Structured Representation

2025-05-17

AI Summary

This work addresses a fundamental challenge in representation learning: how to construct stable, transferable invariant representations that preserve task relevance while explicitly specifying the appropriate abstraction level and capturing the underlying system’s essential structure. To this end, we propose a structured representation framework grounded in closed semiring algebra. We formally define invariants as partitions induced by relational path closure in an abstract knowledge space—establishing “partition” as the atomic unit of knowledge storage and learning. Additionally, we introduce cross-partition connectors to enable task-driven dynamic reasoning. The framework provides a rigorous computational foundation for invariant representation learning, unifying invariance and task adaptability. Theoretically, it reveals an intrinsic coupling mechanism between abstraction level and relational structure, thereby advancing the principled design of interpretable, generalizable representations.

Technology Category

• Machine Learning: Representation Learning
• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

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. We posit that interpretation operates at the level of higher-order relational knowledge; hence, 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 representation of the invariant partitions based on closed semiring, a relational algebraic structure.

Problem

• Identifying stable and transferable invariants without suppressing task-relevant signals
• Determining the abstraction level and system aspects for defining invariants
• Formalizing invariant partitions as structured representation primitives using relational algebra

Innovation

• Higher-order relational knowledge partitions
• Closed semiring algebraic structure
• Inter-partition connectors for transitions