发表机构
School of Biomedical Engineering, Southern Medical University; Guangdong Provincial Key Laboratory of Medical Image Processing, Southern Medical University（南方医科大学生物医学工程学院; 南方医科大学广东省医学图像重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出双流形视角，构建KGFT轻量级模块，结合利用与探索模式及深度感知策略，在ResNet等架构的图像分类等任务上取得一致性能提升，验证了方法的通用性与有效性。
AI 中文摘要
深度表示学习主要关注特征如何在网络层间演化，却很大程度上忽略了网络参数中嵌入的结构化几何信息。我们提出双流形视角，其中每个卷积层包含两个耦合的几何空间：由卷积滤波器诱导的核流形（Kernel Manifold）和由中间特征表征构成的数据流形（Data Manifold）。由于这些流形共享同一通道空间，参数几何可提供互补的结构信息以引导特征演化。基于此见解，我们提出核引导特征变换（Kernel-Guided Feature Transform, KGFT），这是一个轻量级模块，它从核Gram矩阵中推导几何引导矩阵，并用其变换特征表征的协方差结构。与传统的对特征响应重新加权的注意力机制不同，KGFT通过将几何信息从核流形传递到数据流形，显式地重塑特征关系。为适配网络层级，我们进一步引入利用（Exploit）和探索（Explore）模式，结合深度感知调度策略与可学习的引导强度，自适应控制几何变换的贡献。该设计在浅层促进几何对齐，同时在深层鼓励特征多样性，且不会对表示学习施加过多约束。理论分析验证了所提变换的有效性，并刻画了其对特征协方差的影响。在基于CNN和Transformer的架构（包括ResNet、ViT和LLaMA-7B）上开展的大量实验，在图像分类和算术推理任务上均取得了一致的性能提升，验证了核引导双流形表示学习的通用性与有效性。代码将公开提供。
英文摘要
Deep representation learning has primarily focused on how features evolve across network layers, while largely overlooking the structured geometry embedded in network parameters. We introduce a dual-manifold perspective in which each convolutional layer contains two coupled geometric spaces: a Kernel Manifold induced by convolutional filters and a Data Manifold characterized by intermediate feature representations. Because these manifolds share the same channel space, parameter geometry can provide complementary structural information to guide feature evolution. Based on this insight, we propose Kernel-Guided Feature Transform (KGFT), a lightweight module that derives a geometric guidance matrix from the kernel Gram matrix and uses it to transform the covariance structure of feature representations. Unlike conventional attention mechanisms that reweight feature responses, KGFT explicitly reshapes feature relationships by transferring geometric information from the kernel manifold to the data manifold. To accommodate network hierarchy, we further introduce Exploit and Explore modes with a depth-aware scheduling strategy and a learnable guidance strength that adaptively controls the contribution of geometric transformation. This design promotes geometric alignment in shallow layers while encouraging feature diversity in deeper layers, without imposing excessive constraints on representation learning. Theoretical analysis establishes the validity of the proposed transformation and characterizes its effect on feature covariance. Extensive experiments across CNN- and Transformer-based architectures, including ResNet, ViT, and LLaMA-7B, demonstrate consistent improvements on image classification and arithmetic reasoning tasks, validating the generality and effectiveness of kernel-guided dual-manifold representation learning. Code will be publicly available.
