arxiv: 2604.23239 · v1 · submitted 2026-04-25 · 💻 cs.AI

Recognition: unknown

AdaMamba: Adaptive Frequency-Gated Mamba for Long-Term Time Series Forecasting

Xudong Jiang , Mingshan Loo , Hanchen Yang , Wengen Li , Mingrui Zhang , Yichao Zhang , Jihong Guan , Shuigeng Zhou

Authors on Pith no claims yet

Pith reviewed 2026-05-08 08:13 UTC · model grok-4.3

classification 💻 cs.AI

keywords long-term time series forecastingMambafrequency domainadaptive gatingstate-space modelsmultivariate time seriestime-frequency integration

0 comments

The pith

AdaMamba adds input-dependent frequency bases to Mamba state updates so the model can adapt to frequency differences across variables in long time series.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to show that real-world time series often hide important periodic differences across variables that only become visible in the frequency domain. By generating those frequency bases inside the Mamba update itself and folding them into a single time-frequency forgetting gate, the method lets the state-space model recalibrate its memory on the fly for each input. If the approach works, forecasters gain accuracy on heterogeneous data while keeping the linear-time scaling that makes Mamba attractive for long horizons.

Core claim

AdaMamba endogenizes adaptive frequency analysis inside the Mamba state-space process. An interactive patch encoder first models inter-variable dynamics; then an adaptive frequency-gated module produces input-dependent frequency bases and replaces the standard temporal gate with a unified time-frequency gate. This lets the model scale state transitions according to learned frequency importance while retaining Mamba's long-range dependency modeling. On seven public LTSF benchmarks and two domain-specific sets the method records higher accuracy than prior state-of-the-art approaches at comparable computational cost.

What carries the argument

The adaptive frequency-gated state-space module that creates input-dependent frequency bases on the fly and merges them into a single time-frequency forgetting gate inside each Mamba block.

If this is right

Forecast accuracy rises on multivariate series whose variables differ in dominant frequencies even when they appear aligned in the time domain.
Computational cost stays close to standard Mamba because the frequency adaptation is folded into the existing state update rather than added as a separate module.
The same architecture can be applied to domain-specific series without requiring hand-crafted frequency features for each new domain.
Long-range dependency modeling remains intact because the frequency gate operates alongside rather than replacing the original Mamba recurrence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same input-dependent frequency mechanism could be dropped into other linear-time state-space architectures to test whether the gain is specific to Mamba or general to the state-space family.
If the adaptive bases prove stable, the method offers a route to remove separate frequency preprocessing steps that currently sit outside most deep forecasters.
On very high-dimensional series the interactive patch encoder may become a bottleneck, suggesting a natural next test of whether the frequency gating alone is sufficient when variable count grows.

Load-bearing premise

Real-world time series contain enough measurable frequency heterogeneity across variables that an input-dependent basis generated inside the Mamba update can exploit it without causing extra overfitting or training instability.

What would settle it

If an ablation that replaces the learned input-dependent frequency bases with fixed, non-adaptive bases produces equal or better accuracy on the same seven benchmarks, the value of the adaptive component is falsified.

Figures

Figures reproduced from arXiv: 2604.23239 by Hanchen Yang, Jihong Guan, Mingrui Zhang, Mingshan Loo, Shuigeng Zhou, Wengen Li, Xudong Jiang, Yichao Zhang.

**Figure 1.** Figure 1: A motivating example of the ETTm1 dataset in view at source ↗

**Figure 2.** Figure 2: The architecture of AdaMamba which mainly consists of two modules, i.e., interactive patch encoding module and view at source ↗

**Figure 3.** Figure 3: Visualization of forecasting results. 4.3 Ablation Studies To evaluate the contributions of the main components in AdaMamba , we conduct ablation studies by constructing multiple variants as listed below. Case I: The full AdaMamba that includes both the interactive patch encoding module and the adaptive frequency-gated statespace module. Case II: The interactive patch encoding module in AdaMamba is replac… view at source ↗

