KANMixer: Adaptive KAN for Forecasting

• KANMixer is a long-term time series forecasting architecture that uses adaptive Kolmogorov-Arnold Networks to modulate nonlinearities.
• It integrates a multi-scale mixing backbone to capture hierarchical locality and sequential biases, offering a clear advantage over traditional MLP-based models.
• Empirical evaluations show state-of-the-art results in 16 of 28 experiments, highlighting its practical efficacy in LTSF.

Searching arXiv for KANMixer and closely related KAN-based mixer architectures in time-series forecasting. Searching arXiv for KANMixer and closely related KAN-based mixer architectures in time-series forecasting. KANMixer is a long-term time series forecasting (LTSF) architecture introduced to investigate whether Kolmogorov-Arnold Networks (KAN) can serve as a new modeling core for the task. It is described as a concise architecture that integrates a multi-scale mixing backbone to fully leverage KAN’s adaptive capabilities, and it is motivated by the view that existing MLP-based forecasters, despite their success, often rely on hand-crafted external modules while neglecting hierarchical locality and sequential inductive biases essential for time-series modeling. In the reported evaluation, KANMixer achieves state-of-the-art performance in 16 out of 28 experiments across seven benchmark datasets, and the accompanying analysis frames the contribution not only as a new model but also as an empirical study of how KAN changes the role of structural priors in forecasting systems (Jiang et al., 3 Aug 2025).

1. Conceptual basis

KANMixer emerges from a specific tension in recent forecasting research. On one hand, MLP-based deep learning models have demonstrated remarkable success in LTSF. On the other hand, the dominant pattern in that line of work has been to augment flat MLP backbones with hand-crafted external modules intended to compensate for architectural limitations. The KANMixer paper positions this strategy as increasingly constrained: the added modules may improve performance, but they do not by themselves restore hierarchical locality or sequential inductive bias, and recent studies are said to indicate diminishing performance improvements (Jiang et al., 3 Aug 2025).

The alternative proposed by KANMixer is to treat KAN as the backbone rather than as an accessory. In related KAN literature, a KAN layer is formulated as a sum of learnable univariate edge functions,

$$x^{(\ell+1)}_j=\sum_{i=1}^{n_\ell}\varphi^{(\ell)}_{j,i}\!\big(x^{(\ell)}_i\big),$$

in contrast to the usual MLP pattern of linear weights followed by fixed node activations (Guo et al., 21 Nov 2025). For forecasting, the relevant property is not only universal function approximation in the abstract, but adaptive basis functions capable of granular, local modulation of nonlinearities. KANMixer adopts this property as the central modeling mechanism rather than as a marginal substitution (Jiang et al., 3 Aug 2025).

This positioning distinguishes KANMixer from a merely cosmetic “KAN-ized” MLP. The model is framed around the question of whether KAN can become the organizing principle of LTSF architecture design. That question is significant because much of the prior KAN-related forecasting literature had explored targeted insertion, expert routing, or local replacements, rather than an explicit re-centering of the forecasting backbone around KAN itself (Jiang et al., 3 Aug 2025).

2. Architectural role in long-term forecasting

At the architectural level, KANMixer is defined by two stated commitments: a KAN-centered design and a multi-scale mixing backbone. The paper characterizes the architecture as concise, suggesting an attempt to avoid the proliferation of auxiliary modules that had become common in MLP-based LTSF systems, while still exploiting multi-scale structure (Jiang et al., 3 Aug 2025).

That description places KANMixer within a broader class of forecasting models that use mixing operations to organize information flow across scales, variables, or temporal positions, but it does so with a distinct claim: KAN’s adaptive basis functions materially alter how backbone structure interacts with performance. This is more ambitious than simply replacing an output layer or a single temporal block.

A concise way to situate KANMixer relative to nearby models is the following.

Model	Domain	Relation to KANMixer
KANMixer	LTSF	KAN as a new modeling core with a multi-scale mixing backbone
TSKANMixer	Multivariate forecasting	KAN inserted into temporal components of TSMixer
KFS	LTSF	KAN-based adaptive Frequency Selection architecture with feature mixing
RMoK	Multivariate forecasting	Mixture-of-KAN experts with RevIN

TSKANMixer modifies TSMixer by introducing a two-depth KAN layer into temporal components, either as temporal projection or as an extra time-mixing layer, while retaining ordinary MLP feature-mixing blocks (Hong et al., 25 Feb 2025). KFS combines multi-scale decomposition, spectral dominant-frequency selection, KAN-based modeling, timestamp embedding alignment, and a residual feature mixing module (Wu et al., 1 Aug 2025). RMoK, introduced in the study of KAN effectiveness for multivariate forecasting, uses RevIN and a single mixture-of-KAN-experts layer rather than a mixer stack (Han et al., 2024). Against this background, KANMixer is best understood as an attempt to move from partial substitution toward a KAN-native forecasting core (Jiang et al., 3 Aug 2025).

3. Empirical performance

The central empirical claim of KANMixer is straightforward: extensive evaluation shows state-of-the-art performance in 16 of 28 experiments across seven benchmark datasets (Jiang et al., 3 Aug 2025). Within the paper’s framing, that result is important not only because of the win count, but because it is used to support the viability of KAN as a backbone-level choice for LTSF rather than as a narrow module replacement.

Related work supplies useful comparative context. TSKANMixer reports that one of its two variants beats TSMixer on 8 of 10 datasets in either MSE or MAE, with particularly strong gains on several ETT settings, but also with severe training-time penalties and failures on CIF 2016 and FRED-MD (Hong et al., 25 Feb 2025). KFS reports state-of-the-art performance across multiple real-world time series datasets through a combination of spectral filtering, KAN nonlinear modeling, timestamp alignment, and scale fusion (Wu et al., 1 Aug 2025). RMoK is often best or among the best on seven forecasting datasets, yet is weaker on Traffic, where intricate spatiotemporal correlations among variables appear to matter more strongly (Han et al., 2024).

