Time-series forecasting is foundational to a wide spectrum of web-scale services, spanning personalized recommendations, energy scheduling, and infrastructure capacity planning. Accurate long-term time series forecasting (LTSF) requires models to capture long-range temporal dependencies while adapting to periodic patterns that vary across variables. Although frequency-aware methods offer a global view of temporal dynamics, they typically rely on inflexible heuristic designs, such as predefined period lengths, manually selected or randomly sampled top-k frequency components, and separate spectral transformations. Consequently, they fail to account for time-frequency heterogeneity, where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Meanwhile, Mamba-based forecasters, despite their efficiency in long-range modeling, introduce frequency information only as auxiliary signals, leaving spectral evidence disconnected from state transitions. In this work, we propose AdaMamba, a novel approach that explicitly internalizes input-dependent frequency information into the modeling of temporal dependencies. AdaMamba comprises an interaction learning module and an adaptive frequency-gated state space module: the former captures cross-variable dependencies and multi-scale temporal context, while the latter generates context-dependent frequency bases and unifies temporal forgetting into a single time-frequency gate that directly modulates state evolution. Extensive experiments on seven public LTSF benchmarks and four domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art baselines while maintaining competitive computational efficiency.

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