💻 computer science

Rethinking Time Series with Kolmogorov-Arnold Networks: A Systematic Review

This systematic review evaluates the suitability of Kolmogorov-Arnold Networks (KANs) for time series analysis, concluding that while they excel in interpretable, short-horizon forecasting with smooth patterns across various domains, their current application is limited by heterogeneous evidence, challenges in handling long-range dependencies and regime shifts, and a need for standardized benchmarks and rigorous interpretability validation.

Original authors: Antoni Mól, Dariusz Jemielniak, Leon Ciechanowski

Published 2026-07-14

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Antoni Mól, Dariusz Jemielniak, Leon Ciechanowski

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you're trying to predict the future. Maybe you want to know how much electricity your neighborhood will use tomorrow, how a battery in your phone will hold up, or even what the weather will do. For years, the go-to tools for this job have been like giant, black-box robots (called Deep Learning models) that are great at guessing but terrible at explaining why they guessed what they did. They are also sometimes clumsy with long-term patterns.

Enter Kolmogorov-Arnold Networks, or KANs for short. Think of KANs not as a black box, but as a master chef who doesn't just throw ingredients into a pot; they can show you the exact recipe, step-by-step, explaining exactly how each spice changes the flavor.

Here is the scoop on a new systematic review that tasted-test these KANs against the old robots to see if they're ready for the main course.

The Main Dish: What KANs Actually Do

Traditional neural networks are like a factory assembly line where the machines (neurons) are fixed, and only the conveyor belts (weights) get adjusted. KANs flip the script. Instead of fixed machines, they use adjustable, learnable functions on the connections between the nodes.

Imagine a standard network is a rigid pipe system where water flows through fixed bends. A KAN is like a pipe system where the bends themselves can stretch, shrink, and reshape themselves to fit the water perfectly. This allows them to learn complex, smooth patterns in data much more efficiently.

The Taste Test: Where KANs Shine

The researchers reviewed 36 studies and found that KANs are absolutely crushing it in specific, structured environments.

Energy & Batteries: In the world of power grids and electric car batteries, KANs are like super-precise mechanics. In one study, a KAN model predicted battery health with an error (RMSE) of just 0.00570, beating the old model's 0.00607. In another, it predicted how much charge an electric car battery had left with an accuracy (R²) of 0.9755, while the old model only hit 0.9693.
Nature & Infrastructure: When predicting river flows (streamflow) or how much a dam might bend under pressure, KANs are the stars. For 1-day river flow predictions, KANs hit an accuracy (R²) of 0.975 for the Rhine river, while the previous champion (Transformers) only managed 0.955.
The "Small Data" Superpower: One of the coolest tricks? KANs are tiny. In one anomaly detection test, a KAN model did the job with only 274 parameters (the brain's "memory slots"), whereas the old model needed 10,421. That's a 97% reduction! It's like solving a puzzle with a tiny handful of pieces instead of a whole box.

The "Not So Fast" Zone: Where KANs Stumble

Here is the part where the paper puts on the brakes. KANs are not a magic wand for everything.

The Financial Market Trap: If you think KANs will predict the stock market or crypto prices like a wizard, the paper says: Think again. In financial markets, where prices jump around wildly and change rules suddenly (like a game where the goalposts move every second), KANs struggled. One model trying to predict crypto prices only got an accuracy (R²) of 0.1378 to 0.1796. The paper suggests this is because financial markets are too chaotic and "rough" for the smooth, mathematical curves KANs love to draw.
Long-Term Guessing: KANs are great at short-term predictions (like 1 to 3 days), but as you try to look further into the future, their advantage fades away, and they start performing just like the older models.
The "Slow Cooker" Problem: While KANs are efficient in size, they can be slow to train. In one study, a KAN model took 843 seconds to train, while the baseline model finished in just 244 seconds. It's like a slow-cooker meal that tastes amazing but takes three times longer to prepare.

The "Explainability" Mystery: Can We Actually Read the Recipe?

The biggest selling point of KANs is that they are supposed to be "interpretable." You should be able to look at the model and see the math formula it learned, like seeing the recipe: $X_{t+1} = e^{X_t^2} + \sin(3.14 \cdot X_{t-1})$ .

The paper confirms that yes, they can spit out these formulas. However, there's a catch. The authors warn that just because you can see the formula doesn't mean a human expert actually understands it or trusts it more than a black box.

