The Illusion of Thinking
Strengths and Limitations of Reasoning Models via Problem Complexity
Parshin Shojaee, Iman Mirzadeh, Keivan Alizadeh, Maxwell Horton, Samy Bengio, Mehrdad Farajtabar
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The Illusion of Thinking (Shojaee, Mirzadeh, Alizadeh, Horton, Bengio & Farajtabar — NeurIPS 2025, Apple) asks a deceptively simple question: do Large Reasoning Models actually reason, or do they perform a sophisticated kind of pattern-matching that happens to be wrapped in explanatory prose?
Standard math and coding benchmarks like MATH, AIME, HumanEval and MMLU are contaminated by pre-training data and only score the final answer — they can't tell you whether the model's long chain-of-thought was genuinely deriving the answer or hallucinating a plausible path to a memorized target. The authors replace these benchmarks with controllable puzzle environments — Tower of Hanoi, Checker Jumping, River Crossing and Blocks World — where the problem complexity is a tunable parameter , every instance is algorithmically generated (no contamination), and correctness can be mechanically verified step by step.
The three findings that reframe LRM evaluation:
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Three performance regimes. At low complexity, standard (non-thinking) models actually beat Large Reasoning Models — extra chain-of-thought is wasted effort. At medium complexity, LRMs pull ahead. At high complexity, both collapse to near-zero accuracy — the thinking prefix buys nothing past a critical threshold .
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The reasoning-token collapse. As increases toward , LRMs spend more thinking tokens — exactly as you'd expect. But past , the number of thinking tokens shrinks even though the generation budget is untouched. The model has the compute to keep reasoning; it just stops.
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Algorithmic execution failure. Even when the correct step-by-step algorithm is given in the prompt, LRMs still fail at roughly the same . The bottleneck isn't 'doesn't know how to solve it' — the model cannot reliably execute a known procedure once the required step count crosses a threshold.
Why this matters. The paper doesn't claim LRMs are useless — it claims current benchmarks systematically hide their limits. If an LRM that nails MATH still collapses on an 8-disk Tower of Hanoi (a problem a competent undergraduate can simulate on paper), our evaluation pipeline is telling us the wrong thing about what these models can do. The controllable-puzzle methodology is portable: any future reasoning model can be plotted on the same complexity axis and compared directly, without new benchmarks to curate or contaminate.
Chapter Roadmap
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Pipeline Summary
Large Reasoning Models emit a thinking prefix before the answer — but current benchmarks only score the answer.
Benchmark Contamination
MATH, AIME and friends are scraped from the same internet LRMs train on — memorization masquerades as reasoning.
Controllable Puzzles
Four puzzle families (Hanoi, Checker Jumping, River Crossing, Blocks World) with a single integer complexity knob N.
Three Regimes
Low-N: non-thinking wins. Medium-N: LRM wins. High-N: both collapse past a critical threshold N_c.
Token Collapse
Thinking-token count rises with complexity — then falls past N_c despite the full generation budget being unused.
Algorithm Execution
Giving the model the algorithm in the prompt does not shift N_c — the failure is execution, not knowledge.
Trace Pathologies
Overthink on easy problems (correct answer abandoned) and underthink on hard ones (early commit, no search).
The paper's argument in one picture — from a thinking-model's inference path, through the four puzzle environments and their complexity dial, to the three-regime accuracy curve and the token-collapse finding that defines the paper's headline claim.
Key Points
Large Reasoning Models (LRMs) emit a long thinking prefix before the final answer — o1-style, Claude extended thinking, DeepSeek-R1 style
Standard benchmarks score only the final answer — contamination + hidden failure modes
Controllable puzzles (Tower of Hanoi, Checker Jumping, River Crossing, Blocks World) give a complexity dial and mechanically-verified step-by-step correctness
Low complexity: non-thinking models match or beat LRMs — thinking is wasted
Medium complexity: LRMs genuinely help — the regime where chain-of-thought pays off
High complexity: both collapse — accuracy → 0 past a critical threshold
Reasoning-token collapse: thinking tokens grow then shrink past despite unused budget
Giving the model the algorithm does not move — the failure is in execution, not knowledge
Plot accuracy as a function of complexity: is high and flat for , declines steeply near , and is ~0 for . LRMs shift rightward on medium-hard problems but not on the hardest ones — the wall is real, and every current LRM has one.