提出用关系闭包构建稳定可迁移的结构化表示,解决表征学习中不变性与任务相关性的矛盾。
Structured Relational Representations
- 基于关系闭包定义抽象知识空间中的不变分区,作为核心表征单元
- 通过分区间连接器实现任务相关转换的部署,兼顾不变性与实用性
- 采用闭半环代数形式化基础,为关系型表征提供数学支撑
不变表征是表征学习的核心,但关键挑战仍在于发现既稳定又可迁移的不变性,同时不压制任务相关的信号。这引出了根本性问题:不变性应在何种抽象层次上定义?应刻画系统的哪些方面?环境解读依赖于抽象知识结构来理解当前状态,从而引发互动,成为学习与知识获取的关键驱动力。这种解读发生在更高阶的关系知识层面,因此我们主张不变结构必须是知识所居之处,具体表现为在抽象知识空间中由关系路径闭包定义的划分。这些划分构成核心不变表征,形成知识存储和学习的结构性基础。另一方面,分区间的连接器则支持编码任务相关转换的知识分区的部署。因此,不变划分构成了结构化表征的基础原语。我们基于闭半环——一种关系代数结构——形式化了不变划分的结构化关系表征的计算基础。
原文摘要 · Abstract (English)
Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring further inquiry, about the appropriate level of abstraction at which such invariants should be defined and which aspects of a system they should characterize. Interpretation of the environment relies on abstract knowledge structures to make sense of the current state, which leads to interactions, essential drivers of learning and knowledge acquisition. Interpretation operates at the level of higher-order relational knowledge; hence, we propose that invariant structures must be where knowledge resides, specifically as partitions defined by the closure of relational paths within an abstract knowledge space. These partitions serve as the core invariant representations, forming the structural substrate where knowledge is stored and learning occurs. On the other hand, inter-partition connectors enable the deployment of these knowledge partitions encoding task-relevant transitions. Thus, invariant partitions provide the foundational primitives of structured representation. We formalize the computational foundations for structured relational representations of the invariant partitions based on closed semiring, a relational algebraic structure.
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