From Facts to Insight: Bridging the Compositionality Gap in Language Models

Large language models (LLMs) such as GPT-3 have transformed natural language understanding by memorizing vast amounts of text. Yet, when faced with questions that require combining multiple pieces of knowledge—so-called compositional reasoning—even the biggest models stumble. In their paper Measuring and Narrowing the Compositionality Gap in Language Models, Press et al. introduce a new metric for this shortfall, show that it persists despite model scale, and propose practical prompting techniques to close it.

The Compositionality Gap: What and Why

Compositional reasoning asks a model not simply to recall one fact but to stitch together two or more facts in novel ways. For example:

“What is the calling code of the birthplace of Frida Kahlo?”

Even if an LLM knows:

1. Frida Kahlo was born in Coyoacán.
2. Mexico’s calling code is +52.

it may still fail to produce +52 as the combined answer. To quantify this failure mode, Press et al. define the compositionality gap:

Compositionality Gap =
(Number of 2-hop questions answered incorrectly despite both sub-questions being answered correctly)
÷ (Number of 2-hop questions for which both sub-questions are answered correctly)

This metric exposes how often an LM “knows” the pieces yet cannot compose them into the final answer.

Crafting a Diagnostic Benchmark: Compositional Celebrities

To systematically measure the gap, the authors introduce Compositional Celebrities (CC)—an 8.6 K-question, automatically generated dataset of 2-hop queries:

1. Select a celebrity (e.g., Justin Bieber).
2. Retrieve two facts about their birth (e.g., birth year = 1994; Masters Tournament champion = José María Olazábal).
3. Combine them into a compositional query:

   “Who won the Master’s Tournament in the year Justin Bieber was born?”

Key properties of CC:

• Unlikely combinations: The paired facts are common individually, but their conjunction rarely appears in any text corpus.
• Decomposability: Every question naturally splits into two sub-questions, allowing measurement of memorization vs. composition.

Scaling Alone Doesn’t Solve Composition

A natural hope is that simply increasing model size would improve both factual recall and reasoning. Press et al. evaluate the GPT-3 family (Ada → Davinci) on CC:

• 1-hop accuracy climbs steeply with size.
• 2-hop accuracy improves only marginally.
• Compositionality gap stays near ~40 % across all sizes (0.35 B → 175 B parameters).

This reveals that while larger models memorize ever more facts, they do not proportionally enhance their ability to compose learned knowledge.

Elicitive Prompting: Encouraging “Thought” in LLMs

To tackle this, the authors borrow and extend the idea of prompting LMs to “think aloud.” Two key methods emerge:

1. Chain-of-Thought (CoT)

• The model generates a free-form reasoning trace before the final answer.
• Improves multi-hop accuracy, but can be verbose or hard to parse.

2. Self-Ask Prompting

• A structured approach:
  1. Model decides if follow-up questions are needed.
  2. It explicitly emits each Follow up: sub-question.
  3. It provides each Intermediate answer: in turn.
  4. Finally, it states So the final answer is: in concise form.
• By scaffolding decomposition and retrieval, self-ask dramatically narrows the compositionality gap.

Hybrid Reasoning: Plugging in a Search Engine

Self-ask’s clear sub-question boundaries make it trivial to integrate an external search API:

1. LM generates Follow up: When was X born?
2. System sends that to a search engine and retrieves “1994.”
3. LM continues, using the fetched answer as if it were its own.

This Self-Ask + Search Engine (SA+SE) requires no fine-tuning or prompt changes—and yields further accuracy gains (often +10 pp) on CC and complementary benchmarks like 2WikiMultiHopQA, Musique, and Bamboogle.

Empirical Highlights

Implications for LLM Development

1. Diagnostic Clarity
   The compositionality gap provides a targeted metric for multi-step reasoning beyond aggregate accuracy.

2. Prompt Engineering Matters
   Structured elicitive prompts like self-ask can unlock reasoning abilities that mere scale cannot.

3. Hybrid Systems Are Powerful
   Seamlessly combining LMs with external tools (search, databases) can bridge knowledge or reasoning shortfalls without retraining.

Future Directions

• Deeper Multi-Hop: Extend evaluation to 3-, 4-, or higher-order reasoning tasks.
• Multilingual & Multimodal: Test compositional abilities across languages and modalities (e.g., text + images).
• Architectural Innovations: Design model architectures that internalize explicit decomposition, rather than relying solely on prompting.

Conclusion
Press et al.’s work shines a spotlight on a critical blind spot of today’s LLMs: the gulf between knowing facts and combining them intelligently. By defining the compositionality gap and demonstrating that structured prompting and smart tool integration can dramatically narrow it, they offer both a diagnostic lens and a practical toolkit for the next generation of reasoning-capable language models.

🔗 Read the full paper:
Measuring and Narrowing the Compositionality Gap in Language Models (arXiv:2210.03350)