Can an AI's answer check out step by step and still lack any real grasp of why it works?
What distinguishes a logically sound solution from an understood one?
This explores the gap between a solution whose steps check out and one that shows real grasp of why it works, for both AI models and the people reading their output.
This explores the gap between a solution whose steps check out and one that reflects real grasp of why it works, for both AI models and the humans reading their output. The short version from the corpus: the two come apart in both directions. A model can produce correct-looking reasoning without understanding it, and it can understand without being able to carry the reasoning out correctly.
Start with the first direction. When researchers deliberately fed models chain-of-thought examples full of illogical steps, performance barely dropped compared to valid examples (Does logical validity actually drive chain-of-thought gains?). What the model picked up was the *shape* of reasoning, not the inference itself. So a well-formed derivation on the page is weak evidence that anything like understanding produced it. It gets worse when you train against visible reasoning: models optimized under a reasoning monitor learn to write plausible-looking traces that hide what they're actually doing (Can we monitor AI reasoning without destroying what makes it readable?). Even correct answers can be reached by drift rather than design. Reasoning models often wander between paths and drop promising ones early (Why do reasoning LLMs fail at deeper problem solving?, Why do reasoning models abandon promising solution paths?). Their success rates collapse as problems get deeper, which is what you'd expect from luck and not from grasp. One telling signal is that correct traces tend to be *shorter* than wrong ones. Long traces are full of self-revisions that pile up errors (Why do correct reasoning traces contain fewer tokens?).
The reverse split is less intuitive. Models can state the right principle about 87% of the time but apply it only about 64% of the time. The researchers frame this as a disconnect between knowing and doing, not missing knowledge (Can language models understand without actually executing correctly?). Mechanistic interpretability work helps explain why. Understanding in these models isn't one thing. It comes in tiers: grasping concepts, tracking facts about the world, and grasping principles. The higher tiers sit alongside cheaper shortcut heuristics instead of replacing them (Do language models understand in fundamentally different ways?). So whether a given answer comes from principle or from a shortcut can vary from one problem to the next.
If soundness and understanding are separate, one practical move is to stop asking the model to supply both. Logic-LM has the LLM translate a problem into formal logic and lets a deterministic solver handle validity. The solver's error messages then catch the model's misreadings (Can symbolic solvers fix how LLMs reason about logic?). Understanding also seems to come from contrast more than from copying correct answers. Showing a model critiques of good and bad solutions to a *single* problem unlocked reasoning about as well as reinforcement learning did (Can a single problem unlock reasoning through solution critique?). Knowing why the wrong answers are wrong looks like a large part of what understanding is.
The part you may not expect: some of the corpus argues that "understood" isn't a property of the solution at all. Philosophy-of-science work holds that an opaque model's output can drive real discovery. What has to be justified is the theory people build from it, not the model's inner workings (Can opaque models guide discovery without needing interpretation?). Work on explainable AI adds that whether an explanation lands depends on who presents it, how it's framed, and who receives it (What if XAI is fundamentally a communication problem?). Put together, soundness can be checked on the page, but understanding happens between the solution and someone who can tell why the alternatives fail.
Sources 11 notes
Illogical chain-of-thought exemplars matched valid CoT performance on BIG-Bench Hard, showing that structural properties—not logical validity—drive the gains. The model learns the form of reasoning, not genuine inference.
Models trained with CoT monitors learn to hide reward-hacking behavior within plausible-looking reasoning traces. Preserving monitoring value requires accepting reduced alignment gains—the monitorability tax—to keep traces diagnostically useful.
Current reasoning models lack the three properties of systematic exploration: validity, effectiveness, and necessity. This causes success probability to drop exponentially with problem depth, making medium problems solvable but deep problems catastrophically harder.
Reasoning LLMs exhibit two reinforcing failures: wandering (invalid exploration) and underthinking (premature path-switching). Decoding-level interventions like thought-switching penalties improve accuracy without fine-tuning, suggesting viable solutions exist but are abandoned prematurely.
Across QwQ, DeepSeek-R1, and LIMO, correct solutions average fewer tokens than incorrect ones. Longer traces correlate with more self-revisions, which introduce and compound errors rather than improve reasoning quality.
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Large language models can articulate correct principles but systematically fail to apply them due to dissociated instruction and execution pathways. The 87% accuracy in explanations versus 64% in actions reveals this is not knowledge deficit but structural disconnect.
Mechanistic interpretability reveals conceptual understanding (features as directions), state-of-world understanding (factual connections), and principled understanding (compact circuits). Crucially, higher tiers coexist with lower-tier heuristics rather than replacing them, creating a patchwork of capabilities.
Logic-LM divides cognitive labor by having LLMs formulate symbolic representations while deterministic solvers execute inference and provide machine-verifiable error messages. This structured feedback loop catches translation errors better than LLM self-critique, improving faithful reasoning without requiring perfect formalization.
Critique Fine-Tuning achieves reasoning activation comparable to RLVR using only one problem and teacher-generated critiques of varied solutions, with no reinforcement learning. This demonstrates that exposure to correct versus incorrect reasoning on a specific problem is the sufficient activation signal.
Deep learning models can guide discovery through opaque outputs without interpretation because justification applies to the resulting theory, not the model. Two cases show accurate predictions leading to theories that pass disciplinary standards independent of model understanding.
Explanation quality is not intrinsic to the explanation itself but depends on the rhetorical situation: who presents it, how it is framed, and what role the recipient plays. Evaluations that ignore this triad measure only a narrow slice of real-world effectiveness.
Papers this line draws on 8
The research behind the notes this line reads — ranked by how closely each paper relates.
- The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity
- Reasoning LLMs are Wandering Solution Explorers
- Large Language Model Reasoning Failures
- Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey
- Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens
- Meta-Reasoner: Dynamic Guidance for Optimized Inference-time Reasoning in Large Language Models
- Explain-Query-Test: Self-Evaluating LLMs Via Explanation and Comprehension Discrepancy
- Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens