Demystifying Reasoning Dynamics with Mutual Information: Thinking Tokens are Information Peaks in LLM Reasoning
Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM’s reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model’s prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as “Hmm”, “Wait” and “Therefore,” which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM’s reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM’s reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.
By undergoing reasoning-intensive training on foundational LLMs, recent large reasoning models (LRMs) such as OpenAI’s o1 [21], DeepSeek’s R1 [18], and QwQ [42] have demonstrated exceptional reasoning capabilities, significantly pushing the boundaries of complex problem-solving. However, despite recent advances, the mechanisms underlying these capabilities remain largely under-explored. The internal dynamics of the reasoning process, as well as the influence of each intermediate step on the final answer, are still largely a “black box.” While some research in the field of trustworthy AI suggests the existence of "critical tokens" that directly impact the safety of the LLM’s answers [60, 26, 33], a natural question arises: are there critical reasoning steps or intermediate states that significantly affect the final results in the reasoning process of LRMs?
In this paper, we explore this question from an information-theoretic [3, 24] perspective. Specifically, given a question, we dynamically calculate the mutual information (MI) between the LRM’s representation at each step of reasoning process and the golden answer (i.e., the ground-truth response), observing how the MI evolves. Interestingly, we find that certain steps’ representations exhibit a sudden and significant increase in MI with the golden answer. As shown in Figure 1(a), these representations with MI peaks are sparse and occur non-uniformly throughout the reasoning process.
This suggests that at certain crucial reasoning steps, LRMs’ representation becomes highly informative about the correct answer. Naturally, this raises a question: are these MI peaks potentially related to model’s reasoning performance? Theoretically, we provide preliminary insights into the MI peaks phenomenon, demonstrating that as the cumulative MI between the representations and the golden answer increases, the probability of LRM’s wrong prediction lowers. Furthermore, our experiments show that the base models corresponding to these LRMs (e.g., LLaMA-3.1-8B [16]), does not exhibit this MI Peaks phenomenon as clearly. These analyses suggest that the distinct MI peaks observed during LRM reasoning are potentially stemming from the reasoning-intensive training, and may hold a potential relationship with LRM’s advanced reasoning abilities.
This naturally leads to the question: what semantic roles do the representations at MI peaks play during reasoning? Intriguingly, we find that these representations with MI peaks predominantly correspond to tokens such as “Wait,” “Hmm,” “Therefore,” “So,” which typically express reflectiveness, self-correcting, or transitions, as shown in Figure 1(b). Here, we refer to these tokens with MI peaks as “thinking tokens”. Since these thinking tokens explicitly prompt the model to reflect and reason, and their representations carry enriched information with the golden answer, we hypothesize that these thinking tokens may play a critical role in the model’s reasoning ability. To validate this hypothesis, we suppress the generation of these thinking tokens and observe how the model’s reasoning performance changes. As shown in Figure 5, fully suppressing the generation of these thinking tokens significantly harms the model’s reasoning performance, while randomly suppressing the same number of tokens has little impact. This indicates that these thinking tokens are indeed crucial to LRM’s reasoning ability.
Finally, drawing insights from the above analyses, we propose to improve the reasoning performance of LRMs in two training-free ways.
By allowing the representations at MI Peaks to undergo multiple iterations within the model, we propose a method called Representation Recycling (RR). RR encourages the model to better exploit these informative representations. Experiments show that RR consistently improves the LRMs’ reasoning performance across several benchmarks. For instance, it improves the accuracy of DeepSeek-R1-Distill-LLaMA-8B by 20% relatively on AIME24.
Motivated by our analysis of thinking tokens, we propose Thinking Token based Test-time Scaling (TTTS). That is, when additional token budget remains, we force the model to continue reasoning by begin with the thinking tokens.
Experiments show that TTTS leads to steady performance improvements as the token budget increases compared to the original LRMs. These applications further demonstrate that our observations can offer new insights into enhancing the reasoning abilities of LRMs.