Apple's Illusion of Thinking Paper, Explained

What The Illusion of Thinking Actually Tested

Apple's The Illusion of Thinking tested whether named language models could produce completely valid solutions to four controlled puzzles as the puzzles became more complex. It found a recurring pattern: non-thinking models could lead on easier cases, reasoning models gained an advantage in the middle, and both eventually approached zero accuracy in the reported high-complexity configurations.

That is an important result. It is not proof that artificial intelligence cannot reason. It is not a product benchmark. It is not a comparison between an unaided model and a production system with tools. The paper answers a narrower question about model behavior under a specific experimental design.

Start with the paper version

The first version appeared on June 7, 2025. The current arXiv record is version 3, posted November 20, 2025, and identified as the NeurIPS 2025 camera-ready paper with additional discussion in the appendix. Apple's research page points to the paper and preserves the official abstract.

Version matters because public criticism arrived between those dates. The current appendix addresses objections about output length, random sampling, impossible River Crossing configurations, explicit algorithms, and tool use. A June 2025 summary describes version 1. A current explainer should describe version 3 and show where the argument changed.

The researchers built four adjustable puzzle environments

The paper uses Tower of Hanoi, Checker Jumping, River Crossing, and Blocks World. Each puzzle has explicit rules, a known goal state, and a simulator that can check every proposed move.

Complexity changes by adding disks, checkers, actor-agent pairs, or blocks. The rules remain broadly stable while the required state tracking or sequence grows. That lets the researchers study behavior across a controlled range instead of comparing unrelated benchmark questions.

The simulator-based grading is a real strength. A fluent explanation cannot hide an illegal move. It also creates a strict success rule: one invalid move can make a long answer a failure even when much of the sequence is correct.

Which models were compared

Most matched comparisons use Claude 3.7 Sonnet with and without extended thinking and DeepSeek R1 versus DeepSeek V3. The authors chose those pairs because they could compare thinking and non-thinking variants and inspect the available reasoning traces. Final-answer experiments also include o3-mini configurations.

The current paper says each puzzle instance and complexity level used 25 samples per model after filtering for the requested response format. Claude and DeepSeek runs were allowed generation lengths up to 64,000 tokens.

Those details define the population. The paper does not test every reasoning model, every prompt, every sampling policy, every tool configuration, or every later model version.

The three reported regimes

The headline result is easier to understand as a curve than as a verdict.

flowchart LR
    A["Lower complexity"] --> B["Non-thinking models can match or lead"]
    B --> C["Intermediate complexity"]
    C --> D["Reasoning variants gain an advantage"]
    D --> E["Higher tested complexity"]
    E --> F["Both categories approach zero accuracy"]

The reasoning models delayed the reported collapse but did not avoid it. The authors also observed that thinking-token use increased with complexity and then fell near the point where accuracy collapsed. They interpreted that decline as evidence of an inference-time scaling limitation.

The paper goes beyond final accuracy by inspecting intermediate proposed solutions. In easier cases, a model sometimes found a correct path and then reasoned itself away from it. In harder cases, it could fixate on an early error and fail to recover.

These are observations about generated traces and outputs. Words such as "thinks," "knows," or "gives up" are metaphors unless the paper supplies a measurable operational definition.

Why Tower of Hanoi became controversial

Tower of Hanoi requires (2^n - 1) moves in the standard optimal solution. As disk count rises, an explicitly enumerated answer becomes long even though the recursive algorithm is familiar.

A. Lawsen's comment argues that the experiment mixed reasoning with output execution. It reports preliminary tests in which models generated a compact program for a larger puzzle rather than listing every move. The models performed well in that representation.

The current Apple paper answers that the first invalid move often appeared well before the output budget was exhausted. It also reports temperature-zero tests and says removing sampling did not remove the collapse.

A later replication, Rethinking the Illusion of Thinking, used stepwise prompting and agentic dialogue. It found that output constraints did not explain everything. Its tested models still struggled as Tower of Hanoi reached roughly eight disks.

These findings can coexist. Generating a recursive program, executing a long exact sequence, and maintaining state across an interactive workflow are different tasks. A model may succeed at one and fail at another.

River Crossing exposed a task-validity problem

The original experiment increased the number of actor-agent pairs while using a boat capacity of three for larger cases. Formal solvability constraints mean some configurations above five pairs cannot be solved with that capacity.

Scoring an impossible instance as a reasoning failure is invalid. Both Lawsen and the later replication raised this point. The current Apple appendix acknowledges that the dynamics change at six or more pairs and narrows its response to smaller configurations. The authors argue that model failures at three pairs still matter because that case has an eleven-move solution.

The later replication reports strong results on larger solvable configurations after changing the capacity. That qualifies the broad River Crossing story. It does not erase the earlier valid-case failures.

Tools change the unit of analysis

The original paper intentionally withholds tools because it wants to examine unaided model reasoning and sequential execution. The authors compare that choice to assessing a student's method rather than letting software supply an answer.

The agentic-gap comment asks a different question. It argues that tool access, iterative action, and feedback can reverse some text-only failures. That is relevant to products, where models often search, calculate, run code, query databases, and verify outputs.

Neither unit replaces the other. A model-only test can reveal a component weakness. A system test can show whether an engineered configuration compensates for it. A tool-assisted success does not prove that the base model never failed. A base-model failure does not reveal the end-to-end failure rate of a product that was never tested.

What the paper supports

The paper supports a claim that several frontier reasoning models in 2025 showed sharp, configuration-specific failures on controlled planning puzzles. It supports a claim that more thinking tokens did not reliably create more accurate answers. It supports closer study of state tracking, exact sequential execution, task structure, and reasoning traces.

The paper does not support a universal claim that models do not reason. It does not prove an inherent limit across every architecture. It does not establish the reliability of a tool-using agent or a deployed product. The responses do not prove the reverse.

The most useful lesson is methodological. Before repeating a research headline, identify the paper version, model, task, prompt, tools, budget, sample, filtering, grader, success rule, and inference. [[How to Read an AI Reasoning Paper Critically]] turns those fields into a reusable method. [[Model Capability Is Not System Capability]] shows how the unit changes when the model becomes one part of a product.

This explainer was freshly written from the preserved E072 transcript, the current paper, and formal response papers reviewed on July 28, 2026. AI assistance was used for research organization, drafting, and validation. Publication remains unauthorized.