Parameterization of Hypercomplex Multiplications

The Hamilton product (4D hypercomplex multiplication) enables learning effective representations while saving up to 75% parameters… However, one key caveat is that hypercomplex space only exists at very few predefined dimensions . This restricts the flexibility of models that leverage hypercomplex multiplications . To this end, we propose parameterizing hypercomplex . multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined . As a result, our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hyper complex space, providing more architectural flexibility . Experiments of applications to LSTM and Transformer on natural language inference, machine translation, text style transfer, and subject verb agreement demonstrate .

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Keywords : hypercomplex - multiplications - predefined - hamilton - space -

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