Reasoning Effort and Problem Complexity: A Scaling Analysis in LLMs (2503.15113v1)

Abstract: LLMs have demonstrated remarkable text generation capabilities, and recent advances in training paradigms have led to breakthroughs in their reasoning performance. In this work, we investigate how the reasoning effort of such models scales with problem complexity. We use the infinitely scalable Tents puzzle, which has a known linear-time solution, to analyze this scaling behavior. Our results show that reasoning effort scales with problem size, but only up to a critical problem complexity. Beyond this threshold, the reasoning effort does not continue to increase, and may even decrease. This observation highlights a critical limitation in the logical coherence of current LLMs as problem complexity increases, and underscores the need for strategies to improve reasoning scalability. Furthermore, our results reveal significant performance differences between current state-of-the-art reasoning models when faced with increasingly complex logical puzzles.

Scaling of Reasoning Effort in LLMs

The paper "Reasoning Effort and Problem Complexity: A Scaling Analysis in LLMs" aims to analyze how the reasoning capabilities of LLMs scale with problem complexity. This research investigates the scalability of reasoning effort using the Tents puzzle, a logic problem with a known linear-time solution, serving as a controlled testbed for algorithmic reasoning. The examination focused on understanding how computational demands, delineated as token usage, evolve with problem size.

The authors present compelling evidence that reasoning effort, indicated by the number of tokens generated, scales with problem size, but this relationship holds only up to a threshold of problem complexity. Beyond this critical threshold, reasoning effort does not increase as expected; in some cases, it even decreases. This phenomenon demonstrates a limitation in the logical coherence of state-of-the-art reasoning models, particularly when tasked with more complex problem sets. The analysis highlights significant discrepancies in performance across several advanced LLMs, such as Gemini 2.0 Flash Thinking, OpenAI o3-mini, DeepSeek R1, and Qwen/QwQ-32B-Preview.

The research methodically evaluates reasoning effort through key metrics—success rate and token usage—across different problem sizes. Notably, DeepSeek R1 and OpenAI o3-mini manifest linear reasoning effort scaling with problem size for puzzles they could solve. It is worth highlighting a critical observation related to OpenAI o3-mini: reasoning effort increases initially but drops past a problem size of 100, suggesting a "frustration effect" where logical complexity ceases to compel further reasoning effort in the model.

Furthermore, o3-mini demonstrates distinct problem-solving capabilities, successfully tackling the largest problem instances compared to its peers, affirming its capability to adjust reasoning effort up to a certain problem complexity. In contrast, Qwen/QwQ-32B-Preview underperforms at increasing problem sizes, failing with instances larger than 25, highlighting notable limitations within its architecture or training strategies. The paper also indicates that reasoning effort strategies using low, medium, and high strategies significantly impact models' utility and limitations in complex problem-solving scenarios. High reasoning effort enables solving larger puzzles, yet increases token usage even for smaller ones.

Concerning the paper's findings, LLMs show the potential to adapt reasoning effort to match problem complexity but within identifiable logical limits. The implications are significant for the AI research landscape. Understanding how LLMs scale reasoning capabilities can guide enhancements in structuring algorithms that optimize reasoning resources. It also underscores the necessity for new architectures or techniques that enhance reasoning coherence for complex task demands, potentially through length optimization of reasoning paths or refined model prompting.

This paper provides a foundational framework for future research into scaling reasoning in LLMs. The authors successfully isolate reasoning processes from actuation complexities, offering a clear view of current models' capabilities and limitations. It serves as a precursor for extended investigations into various logic puzzles with varying complexity profiles, leading to broader benchmarks for reasoning abilities.

Expanding scalability tests over a wide range of logic problems will allow further assessment of algorithmic complexity impacts on reasoning efforts, which could influence developments of new models or adjustments in current training methods. Understanding these dimensions ultimately contributes to the broader scope of enhancing AI's problem-solving capabilities, making scalable and efficient LLMs attainable goals for future AI advancements.