Academic

Hardware-Oriented Inference Complexity of Kolmogorov-Arnold Networks

arXiv:2604.03345v1 Announce Type: new Abstract: Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful architecture for various machine learning applications. However, their unique structure raises significant concerns regarding their computational overhead. Existing studies primarily evaluate KAN complexity in terms of Floating-Point Operations (FLOPs) required for GPU-based training and inference. However, in many latency-sensitive and power-constrained deployment scenarios, such as neural network-driven non-linearity mitigation in optical communications or channel state estimation in wireless communications, training is performed offline and dedicated hardware accelerators are preferred over GPUs for inference. Recent hardware implementation studies report KAN complexity using platform-specific resource consumption metrics, such as Look-Up Tables, Flip-Flops, and Block RAMs. However, these metrics require a full hardware design and synthesis stage that limits their u

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Bilal Khalid, Pedro Freire, Sergei K. Turitsyn, Jaroslaw E. Prilepsky · · 1 min read · 13 views
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arXiv:2604.03345v1 Announce Type: new Abstract: Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful architecture for various machine learning applications. However, their unique structure raises significant concerns regarding their computational overhead. Existing studies primarily evaluate KAN complexity in terms of Floating-Point Operations (FLOPs) required for GPU-based training and inference. However, in many latency-sensitive and power-constrained deployment scenarios, such as neural network-driven non-linearity mitigation in optical communications or channel state estimation in wireless communications, training is performed offline and dedicated hardware accelerators are preferred over GPUs for inference. Recent hardware implementation studies report KAN complexity using platform-specific resource consumption metrics, such as Look-Up Tables, Flip-Flops, and Block RAMs. However, these metrics require a full hardware design and synthesis stage that limits their utility for early-stage architectural decisions and cross-platform comparisons. To address this, we derive generalized, platform-independent formulae for evaluating the hardware inference complexity of KANs in terms of Real Multiplications (RM), Bit Operations (BOP), and Number of Additions and Bit-Shifts (NABS). We extend our analysis across multiple KAN variants, including B-spline, Gaussian Radial Basis Function (GRBF), Chebyshev, and Fourier KANs. The proposed metrics can be computed directly from the network structure and enable a fair and straightforward inference complexity comparison between KAN and other neural network architectures.

Executive Summary

This article proposes a novel approach to evaluating the hardware inference complexity of Kolmogorov-Arnold Networks (KANs) using platform-independent formulae. The authors derive expressions for Real Multiplications (RM), Bit Operations (BOP), and Number of Additions and Bit-Shifts (NABS) to enable fair and straightforward complexity comparisons between KANs and other neural network architectures. The study extends its analysis across multiple KAN variants, including B-spline, Gaussian Radial Basis Function (GRBF), Chebyshev, and Fourier KANs, and demonstrates the utility of the proposed metrics in early-stage architectural decisions and cross-platform comparisons. This work addresses a significant gap in the existing literature and has far-reaching implications for the development and deployment of KANs in latency-sensitive and power-constrained applications.

Key Points

  • ▸ Derivation of platform-independent formulae for evaluating hardware inference complexity of KANs
  • ▸ Extension of analysis across multiple KAN variants
  • ▸ Utility of proposed metrics in early-stage architectural decisions and cross-platform comparisons

Merits

Strength in Addressing a Significant Gap

The article effectively identifies and addresses a critical limitation in the existing literature, which primarily evaluates KAN complexity using platform-specific resource consumption metrics.

Methodological Rigor

The authors demonstrate a high degree of methodological rigor through the derivation of platform-independent formulae and the extension of analysis across multiple KAN variants.

Demerits

Limited Scope

The study exclusively focuses on KANs and may not be directly applicable to other neural network architectures.

Complexity of Formulae

The proposed formulae may be challenging to compute and interpret, particularly for non-experts in the field.

Expert Commentary

The article represents a significant contribution to the field of neural network complexity analysis, addressing a critical limitation in the existing literature. The proposed metrics have the potential to revolutionize the design and deployment of KANs in latency-sensitive and power-constrained applications. However, further research is needed to extend the analysis to other neural network architectures and to explore the practical implications of the proposed metrics in real-world applications.

Recommendations

  • ✓ Recommendation 1: The authors should consider extending their analysis to other neural network architectures to enable fair and straightforward complexity comparisons across the field.
  • ✓ Recommendation 2: The proposed metrics should be further evaluated and validated through experimental studies in real-world applications to demonstrate their practical utility and implications.

Sources

Original: arXiv - cs.LG

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