This paper explores ways to extend a recurrent neural network (RNN) to a deep RNN. The authors argue that the concept of depth in RNNs is less clear than in feedforward networks. They identify three parts of an RNN that can be made deeper: the input-to-hidden function, the hidden-to-hidden transition, and the hidden-to-output function. Based on this, they propose two novel deep RNN architectures that are orthogonal to previous methods of stacking recurrent layers. They also introduce a new framework based on neural operators to interpret these deep RNNs. The proposed deep RNNs are evaluated on tasks such as polyphonic music prediction and language modeling, showing that they outperform conventional, shallow RNNs. The paper discusses different ways to increase the depth of an RNN, including making the input-to-hidden function deeper, the hidden-to-output function deeper, and the hidden-to-hidden transition deeper. They propose several variants of deep RNNs, including the deep transition RNN (DT-RNN), the deep output RNN (DO-RNN), and the stacked RNN (sRNN). They also introduce the concept of shortcut connections to alleviate the problem of difficult learning introduced by increasing depth. The authors evaluate the performance of these deep RNNs on tasks such as polyphonic music prediction and language modeling. They find that the deep output and deep transition RNN (DOT-RNN) outperforms the conventional RNN and stacked RNN on language modeling tasks. They also show that the proposed deep RNNs benefit from non-saturating activation functions and dropout, similar to feedforward neural networks. The paper concludes that deep RNNs can benefit from depth in a similar way to feedforward neural networks, and that the proposed architectures are effective for modeling complex sequences. However, training deep RNNs remains challenging, and further research is needed to improve their performance and efficiency.This paper explores ways to extend a recurrent neural network (RNN) to a deep RNN. The authors argue that the concept of depth in RNNs is less clear than in feedforward networks. They identify three parts of an RNN that can be made deeper: the input-to-hidden function, the hidden-to-hidden transition, and the hidden-to-output function. Based on this, they propose two novel deep RNN architectures that are orthogonal to previous methods of stacking recurrent layers. They also introduce a new framework based on neural operators to interpret these deep RNNs. The proposed deep RNNs are evaluated on tasks such as polyphonic music prediction and language modeling, showing that they outperform conventional, shallow RNNs. The paper discusses different ways to increase the depth of an RNN, including making the input-to-hidden function deeper, the hidden-to-output function deeper, and the hidden-to-hidden transition deeper. They propose several variants of deep RNNs, including the deep transition RNN (DT-RNN), the deep output RNN (DO-RNN), and the stacked RNN (sRNN). They also introduce the concept of shortcut connections to alleviate the problem of difficult learning introduced by increasing depth. The authors evaluate the performance of these deep RNNs on tasks such as polyphonic music prediction and language modeling. They find that the deep output and deep transition RNN (DOT-RNN) outperforms the conventional RNN and stacked RNN on language modeling tasks. They also show that the proposed deep RNNs benefit from non-saturating activation functions and dropout, similar to feedforward neural networks. The paper concludes that deep RNNs can benefit from depth in a similar way to feedforward neural networks, and that the proposed architectures are effective for modeling complex sequences. However, training deep RNNs remains challenging, and further research is needed to improve their performance and efficiency.