Parallel thinking has emerged as a promising paradigm for reasoning, yet it imposes significant computational burdens. Existing efficiency methods primarily rely on local, per-trajectory signals and lack principled mechanisms to exploit global dynamics across parallel branches. We introduce 2D probing, an interface that exposes the width-depth dynamics of parallel thinking by periodically eliciting intermediate answers from all branches. Our analysis reveals three key insights: non-monotonic scaling across width-depth allocations, heterogeneous reasoning branch lengths, and early stabilization of global consensus. Guided by these insights, we introduce $\textbf{Parallel-Probe}$, a training-free controller designed to optimize online parallel thinking. Parallel-Probe employs consensus-based early stopping to regulate reasoning depth and deviation-based branch pruning to dynamically adjust width. Extensive experiments across three benchmarks and multiple models demonstrate that Parallel-Probe establishes a superior Pareto frontier for test-time scaling. Compared to standard majority voting, it reduces sequential tokens by up to $\textbf{35.8}$% and total token cost by over $\textbf{25.8}$% while maintaining competitive accuracy.
翻译:并行思维已成为一种有前景的推理范式,但其带来了显著的计算负担。现有的效率提升方法主要依赖于局部的、单轨迹信号,缺乏利用并行分支间全局动态的原理性机制。我们引入了二维探测,这是一种通过定期从所有分支获取中间答案来揭示并行思维宽度-深度动态的接口。我们的分析揭示了三个关键发现:宽度-深度分配的非单调缩放特性、推理分支长度的异质性,以及全局共识的早期稳定化。基于这些发现,我们提出了 $\textbf{Parallel-Probe}$,一个无需训练、旨在优化在线并行思维的控制器。Parallel-Probe 采用基于共识的早停机制来调控推理深度,并利用基于偏差的分支剪枝来动态调整宽度。在三个基准测试和多个模型上进行的大量实验表明,Parallel-Probe 为测试时缩放建立了更优的帕累托前沿。与标准多数投票方法相比,它在保持竞争力准确率的同时,将顺序令牌数量减少了高达 $\textbf{35.8}$%,总令牌成本降低了超过 $\textbf{25.8}$%。