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KAN vs LSTM Performance in Time Series Forecasting

This study demonstrates that while baseline Kolmogorov-Arnold Networks (KAN) converge faster during training, Long Short-Term Memory (LSTM) networks significantly outperform them in predictive accuracy for stochastic, non-stationary financial time series, establishing LSTM as the superior choice for accuracy-critical forecasting tasks.

Original authors: Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova, Federico Frascoli

Published 2026-07-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tabish Ali Rather, S M Mahmudul Hasan Joy, Nadezda Sukhorukova, Federico Frascoli

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

The Big Picture: A Race Between Two Forecasters

Imagine you are trying to predict the weather for the next few days, but the weather is chaotic, changing its mind constantly, and doesn't follow a simple rulebook. You have two different "forecasters" (computer models) to help you:

The Veteran Detective (LSTM): This model has been around for a long time. It is famous for being excellent at looking at a story told over time (like a sequence of events) and remembering what happened yesterday to guess what happens tomorrow.
The New Theoretical Genius (KAN): This is a brand-new model based on a fancy mathematical theorem. It promises to be very "transparent"—meaning you can easily see how it makes its decisions. However, it was originally designed for static puzzles, not for stories that unfold over time.

The authors of this paper put these two against each other to see who is better at predicting stock market prices (which are messy, random, and constantly changing).

The Setup: How They Played the Game

The researchers set up a specific challenge:

The Task: Predict future stock prices based on past data (Open, High, Low, Close, Volume).
The Rules: They used a "Direct Multi-Output" method. Imagine asking the model, "Here is the last 20 days of data; tell me exactly what the price will be for the next 1 day, 2 days, or even 100 days all at once."
The Scorecard: They measured success using RMSE (Root Mean Square Error). Think of this as a "mistake score." The lower the number, the better the model is.

The Results: The Veteran Wins Decisively

The results were clear and consistent across all timeframes (1 day, 2 days, and 100 days):

The Veteran (LSTM) was the clear winner. It predicted the stock prices with much higher accuracy. In fact, its mistakes were 6.5 to 10 times smaller than the New Genius's mistakes.
The New Genius (KAN) struggled. While it was theoretically interesting, it made huge errors. It was like trying to solve a moving puzzle by freezing the pieces in place; it just couldn't keep up with the flow of time.

The Analogy:
Imagine you are trying to predict where a runner will be in 10 seconds.

LSTM watches the runner, sees their speed, their stride, and their momentum, and calculates the future path.
Standard KAN takes a photo of the runner, flattens the photo into a single list of numbers (ignoring the order of the steps), and tries to guess the future. It's like trying to predict a movie's ending by looking at a pile of random frames from the middle of the film. It just doesn't work well for sequences.

The "Speed" Trap: Who was Faster?

You might think, "If KAN was so bad, maybe it was at least super fast?"

The Paper says: Yes, KAN finished its training faster (about 35 seconds vs. up to 120 seconds for LSTM).
The Catch: This isn't a fair comparison. It's like comparing a sprinter who ran 100 meters to a marathon runner who only jogged 10 meters.
- LSTM trained for 25 "rounds" (epochs) using small batches of data.
- KAN only did 10 "rounds" using the entire dataset at once.
- Because KAN did so much less work, it finished quickly, but it didn't get a chance to learn as deeply. The paper warns that you can't say KAN is "faster" in a useful way because they didn't run the same amount of training.

Why Did KAN Fail? (The Core Problem)

The paper identifies a fundamental structural flaw in how the standard KAN model was used:

LSTM is built to understand time. It remembers the order of events (Step 1 happened before Step 2).
Standard KAN (the version tested here) treats time as static. To feed data into it, the researchers had to "flatten" the time sequence into a single long list of numbers. This destroyed the timeline. The model lost the context of when things happened, which is the most important part of predicting the future.

The Bottom Line for Practitioners

If you need accuracy: Stick with LSTM. It is the reliable, proven choice for financial forecasting.
If you want the "New Thing" (KAN): Don't use the standard version for stock prediction. It is not ready for this job yet.
The Caveat: The paper explicitly states that there are newer, modified versions of KAN (like "Temporal KAN" or "Time-Frequency KAN") that try to fix this time-tracking problem. However, this study did not test those. It only tested the "base" version.

Summary in One Sentence

When predicting chaotic stock prices, the old-school, time-aware LSTM model crushed the new, theoretically transparent KAN model because the standard KAN couldn't understand the flow of time, turning a sequence of events into a meaningless pile of numbers.

