Position Spaces and Graphs

In this paper, we introduce position graphs, a graph-based reasoning framework based on the formalization of position spaces. This framework utilizes two strict partial orders, representing horizontal and vertical alignment and precedence, to model the relative positions of discrete tokens. Unlike general qualitative spatial calculi, position graphs are constrained by a chain condition and compatibility requirements that focus on rows and columns. We provide a comprehensive theoretical analysis of this representation, beginning with a characterization of graph consistency. Conditions to ensure the consistency of position graphs are established. Furthermore, we investigate the computational complexity of structural pattern discovery, modeled as the induced subgraph isomorphism problem. We demonstrate that this problem remains NP-complete even within the restricted class of position graphs. While initially motivated by document processing, this work focuses on the underlying mathematical properties and algebraic consistency of position-based constraints, providing a formal logical layer that is independent of specific data extraction techniques.

Evolving Idea Graphs with Learnable Edits-and-Commits for Multi-Agent Scientific Ideation

LLM-empowered multi-agent systems offer new potential to accelerate scientific discovery by generating novel research ideas. However, existing methods typically coordinate agents through temporary texts, such as drafts or chat logs; it is difficult to pinpoint the weaknesses in the generated ideas and how the agents refine them. To this end, we introduce \textbf{Evolving Idea Graphs} (EIG), a graph-based multi-agent scientific ideation framework that can generate high-performance research ideas across various benchmark-native metrics, such as novelty, feasibility, and clarity. Instead of coordinating solely through texts, EIG represents a partially formed proposal as an evolving idea graph, where nodes capture scientific claims and edges encode relations (e.g., support and conflict), enabling unresolved weaknesses to remain identifiable throughout the idea evolving process. Specifically, a learned two-head controller operates over the evolving graph to guide the ideation: one head selects graph edits for agents to execute, while the other decides when the graph is ready for commit as final proposal synthesis. On AI Idea Bench 2025 and LiveIdeaBench, EIG outperforms all compared systems on both automatic benchmark scores and blind expert ratings. Ablations further show that explicit graph state provides the main performance gains, and learned edit-and-commit control adds consistent improvements.