True Thinking Score (TTS)

• True Thinking Score (TTS) is a metric that quantifies the causal influence of individual reasoning steps in chain-of-thought traces by comparing model confidence under perturbed and unperturbed conditions.
• Empirical analysis on competitive math datasets shows that most reasoning steps are decorative, with only a small fraction (around 6.4%) exerting significant causal impact on final predictions.
• TTS is computed using Monte Carlo sampling over various perturbations, offering insights into LLM interpretability, trustworthiness, and the potential for controlled model steering.

The True Thinking Score (TTS) quantifies the causal impact of individual reasoning steps in chain-of-thought (CoT) traces generated by LLMs. TTS is designed to distinguish between reasoning steps that genuinely influence the model's final prediction (“true-thinking” steps) and those that merely provide the appearance of reasoning without affecting the output (“decorative” steps). Empirical analysis with competitive math datasets reveals that most CoT steps are decorative, with only a sparse set of steps exerting meaningful control over LLM predictions. This differentiation has significant implications for interpretability, trustworthiness, computational efficiency, and model steering (Zhao et al., 28 Oct 2025).

1. Formal Definition of the True Thinking Score

The formalism treats each step $s$ in a CoT trace as a binary “treatment” variable $\mathbf{X} \in \{0, 1\}$, with $1$ denoting the unperturbed step and $0$ a perturbed version, typically created by altering every numeric token. The context $\mathcal{C}$—comprised of the preceding steps—can similarly be intact ($\mathbf{C} = 1$) or perturbed ($\mathbf{C} = 0$). The final model answer under the full, unperturbed CoT, $y^* = f(q, \mathcal{C}^\star)$, serves as the reference output.

The model’s confidence in $y^*$ following an intervention $(c, x)$ is denoted as $\mathbf{X} \in \{0, 1\}$0. Two context-conditioned average treatment effects (ATEs) are then defined:

• $\mathbf{X} \in \{0, 1\}$1 (necessity, under intact context)
• $\mathbf{X} \in \{0, 1\}$2 (sufficiency, under perturbed context)

The True Thinking Score for step $\mathbf{X} \in \{0, 1\}$3 takes the average of the magnitudes of these effects:

$\mathbf{X} \in \{0, 1\}$4

Thus, TTS directly quantifies the causal influence of step $\mathbf{X} \in \{0, 1\}$5 on the model's final prediction in both clean and corrupted contexts.

2. Algorithm for Computing TTS

TTS is estimated empirically using Monte Carlo sampling over perturbed and unperturbed step/context combinations, typically as follows:

$0$4

The EarlyExitModel computes the model’s predicted confidence (or probability) in $\mathbf{X} \in \{0, 1\}$6 for each intervention. The procedure is repeated for each step in the CoT trace.

3. Thresholds and Interpretation

TTS values lie in $\mathbf{X} \in \{0, 1\}$7, admitting a natural interpretation:

• TTS ≈ $\mathbf{X} \in \{0, 1\}$8: The step is decorative, with negligible causal impact on the final answer.
• TTS ≫ $\mathbf{X} \in \{0, 1\}$9: The step is a true-thinking step, actively contributing to the model's prediction.

In empirical studies, most reasoning steps have TTS values below $1$0. High-confidence true-thinking steps are identified with TTS $1$1. For “steering” experiments, steps with TTS $1$2 are treated as canonical true-thinking, while steps with TTS $1$3 are taken as purely decorative. Moreover, ablation results indicate that steering strength grows approximately linearly within the TTS range, and steps with TTS $1$4 are functionally equivalent to purely decorative steps.

4. Empirical Findings and Case Study

The distribution of TTS across CoT steps is highly long-tailed. For the Qwen-2.5 model evaluated on the AIME dataset:

• Mean TTS ≈ $1$5
• Only $1$6 of steps exceed TTS $1$7
• Only $1$8 of steps exceed TTS $1$9

Similar distributions are observed for other competitive math benchmarks (AMC, MATH). High-TTS steps are sparse and occur interleaved within the CoT sequence, with no strict positional regularity, though there is a slight tendency for true-thinking steps to be positioned later in the trace. Notably, self-verification (“aha moment”) steps sometimes exhibit extremely low TTS values (TTS $0$0; e.g., $0$1 of Qwen self-checks), revealing that explicit checking steps may be verbalized without actual model verification (Zhao et al., 28 Oct 2025).

5. True-Thinking vs. Decorative Steps: Conceptual and Practical Distinctions

High-TTS (true-thinking) steps are those whose perturbation—regardless of whether the prior context is intact (“necessity”) or corrupted (“sufficiency”)—meaningfully shifts the model’s confidence in its final answer. These steps are the causal drivers of model predictions.

In contrast, low-TTS (decorative) steps are effectively post hoc rationalizations or verbal flourishes. They appear in the output sequence but do not affect inference when perturbed, indicating a disconnect between externalized reasoning and the model's internal calculation.

A summary of these distinctions appears in the following table:

Step Type	TTS Value	Causal Impact on Output
True-thinking	$0$2	High
Decorative	$0$3	Negligible

The predominance of decorative steps challenges common assumptions about the faithfulness of CoT traces and has implications for interpretability, safety monitoring, and computational efficiency. A plausible implication is that surface rationales in LLM generation should not be treated as reliable evidence of internal calculation, and naive manipulation or inspection of rationales may be fundamentally misleading.

6. Model Steering and the TrueThinking Direction

Empirical results establish the existence of a “TrueThinking direction” in the latent space of LLMs. Manipulating the model along this direction can selectively activate or deactivate specific CoT steps when computing the final output. This steering can convert decorative steps (low TTS) into causally active true-thinking steps, or vice versa. Such capability points to the possibility of controlling the engagement of internal reasoning for select steps, with potential ramifications for model robustness and alignment (Zhao et al., 28 Oct 2025).

7. Limitations and Open Questions

TTS operates as a greedy probe and does not reconstruct the complete causal structure of multi-step reasoning. It is inherently dependent on the detectability of perturbations (e.g., models might sometimes recognize or ignore subtle numeric changes), posing interpretability challenges for the Average Treatment Effect. TTS provides only indirect evidence of internal computation; ground-truth reasoning steps remain unobservable in practice.

Thresholds like 0.7 or 0.9 for true-thinking identification are heuristic, may vary by model size or domain, and their universality is unconfirmed. TTS computation is computationally expensive, limiting its scalability, and results for larger proprietary LLMs are not yet available. An important open research direction is incorporating TTS into training objectives to better align externalized CoT traces with authentic model reasoning, thereby improving both interpretability and trustworthiness of future generations of LLMs (Zhao et al., 28 Oct 2025).