Research map / Large language models / Instruction and fine-tuning
Logically Consistent Language Models via Neuro-Symbolic Integration
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Proposes LoCo-LMs, fine-tuning LLMs with a semantic loss (weighted model counting over logical constraints) so they become more factual and self-consistent without external solvers at inference.
Problem
LLMs contradict themselves on logically related facts (negation, implication, reverse implication) and are often factually inconsistent; existing fixes rely on external solvers at inference or large-scale fine-tuning.
Approach
Use the semantic loss, a probabilistic neuro-symbolic objective that maximizes the probability that LLM beliefs satisfy propositional constraints (computed efficiently via compiled circuits), to fine-tune LLMs on a small KB of facts and rules, with LoRA and 4-bit quantization.
Key results
- On BeliefBank calibration, LoCo-Macaw trained on T1 reaches Tot F1 0.96 and implication consistency 0.99, versus ConCoRD at 0.91 Tot F1 and 0.91 consistency.
- LoCo-LLaMa-2-7b (Super) achieves average consistency 0.77 on the BeliefBank test split, versus 0.55 for LLaMa-2-70b zero-shot.
- On EntailmentBank, LoCo-LLaMa-2-7b (F-IMP) keeps consistency at 0.98 across tree depths 1-5 versus 0.59-0.87 for the LLaMa-2-7b baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply semantic-loss fine-tuning on implication constraints instead of using ConCoRD | Macaw-Large · BeliefBank silver, T1 | Imp: 0.91 -> 0.99 | Helped |
| Use semantic-loss rather than XENT fine-tuning on T1+T2 (5%) | Macaw-Large · BeliefBank silver, T1+T2 (5%) | Imp: 0.82 -> 0.92 | Helped |
| Fine-tune on combined negation and factual implication constraints | LLaMa-2-7b · BeliefBank test | AVG: 0.55 -> 0.77 | Helped |
| Fine-tune on negation constraints only (ablation) | LLaMa-2-7b · BeliefBank test | NEG: 0.42 -> 0.96 | Helped |
| Fine-tune on factual implication constraints (ablation) | LLaMa-2-7b · BeliefBank test | IMP: 0.52 -> 0.99 | Helped |
| Use factual implication constraints only rather than combined negation and implication constraints (ablation) | LLaMa-2-7b · BeliefBank test | NEG: 0.96 -> 0.00 | Hurt |
| Use negation constraints only rather than combined negation and implication constraints (ablation) | LLaMa-2-7b · BeliefBank test | AVG: 0.52 -> 0.77 | Hurt |
| Fine-tune on factual implication constraints (ablation) | LLaMa-2-7b · EntailmentBank test, depth 1 | Consistency: 0.87 -> 0.98 | Helped |
| Fine-tune on negation constraints only (ablation) | LLaMa-2-7b · EntailmentBank test, depth 1 | Consistency: 0.87 -> 0.51 | Hurt |
Surprising findings
- Fine-tuning on negation alone (NEG) did not improve over baseline on EntailmentBank consistency, and factual-implication-only training gave near-zero reverse implication consistency.
- Standard XENT fine-tuning on true/false facts led the model to label almost everything false due to class imbalance.
Limitations
- Sensitivity to prompt format; consistency gains do not always transfer across formats.
- Assumes conditional independence of fact probabilities and correct constraints in the KB.
- Only implications and exclusive ORs are used for training in practice.
Experimental setup
Datasets: BeliefBank EntailmentBank WikiText
Benchmarks: BeliefBank EntailmentBank
Metrics: F1 implication consistency reverse implication consistency negation self-consistency perplexity
Baselines: ConCoRD Macaw-Large Macaw+XENT LLaMa-2-7b LLaMa-2-70b LLaMa-2-7b + XENT
Builds on: semantic loss ConCoRD LoRA QLoRA
Closest papers by meaning
- Logical Consistency of Large Language Models in Fact-Checking (ICLR 2025 · similarity 0.89)
- Calibrating Reasoning in Language Models with Internal Consistency (NeurIPS 2024 · similarity 0.89)
- Journey to the Center of the Knowledge Neurons: Discoveries of Language-Independent Knowledge Neurons and Degenerate Knowledge Neurons (AAAI 2024 · similarity 0.89)
- Inductive Learning of Logical Theories with LLMs: A Expressivity-graded Analysis (AAAI 2025 · similarity 0.88)
- Improving Factuality and Reasoning in Language Models through Multiagent Debate (ICML 2024 · similarity 0.88)
- Content-free Logical Modification of Large Language Model by Disentangling and Modifying Logic Representation (AAAI 2025 · similarity 0.88)
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