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Improving Neural Logic Machines via Failure Reflection

ICML 2024 · Large language models › Agents, code and math · approach: Inductive and abstract reasoning evaluation

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Proposes Failure Reflection Guided Regularizer (FRGR), which mines root-cause subprograms from repeated errors in neural logic machines and penalizes them during training to improve performance, generalization, and efficiency.

Problem

Neural logic machines (NLM and DLM) repeat similar mistakes during training, causing oscillation around ill-performing local optima and sub-optimal performance on inductive logic programming and reasoning tasks.

Approach

Extracts the induced program from the NLM at each erroneous training step, uses Apriori frequent-itemset mining over a history queue of erroneous programs to identify the recurring root-cause subprogram, and adds an L1 repetition regularizer that penalizes that subprogram in future iterations.

Key results

• On IsMGUncle (data-rich), NLM w/ FRGR reaches 100% IID and 60.44% generalization at n=100 versus 10.04% for NLM.
• On IsUncle, NLM w/ FRGR needs 45.44% fewer epochs than NLM to converge; DLM w/ FRGR needs 12.70% fewer epochs than DLM.
• In the data-scarce setting (1/500 data), DLM on IsUncle keeps 80% performance and generalization with FRGR versus 60%/40% without.

Measured effects reported in the paper

Surprising findings

• The authors could not reproduce the reinforcement learning results reported in the original DLM paper.
• FRGR slightly increased epochs on simple tasks such as HasFather, 1-OutDegree, and 4-Connectivity.

Limitations

• Extra overhead from periodic frequent itemset mining every m epochs and program extraction.
• Fewer epochs not achieved on some simple tasks, where regularization slows learning.
• Evaluated only on NLM and DLM architectures and ILP/RL reasoning tasks, not on broader domains.

Experimental setup

Datasets: Family Tree reasoning tasks General Graph reasoning tasks Sorting Path BlocksWorld

Benchmarks: Family Tree reasoning (IsUncle, IsMGUncle, HasSister, HasFather, IsGrandparent) Graph reasoning (k-OutDegree, k-Connectivity) Sorting Path BlocksWorld

Metrics: success rate (performance) generalization success rate graduation ratio epochs to convergence unary atom ratio

Baselines: NLM DLM

Builds on: Neural Logic Machines Differentiable Logic Machines Apriori algorithm REINFORCE

Closest papers by meaning

• Efficient Reasoning for Large Reasoning Language Models via Certainty-Guided Reflection Suppression (AAAI 2026 · similarity 0.85)
• SuperCorrect: Advancing Small LLM Reasoning with Thought Template Distillation and Self-Correction (ICLR 2025 · similarity 0.85)
• GLoRe: When, Where, and How to Improve LLM Reasoning via Global and Local Refinements (ICML 2024 · similarity 0.85)
• LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision (ICLR 2026 · similarity 0.84)
• Stop Unnecessary Reflection: Training LRMs for Efficient Reasoning with Adaptive Reflection and Length Coordinated Penalty (ICLR 2026 · similarity 0.84)
• General-Reasoner: Advancing LLM Reasoning Across All Domains (NeurIPS 2025 · similarity 0.84)