We replace the multiplication and sigmoid function of the conventional recurrent gate with addition and ReLU activation. This mechanism is designed to maintain long-term memory for sequence processing but at a reduced computational cost, thereby opening up for more efficient execution or larger models on restricted hardware. Recurrent Neural Networks (RNNs) with gating mechanisms such as LSTM and GRU have been widely successful in learning from sequential data due to their ability to capture long-term dependencies. Conventionally, the update based on current inputs and the previous state history is each multiplied with dynamic weights and combined to compute the next state. However, multiplication can be computationally expensive, especially for certain hardware architectures or alternative arithmetic systems such as homomorphic encryption. It is demonstrated that the novel gating mechanism can capture long-term dependencies for a standard synthetic sequence learning task while significantly reducing computational costs such that execution time is reduced by half on CPU and by one-third under encryption. Experimental results on handwritten text recognition tasks furthermore show that the proposed architecture can be trained to achieve comparable accuracy to conventional GRU and LSTM baselines. The gating mechanism introduced in this paper may enable privacy-preserving AI applications operating under homomorphic encryption by avoiding the multiplication of encrypted variables. It can also support quantization in (unencrypted) plaintext applications, with the potential for substantial performance gains since the addition-based formulation can avoid the expansion to double precision often required for multiplication.

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