Bitwise Optimization for Rapid Tanh Function Evaluation

The hyperbolic tangent activation function plays a pivotal role across diverse domains like NLP, speech and image recognition, RNNs, and seq2seq models. This work introduces BitTanh, a method that computes the hyperbolic tangent function much faster than the standard numpy's hyperbolic tangent function by leveraging bit manipulation techniques. BitTanh exhibits remarkable performance gains, especially when coupled with Normal Xavier Glorot's initialization, ensuring controlled variance for optimal activation function utilization. BitTanh demonstrates exceptional speed, enabling substantially accelerated neural network computations. Moreover, the analysis reveals that the BitTanh algorithm, implemented in C with a time complexity of O(1) when processed for a floating number, showcases remarkable efficiency gains. The algorithm's constant time complexity ensures swift execution, facilitating expedited neural network computations. However, its efficacy is prominent when the components of the input vector are near zero, prompting the question of the utility of activation in such cases. Yet, for tasks requiring nonlinear transformations or intricate feature extraction, activation functions like hyperbolic tangent function are indispensable. They introduce crucial nonlinearities, facilitating the learning of complex data patterns. Despite initial approximations, BitTanh offers close outputs that can be refined using optimization techniques like Newton's method. Even after optimization, it remains faster than numpy's standard method for calculating hyperbolic tangent function. Its suitability lies in scenarios where we need a large number of neurons in the neural network layer.