Kun Zhou

Yifan Du, Kun Zhou, Yingqian Min et al.

We study how different Chain-of-Thought (CoT) designs affect the acquisition of the generalizable visual reasoning ability in vision-language models (VLMs). While CoT data, especially long or visual CoT such as "think with image", has been widely used to supervise intermediate reasoning, it remains unclear why specific CoT designs help and which ones truly support generalizable reasoning. To systematically evaluate this, we focus on a controlled maze-solving benchmark where reasoning rules are fully visual, difficulty can be tuned by grid size, and all the intermediate steps can be automatically generated. Using Qwen2.5-VL-7B under a standard SFT-then-RL pipeline, we compare three representative CoT formats: Language CoT, Grounding CoT (with spatial coordinate trajectories), and Visual CoT (with image manipulations). Our experiments reveal that visual and longer CoT mainly accelerate convergence but do not lift the final performance ceiling; concise CoT containing only essential grounding steps outperforms longer traces; and, strikingly, CoT retaining only the minimal grounding results generalizes best across different maze sizes. We further validate these insights on other vision-centric tasks. These findings highlight a "short is long" effect and provide practical guidance for constructing more generalizable SFT datasets for visual reasoning.

Siyuan Shen, Tianjia Shao, Kun Zhou et al.

While the superior performance of second-order optimization methods such as Newton's method is well known, they are hardly used in practice for deep learning because neither assembling the Hessian matrix nor calculating its inverse is feasible for large-scale problems. Existing second-order methods resort to various diagonal or low-rank approximations of the Hessian, which often fail to capture necessary curvature information to generate a substantial improvement. On the other hand, when training becomes batch-based (i.e., stochastic), noisy second-order information easily contaminates the training procedure unless expensive safeguard is employed. In this paper, we adopt a numerical algorithm for second-order neural network training. We tackle the practical obstacle of Hessian calculation by using the complex-step finite difference (CSFD) -- a numerical procedure adding an imaginary perturbation to the function for derivative computation. CSFD is highly robust, efficient, and accurate (as accurate as the analytic result). This method allows us to literally apply any known second-order optimization methods for deep learning training. Based on it, we design an effective Newton Krylov procedure. The key mechanism is to terminate the stochastic Krylov iteration as soon as a disturbing direction is found so that unnecessary computation can be avoided. During the optimization, we monitor the approximation error in the Taylor expansion to adjust the step size. This strategy combines advantages of line search and trust region methods making our method preserves good local and global convergency at the same time. We have tested our methods in various deep learning tasks. The experiments show that our method outperforms exiting methods, and it often converges one-order faster. We believe our method will inspire a wide-range of new algorithms for deep learning and numerical optimization.