Rethinking the Combined and Individual Orders of Derivative of States for Differential Recurrent Neural Networks: Deep Differential Recurrent Neural Networks

Due to their special gating schemes, Long Short-Term Memory (LSTM) has shown greater potential to process complex sequential information than the traditional Recurrent Neural Network (RNN). The conventional LSTM, however, fails to take into consideration the impact of salient spatio-temporal dynamics present in the sequential input data. This problem was first addressed by the differential Recurrent Neural Network (dRNN), which uses a differential gating scheme known as Derivative of States (DoS). DoS uses higher orders of internal state derivatives to analyze the change in information gain originated from the salient motions between the successive frames. The weighted combination of several orders of DoS is then used to modulate the gates in dRNN. While each individual order of DoS is good at modeling a certain level of salient spatio-temporal sequences, the sum of all the orders of DoS could distort the detected motion patterns. To address this problem, we propose to control the LSTM gates via individual orders of DoS. To fully utilize the different orders of DoS, we further propose to stack multiple levels of LSTM cells in an increasing order of state derivatives. The proposed model progressively builds up the ability of the LSTM gates to detect salient dynamical patterns in deeper stacked layers modeling higher orders of DoS; thus, the proposed LSTM model is termed deep differential Recurrent Neural Network (d²RNN). The effectiveness of the proposed model is demonstrated on three publicly available human activity datasets: NUS-HGA, Violent-Flows, and UCF101. The proposed model outperforms both LSTM and non-LSTM based state-of-the-art algorithms.