AI 中文总结
本文提出TDIR算法，通过正交子空间分解历史照片的日期与内容分量，实现兼具时间结构与检索有效性的表示，在组合历史图像检索任务中表现出色。
AI 中文摘要
时间沿线性方向演变，而神经嵌入空间的几何结构本质上是多维的，往往杂乱无章且难以解释。原则上，人们可以将嵌入空间限制在单一时间维度上；然而，这种降维会牺牲下游任务的性能，因为一维嵌入无法保留足够的表达能力。本文探究是否有可能学习到既保留时间结构又对图像和物体检索有效的表示，并通过构建此类系统的数学基础回答了该问题。我们提出了时间可分解图像表示（Temporally Decomposable Image Representations, TDIR），这是一种表示学习算法，通过正交子空间将历史照片分解为独立的日期和内容分量。我们定义并证明了实现此类分解的条件，表征了当这些条件仅部分满足时产生的误差，并表明时间子空间与分类子空间之间的正交性会在联合优化中自然出现，无需显式施加。除几何特性外，TDIR还支持嵌入空间上的一类可传递操作：无需标签监督，即可将一张图像的时间信息提取并注入另一张图像的表示中。所有理论特性均在历史照片的组合图像检索这一现实问题中得到验证，其中查询同时通过标签或示例图像指定物体内容和目标时间段。这种真实场景为我们推导的命题提供了具体支撑，在保持日期估计和物体检索均具有竞争力性能的同时，提供了一种直观且可解释的方式来浏览照片档案。
英文摘要
While time evolves linearly, the geometry of neural embedding spaces is inherently multi-dimensional, often chaotic, and difficult to interpret. In principle, one could constrain an embedding space to a single temporal dimension; however, such a reduction would sacrifice performance on downstream tasks, as one-dimensional embeddings cannot retain sufficient expressive capacity. This paper asks whether it is possible to learn representations that preserve temporal structure while remaining effective for image and object retrieval, and answers this question by building the mathematical foundations of such a system. We propose Temporally Decomposable Image Representations (TDIR), a representation learning algorithm that decomposes historical photographs into separate date and content components through orthogonal subspaces. We define and prove the conditions under which such a decomposition is achievable, characterize the error incurred when those conditions are only partially met, and show that orthogonality between temporal and categorical subspaces emerges naturally from the joint optimization, without requiring it to be imposed explicitly. Beyond its geometric properties, TDIR enables a class of transitive operations on embedding spaces: the temporal information of one image can be extracted and injected into the representation of another, with no label supervision required. All theoretical properties are grounded and validated in the real-world problem of Composed Image Retrieval on historical photographs, where a query simultaneously specifies object content and a target time period, either through labels or through example images. This in-the-wild setting serves as a concrete backing for the propositions we derive, offering an intuitive and interpretable way to navigate photographic archives while maintaining competitive performance in both date estimation and object retrieval.
CommentsAccepted at BMVC2026
