Sample-Efficiency of Kolmogorov-Arnold Networks

summary

Video file (mp4)

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.

In short

Kolmogorov-Arnold Networks (KANs) are a new neural network type that replaces fixed weights with learnable functions, aiming for better sample efficiency. Experiments show KANs achieve similar performance to traditional models using 40% fewer samples. The biggest gains happen early in training, making them useful for expensive data collection tasks.

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.

Terminology used across episodes

This episode discusses

The paper

Sample-Efficiency of Kolmogorov-Arnold Networks · Read on arXiv

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

ETH Zürich

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

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 >

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