AI 中文总结
该研究提出两阶段师生训练仓本梯度流系统的方法，含74个振荡器的系统在MNIST、Fashion-MNIST上分别获96.711%、86.399%平均测试准确率，实现高精度有限时间推理。
AI 中文摘要
物理推理中的核心问题是，强约束动力系统能否通过自身的有限时间演化实现准确的输入-输出映射。我们在仓本（Kuramoto）相位网络中研究该问题，其确定性动力学形成输入条件梯度流，预测结果直接从输出振荡器读取。作为一种构造性训练方法，我们提出两阶段师生程序：首先将神经教师转换为显式相位轨迹，其终端振荡器激活值复现教师输出；再通过沿该规定路径匹配学生向量场来训练仓本（Kuramoto）参数。由于准确的教师强制路径匹配无法确保准确的自主推理，我们随后对自主有限时间展开进行求导，使其终端输出直接与神经目标对齐。该含74个振荡器的振荡器系统在MNIST上达到平均测试准确率96.711%，在Fashion-MNIST上达到86.399%。此能力在神经教师架构、匹配系统规模、热扰动及积分网格细化中均保持。综上，这些结果构造性证明，强约束的小型仓本（Kuramoto）梯度流系统可通过直接振荡器读取训练以实现高精度有限时间推理。
英文摘要
A central question in physical inference is whether strongly constrained dynamical systems can realize accurate input--output maps through their own finite-time evolution. We study this question in Kuramoto phase networks, whose deterministic dynamics form an input-conditioned gradient flow and whose predictions are read directly from output oscillators. As a constructive training approach, we develop a two-stage teacher--student procedure. A neural teacher is first converted into an explicit phase trajectory whose terminal oscillator activations reproduce the teacher outputs, and the Kuramoto parameters are trained by matching the student vector field along this prescribed path. Because accurate teacher-forced path matching does not ensure accurate autonomous inference, we then differentiate through the autonomous finite-time rollout and directly align its terminal output with the neural target. The resulting oscillator system, with $74$ oscillators, reaches mean test accuracies of $96.711\%$ on MNIST and $86.399\%$ on Fashion-MNIST. This capability persists across neural-teacher architectures, matched system sizes, thermal perturbations, and integration-grid refinement. Together, these results provide a constructive demonstration that a strongly constrained, small-sized Kuramoto gradient-flow system can be trained for high-accuracy finite-time inference through a direct oscillator readout.
