The Molecular Structure of Thought: Mapping the Topology of Long Chain-of-Thought Reasoning

Glad to share our recent exploratory project:

🧪 Title: The Molecular Structure of Thought: Mapping the Topology of Long Chain-of-Thought Reasoning
🌐 arXiv: 2601.06002
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🧐 Why revisit Long CoT?
Recent work often focuses on “making CoT longer,” but longer traces are more likely to derail—e.g., drifting off-track, breaking logical continuity, or amplifying hallucinations—especially when attempting to cold-start genuine long-horizon reasoning from a standard instruction-tuned model.
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A key observation is that many trajectories that merely look like long reasoning (e.g., distilling from randomly sampled ICL demonstrations, or using human-written long step-by-step solutions) are not behaviorally stable, and models frequently fail to learn robustly from them.
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😭 Why imitation often fails

• “Long” human CoT is not necessarily effective: Fine-tuning on human-written long CoT does not reliably reproduce the gains achieved by distilling from a strong reasoning model.
• Distill from Weak instruct model + random ICL demonstrations largely fails: Using randomly chosen 1-shot ICL examples to “fake” long reasoning for distillation leads to significant degradation, suggesting that superficial formatting is insufficient.
  ​- Keywords are not the driver: Replacing surface tokens (e.g., “wait”) while preserving the underlying reasoning trajectory and behavioral pattern yields similar performance, indicating that SFT primarily learns structure/behavior rather than prompt-specific keywords.
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  🔍 Early evidence: Long CoT has stable “structural fingerprints”
• We observe a stable behavioral transfer graph: across different strong reasoning models and tasks, the induced distributional characteristics appear highly consistent.
  ​- In semantic space, we see “linking–folding” patterns: deep reasoning tends to form locally dense structures; self-reflection tends to create backward links for validation/correction; and exploration tends to form weaker cross-cluster connections.
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💡 Core hypothesis: effective Long CoT as a “molecular structure”
High-quality Long CoT is not merely a linear chain; it is stabilized by three interaction types—analogous to chemical bonds—that organize and constrain reasoning trajectories:
​- Deep Reasoning (covalent-bond-like): forms the main reasoning backbone; if it breaks, the solution collapses.
​- Self-Reflection (hydrogen-bond-like): folds later steps back to earlier ones to verify assumptions, detect errors, and correct the path.
​- Self-Exploration (van der Waals-like): weak but important cross-domain probing that broadens coverage and discovers alternative routes.
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An additional observation is that the Gibbs–Boltzmann energy formulation is closely aligned with the attention formulation; hence, the “energy distributions” of different bonds can be estimated directly from attention, exhibiting a stable ordering reminiscent of real chemical bond energies.
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🍎 “Semantic isomers” of Long CoT

• For the same problem, trajectories can be semantically close yet differ in the distribution and transitions of bonds, yielding distinct “isomers” with dramatically different trainability and downstream performance.
  ​- Two isomers that appear similar may still be incompatible: mixing them during training can trigger structural conflicts and degrade performance.
  ​- ICL is not inherently ineffective; it helps when demonstrations are selected such that their structural distribution aligns with the target high-quality isomer.
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🔧 Solution: MOLE-SYN
We propose MOLE-SYN: first estimate a behavioral transfer graph from a strong reasoning model, then use it to guide a pure instruct LLM to synthesize Long CoT trajectories.
​- Empirically, distilling Qwen-2.5 with MOLE-SYN–generated trajectories can approach the effectiveness of distillation from QwQ.
​- This initialization also exhibits strong RL potential: it yields more stable RL training curves and sustained improvement headroom.

• Finally, different behaviors have distinct global effects: deep reasoning makes the core logic more compact, self-reflection increases overall “folding” tightness, and self-exploration expands the reachable search space.
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👀 A practical implication is that when CoT is heavily summarized or compressed, the “molecular structure” distribution can be destroyed, and distilled models may underperform even the original teacher.
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If a prior viewpoint treated CoT behaviors as nodes, this work reframes them as edges that link logical states: the training target may not be “longer answers,” but a more stable reasoning skeleton controlled by structured reasoning behaviors.
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