remaining interpretable via explicit centers and bandwidths. To scale, we implement filters with Chebyshev polynomial expansions, avoiding eigendecompositions. We further propose Transferable Adaptive Spectral Shaping (TASS): the baseline kernel is learned on source graphs and, on a target graph, kept fixed while only the shaping parameters are adapted, enabling few-shot transfer under matched compute. Across controlled synthetic benchmarks spanning graph families and signal regimes, Adaptive Spectral Shaping reduces reconstruction error relative to fixed-prototype wavelets and learned linear banks, and TASS yields consistent positive transfer. The framework provides compact spectral modules that plug into graph signal processing pipelines and graph neural networks, combining scalability, interpretability, and cross-graph generalization.

翻译：本文提出自适应谱形（Adaptive Spectral Shaping）这一数据驱动的图滤波框架，该方法学习一个可复用的基线谱核，并通过少量高斯因子对其进行调制。由此产生的多峰、多尺度响应将能量分配到拉普拉斯谱的异质区域，同时通过显式的中心频率和带宽保持可解释性。为实现可扩展性，我们采用切比雪夫多项式展开实现滤波器，避免了特征分解。我们进一步提出可迁移自适应谱形（Transferable Adaptive Spectral Shaping, TASS）：基线核在源图上学习获得，在目标图上则保持固定，仅调整谱形参数，从而在匹配的计算量下实现少样本迁移。在涵盖不同图族与信号机制的受控合成基准测试中，自适应谱形相比固定原型小波与学习型线性滤波器组降低了重构误差，且TASS实现了持续的正向迁移。该框架提供了紧凑的谱模块，可嵌入图信号处理流程与图神经网络中，兼具可扩展性、可解释性与跨图泛化能力。