Technical Summary: Kolmogorov Arnold Network vs Long Short Term Memory Performance in Time Series Forecasting

Problem Statement
Financial markets are characterized by stochastic, non-stationary processes with complex nonlinear dependencies. While Long Short-Term Memory (LSTM) networks have become the standard for modeling such sequential data, their "black-box" nature limits interpretability in high-stakes decision-making. Kolmogorov-Arnold Networks (KAN), grounded in the Kolmogorov-Arnold representation theorem, offer a theoretically interpretable alternative by replacing fixed activation functions with learnable spline-based functions. However, a significant gap exists in the literature: there is no controlled empirical comparison between baseline KAN (as implemented in the PyKAN library) and established LSTM architectures on stochastic financial time series. Prior studies often compare KAN against Multi-Layer Perceptrons (MLPs) or evaluate specialized temporal variants (e.g., TKAN, TFKAN) rather than isolating the performance of the standard KAN formulation. This study addresses this gap by benchmarking baseline KAN against baseline LSTM to determine if the standard KAN architecture is viable for sequential forecasting without temporal modifications.

Methodology
The study employs a controlled experimental design using historical stock price data (Open, High, Low, Close, Volume) obtained via the yfinance API.

Data Preprocessing: Features were scaled to the range $[0, 1]$ using Min-Max scaling fitted on the entire dataset prior to splitting. A direct multi-output forecasting protocol was used: given a look-back window $L$ , models predict $H$ future time steps simultaneously. Prediction horizons tested were 1, 2, and 100 days.
Model Architectures:
- LSTM: Implemented via TensorFlow/Keras with stacked unidirectional layers, dropout regularization, and RMSprop optimization. Inputs were treated as 3D tensors $(batch, L, features)$, preserving temporal ordering.
- KAN: Implemented via PyKAN (PyTorch). Crucially, standard KAN accepts only 2D input; therefore, the sequential input was flattened into a 1D vector of length $L \times |F|$ , effectively discarding temporal ordering. Optimization used LBFGS (full-batch, second-order) with B-spline activation functions.
Evaluation Metrics: Performance was measured using Root Mean Square Error (RMSE) computed in the normalized feature space.
Experimental Asymmetries: The authors explicitly note several asymmetries in the protocol: LSTM used mini-batch stochastic optimization (25 epochs), while KAN used full-batch second-order optimization (10 LBFGS steps). Random seeds were fixed for KAN but not for LSTM. These factors are acknowledged as confounds that prevent attributing performance differences solely to architectural capacity.

Key Results
The study finds that baseline LSTM substantially outperforms baseline KAN across all tested prediction horizons and market conditions (normal, volatile, trending).

Predictive Accuracy: LSTM achieved RMSE values 6.5 to 10.0 times lower than KAN.
- At the 1-day horizon, the best LSTM configuration achieved a test RMSE of 0.039, while the best KAN configuration achieved 0.152.
- At the 100-day horizon, LSTM maintained a 6.5 to 7.2 times advantage.
- KAN was the only model tested at the 200-day horizon (due to LSTM configuration limits), yielding high RMSE values (0.645–0.670), though the authors note the absence of a naive baseline (e.g., persistence) makes it unclear if this represents a meaningful improvement over trivial strategies.
Training Efficiency: KAN completed training faster (average 35.12 seconds) compared to LSTM (11–120 seconds). However, the authors caution that this is not a fair comparison of architectural efficiency, as KAN performed significantly fewer parameter updates (10 full-batch steps) compared to LSTM (25 epochs of mini-batch updates).
Architectural Insight: The primary driver of the performance gap is identified as the input representation. LSTM preserves temporal structure through recurrent gating, whereas standard KAN flattens the sequence, removing the sequential dependencies essential for time series forecasting. Simpler LSTM configurations (2-layer, 10 units) outperformed deeper ones, consistent with vanishing gradient issues in deep RNNs.

Key Contributions

Empirical Baseline: The study establishes the first controlled empirical baseline for standard KAN (PyKAN) against standard LSTM on stochastic financial data.
Identification of Limitations: It demonstrates that without temporal modifications (such as recurrent gating or frequency-domain processing), standard KAN is not competitive for sequential forecasting tasks due to the loss of temporal structure upon input flattening.
Transparency on Constraints: The paper explicitly details methodological limitations, including optimizer asymmetry, lack of fixed random seeds for LSTM, and data leakage from global scaling, ensuring that the magnitude of the performance gap is interpreted with appropriate caution.

Significance and Claims
The authors modestly conclude that baseline KAN in its standard form is not competitive with established LSTM for accuracy-critical financial forecasting. The study does not claim KAN is useless; rather, it posits that the theoretical interpretability of KAN comes at a severe cost to predictive accuracy in its current standard implementation.

The significance of the work lies in:

Validating the necessity of temporal variants: The results support the existence of specialized KAN variants (TKAN, TFKAN) designed to restore sequential processing, suggesting these modifications are necessary, not optional, for competitive performance.
Guidance for Practitioners: For applications requiring high accuracy, LSTM remains the preferred choice. Practitioners interested in KAN's interpretability for financial applications are advised to utilize temporal variants rather than the baseline PyKAN implementation.
Future Research Directions: The paper calls for future work to include matched compute budgets, naive baselines (persistence, ARIMA), and evaluations of specialized KAN variants to determine if architectural modifications can close the accuracy gap. It also highlights the need for further mathematical research into efficient free-knot polynomial spline approximation to address the non-smooth, non-convex optimization challenges inherent to KAN.