基于张量的混沌感知
Tensor-Based Chaotic Perception
AI总结：
本文提出基于张量的混沌感知方法，利用三阶张量映射输入为混沌序列，通过吸引子拓扑指纹实现对象识别，并在Sonar和KTH-TIPS2-a数据集上验证了类别区分与感知恒常性。
AI中文摘要：
符号可以为复杂的感觉信息提供紧凑的表示。在数学上，混沌吸引子可以为这类表示提供基础，其中对象身份编码在吸引子的拓扑组织中。在三维相空间中，这种组织可以通过不稳定周期轨道的链接矩阵来表征，该矩阵作为拓扑指纹。由于链接矩阵对可学习参数没有闭式依赖，我们学习生成目标吸引子的混沌序列，而不是直接优化该不变量；重建的吸引子随后通过其拓扑确定其不稳定周期轨道和链接矩阵。在本文中，我们提出一个三阶张量，将输入映射到生成相应混沌序列的连接矩阵。利用向量与其作为序列的序贯表示之间的对偶性，我们将输入提升到更高维空间并重新排序其分量，从而允许输入以序贯方式而非同时方式呈现。我们首先证明该表示能够区分Sonar数据集中的类别。然后，我们使用KTH-TIPS2-a数据集考察感知恒常性，其中类别内的颜色和纹理变化被映射到与同一拓扑吸引子类别相关联的不同混沌序列。结果表明，所提出的基于张量的映射能够在适应对象感觉实现变化的同时保持吸引子类别。
英文摘要：
Symbols can provide compact representations of complex sensory information. Mathematically, chaotic attractors can provide a basis for such representations, with object identity encoded in the topological organization of the attractor. In three-dimensional phase space, this organization can be characterized by the linking matrix of unstable periodic orbits, which serves as a topological fingerprint. Because the linking matrix has no closed-form dependence on the learnable parameters, we learn the chaotic series generating the target attractors rather than optimizing the invariant directly; the reconstructed attractor then determines its unstable periodic orbits and linking matrix through its topology. In this paper, we propose a third-order tensor that maps inputs to connection matrices that generate the corresponding chaotic series. Exploiting the duality between a vector and its sequential representation as a series, we lift inputs into a higher-dimensional space and reorder their components, allowing the input to be presented sequentially rather than simultaneously. We first demonstrate that this representation can discriminate between classes in the \href{https://archive.ics.uci.edu/dataset/151/connectionist+bench+sonar+mines+vs+rocks}{Sonar} dataset. We then examine perceptual constancy using the \href{https://www.csc.kth.se/cvap/databases/kth-tips/index.html}{KTH-TIPS2-a} dataset, where variations in color and texture within a class are mapped to distinct chaotic series associated with the same topological attractor class. The results demonstrate that the proposed tensor-based mapping can preserve attractor class while accommodating variations in the sensory realization of an object.
