Sample-Efficiency of Kolmogorov-Arnold Networks

arXiv:2610.10627 · cs.LG · Submitted 2026-10-07 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Sample-Efficiency of Kolmogorov-Arnold Networks".

Jane: The gist: Similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture, and that relative performance improvements up to 50% occur during the training process.

Tom: First, who's behind it and why it matters.

Paper summary: Tom: We just covered how KANs can achieve similar performance with forty percent fewer samples across various benchmarks, including the Feynman dataset and Gymnasium RL tests. The core of the paper is proposing Kolmogorov–Arnold Networks as a new architecture for deep reinforcement learning that handles physical relationships better than MLPs >

Jane: They are building these networks on the idea from the Kolmogorov–Arnold representation theorem <ref:2610.10627#pg2>, which lets them represent functions as a finite superposition of univariate functions and summation operators >

Lu: The paper claims that unlike traditional MLPs that use fixed nonlinear activations, KANs replace scalar weights with learnable univariate functions defined along the edges of the network fourteen <ref:2610.10627#pg2,KANs replace scalar weights with learnable univariate functions defined along the edges>. This formulation allows them to directly learn functional relationships between variables >

Meng: So, it’s not just about changing the math; it’s about how they structure the learning process. They claim this direct learning of functional relationships leads to better interpretability >

Tom: They say KANs offer improved interpretability and significantly higher parameter efficiency compared to MLPs while retaining strong approximation capabilities fourteen <ref:2610.10627#pg2,KANs offer improved interpretability and significantly higher parameter efficiency>. This is a key selling point for applications where understanding the underlying structure matters >

Jane: And they tested this by systematically studying sample efficiency using experiments on two main datasets: the Feynman dataset and the Gymnasium RL benchmark >

Lalam: They used fixed Ntest at one thousand in that experiment and varied the training size over Ntrain in range of (one) <ref:2610.10627#pg3>. For RL, they used a proximal policy optimization strategy for PPO learning >

Tom: In the Feynman experiment, they found a clear low-sample crossover in favor of KANs after fifty training samples <ref:2610.10627#pg2>. The best KAN family reduced mean NRMSE from zero point two zero zero to zero point one six three at just fifty samples >

Jane: And they also noted a massive relative improvement, going from about thirteen point nine percent of improvement at just fifty-four samples up to nearly fifty percent improvement after a hundred samples <ref:2610.10627#pg2>.

Lu: The results show that once the target error is below the early-data regime, KANs can match or surpass MLP performance with substantially fewer training samples >

Meng: That means for a real robot or control system, you don't need as much expensive simulation time to get a high-performing policy <ref:2610.10627#pg3>.

Tom: They also looked at the Gymnasium experiment across Acrobot, CartPole, MountainCar, and Pendulum >

Jane: Across those environments, the advantage of KANs peaked at about forty-one point six percent when using two thousand two hundred fifty episodes <ref:2610.10627#pg3>, but it narrowed to about seven point five percent on average at the final checkpoint >

Lalam: The sample-reduction curves show that similar performances can be achieved with about forty percent fewer samples using KANs, and these gains are robust to varying levels of noise in rewards > <ref:2610.10627#pg1,gains are robust to varying levels of noise in rewards>

Tom: These findings from "Sample-Efficiency of Kolmogorov-Arnold Networks" really highlight the practical value of this architecture when dealing with costly simulation or measurement data >

Conclusion: Jane: So looking at the paper, "Sample-Efficiency of Kolmogorov-Arnold Networks," we see that the authors are focused on proving how much less data is needed to train effective control models >

Tom: Right. The title itself sets up a direct comparison between what KANs can do and what traditional architectures like MLPs can do when it comes to sample efficiency >

Lu: Essentially, the paper establishes that KANs are a promising architecture for learning physical relationships in control problems because of their superior parameter efficiency <ref:2610.10627#pg2>.

Meng: The implication here is that if we are working on problems where getting real-world data is hard, like in robotics, KANs give us a much better starting point for training >

Jane: They’ve shown that the gains are most pronounced in the early and middle stages of training, which is crucial when simulator calls or hardware trials are expensive >

Tom: The authors suggest that a practical approach is to train with these KANs during the scarce-sample phase and then distill that learned policy into a simpler MLP for deployment >

Lalam: This means we can leverage the KAN structure for initial learning, and then simplify it down when inference cost becomes the bottleneck >

Tom: So, in short, they show that similar performance with forty percent fewer samples is achievable with KANs, and this efficiency is robust to reward noise >

Kevin Riehl, Shaimaa K. El-Baklish, Fan Wu, Anastasios Kouvelas

ETH Zürich

cs.LG

Submitted: 2026-10-07

Updated: 2026-10-07

Code: https://github.com/DerKevinRiehl/neurips26_kan_training

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 82/100

The gist: The gist: Similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture, and that relative performance improvements up to 50% occur during the training process.

Key concepts

Kolmogorov–Arnold Networks (KANs): These networks are inspired by a mathematical theorem that suggests complex functions can be built from simple univariate functions. Instead of using standard fixed weights, KANs use learnable functions along the network edges to directly model functional relationships between variables.
Sample Efficiency: This measures how much data (samples) a model needs to reach a certain level of performance. The study found that KANs are more sample-efficient, meaning they can achieve better accuracy with significantly fewer training examples compared to standard neural networks.
Low-Sample Crossover: This refers to the point during training where the performance advantage of one model (KANs) over another (MLPs) becomes clear. In this study, KANs showed a clear crossover point after only 50 training samples, indicating they quickly become superior.
Early-Data Regime: This is the initial phase of training where the model learns the most significant functional relationships from limited data. The results indicate that KANs perform exceptionally well in this regime, which is crucial when data collection is costly.