**Figure 4.** Figure 4: The visualization of frequency analysis. view at source ↗

**Figure 5.** Figure 5: Comparison of AdaMamba and six baseline models view at source ↗

**Figure 6.** Figure 6: Performance gains and computational overhead of view at source ↗

**Figure 8.** Figure 8: Sensitivity analysis of multi-scale patch. view at source ↗

**Figure 7.** Figure 7: Analysis of the hyperparameter sensitivity. view at source ↗

read the original abstract

Accurate long-term time series forecasting (LTSF) requires the capture of complex long-range dependencies and dynamic periodic patterns. Recent advances in frequency-domain analysis offer a global perspective for uncovering temporal characteristics. However, real-world time series often exhibit pronounced cross-domain heterogeneity where variables that appear synchronized in the time domain can differ substantially in the frequency domain. Existing frequency-based LTSF methods often rely on implicit assumptions of cross-domain homogeneity, which limits their ability to adapt to such intricate variability. To effectively integrate frequency-domain analysis with temporal dependency learning, we propose AdaMamba, a novel framework that endogenizes adaptive and context-aware frequency analysis within the Mamba state-space update process. Specifically, AdaMamba introduces an interactive patch encoding module to capture inter-variable interaction dynamics. Then, we develop an adaptive frequency-gated state-space module that generates input-dependent frequency bases, and generalizes the conventional temporal forgetting gate into a unified time-frequency forgetting gate. This allows dynamic calibration of state transitions based on learned frequency-domain importance, while preserving Mamba's capability in modeling long-range dependencies. Extensive experiments on seven public LTSF benchmarks and two domain-specific datasets demonstrate that AdaMamba consistently outperforms state-of-the-art methods in forecasting accu racy while maintaining competitive computational efficiency. The code of AdaMamba is available at https://github.com/XDjiang25/AdaMamba.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

AdaMamba adds an input-dependent frequency gate to Mamba but the change to the forgetting mechanism lacks a derivation that it preserves the original SSM stability.

read the letter

The main point is that this paper takes Mamba and tries to make its state update adapt to frequency content on the fly. The interactive patch encoder and the adaptive frequency-gated module are the concrete additions. They generate frequency bases from the input and fold them into a single time-frequency forgetting gate. That addresses the observation that variables can look aligned in time but differ in their periodic structure across domains. The abstract reports stronger long-term forecast numbers on seven standard benchmarks plus two domain datasets, with runtimes that stay competitive. Code is released, which lets others check the implementation directly. Those are the parts that actually move the needle beyond prior Mamba and frequency work. The soft spot sits in the central modification. The stress-test note is right that the paper does not show how the frequency term alters the state matrix A or the discretization step while keeping the selective SSM properties intact. Without that step, it is hard to know whether the new gate still supports reliable long-range modeling or whether it adds coupling that could hurt on some series. The benchmark wins are stated clearly, but the abstract gives no error bars, ablation tables, or statistical tests, so the size of the real gain is still provisional. This is useful reading for anyone already working with state-space models on forecasting tasks. The design is a straightforward extension rather than a foundational change, but it is concrete enough that a referee could evaluate the equations and the experiments in one pass. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper proposes AdaMamba, a Mamba-based model for long-term time series forecasting that adds an interactive patch encoding module for inter-variable dynamics and an adaptive frequency-gated state-space module. The latter generates input-dependent frequency bases and generalizes the temporal forgetting gate into a unified time-frequency gate to dynamically adjust state transitions according to learned frequency importance while aiming to retain long-range dependency modeling. Experiments on seven public LTSF benchmarks plus two domain-specific datasets are reported to show consistent accuracy gains over state-of-the-art methods at competitive computational cost.

Significance. If the adaptive frequency integration can be shown to preserve the selective SSM stability and discretization properties while capturing cross-domain frequency heterogeneity, the approach would offer a concrete mechanism for hybrid time-frequency modeling in forecasting tasks where periodic patterns vary across variables or domains. The public code release supports reproducibility.

major comments (2)

