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A unique feature of Recurrent Neural Networks (RNNs) is that it incrementallyprocesses input sequences. In this research, we aim to uncover the inherentgeneralization properties, i.e., inductive bias, of RNNs with respect to howfrequently RNNs switch the outputs through time steps in the sequenceclassification task, which we call output sequence frequency. Previous workanalyzed inductive bias by training models with a few synthetic data andcomparing the model's generalization with candidate generalization patterns.However, when examining the output sequence frequency, previous methods cannotbe directly applied since enumerating candidate patterns is computationallydifficult for longer sequences. To this end, we propose to directly calculatethe output sequence frequency for each model by regarding the outputs of themodel as discrete-time signals and applying frequency domain analysis.Experimental results showed that Long Short-Term Memory (LSTM) and GatedRecurrent Unit (GRU) have an inductive bias towards lower-frequency patterns,while Elman RNN tends to learn patterns in which the output changes at highfrequencies. We also found that the inductive bias of LSTM and GRU varies withthe number of layers and the size of hidden layers.

Empirical Analysis of the Inductive Bias of Recurrent Neural Networks by Discrete Fourier Transform of Output Sequences