Feed-Forward Neural Networks Need Inductive Bias to Learn Equality Relations
This addresses a fundamental limitation in neural network learning for relational data, which is crucial for tasks in relational learning, though it is incremental as it builds on existing methods by adding specific units.
The study tackled the problem of standard feed-forward neural networks failing to generalize in learning basic binary relations like equality on binary vectors, even with extensive training data, and introduced differential rectifier (DR) units to create an inductive bias, enabling reliable generalization from small datasets without negative effects.
Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation fails with standard feed-forward networks on binary vectors. Even when trained with maximal training data, standard networks do not reliably detect equality.We introduce differential rectifier (DR) units that we add to the network in different configurations. The DR units create an inductive bias in the networks, so that they do learn to generalise, even from small numbers of examples and we have not found any negative effect of their inclusion in the network. Given the fundamental nature of these relations, we hypothesize that feed-forward neural network learning benefits from inductive bias in other relations as well. Consequently, the further development of suitable inductive biases will be beneficial to many tasks in relational learning with neural networks.