Study Reveals Fundamental Limitations of Learning Tanh Neural Networks Under Finite Precision
Researchers have identified fundamental constraints on training tanh neural networks when using finite-precision computations, showing that adaptive randomized algorithms cannot exceed Monte Carlo convergence rates without exponentially larger sampling budgets. The work extends previous theoretical findings about ReLU networks to the tanh activation function setting. These findings have implications for understanding the theoretical boundaries of neural network learning in practical computing environments with limited precision.
A new theoretical study published on arXiv investigates how finite-precision arithmetic affects the learnability of tanh neural networks trained from point evaluations. The researchers developed a novel construction using sharply localized bump functions created through iterated tanh activations to prove their main result: no adaptive randomized algorithm using m samples can achieve convergence rates better than O(m^-1/p) in the Lp norm without the sampling budget growing exponentially with network size and architecture parameters. This work builds on prior research by Berner, Grohs, and Voigtländer (2023) and extends theoretical limitations previously established for ReLU networks to the tanh setting. The findings reveal fundamental constraints imposed by computational precision on which function classes can be efficiently learned, contributing to the theoretical understanding of neural network optimization in realistic computing scenarios.
What's missing
The study's own limitations and open questions are not detailed in the abstract provided. Specifically, the abstract does not discuss: whether these theoretical bounds are tight or could be improved; practical implications for real-world neural network training where precision constraints vary; or whether similar limitations apply to other activation functions beyond tanh and ReLU.
What different sources said
- arXiv cs.LGCenter
Limitations of Learning Tanh Neural Networks with Finite Precision
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