Expressive Power of Floating-Point Neural Networks with Arbitrary Reduction Orders and Inexact Activation Implementations
arXiv:2605.28704v1 Announce Type: new Abstract: Most existing expressivity theories for neural networks assume exact real arithmetic, whereas practical neural networks are executed under finite-precision floating-point arithmetic with implementation-dependent execution semantics. Recent works have begun studying the expressive power of floating-point neural networks, but existing results are limited to highly restricted activation functions and idealized assumptions such as fixed left-to-right reduction orders and correctly rounded activation implementations. In this work, we study the express
This research is emerging now as the practical limitations of floating-point arithmetic in AI models become more salient with increasing model size and complexity, demanding deeper theoretical understanding.
A more precise understanding of floating-point arithmetic's impact on neural network expressivity is crucial for developing more robust, efficient, and reliable AI systems, especially in resource-constrained or sensitive applications.
The theoretical foundation for designing and optimizing neural networks will evolve to explicitly account for the realities of finite-precision computation, rather than relying solely on ideal real arithmetic assumptions.
- · AI hardware manufacturers
- · AI algorithm researchers
- · Developers of embedded AI systems
- · Developers relying solely on exact arithmetic assumptions
- · Hardware designers not accounting for floating-point nuances
Improved understanding of neural network behavior on real-world hardware, leading to more predictable performance.
Development of specialized hardware and activation functions optimized for specific floating-point behaviors and reduction orders.
New classes of neural network architectures emerge that inherently account for finite-precision effects, potentially enabling more efficient and smaller models.
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Read at arXiv cs.LG