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Mathematical Explanation for Faster Convergence of Attention-Based Models vs. RNNs

Establish, through formal mathematical analysis, why transformer attention mechanisms often converge faster than recurrent neural networks (RNNs) when trained on natural language processing tasks.

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Background

The paper highlights the empirical effectiveness of attention mechanisms and their central role in modern LLMs such as GPT, LLaMA, and DeepSeek.

However, the authors explicitly note the absence of a mathematical explanation for the observed faster convergence of attention-based models compared to RNNs, posing a formal theoretical analysis as an outstanding problem.

References

It is clear that the attention mechanism has shown its effictiveness. It is at the heart of LLMs, like GPT, LLAMA, DeepSeek,... We have not analyze from a mathematical perspective why it converges faster than RNN.

— The algebra and the geometry aspect of Deep learning (2510.18862 - Aristide, 21 Oct 2025) in Section 7. Training Neural network for Natural language processing tasks