Taken together, these results suggest a broader empirical pattern: KAN-based forecasting systems can be highly competitive, but their success depends on how KAN is embedded into the architecture. KANMixer’s reported 16-of-28 state-of-the-art record is therefore notable because it accompanies an explicit claim that KAN is no longer peripheral to the forecasting pipeline (Jiang et al., 3 Aug 2025).

4. KAN versus MLP as the modeling core

A defining contribution of KANMixer is its comparison with traditional MLP architectures. The paper states that it systematically analyzes the strengths and limitations of KANMixer against such baselines and finds that the adaptive flexibility of KAN’s learnable basis functions significantly transforms the influence of network structural prior on forecasting performance (Jiang et al., 3 Aug 2025).

That finding has methodological significance. In flat MLP-style forecasters, structural prior is often carried by external architectural interventions: decomposition branches, patching, multi-scale blocks, or hand-crafted mixers. KANMixer argues that once the nonlinear basis itself becomes adaptive and locally modulatable, the dependence of performance on those priors changes. This suggests that architectural choices in KAN-based forecasters should not be interpreted through the same lens as in ordinary MLP systems.

The broader literature supports a cautious version of that conclusion. RMoK shows that direct KAN replacement inside a Transformer is not uniformly beneficial, whereas a mixture-of-KAN design integrates more effectively (Han et al., 2024). In human activity recognition, the hybrid “KAN-MLP-Mixer” reports that replacing the Feature Mixer module with KAN variants generally resulted in substantial performance degradation, while selective placement of EfficientKAN in data embedding and LarctanKAN in the classifier improved the average macro F1 score relative to the pure-MLP baseline by 5.33% (Liu et al., 18 May 2026). TSKANMixer likewise keeps feature-mixing MLPs intact while targeting temporal components with KAN (Hong et al., 25 Feb 2025).

A common misconception is therefore that KAN-based mixer research uniformly supports replacing every MLP with a KAN. The available evidence does not support that interpretation. KANMixer is better read as an argument that KAN can be the core of an LTSF architecture when the backbone is designed to exploit it, not as a blanket prescription that every MLP sublayer should disappear (Jiang et al., 3 Aug 2025).

5. Design factors and practical guidance

The KANMixer paper states that it identifies critical design factors affecting forecasting accuracy and offers practical insights for effectively utilizing KAN in LTSF. It further claims that these insights constitute the first empirically grounded guidelines for effectively leveraging KAN in LTSF (Jiang et al., 3 Aug 2025). Even without enumerating those factors in detail here, that claim marks an important transition from proof-of-concept substitution toward design methodology.

Related studies make clear what kinds of issues such guidance must address. In RMoK, basis choice matters materially: B-spline, wavelet, Taylor, and Jacobi variants do not behave identically, and mixture-of-experts routing is used in part to mitigate that sensitivity (Han et al., 2024). KFS indicates that KAN-based multi-scale systems may benefit from explicit spectral denoising, aligned timestamp embeddings, and cross-scale feature mixing rather than relying on KAN alone (Wu et al., 1 Aug 2025). TSKANMixer shows that KAN can improve temporal modeling yet introduce severe computational overhead, with some ETT settings reported as up to about 50 times slower than TSMixer during training (Hong et al., 25 Feb 2025).

A plausible implication is that “using KAN in LTSF” is not a single design decision but a bundle of interdependent decisions about where adaptive basis functions should act, what multiscale structure accompanies them, and how much structural prior the backbone should retain. KANMixer is significant precisely because it treats these interactions as a first-class empirical object rather than as incidental implementation detail (Jiang et al., 3 Aug 2025).

The paper also reports that code is available in the supplementary file, which is consistent with the broader reproducibility emphasis seen across recent KAN forecasting work (Jiang et al., 3 Aug 2025).

6. Naming, related usage, and open questions

The name “KANMixer” belongs to a broader and somewhat confusing family of KAN-and-mixer terminology. “TSKANMixer” is a KAN-augmented TSMixer for multivariate time-series forecasting (Hong et al., 25 Feb 2025). “KAN-Mixers” refers to a fully KAN-based image-classification architecture that replaces both token-mixing and channel-mixing MLPs in an MLP-Mixer-like design (Canuto et al., 11 Mar 2025). “KAN-MLP-Mixer” refers to a hybrid human-activity-recognition architecture that uses EfficientKAN for input embedding, MLP for feature mixing, and LarctanKAN for classification (Liu et al., 18 May 2026). These models are related by motif, not by identity.

That naming overlap matters because it clarifies what is and is not distinctive about KANMixer. The 2025 LTSF model is not simply another instance of “put KAN somewhere inside a mixer.” Its explicit claim is stronger: KAN may serve as a new modeling core for long-term time series forecasting (Jiang et al., 3 Aug 2025).

Several open questions remain. Related forecasting studies show that KAN integration can improve accuracy yet remain computationally expensive (Hong et al., 25 Feb 2025), that basis choice and expert routing can strongly affect outcomes (Han et al., 2024), and that channel interaction may still challenge simple KAN-centered systems on datasets with intricate cross-variable structure (Han et al., 2024). These findings do not weaken KANMixer’s contribution; rather, they define its research agenda. The model stands at the point where KAN research in forecasting shifts from isolated substitutions toward backbone design, empirical principles, and a more explicit theory of when adaptive basis functions should dominate architectural prior (Jiang et al., 3 Aug 2025).