On the Practical Computational Power of Finite Precision RNNs for Language Recognition (1805.04908v1)

Abstract: While Recurrent Neural Networks (RNNs) are famously known to be Turing complete, this relies on infinite precision in the states and unbounded computation time. We consider the case of RNNs with finite precision whose computation time is linear in the input length. Under these limitations, we show that different RNN variants have different computational power. In particular, we show that the LSTM and the Elman-RNN with ReLU activation are strictly stronger than the RNN with a squashing activation and the GRU. This is achieved because LSTMs and ReLU-RNNs can easily implement counting behavior. We show empirically that the LSTM does indeed learn to effectively use the counting mechanism.

Essay on the Computational Capabilities of Finite Precision RNNs in Language Recognition

The paper "On the Practical Computational Power of Finite Precision RNNs for Language Recognition" by Gail Weiss, Yoav Goldberg, and Eran Yahav presents a rigorous analysis of recurrent neural network (RNN) models under the constraints of finite precision. While theoretical results have established the Turing completeness of RNNs with infinite precision, practical applications in NLP often rely on models constrained by finite precision and bounded computation time. This work scrutinizes such constraints and evaluates the computational capacity of different RNN variants, including the LSTM, Elman-RNN, and GRU architectures.

Differentiating Computational Power Across RNN Variants

The authors begin by highlighting the limitations of prior conclusions regarding RNN Turing completeness, which were based on assumptions of infinite precision and unbounded computation times. They instead focus on practical implementations where RNNs operate at finite precision and are subjected to constraints such as those imposed by GPUs with standard 32-bit floating point computations.

Crucially, the paper delineates how different RNN architectures diverge in their computational prowess under these conditions. The paper establishes that LSTMs and Elman-RNNs with ReLU activation possess a superior computational strength relative to RNNs with squashing activations and GRUs. Notably, this increased capacity stems from the ability of LSTMs and ReLU-RNNs to efficiently implement a counting mechanism, a feature deemed infeasible for GRUs and SRNNs with finite precision.

Empirical Findings Supporting Theoretical Claims

Empirical evidence is presented to corroborate the theoretical findings. The authors train LSTM and GRU models on languages such as $a^nb^n$ and $a^nb^nc^n$, which necessitate a counting mechanism for accurate recognition. It is observed that LSTMs not only learn these languages efficiently via back-propagation but also generalize well to longer sequences than encountered during training. This behavior contrasts starkly with that of GRUs, which demonstrate limited generalization and lack clear counting capabilities.

A noteworthy aspect of this work is the visualization of RNN activations, which provides granular insights into how LSTMs allocate certain dimensions to implement counting, a capability absent in GRUs. The empirical tests underline the superior accuracy of LSTMs over GRUs in recognizing specified languages, further emphasizing the disparity in their computational strengths.

Theoretical and Practical Implications

The findings presented in this work have significant implications for both theoretical understanding and practical deployment of RNN models in NLP tasks. Theoretically, the elucidation of the constraints under finite precision sheds light on the inherent computational limitations and possibilities of different RNN architectures. The practical ramifications are equally pertinent; models like LSTMs, which exhibit the ability to implement complex functionalities such as counting, align more closely with the demands of real-world NLP applications where nuanced sequence processing is paramount.

This work also suggests a potential avenue for future exploration: the architectural design and optimization of neural networks that balance theoretical capabilities with training stability and efficient resource utilization. The distinct computational capacities identified here recommend careful selection of RNN architectures based on task-specific requirements, particularly when dealing with languages or sequences involving memory and counting.

In conclusion, this paper provides a comprehensive exploration of the computational capabilities of finite precision RNNs, offering valuable insights that can guide both the theoretical understanding and practical application of RNNs in diverse language processing contexts.