RNNs can generate bounded hierarchical languages with optimal memory
This provides foundational theoretical insight into RNNs' success in language generation, addressing a key problem in computational linguistics and AI.
The paper tackles the theoretical understanding of RNNs in generating natural language by proving that RNNs can efficiently generate bounded hierarchical languages like Dyck-(k,m) with optimal memory. It shows an RNN requires only O(m log k) hidden units, an exponential reduction from previous O(k^(m/2)), and proves this is optimal with a lower bound of o(m log k).
Recurrent neural networks empirically generate natural language with high syntactic fidelity. However, their success is not well-understood theoretically. We provide theoretical insight into this success, proving in a finite-precision setting that RNNs can efficiently generate bounded hierarchical languages that reflect the scaffolding of natural language syntax. We introduce Dyck-($k$,$m$), the language of well-nested brackets (of $k$ types) and $m$-bounded nesting depth, reflecting the bounded memory needs and long-distance dependencies of natural language syntax. The best known results use $O(k^{\frac{m}{2}})$ memory (hidden units) to generate these languages. We prove that an RNN with $O(m \log k)$ hidden units suffices, an exponential reduction in memory, by an explicit construction. Finally, we show that no algorithm, even with unbounded computation, can suffice with $o(m \log k)$ hidden units.