On the Memory Mechanism of Tensor-Power Recurrent Models

• URL: http://arxiv.org/abs/2103.01521v1
• Date: Tue, 2 Mar 2021 07:07:47 GMT
• Title: On the Memory Mechanism of Tensor-Power Recurrent Models
• Authors: Hejia Qiu, Chao Li, Ying Weng, Zhun Sun, Xingyu He, Qibin Zhao
• Abstract summary: We investigate the memory mechanism of TP recurrent models. We show that a large degree p is an essential condition to achieve the long memory effect. New model is expected to benefit from the long memory effect in a stable manner.
• Score: 25.83531612758211
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Tensor-power (TP) recurrent model is a family of non-linear dynamical systems, of which the recurrence relation consists of a p-fold (a.k.a., degree-p) tensor product. Despite such the model frequently appears in the advanced recurrent neural networks (RNNs), to this date there is limited study on its memory property, a critical characteristic in sequence tasks. In this work, we conduct a thorough investigation of the memory mechanism of TP recurrent models. Theoretically, we prove that a large degree p is an essential condition to achieve the long memory effect, yet it would lead to unstable dynamical behaviors. Empirically, we tackle this issue by extending the degree p from discrete to a differentiable domain, such that it is efficiently learnable from a variety of datasets. Taken together, the new model is expected to benefit from the long memory effect in a stable manner. We experimentally show that the proposed model achieves competitive performance compared to various advanced RNNs in both the single-cell and seq2seq architectures.

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