The Trade-off: To get a model simple enough to read the recipe, you often have to make the model less accurate. In one test, the "readable" version of the KAN was significantly worse at its job than the "unreadable" version.
The Missing Proof: The paper points out that while we have the formulas, no one has actually asked human experts (like doctors or engineers) if these formulas help them make better decisions. It's like having a map that looks beautiful, but we haven't tested if it actually helps you find your way.

The Verdict: A Specialized Tool, Not a Universal Fix

So, what's the final takeaway?

The paper suggests that KANs are a promising, specialized tool for problems where the data is smooth, structured, and short-term—like predicting electricity use, river levels, or battery health. In these areas, they are often more accurate, smaller, and more transparent than the old models.

However, they are not a universal fix. They are not ready to replace all other models, especially in chaotic fields like finance or for very long-term predictions. The authors also note that the field is still young; many studies didn't report how long the models took to run or how much memory they used, making it hard to say for sure if they are ready for the real world.

In short: KANs are a brilliant new instrument in the orchestra of AI, perfect for playing smooth, complex melodies, but they might get lost in the noise of a chaotic rock concert. We need more practice (and more testing) before we let them lead the band.

Technical Summary: Rethinking Time Series with Kolmogorov-Arnold Networks: A Systematic Review

1. Problem Statement

Time series analysis is critical across domains such as finance, healthcare, energy, and climate science, yet it faces persistent challenges that existing methodologies struggle to address. Traditional statistical methods (e.g., ARIMA) often fail due to restrictive linearity and stationarity assumptions, unable to adapt to non-stationary data or concept drift. Deep learning architectures, including Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks, suffer from vanishing/exploding gradients, computational inefficiencies in sequential processing, and catastrophic forgetting. More recently, Transformer architectures have been applied to time series but face architectural mismatches, such as the permutation-invariant nature of self-attention conflicting with temporal order, quadratic computational complexity, and a tendency to overfit on smaller datasets. Furthermore, existing models often lack interpretability and robust mechanisms to handle concept drift—the evolution of underlying data distributions over time.

The paper posits that Kolmogorov-Arnold Networks (KANs), a novel architecture based on the Kolmogorov-Arnold representation theorem, offer a fundamentally different modeling paradigm. Unlike Multi-Layer Perceptrons (MLPs) that use fixed activation functions and learn linear weights, KANs place learnable, non-linear univariate functions (typically B-splines) on the edges of the network. This structure theoretically allows for more efficient function approximation and inherent interpretability, potentially addressing the gaps left by current time series models.

2. Methodology

This work is a systematic review of the suitability of KANs for time series analysis.

Search Strategy: The authors searched four databases (ScienceDirect, IEEE Xplore, Springer, and arXiv) for literature published between April 2024 and November 2025. The search string combined terms for "Kolmogorov–Arnold Network" with "time series," "temporal data," and "forecasting/prediction."
Selection Criteria: From an initial pool of 243 records, 36 studies were selected for detailed analysis. Inclusion criteria required empirical evaluation of KANs on time series tasks, reporting of performance metrics (accuracy, generalization, adaptability), and sufficient methodological transparency. Studies focusing solely on theory without empirical application or those lacking time series relevance were excluded.
Analysis Framework: The review synthesizes evidence across six key domains: energy systems, environmental monitoring, biomedical signals, finance, infrastructure, and general forecasting benchmarks. The analysis focuses on three primary research questions (RQs):
1. Under what conditions do KANs outperform established architectures?
2. How does the qualitative interpretability of KANs compare to post-hoc explainability methods (e.g., SHAP, LIME) in terms of user comprehension and trust?
3. What are the computational efficiency–accuracy trade-offs (training complexity, inference, model size) compared to conventional models?

3. Key Contributions

The paper provides a comprehensive synthesis of the current state of KANs in time series, offering:

A Domain-Specific Performance Synthesis: A detailed mapping of KAN performance across diverse sectors, identifying where the architecture excels (structured, smooth patterns) and where it struggles (high volatility, abrupt regime shifts).
Critical Assessment of Interpretability: A rigorous evaluation distinguishing between the capability to visualize learned functions and the practical utility of those visualizations for decision-making. The review highlights a lack of empirical validation from domain experts regarding KAN interpretability claims.
Computational Benchmarking Analysis: An analysis of the trade-offs between parameter efficiency and training time, noting a significant gap in reported computational metrics across the reviewed literature.
Identification of Research Gaps: The authors identify critical limitations in the current evidence base, particularly regarding concept drift evaluation, statistical significance testing, and the absence of standardized benchmarks for KAN-specific drift adaptation.

