ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models

Qwen3-4B with Ministral-3B-R, blue is the text ThinkFuse took from the auxiliary model

Method

1. Step 1

   Token uncertainty over fixed-length segments

   ThinkFuse monitors uncertainty at the segment level rather than relying directly on isolated token-level signals, which can be sensitive to local lexical or discourse fluctuations. Segments have a fixed length of \(T\) tokens. For each token of the segment \(s_k^p\) that the primary model \(M_p\) generates from the context \(c_k\), it computes normalized Shannon entropy over the top-\(r\) log-probability distribution:

   \[u_{k,i}^{p} = -\frac{\sum_{v \in \mathcal{V}_{k,i}} \tilde{p}_{k,i}(v) \log \tilde{p}_{k,i}(v)}{\log \lvert \mathcal{V}_{k,i} \rvert}\]

   Here \(\mathcal{V}_{k,i}\) is the set of the \(r\) highest-probability candidate tokens at position \(i\), and \(\tilde{p}_{k,i}\) is the distribution renormalized over that set.

2. Step 2

   Segment uncertainty with EWCA

   Exponentially Weighted Causal Aggregation (EWCA) turns the token uncertainties into one segment-level signal. Each token uncertainty is weighted by its relative position and by the uncertainty accumulated over the preceding tokens:

   \[w_{k,i} = \exp(\alpha \cdot i) \cdot \prod_{j<i} \bigl(1 + \beta \cdot u_{k,j}^{p}\bigr)\]

   where \(\alpha\) controls later-token emphasis and \(\beta\) controls uncertainty accumulation. The segment-level uncertainty of the \(k\)-th segment is

   \[U_k^p = \frac{\sum_{i=1}^{T_k} w_{k,i}\, u_{k,i}^p}{\sum_{i=1}^{T_k} w_{k,i}}\]

3. Step 3

   Adaptive threshold with a soft budget

   The same uncertainty value can have different implications depending on the recent reasoning trajectory. The mean uncertainty \(\mu_k\) and deviation scale \(\sigma_k\) of the trajectory are updated by an exponential moving average with decay factor \(\eta\), and they set the threshold

   \[\begin{aligned} \mu_k &= (1-\eta)\,\mu_{k-1} + \eta\, U_k^p \\ \sigma_k &= (1-\eta)\,\sigma_{k-1} + \eta\, \lvert U_k^p - \mu_{k-1} \rvert \\ \theta_k &= (\mu_{k-1} + \tau \cdot \sigma_{k-1}) \cdot (1 + \lambda \cdot R_{k-1}^2) \end{aligned}\]

   where \(\tau\) controls the deviation margin and \(R_{k-1}\) is the cumulative fusion ratio, scaled by the soft budget parameter \(\lambda\). The quadratic term raises the threshold as fusions accumulate, and fusion is triggered only when \(U_k^p \ge \theta_k\).

4. Step 4

   Trajectory compatibility scoring

   When the trigger activates, the auxiliary reasoning model \(M_a\) generates an alternative segment \(s_k^a\) from the same context. The primary model scores both candidates as a trajectory-compatibility scorer, \(\ell_k(s) = \mathrm{PPL}_{M_p}(s \mid c_k)\), and the selected segment is

   \[s_k^\star = \begin{cases} s_k^p, & U_k^p < \theta_k \\ \arg\min\limits_{s \in \{s_k^p,\, s_k^a\}} \ell_k(s), & U_k^p \ge \theta_k \end{cases}\]

   It is appended to the reasoning context, \(c_{k+1} = c_k \oplus s_k^\star\), and the primary model continues generation from the updated context until the reasoning trajectory reaches a terminal state.

Fusion Dynamics and Downstream Performance

The fusion methods differ in how many auxiliary reasoning tokens they fuse and in how this changes the length of the thinking stage. Cool-Fusion fuses the most auxiliary tokens, yet its thinking stage is the shortest on four of the five benchmarks. This suggests that excessive fusion can overwrite or prematurely redirect the primary model's reasoning trajectory, explaining its large performance drops. AdaFuse uses fewer auxiliary tokens but still shortens the thinking stage on reasoning-intensive benchmarks such as AIME24 and GPQA, indicating that simply limiting auxiliary usage is insufficient for preserving reasoning quality.

ThinkFuse uses auxiliary tokens much more sparsely than Cool-Fusion. Combined with its accuracy gains, this analysis suggests that effective test-time fusion requires selective and trajectory-aware intervention, rather than frequent or locally determined auxiliary fusion.

Ablation Study

BibTeX

@article{kang2026thinkfuse,
  title={ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models},
  author={Kang, Myunghoon and Lee, Jungseob and Seo, Jaehyung and Lim, Heuiseok},
  journal={arXiv preprint arXiv:2610.07803},
  year={2026}
}