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Logically Consistent Language Models via Neuro-Symbolic Integration

Diego Calanzone, Stefano Teso, Antonio Vergari

TL;DR

This work introduces a loss based on neuro-symbolic reasoning that teaches an LLM to be logically consistent with an external set of facts and rules and improves self-consistency even when the LLM is fine-tuned on a limited set of facts.

Abstract

Large language models (LLMs) are a promising venue for natural language understanding and generation. However, current LLMs are far from reliable: they are prone to generating non-factual information and, more crucially, to contradicting themselves when prompted to reason about relations between entities of the world. These problems are currently addressed with large scale fine-tuning or by delegating reasoning to external tools. In this work, we strive for a middle ground and introduce a loss based on neuro-symbolic reasoning that teaches an LLM to be logically consistent with an external set of facts and rules and improves self-consistency even when the LLM is fine-tuned on a limited set of facts. Our approach also allows to easily combine multiple logical constraints at once in a principled way, delivering LLMs that are more consistent w.r.t. all constraints and improve over several baselines w.r.t. a given constraint. Moreover, our method allows LLMs to extrapolate to unseen but semantically similar factual knowledge, represented in unseen datasets, more systematically.

Logically Consistent Language Models via Neuro-Symbolic Integration

TL;DR

This work introduces a loss based on neuro-symbolic reasoning that teaches an LLM to be logically consistent with an external set of facts and rules and improves self-consistency even when the LLM is fine-tuned on a limited set of facts.

Abstract

Large language models (LLMs) are a promising venue for natural language understanding and generation. However, current LLMs are far from reliable: they are prone to generating non-factual information and, more crucially, to contradicting themselves when prompted to reason about relations between entities of the world. These problems are currently addressed with large scale fine-tuning or by delegating reasoning to external tools. In this work, we strive for a middle ground and introduce a loss based on neuro-symbolic reasoning that teaches an LLM to be logically consistent with an external set of facts and rules and improves self-consistency even when the LLM is fine-tuned on a limited set of facts. Our approach also allows to easily combine multiple logical constraints at once in a principled way, delivering LLMs that are more consistent w.r.t. all constraints and improve over several baselines w.r.t. a given constraint. Moreover, our method allows LLMs to extrapolate to unseen but semantically similar factual knowledge, represented in unseen datasets, more systematically.
Paper Structure (30 sections, 16 equations, 3 figures, 13 tables)

This paper contains 30 sections, 16 equations, 3 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Logical consistency through the lenses of probabilistic reasoning
  3. Factuality.
  4. Negation consistency.
  5. Implication consistency.
  6. Reverse implication consistency.
  7. More complex constraints.
  8. Logically-consistent LLMs via NeSy integration
  9. Related Work
  10. LLMs and factual reasoning.
  11. More complex reasoning with LLMs.
  12. Semantic loss & other NeSy approaches
  13. Experiments
  14. RQ1: How do LoCo-LMs perform compared to external solvers?
  15. RQ2: How do LoCo-LMs deal with different logical constraints?
  16. ...and 15 more sections

Figures (3)

  • Figure 1: Our Logically Consistent (LoCo) LLMs can be fine-tuned in a unified way to be more factual and consistent to several different forms of logical constraints such as direct (left), reverse (middle) implications, negation and combinations thereof (\ref{['sec:methodology']}) when compared to a pre-trained LLaMa 2 70B or fine-tuned baseline such as LLaMa 2 7B.viva la semantic loss antifascista
  • Figure 2: An illustration of an entailment tree, namely a "prof", from EntailmentBank dalvi2022explaining. Blue nodes are premises in logical conjunction, orange nodes are implications and the green node denote the hypothesis to prove.
  • Figure 3: Pairwise cosine similarities between entities in the training distribution (calibration, rows) and the test distribution (silver, columns).