Bridging the Empirical-Theoretical Gap in Neural Network Formal Language Learning Using Minimum Description Length
This addresses the empirical-theoretical gap in neural network learning for formal languages, which is incremental as it applies an existing MDL principle to a specific domain.
The paper tackled the problem of neural networks failing to achieve perfect generalization in formal language learning, even when theoretical solutions exist, and found that using the Minimum Description Length (MDL) objective makes the correct solution an optimum, unlike standard objectives with regularization.
Neural networks offer good approximation to many tasks but consistently fail to reach perfect generalization, even when theoretical work shows that such perfect solutions can be expressed by certain architectures. Using the task of formal language learning, we focus on one simple formal language and show that the theoretically correct solution is in fact not an optimum of commonly used objectives -- even with regularization techniques that according to common wisdom should lead to simple weights and good generalization (L1, L2) or other meta-heuristics (early-stopping, dropout). On the other hand, replacing standard targets with the Minimum Description Length objective (MDL) results in the correct solution being an optimum.