Benchmarking Neural Network Generalization for Grammar Induction

TL;DR

This paper introduces a formal language-based benchmark to evaluate neural network generalization in grammar induction, revealing that MDL-trained models outperform standard ones in data efficiency and generalization.

Contribution

It proposes a new formal language-based benchmark for neural network generalization and demonstrates that MDL training improves generalization over standard loss functions.

Findings

MDL-trained networks generalize better with less data

The benchmark includes languages like a^nb^n and Dyck-1, 2

Networks' generalization scores correlate with training data size

Abstract

How well do neural networks generalize? Even for grammar induction tasks, where the target generalization is fully known, previous works have left the question open, testing very limited ranges beyond the training set and using different success criteria. We provide a measure of neural network generalization based on fully specified formal languages. Given a model and a formal grammar, the method assigns a generalization score representing how well a model generalizes to unseen samples in inverse relation to the amount of data it was trained on. The benchmark includes languages such as $a^nb^n$, $a^nb^nc^n$, $a^nb^mc^{n+m}$, and Dyck-1 and 2. We evaluate selected architectures using the benchmark and find that networks trained with a Minimum Description Length objective (MDL) generalize better and using less data than networks trained using standard loss functions. The benchmark is available at https://github.com/taucompling/bliss.