# Deductive Closure Training of Language Models for Coherence, Accuracy, and Updatability

arXiv: https://arxiv.org/abs/2401.08574 · HTML: https://mlsanity.com/paper/2401.08574/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 47 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 28 of 28)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Memory-Based Model Editing at Scale](https://mlsanity.com/paper/2206.06520/) (2022)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Asking and Answering Questions to Evaluate the Factual Consistency of Summaries](https://mlsanity.com/paper/2004.04228/) (2020)
- [MQuAKE: Assessing Knowledge Editing in Language Models via Multi-Hop Questions](https://mlsanity.com/paper/2305.14795/) (2023)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [Maieutic Prompting: Logically Consistent Reasoning with Recursive Explanations](https://mlsanity.com/paper/2205.11822/) (2022)
- [Q2: Evaluating Factual Consistency in Knowledge-Grounded Dialogues via Question Generation and Question Answering](https://mlsanity.com/paper/2104.08202/) (2021)
- [StreamingQA: A Benchmark for Adaptation to New Knowledge over Time in Question Answering Models](https://mlsanity.com/paper/2205.11388/) (2022)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Towards LLM-based Fact Verification on News Claims with a Hierarchical Step-by-Step Prompting Method](https://mlsanity.com/paper/2310.00305/) (2023)
- [CREAK: A Dataset for Commonsense Reasoning over Entity Knowledge](https://mlsanity.com/paper/2109.01653/) (2021)
- [Answering Questions by Meta-Reasoning over Multiple Chains of Thought](https://mlsanity.com/paper/2304.13007/) (2023)
- [Improved Natural Language Generation via Loss Truncation](https://mlsanity.com/paper/2004.14589/) (2020)
- [Language Model Self-improvement by Reinforcement Learning Contemplation](https://mlsanity.com/paper/2305.14483/) (2023)
- [Prompt-and-Rerank: A Method for Zero-Shot and Few-Shot Arbitrary Textual Style Transfer with Small Language Models](https://mlsanity.com/paper/2205.11503/) (2022)
- [Benchmarking and Improving Generator-Validator Consistency of Language Models](https://mlsanity.com/paper/2310.01846/) (2023)
- [Entailer: Answering Questions with Faithful and Truthful Chains of Reasoning](https://mlsanity.com/paper/2210.12217/) (2022)
- [Natural Language Deduction through Search over Statement Compositions](https://mlsanity.com/paper/2201.06028/) (2022)

## Built on by (most cited first, 22 of 22)

- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Rethinking Interpretability in the Era of Large Language Models](https://mlsanity.com/paper/2402.01761/) (2024)
- [Self-Adapting Language Models](https://mlsanity.com/paper/2506.10943/) (2025)
- [Synthetic continued pretraining](https://mlsanity.com/paper/2409.07431/) (2024)
- [Beyond Preferences in AI Alignment](https://mlsanity.com/paper/2408.16984/) (2024)
- [Human-LLM Compound System for Scientific Ideation through Facet Recombination and Novelty Evaluation](https://mlsanity.com/paper/2409.14634/) (2024)
- [On the generalization of language models from in-context learning and finetuning: a controlled study](https://mlsanity.com/paper/2505.00661/) (2025)
- [Bias-Augmented Consistency Training Reduces Biased Reasoning in Chain-of-Thought](https://mlsanity.com/paper/2403.05518/) (2024)
- [A Probabilistic Framework for LLM Hallucination Detection via Belief Tree Propagation](https://mlsanity.com/paper/2406.06950/) (2024)
- [Teaching Models to Verbalize Reward Hacking in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.22777/) (2025)
- [CodeUpdateArena: Benchmarking Knowledge Editing on API Updates](https://mlsanity.com/paper/2407.06249/) (2024)
- [Latent learning: episodic memory complements parametric learning by enabling flexible reuse of experiences](https://mlsanity.com/paper/2509.16189/) (2025)
- [Crafting Interpretable Embeddings by Asking LLMs Questions](https://mlsanity.com/paper/2405.16714/) (2024)
- [Assessing the Reasoning Capabilities of LLMs in the context of Evidence-based Claim Verification](https://mlsanity.com/paper/2402.10735/) (2024)
- [Language Modeling with Editable External Knowledge](https://mlsanity.com/paper/2406.11830/) (2024)
- [Always Tell Me The Odds: Fine-grained Conditional Probability Estimation](https://mlsanity.com/paper/2505.01595/) (2025)
- [BottleHumor: Self-Informed Humor Explanation using the Information Bottleneck Principle](https://mlsanity.com/paper/2502.18331/) (2025)
- [Do explanations generalize across large reasoning models?](https://mlsanity.com/paper/2601.11517/) (2026)
- [Uncovering Gaps in How Humans and LLMs Interpret Subjective Language](https://mlsanity.com/paper/2503.04113/) (2025)
- [PropMEND: Hypernetworks for Knowledge Propagation in LLMs](https://mlsanity.com/paper/2506.08920/) (2025)
- [Can Gradient Descent Simulate Prompting?](https://mlsanity.com/paper/2506.20989/) (2025)
- [Using LLMs for Explainable, Data-Driven Insight Generation from Time Series](https://mlsanity.com/paper/2607.18271/) (2026)

## Abstract (arXiv)

While language models (LMs) can sometimes generate factually correct text and estimate truth values of individual claims, these generally do not reflect a globally coherent, manipulable model of the world. As a consequence, current LMs also generate incorrect or nonsensical content, and are difficult to edit and bring up to date. We present a method called Deductive Closure Training (DCT) that uses LMs themselves to identify implications of (and contradictions within) the text that they generate, yielding an efficient self-supervised procedure for improving LM factuality. Given a collection of seed documents, DCT prompts LMs to generate additional text implied by these documents, reason globally about the correctness of this generated text, and finally fine-tune on text inferred to be correct. Given seed documents from a trusted source, DCT provides a tool for supervised model updating; if seed documents are sampled from the LM itself, DCT enables fully unsupervised fine-tuning for improved coherence and accuracy. Across the CREAK, MQUaKE, and Reversal Curse datasets, supervised DCT improves LM fact verification and text generation accuracy by 3-26%; on CREAK fully unsupervised DCT improves verification accuracy by 12%. These results show that LMs' reasoning capabilities during inference can be leveraged during training to improve their reliability.