4. Results

4.1 Performance Patterns

Success Cases: KANs consistently demonstrate superior or comparable performance in domains characterized by smooth, structured temporal patterns and physical constraints.
- Energy & Infrastructure: In streamflow forecasting, KANs outperformed Transformers for 1–3 day horizons (R² > 0.95). In energy load forecasting, KANs achieved 20–34% RMSE improvements over baselines.
- Biomedical: KANs showed strong results in battery state-of-charge (SoC) estimation (R² = 0.9755) and ECG abnormality detection, often with fewer parameters than MLPs or LSTMs.
- Parameter Efficiency: In 9 out of 12 studies reporting parameter counts, KAN variants required substantially fewer parameters (reductions of 61% to 98%) to achieve comparable or better performance than baselines.
Limitations:
- Financial Forecasting: KANs struggled in financial markets characterized by high volatility and non-stationarity. R² values for cryptocurrency prediction were low (0.13–0.18), suggesting spline-based smooth function approximation is ill-suited for adversarial, regime-switching dynamics.
- Long-Horizon Forecasting: Performance advantages often diminish beyond 3-day horizons, converging with Transformer performance at 7 days.
- Specific Failures: KANs underperformed baselines in probabilistic load forecasting (vs. Quantile-ANN), real estate price prediction (vs. XGBoost), and specific long-term benchmark suites.

4.2 Computational Efficiency

Training Time: Contrary to parameter efficiency, KANs consistently required longer training times than baselines in the majority of reported studies (e.g., 1.77x to 3.45x longer). This is attributed to the computational overhead of optimizing spline coefficients during backpropagation.
Inference & Memory: GPU memory consumption was lower for KANs in reported cases (e.g., 85% reduction in one study), aligning with their parameter efficiency. However, inference latency data is scarce.
Reporting Gap: A significant finding is the lack of computational benchmarking data; only a minority of the 36 studies reported training time, inference latency, or memory usage, limiting definitive conclusions about deployment feasibility.

4.3 Interpretability

Mechanisms: KANs offer built-in interpretability via B-spline visualizations, edge-weight graphs, and the ability to extract symbolic mathematical formulas (e.g., $X_{t+1} = e^{X_t^2} + \sin(3.14 \cdot X_{t-1})$ ).
Critical Evaluation: The review finds that while these mechanisms exist, their practical utility is unproven.
- There is a lack of user studies validating whether domain experts find KAN visualizations more comprehensible or actionable than post-hoc methods like SHAP.
- Trade-offs: Achieving visual interpretability often requires simplifying the network architecture, which can lead to significant performance degradation (e.g., a drop in F1-score from 0.70 to 0.54 in one study).
- Complexity: Interpreting dense networks with hundreds of B-spline plots remains cognitively demanding, and the extraction of symbolic formulas often requires complex post-hoc processing (pruning), challenging the claim of "interpretability by design."

4.4 Concept Drift

Current evidence on KANs and concept drift is preliminary. While some architectures (e.g., WormKAN) show promise in identifying regime shifts, systematic evaluation against established drift detection benchmarks (e.g., ADWIN, DDM) is absent. The field lacks controlled studies on how KANs adapt to sudden vs. gradual distributional shifts.

5. Significance and Claims

The paper concludes that Kolmogorov-Arnold Networks represent a promising but selective architectural innovation for time series analysis.

Selective Deployment: KANs are most suitable for domains with smooth, physically constrained temporal patterns (e.g., energy, hydrology, biomedical signals) where parameter efficiency and the potential for interpretability are valuable.
Not a Universal Solution: They are not a universal improvement over state-of-the-art models, particularly failing in high-volatility financial forecasting and long-range prediction tasks.
Methodological Maturity: The authors emphasize that the current evidence base is preliminary, heterogeneous, and unevenly reported. The field suffers from a lack of statistical significance testing, standardized benchmarks, and rigorous validation of interpretability claims.
Future Directions: The paper calls for future work to prioritize standardized benchmarks, statistical testing, concept-drift evaluation, and user-centered studies to validate whether the theoretical interpretability of KANs translates into improved human decision-making.

In summary, the paper advocates for a cautious, evidence-based adoption of KANs, urging the community to move beyond technical demonstrations of symbolic extraction toward rigorous empirical validation of their practical utility and limitations.