arXiv:2606.11104v1 Announce Type: new Abstract: We investigate limitations of learning $\tanh$ neural networks from point evaluations under finite-precision computations and $L^p$ accuracy guarantees, building on Berner, Grohs, and Voigtl\"ander (2023). Our approach is based on a novel construction of sharply localized bump functions via iterated $\tanh$ activations. Using this mechanism, we show that, in a finite-precision setting, no adaptive randomized algorithm based on $m$ samples can achieve a convergence rate higher than the Monte Carlo rate $O(m^{-1/p})$ in the $L^p$ norm, unless the s
This research provides theoretical bounds on the performance of a specific type of neural network in finite precision, offering a foundational understanding of a current limitation in AI model development.
A strategic reader should care because this highlights a fundamental, if currently theoretical, constraint affecting the scalability and performance of certain AI architectures, particularly as computational resources become more constrained or specialized.
This research doesn't immediately change current AI practices but provides a theoretical basis that could influence future hardware design and algorithm development for robust AI.
- · AI researchers focusing on theoretical limits
- · Developers of custom AI hardware optimized for precision
- · Academic institutions
- · Developers relying solely on current tanh activation optimizations
- · Hardware developers ignoring precision implications
The findings suggest a fundamental performance ceiling for tanh-based neural networks under finite precision.
This could lead to increased focus on alternative activation functions or precision-aware neural network designs to overcome these limitations.
Long-term, this theoretical understanding may influence the design of future AI chips and a shift towards computational paradigms less susceptible to finite-precision issues.
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Read at arXiv cs.LG