📊 statistics

DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

DecompKAN is a lightweight, attention-free time series forecasting architecture that utilizes trend-residual decomposition and B-spline Kolmogorov-Arnold Networks (KAN) to achieve competitive predictive accuracy while providing model transparency through inspectable, visualized edge functions.

Original authors: Naveen Mysore

Published 2026-04-28

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Naveen Mysore

Original paper licensed under CC BY 4.0 (http://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 are a doctor trying to predict a patient's heart rate for the next hour, or a meteorologist trying to predict tomorrow's storm. You don't just want a "guess"; you want to know why the computer made that guess. You want to see the logic.

Current AI models (like the famous "Transformers") are like "Black Box" geniuses. They are incredibly accurate, but if you ask them, "Why did you predict a storm?" they can only point to certain parts of the data and say, "I looked at this part." They can't explain the actual math or the "shape" of the logic they used.

This paper introduces DecompKAN, a new type of AI that is both smart and transparent.

The Core Idea: The "Transparent Chef"

Think of traditional AI like a Magic Blender. You throw in ingredients (data), press a button, and out comes a smoothie (the prediction). It tastes great, but you have no idea how the ingredients were transformed inside.

DecompKAN is more like a Master Chef with a Glass Kitchen.

Instead of a blender, it uses a series of specialized stations. You can look through the glass and see exactly how the ingredients are being handled: one station is slicing, one is sautéing, and one is seasoning. In DecompKAN, these "stations" are called KAN edges, and they don't just hide the math—they draw it out for you like a beautiful, wavy graph.

How It Works (The Three-Step Recipe)

To make sense of messy, wiggly data (like weather or heartbeats), DecompKAN uses a three-step process:

1. The "Separation of Concerns" (Decomposition)

Imagine you are looking at a song. You hear the heavy, slow bassline and the fast, frantic drumbeat at the same time. It’s hard to analyze both at once.
DecompKAN acts like a high-end audio splitter. It separates the data into two tracks:

The Trend: The slow, steady "bassline" (e.g., the gradual warming of the planet).
The Residual: The fast, jumpy "drumbeat" (e.g., a sudden afternoon thunderstorm).
By looking at them separately, the AI doesn't get confused.

2. The "Patchwork Quilt" (Patching)

Instead of trying to swallow a whole long history of data in one gulp, the AI cuts the data into small, manageable "patches"—like cutting a long piece of fabric into small squares to make a patchwork quilt. This makes it much easier to spot local patterns.

3. The "Mathematical Artist" (The KAN)

This is the secret sauce. Most AIs use "MLPs," which are like rigid, straight-edged rulers. They can only draw straight lines.
DecompKAN uses KANs (Kolmogorov-Arnold Networks), which are like flexible, bendable wires. Because these wires are "B-splines" (mathematical curves), they can bend and wiggle into any shape.

Why This Matters: The "Inspectable" Magic

The most exciting part of this paper is the Visual Inspection.

Because the AI uses these "bendable wires" (edge functions), the researchers can actually print out a picture of what the AI learned.

When looking at Weather data, the AI's "wires" turned into waves (oscillatory patterns), because weather moves in cycles.
When looking at Medical (PPG) data, the "wires" turned into steps (threshold patterns), because biological signals often jump when a certain limit is hit.

This is a game-changer for safety. If a doctor uses this AI to monitor a patient, they can look at the "shape" of the AI's logic. If the AI's logic looks "wavy" when it should look "stepped," the doctor knows the AI is making a mistake before it gives a wrong prediction.

Summary

DecompKAN isn't just trying to be the smartest student in the class; it's trying to be the student who shows their work on the chalkboard. It’s a lightweight, efficient, and—most importantly—honest way to predict the future.

Technical Summary: DecompKAN: Decomposed Patch-KAN for Long-Term Time Series Forecasting

1. Problem Statement

Long-term time series forecasting (LTSF) is critical in scientific domains (e.g., climate modeling, physiological monitoring, energy systems). While Transformer-based models achieve high accuracy, they suffer from two major limitations in these fields:

Lack of Mechanistic Transparency: Attention weights only indicate which tokens are relevant, not what functional transformations are applied to the features. Post-hoc explanation methods (like SHAP) often provide only local approximations rather than exposing the model's actual internal computations.
Complexity vs. Interpretability: In safety-critical applications, practitioners need to verify if a model captures known physical or physiological relationships (e.g., diurnal cycles or heart rate dynamics) rather than just learning spurious correlations.

2. Methodology

The authors propose DECOMPKAN, a lightweight, attention-free architecture that replaces the standard MLP or Transformer core with B-spline Kolmogorov–Arnold Network (KAN) edge functions. The architecture follows a four-stage channel-independent pipeline:

Stacked Normalization: To handle non-stationarity, the model uses RevIN (Reversible Instance Normalization) to remove window-level drift, followed by a Learned Adaptive Normalization module. This module uses a small MLP to learn dataset-specific scale and shift adjustments based on the temporal shape of the normalized signal.
Trend–Residual Decomposition: The input is split into a trend component (via a moving-average filter) and a residual component. This allows the model to separate slow-moving dynamics from fast oscillations.
Patch-KAN Branches: Each component is processed by an independent branch. The sequence is divided into overlapping patches, which are linearly embedded. These embeddings are then processed by a KAN consisting of three layers. Instead of fixed activation functions, each KAN edge learns a 1D scalar function $\phi(x)$ using cubic B-splines with local support.
Denormalization: The outputs from the trend and residual branches are summed and passed through an adaptive denormalization head and the inverse RevIN transform to restore the original scale.

3. Key Contributions

Architectural Transparency: Unlike attention-based models, every edge in the KAN is a directly inspectable 1D nonlinear transformation. This allows for the visualization of the actual mathematical functions the model uses to transform latent features.
Lightweight Design: The model is highly efficient, utilizing only 1.9–3.6M parameters, making it significantly smaller than many large-scale foundation models.
Domain-Adaptive Nonlinearities: The model demonstrates that KANs can autonomously learn different "functional vocabularies" depending on the data (e.g., oscillatory functions for weather vs. threshold-like functions for physiological signals).
Pipeline-Centric Performance: Through ablation, the authors prove that the architectural pipeline (decomposition, patching, and normalization) is a more significant driver of performance than the specific choice of the nonlinear layer (KAN vs. MLP/Attention).

4. Results

Accuracy: DECOMPKAN achieves best or tied-best MSE on 15 of 32 dataset–horizon combinations against published baselines. It shows particular strength in datasets with smooth temporal dynamics, such as Solar ( $-17\%$ MSE vs. iTransformer) and ECL ( $-10\%$ MSE vs. iTransformer).
Controlled Comparison: When retrained under a unified protocol, DECOMPKAN remained competitive or superior on physics-structured datasets like Weather and PPG-DaLiA.
Interpretability Findings:
- Visualization: Edge functions in the trend branch are smooth and slowly varying, while residual branch functions are sharper and oscillatory.
- Structured Sparsity: The first KAN layer acts as a feature selector, where many edges learn near-zero functions, concentrating representational capacity in deeper layers.
Limitations: The model underperforms on datasets dominated by complex regime changes (e.g., ETTh1, Traffic) or those requiring heavy cross-variate dependency modeling, due to its channel-independent design.

5. Significance

DECOMPKAN represents a shift from "black-box" accuracy-driven forecasting toward "inspectable" forecasting. By utilizing the Kolmogorov–Arnold representation, the model provides a mathematical bridge between deep learning and scientific interpretability. This makes it highly relevant for high-stakes environments (clinical, meteorological, and industrial) where understanding the why behind a prediction is as important as the prediction itself.