Floating-Point Networks with Automatic Differentiation Can Represent Almost All Floating-Point Functions and Their Gradients
arXiv:2605.01702v2 Announce Type: replace Abstract: Theoretical studies show that for any differentiable function on a compact domain, there exists a neural network that approximates both the function values and gradients. However, such a result cannot be used in practice since it assumes real parameters and exact internal operations. In contrast, real implementations only use a finite subset of reals and machine operations with round-off errors. In this work, we investigate whether a similar result holds for neural networks under floating-point arithmetic, when the gradient with respect to th
This research is emerging as the practical application and scaling of AI, particularly neural networks, increasingly relies on efficient and precise computation in real-world floating-point environments.
A strategic reader should care because theoretical guarantees for neural network capabilities, specifically their ability to represent functions and gradients under floating-point arithmetic, validate current practices and open new avenues for more robust and reliable AI systems.
This research provides a stronger theoretical foundation for the practical efficacy of floating-point neural networks, potentially leading to more targeted architectural optimizations and improved deployment confidence in AI applications.
- · AI researchers and developers
- · Deep learning framework providers
- · High-performance computing industry
- · Industries deploying AI at scale
- · Skeptics of AI's theoretical foundations in practical contexts
The theoretical understanding of floating-point neural networks and their gradient representation is significantly advanced.
This improved understanding may accelerate the development of more stable, efficient, and provably reliable AI models for critical applications.
Enhanced trust in the computational integrity of AI systems could broaden their adoption in extremely sensitive domains like autonomous systems and financial modeling.
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Read at arXiv cs.LG