Simple strategies to encode tree automata in sigmoid recursive neural networks

Recently, a number of authors have explored the use of recursive neural nets (RNN) for the adaptive processing of trees or tree-like structures. One of the most important language-theoretical formalizations of the processing of tree-structured data is that of deterministic finite-state tree automata (DFSTA). DFSTA may easily be realized as RNN using discrete-state units, such as the threshold linear unit. A recent result by J. Sima (1997) shows that any threshold linear unit operating on binary inputs can be implemented in an analog unit using a continuous activation function and bounded real inputs. The constructive proof finds a scaling factor for the weights and reestimates the bias accordingly. We explore the application of this result to simulate DFSTA in sigmoid RNN (that is, analog RNN using monotonically growing activation functions) and also present an alternative scheme for one-hot encoding of the input that yields smaller weight values, and therefore works at a lower saturation level.