Summary

The gist: Similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture, and that relative performance improvements up to 50% occur during the training process.

Kolmogorov–Arnold Networks (KANs) Architecture

Kolmogorov–Arnold Networks are a recently proposed class of neural network architectures inspired by the Kolmogorov–Arnold representation theorem, which states that any continuous multivariate function can be expressed as a finite superposition of univariate functions and summation operators. Unlike traditional neural networks such as multilayer perceptrons (MLPs), which rely on linear transformations followed by fixed nonlinear activation functions, KANs replace scalar weights with learnable univariate functions defined along the edges of the network. This formulation allows the model to directly learn functional relationships between variables rather than approximating them only through weighted sums of fixed activation functions. As a result, KANs offer improved interpretability and significantly higher parameter efficiency while retaining strong approximation capabilities.

Sample-Efficiency Assessment Methodology

The study systematically assesses sample efficiency using computational experiments covering the Feynman dataset and the Gymnasium RL benchmark. The comparison involves matching model complexities between KANs and MLPs to ensure a fair comparison. For the Feynman experiment, the protocol fixed Ntest = 1000 and varied the training size over Ntrain ∈ (1). The comparison in RL involves using proximal policy optimization (PPO) learning strategy.

Results on Sample Efficiency

The Feynman experiment shows a clear low-sample crossover in favor of KANs after 50 training samples. The best KAN family reduces mean NRMSE from 0.200 to 0.163 (at 50 samples) and from 0.127 to 0.060 (at 1,00, corresponding to a relative improvement from 13.9% (at 5,4 samples) to 49.3% (at). Equivalently, KANs reach several MLP error levels with substantially fewer training samples once the target error is below the early-data regime. In the Gymnasium experiment, across Acrobot, CartPole, MountainCar, and Pendulum, the advantage of KANs peaks at about 41.6% (2250 episodes) and then narrows to about 7.5% (final checkpoint) on average. The sample-reduction curves show that similar performances can be achieved with about 40% fewer samples using KANs.

Robustness to Noise

The noisy-reward benchmark indicates that these gains are not an artifact of clean reward feedback. Adding Gaussian reward noise increases variance, but the KAN and MLP comparison keeps the same qualitative shape across the tested noise scales.

Conclusion on Application

The experiments highlight that KAN architectures improve sample efficiency when the task contains smooth low-dimensional structure. The strongest gains occur in the early and middle part of training, which is the regime that matters most when simulator calls, measurements, or hardware trials are expensive. The results suggest that KANs can be useful for low-data control problems. A practical route for deployment is to train with KANs during the scarce-sample phase and then distill the learned policy into a cheaper MLP when inference cost is the bottleneck.

Experiment Setup Details

The Feynman benchmark consists of analytic equations with named input variables and prescribed sampling ranges. For each equation, one fixed train pool and one fixed test set are sampled, and model initializations are varied across random seeds. The Gymnasium benchmark uses low-dimensional state vectors for observations. The KAN sweep includes B-spline KANs and Gaussian RBF KANs with hidden dimensions [2], [4], [8], [4, 4], and [8, 8]. The PPO training involves Adam with learning rate 3 × 10−4. The KAN and MLP models were matched by model complexity (number of parameters) to ensure a fair comparison. The primary setting uses a fixed architecture recipe for each model family.

Improvements for AI systems

Improve sample efficiency in control tasks by utilizing Kolmogorov-Arnold Networks (KANs). The results show that similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture and relative performance improvements up to 50% occur during the training process. This allows for learning effective controllers in real-world applications with substantially reduced environment interaction costs.
Develop more robust reinforcement learning agents by leveraging KANs for policy approximation under noisy feedback. The study indicates that the observed gains are robust to varying levels of noise in rewards, meaning KANs maintain their sample efficiency advantage even when Gaussian reward noise increases variance. This leads to controllers that perform reliably despite imperfect or noisy real-world measurements.
Create interpretable and verifiable control policies by employing KANs for function approximation. The paper highlights that KANs offer improved interpretability compared to Multi-Layer-Perceptron architectures, allowing researchers to understand the underlying functional structure of learned relationships in control problems. This is particularly useful for safety-critical settings where neural policies are difficult to inspect, verify, or translate into controller equations.
Optimize deployment pipelines by implementing a two-stage training strategy. The results suggest that a practical route for deployment is to train with KANs during the scarce-sample phase and then distill the learned policy into a cheaper MLP when inference cost is the bottleneck. This allows for maximizing sample efficiency early on while maintaining deployable, computationally lighter models later.

Abstract

Deep reinforcement learning has achieved substantial performance gains over classical control approaches. Yet, a central challenge to learning in real-world applications is acquiring costly samples. Kolmogorov-Arnold Networks are a recently proposed architecture that can learn physical relationships in control problems effectively, with significantly higher parameter efficiency and interpretability when compared to Multi-Layer-Perceptron architectures. In this work, we systematically study sample-efficiency using computational experiments, covering the Feynman dataset and the Gymnasium RL benchmark. The results show that similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture, and that relative performance improvements up to 50% occur during the training process. The observed gains are robust to varying levels of noise in rewards. These results highlight the potential of the Kolmogorov-Arnold architectures for more sample-efficient reinforcement learning. Code: https://github.com/DerKevinRiehl/neurips26 kan training