If you train an AI on maps of what must come first, does it get better at 'A needs B needs C' thinking?
Can curriculum graphs as training data improve model understanding of prerequisite chains?
This explores whether training a model on data built from dependency graphs (maps of what has to come before what) makes it better at reasoning through 'A needs B needs C' chains.
This explores whether training a model on data built from dependency graphs (maps of what has to come before what) makes it better at reasoning through 'A needs B needs C' chains. The corpus has no study of prerequisite chains specifically, but the nearest evidence is encouraging. A 32B model fine-tuned on 24,000 reasoning tasks generated from paths through a medical knowledge graph reached state-of-the-art results across 15 medical domains, and the note reads this as structured, bottom-up composition of small building blocks mattering more than raw scale Can knowledge graphs teach models deep domain expertise?. A path through a graph is a chain, so the training signal has the same shape as a prerequisite chain, with medical relations in place of 'learn this first'.
The order in which the model meets the chain looks like a separate lever from the graph itself. Reverse curriculum RL starts the model near the end of a solution and slides the starting point backward. That exposes which step breaks using only a right-or-wrong final answer, with no human step-by-step labels Can curriculum learning approximate expensive process supervision?. This enforces a prerequisite structure through the schedule: master the last link, then the one before it. Sequencing has measurable effects elsewhere too. In Omni-Thinker, training structured tasks first beat mixing everything together by 6.2%, because it stopped entropy collapse from damaging open-ended skills Does training order reshape how models handle different task types?. A graph would give you a principled order for both. Separately, teacher-refined data can hurt when it sits beyond the student's current learning frontier, even if it is objectively better Does teacher-refined data always improve student model performance?. A prerequisite graph is arguably a map of that frontier, but no note here tests that directly.
The catch is what counts as understanding. Models trained on deliberately wrong instructions score about the same as models trained on correct ones (43% vs a 42.6% baseline), because what transfers is the shape of the output, not the task Does instruction tuning teach task understanding or output format?. Chain-of-thought work finds something similar. Models reproduce the form of reasoning and fail predictably when the task, length or format shifts Does chain-of-thought reasoning actually generalize beyond training data?, Does chain-of-thought reasoning reveal genuine inference or pattern matching?. A model trained on graph paths could therefore look fluent about prerequisites while only having learned what graph-shaped answers look like. The test that would separate the two is chains longer than anything in training, or chains in an unfamiliar domain. Length shift is one of the conditions used to break chain-of-thought in those experiments.
Two other findings affect whether training on a graph is the right move at all. Prompting can only activate knowledge a model already has and cannot supply what is missing Can prompt optimization teach models knowledge they lack?. If the model lacks the domain's dependencies, training on them is the only route. But the model may not need to internalize the graph. LogicRAG builds a directed graph from each query at inference time, which avoids the construction cost and staleness of a pre-built graph while keeping multi-hop reasoning Can query-time graph construction replace pre-built knowledge graphs?. Baking the graph in suits stable, deep domains like medicine, and building it on demand suits prerequisites that change.
Whether the skill of following dependencies transfers beyond the graph's own domain is unresolved. Reasoning generalization appears to come from broad procedural knowledge spread across many kinds of documents Does procedural knowledge drive reasoning more than factual retrieval?. A single-domain graph may therefore teach that domain's facts more than a portable habit of walking backward through dependencies. The corpus doesn't settle this.
Sources 10 notes
Fine-tuning a 32B model on 24,000 reasoning tasks derived from medical knowledge graph paths produces state-of-the-art performance across 15 medical domains, demonstrating that structured knowledge composition matters more than scale.
R3 progressively slides the reasoning start state backward from near-completion, creating a curriculum that reveals step-level failure modes using only outcome feedback. This achieves process supervision granularity without expensive human step annotations.
Omni-Thinker shows structured domains decrease output entropy while creative domains increase it. BWT-guided scheduling—training structured tasks first—yields 6.2% gains over joint training by preventing entropy collapse from damaging open-ended capabilities.
Teacher-refined data degrades performance when it exceeds the student's learning frontier, even if objectively higher quality. Students should filter refinements using their own statistical profile to retain only compatible improvements.
Models trained on semantically empty or deliberately incorrect instructions achieve comparable performance to those trained on full correct instructions, achieving 43% vs random baseline 42.6%. The semantic content of instructions appears largely irrelevant; what transfers is knowledge of the output space.
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DataAlchemy experiments show CoT fails systematically under distributional shifts in task, length, and format. Models produce fluent but logically inconsistent reasoning — imitating reasoning form without valid underlying logic.
CoT works by constraining models to reproduce familiar reasoning patterns from training, not by enabling novel symbolic reasoning. Performance degrades predictably under distribution shifts—the signature of imitation rather than capability emergence.
Prompting works entirely within a model's pre-existing training distribution and cannot supply domain knowledge absent from training data. This creates a hard ceiling: no prompt strategy can compensate for missing foundational knowledge, only reorganize what already exists.
LogicRAG constructs directed acyclic graphs from queries at inference time rather than pre-building corpus-wide graphs, eliminating construction overhead, avoiding staleness, and enabling query-specific retrieval logic without sacrificing multi-hop reasoning capability.
Analysis of 5 million pretraining documents shows reasoning relies on broad, transferable procedural knowledge from diverse sources, unlike factual recall which depends on narrow, document-specific memorization of target facts.
Papers this line draws on 8
The research behind the notes this line reads — ranked by how closely each paper relates.
- Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens
- CoT is Not True Reasoning, It Is Just a Tight Constraint to Imitate: A Theory Perspective
- When More is Less: Understanding Chain-of-Thought Length in LLMs
- Hierarchical Reasoning Model
- Measuring Faithfulness in Chain-of-Thought Reasoning
- Break the Chain: Large Language Models Can be Shortcut Reasoners
- RAGU: A Multi-Step GraphRAG Engine with a Compact Domain-Adapted LLM
- Can Language Models Solve Graph Problems in Natural Language?