RankGuide: Tensor-Rank-Guided Routing and Steering for Efficient Reasoning
Authors: Jiayi Tian, Yupeng Su, Ryan Solgi, Souvik Kundu, Zheng Zhang
Organizations: University of California, Santa Barbara · Intel Labs
Abstract
Large reasoning models (LRMs) enhance problem-solving capabilities by generating explicit multi-step chains of thought (CoT) reasoning; however, they incur substantial inference latency and computational overhead. To mitigate this issue, recent works have explored model collaboration paradigms, where small reasoning models (SRMs) generate intermediate reasoning steps to achieve a better accuracy--latency trade-off. Despite recent progress, effectively and efficiently detecting and mitigating SRM failures in collaborative systems remains a key challenge. To address this issue, we analyze SRM inference in both the generated text and hidden-state spaces, and identify three types of failure modes: \textit{overconfidence}, \textit{uncertainty}, and \textit{heavy revalidation}. Building on these insights, we propose \textbf{RankGuide}, a framework that improves the efficiency and effectiveness of SRM--LRM collaboration through tensor-rank-guided routing and steering. Specifically, RankGuide leverages a routing signal that incorporates tensor-rank signals derived from consecutive hidden states to detect when SRMs are likely to fail and selectively invoke LRMs. In addition, we introduce a tensor-rank-filtered steering vector extraction method to modulate the reasoning trajectory of SRMs, thereby improving their generation quality. By improving both routing and steering through tensor-rank signals, RankGuide enables SRM--LRM collaborative systems to achieve more efficient reasoning with fewer steps and improved accuracy. Experiments on multiple reasoning benchmarks demonstrate the efficacy of RankGuide in reducing latency by up to 1.75× compared to LRM, while maintaining competitive accuracy relative to prior methods.
Large Reasoning Models (LRMs) achieve strong performance on complex tasks through extended chains of thought but suffer from high inference latency due to autoregressive reasoning. Recent work explores using Small Reasoning Models (SRMs) to accelerate LRM inference. In this paper, we systematically characterize the capability boundaries of SRMs and identify three common types of reasoning risks: (1) path divergence, where SRMs lack the strategic ability to construct an initial plan, causing reasoning to deviate from the most probable path; (2) cognitive overload, where SRMs fail to solve particularly difficult steps; and (3) recovery inability, where SRMs lack robust self-reflection and error correction mechanisms. To address these challenges, we propose TrigReason, a trigger-based collaborative reasoning framework that replaces continuous polling with selective intervention. TrigReason delegates most reasoning to the SRM and activates LRM intervention only when necessary-during initial strategic planning (strategic priming trigger), upon detecting extraordinary overconfidence (cognitive offload trigger), or when reasoning falls into unproductive loops (intervention request trigger). The evaluation results on AIME24, AIME25, and GPQA-D indicate that TrigReason matches the accuracy of full LRMs and SpecReason, while offloading 1.70x - 4.79x more reasoning steps to SRMs. Under edge-cloud conditions, TrigReason reduces latency by 43.9% and API cost by 73.3%. Our code is available at \href{https://github.com/QQQ-yi/TrigReason}{https://github.com/QQQ-yi/TrigReason}
Implicit chain-of-thought (iCoT) methods aim to internalize reasoning in large language models, but often underperform explicit CoT prompting. We empirically find that hidden-state reasoning trajectories exhibit low-rank structure. Motivated by this observation, we propose a low-rank distillation framework that transfers reasoning by aligning teacher and student trajectories in a shared low-rank tensor subspace using first- and second-order statistics. The resulting formulation captures the global structure of reasoning while supporting a compact latent reasoning process. We evaluate the method across multiple model families, including LLaMA and Qwen, at different scales on mathematical reasoning benchmarks. Our approach consistently improves performance, especially on challenging multi-step tasks, approaching explicit CoT accuracy and outperforming prior iCoT distillation methods.
Chain-of-thought (CoT) reasoning improves the reasoning ability of large language models by introducing intermediate computation, but explicit rationales increase decoding length, latency, and context cost. Implicit CoT offers a more efficient alternative by moving intermediate reasoning into continuous latent states. However, latent reasoning can be unstable: successive latent states may become overly similar and collapse toward a shared dominant direction, reducing the diversity of the reasoning trajectory. In this work, we identify latent rank collapse and propose WIDER, a lightweight spectral regularizer for implicit CoT. During training, WIDER estimates the shared direction of each latent trajectory and penalizes projections onto this direction, encouraging latent states to span a broader representational subspace. The method is plug-and-play and leaves the backbone model, latent schedule, and inference-time decoding procedure unchanged. We further formulate this collapse as a geometric bottleneck in implicit reasoning, casting its mitigation as a training-time regularization problem rather than an inference-time decoding change. Extensive experiments show that WIDER improves matched implicit CoT baselines, while mechanistic analyses reveal higher effective rank, lower dominant-direction energy, and reduced redundancy among latent steps. These results highlight latent subspace utilization as an important factor for efficient continuous reasoning, providing a geometric perspective for analyzing and improving implicit CoT. Code is available at https://github.com/whitesweater/WIDER.