# The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity

arXiv: https://arxiv.org/abs/2506.06941 · HTML: https://mlsanity.com/paper/2506.06941/

## Key facts

- Cited by 302 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 34)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [Making Large Language Models Better Reasoners with Step-Aware Verifier](https://mlsanity.com/paper/2206.02336/) (2022)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Reasoning Models Can Be Effective Without Thinking](https://mlsanity.com/paper/2504.09858/) (2025)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!](https://mlsanity.com/paper/2502.07374/) (2025)
- [Optimizing Test-Time Compute via Meta Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.07572/) (2025)
- [Teaching Algorithmic Reasoning via In-context Learning](https://mlsanity.com/paper/2211.09066/) (2022)
- [LLMs Still Can't Plan; Can LRMs? A Preliminary Evaluation of OpenAI's o1 on PlanBench](https://mlsanity.com/paper/2409.13373/) (2024)
- [DeepSeek-R1 Thoughtology: Let's think about LLM Reasoning](https://mlsanity.com/paper/2504.07128/) (2025)
- [Alice in Wonderland: Simple Tasks Showing Complete Reasoning Breakdown in State-Of-the-Art Large Language Models](https://mlsanity.com/paper/2406.02061/) (2024)
- [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022)
- [When Thinking Fails: The Pitfalls of Reasoning for Instruction-Following in LLMs](https://mlsanity.com/paper/2505.11423/) (2025)
- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [The relationship between reasoning and performance in large language models--o3 (mini) thinks harder, not longer](https://mlsanity.com/paper/2502.15631/) (2025)

## Built on by (most cited first, 30 of 302)

- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Is Chain-of-Thought Reasoning of LLMs a Mirage? A Data Distribution Lens](https://mlsanity.com/paper/2508.01191/) (2025)
- [No Free Lunch: Rethinking Internal Feedback for LLM Reasoning](https://mlsanity.com/paper/2506.17219/) (2025)
- [Reinforcement Learning Meets Large Language Models: A Survey of Advancements and Applications Across the LLM Lifecycle](https://mlsanity.com/paper/2509.16679/) (2025)
- [RL Squeezes, SFT Expands: A Comparative Study of Reasoning LLMs](https://mlsanity.com/paper/2509.21128/) (2025)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)
- [The Open Proof Corpus: A Large-Scale Study of LLM-Generated Mathematical Proofs](https://mlsanity.com/paper/2506.21621/) (2025)
- [Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning](https://mlsanity.com/paper/2601.02902/) (2026)
- [Comment on The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.09250/) (2025)
- [Frontier LLMs Still Struggle with Simple Reasoning Tasks](https://mlsanity.com/paper/2507.07313/) (2025)
- [Large Language Model Reasoning Failures](https://mlsanity.com/paper/2602.06176/) (2026)
- [Variation in Verification: Understanding Verification Dynamics in Large Language Models](https://mlsanity.com/paper/2509.17995/) (2025)
- [CME-CAD: Heterogeneous Collaborative Multi-Expert Reinforcement Learning for CAD Code Generation](https://mlsanity.com/paper/2512.23333/) (2025)
- [Technological folie `a deux: Feedback Loops Between AI Chatbots and Mental Illness](https://mlsanity.com/paper/2507.19218/) (2025)
- [How Far Are AI Scientists from Changing the World?](https://mlsanity.com/paper/2507.23276/) (2025)
- [MEML-GRPO: Heterogeneous Multi-Expert Mutual Learning for RLVR Advancement](https://mlsanity.com/paper/2508.09670/) (2025)
- [NeuReasoner: Towards Explainable, Controllable, and Unified Reasoning via Mixture-of-Neurons](https://mlsanity.com/paper/2604.02972/) (2026)
- [Formalizing Learning from Language Feedback with Provable Guarantees](https://mlsanity.com/paper/2506.10341/) (2025)
- [Towards Reliable Benchmarking: A Contamination Free, Controllable Evaluation Framework for Multi-step LLM Function Calling](https://mlsanity.com/paper/2509.26553/) (2025)
- [Context Is What You Need: The Maximum Effective Context Window for Real World Limits of LLMs](https://mlsanity.com/paper/2509.21361/) (2025)
- [Position: The Hidden Costs and Measurement Gaps of Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2509.21882/) (2025)
- [A Unified Reasoning Framework for Holistic Zero-Shot Video Anomaly Analysis](https://mlsanity.com/paper/2511.00962/) (2025)
- [Code Like Humans: A Multi-Agent Solution for Medical Coding](https://mlsanity.com/paper/2509.05378/) (2025)
- [Epistemological Fault Lines Between Human and Artificial Intelligence](https://mlsanity.com/paper/2512.19466/) (2025)
- [Do LLMs Really Need 10+ Thoughts for "Find the Time 1000 Days Later"? Towards Structural Understanding of LLM Overthinking](https://mlsanity.com/paper/2510.07880/) (2025)
- [The Hot Mess of AI: How Does Misalignment Scale With Model Intelligence and Task Complexity?](https://mlsanity.com/paper/2601.23045/) (2026)
- [Recursive Multi-Agent Systems](https://mlsanity.com/paper/2604.25917/) (2026)
- [From Prompts to Constructs: A Dual-Validity Framework for Large Language Model Research in Psychology](https://mlsanity.com/paper/2506.16697/) (2025)

## Abstract (arXiv)

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.