[Abstract / adaptive frequency-gated state-space module description] The description of the adaptive frequency-gated state-space module (abstract and method section) states that the conventional temporal forgetting gate is generalized to a unified time-frequency forgetting gate via input-dependent frequency bases. No explicit equation is supplied showing how the frequency component enters the state matrix A, input matrix B, or the discretization step of the underlying SSM. Without this, it is impossible to verify that the selective long-range dynamics and stability guarantees of the original Mamba are retained; any unanalyzed time-frequency coupling would directly undermine the central performance claim.
[Experiments section] The experimental claims of consistent outperformance rest on benchmark results, yet the manuscript provides no details on the number of independent runs, statistical significance tests, error bars, or ablation studies that isolate the contribution of the input-dependent frequency bases versus the base Mamba architecture. This absence makes it difficult to rule out that observed gains arise from hyper-parameter tuning or other unanalyzed factors rather than the proposed adaptive mechanism.

minor comments (2)

[Abstract] The abstract contains a typographical spacing error: 'accu racy' should read 'accuracy'.
[Method] Notation for the unified time-frequency gate and frequency bases should be introduced with a clear symbol table or inline definitions to avoid ambiguity when the equations are eventually supplied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough and constructive review. We address each major comment below and will revise the manuscript accordingly to improve clarity and rigor.

read point-by-point responses

Referee: [Abstract / adaptive frequency-gated state-space module description] The description of the adaptive frequency-gated state-space module (abstract and method section) states that the conventional temporal forgetting gate is generalized to a unified time-frequency forgetting gate via input-dependent frequency bases. No explicit equation is supplied showing how the frequency component enters the state matrix A, input matrix B, or the discretization step of the underlying SSM. Without this, it is impossible to verify that the selective long-range dynamics and stability guarantees of the original Mamba are retained; any unanalyzed time-frequency coupling would directly undermine the central performance claim.

Authors: We agree that the current description is insufficient for verifying the integration details. The manuscript describes the adaptive frequency-gated state-space module at a conceptual level but does not supply the explicit equations for how input-dependent frequency bases modify the state matrix A, input matrix B, or the discretization step. In the revised version, we will add these precise formulations (including the modified SSM update rules and the unified time-frequency gate) to the method section, along with a brief analysis confirming that selective long-range dynamics and stability properties are preserved. revision: yes
Referee: [Experiments section] The experimental claims of consistent outperformance rest on benchmark results, yet the manuscript provides no details on the number of independent runs, statistical significance tests, error bars, or ablation studies that isolate the contribution of the input-dependent frequency bases versus the base Mamba architecture. This absence makes it difficult to rule out that observed gains arise from hyper-parameter tuning or other unanalyzed factors rather than the proposed adaptive mechanism.

Authors: We acknowledge this gap in experimental reporting. The manuscript presents results across the benchmarks but omits the number of runs, error bars, significance tests, and ablations isolating the frequency bases. We will revise the Experiments section to include: five independent runs per model with reported means and standard deviations; paired t-tests for statistical significance against baselines; and a dedicated ablation comparing the full model to a non-adaptive Mamba variant. These changes will substantiate the contribution of the proposed adaptive mechanism. revision: yes

Circularity Check

0 steps flagged

No circularity: novel adaptive module with independent empirical validation

full rationale

The paper proposes AdaMamba as an extension of Mamba SSMs that introduces an interactive patch encoding module and an adaptive frequency-gated state-space module generating input-dependent frequency bases to create a unified time-frequency forgetting gate. These are presented as architectural innovations with explicit design goals (capturing cross-domain frequency heterogeneity while preserving long-range dependency modeling). The central claims of outperformance rest on experimental results across seven LTSF benchmarks and two domain-specific datasets, not on any definitional equivalence, fitted-parameter renaming, or self-citation chain that reduces the result to its inputs. No load-bearing step equates a derived quantity to a fitted input or prior self-cited result by construction; the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

The central performance claim rests on the effectiveness of two newly introduced modules whose behavior is learned from data; no explicit free parameters, axioms, or invented physical entities are stated in the abstract.

invented entities (1)

adaptive frequency-gated state-space module no independent evidence
purpose: Generates input-dependent frequency bases and unifies time-frequency forgetting to calibrate state transitions
Core novel component introduced to address cross-domain frequency heterogeneity

pith-pipeline@v0.9.0 · 5572 in / 1100 out tokens · 78650 ms · 2026-05-08T08:13:48.099457+00:00 · methodology

discussion (0)

Reference graph

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