Systematic Generalization in Language Models Scales with Information Entropy

TL;DR

This work investigates systematic generalization in sequence-to-sequence models and demonstrates that performance on embedded-sentence generalization scales with training-data entropy, quantified as $H^{\text{train}}_{e_2}(V)$. It formalizes a data-centric framework, generates synthetic data via a modified SCAN grammar, and evaluates four architectures under two entropy-raising strategies: distribution mixing and incremental support, showing that higher entropy facilitates out-of-distribution generalization even without architectural priors. Across experiments, the Transformer generally performs best, while a permutation-equivariant model with built-in priors can solve the zero-entropy (degenerate) case, highlighting the role of priors versus data properties. The findings suggest information efficiency as a lens for systematic generalization and raise its applicability limits at low entropy and in real-world, non-synthetic settings.

Abstract

Systematic generalization remains challenging for current language models, which are known to be both sensitive to semantically similar permutations of the input and to struggle with known concepts presented in novel contexts. Although benchmarks exist for assessing compositional behavior, it is unclear how to measure the difficulty of a systematic generalization problem. In this work, we show how one aspect of systematic generalization can be described by the entropy of the distribution of component parts in the training data. We formalize a framework for measuring entropy in a sequence-to-sequence task and find that the performance of popular model architectures scales with the entropy. Our work connects systematic generalization to information efficiency, and our results indicate that success at high entropy can be achieved even without built-in priors, and that success at low entropy can serve as a target for assessing progress towards robust systematic generalization.

Figures (6)

• Figure 1: Systematic generalization increases with the entropy of the training data for popular sequence-to-sequence models, even without built-in priors.
• Figure 2: A schematic overview of the two approaches to increasing the entropy level. Top: Vertical scaling by distribution mixing. Bottom: Horizontal scaling by incrementing the support of the distribution.
• Figure 3: Example of distributions of verbs for $e_1$ (left) and $e_2$ (right).
• Figure 4: Probabilities in the degenerate case for $e_2$
• Figure 5: Results from the Experiments 1 & 2. The accuracy and standard deviations are from five seeds.

Theorems & Definitions (3)

• Definition 1: CB
• Definition 2: Weak systematicity
• Definition 3: Strong systematicity