TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging

Topological Data Analysis (TDA), particularly persistent homology (PH), provides powerful geometric insights into medical images—such as identifying loops, connected components, and shape characteristics—that standard pixel-level deep learning models often overlook. However, effectively applying TDA is difficult because it requires choosing from a wide variety of topological descriptors (e.g., persistence images, persistence landscapes), each with unique mathematical properties and hyperparameter requirements. Currently, this process is manual, expertise-dependent, and prone to trial-and-error.

TopoAgent is an LLM-based agentic framework designed to automate topology learning. It operates through a Perception--Reasoning--Action--Reflection (PRAR) loop, supported by 21 domain-specific tools and a dual-memory system.

• Perception: The agent analyzes the image's topological profile (e.g., PH statistics) and visual properties to identify the object type.
• Reasoning: It uses a distilled skill set to propose and determine the most suitable topological descriptor and its configuration, specifically designed to avoid anchoring bias by separating proposal from final determination.
• Action: It executes the chosen descriptor using pre-built tools.
• Reflection: It validates the quality of the resulting feature vector and can trigger retries if the output is suboptimal, recording diagnostic information in long-term memory to improve future performance.

To evaluate the framework, the authors introduced TopoBenchmark, a standardized collection of 113,182 samples across 26 medical imaging datasets. Experiments demonstrate that TopoAgent achieves 68.21% average balanced accuracy, significantly outperforming both fixed-descriptor baselines (58.89%) and general-purpose LLMs (46.25%). The framework's ability to adaptively determine descriptors per image—rather than relying on a single, fixed method—is the primary driver of its performance gains, particularly in complex morphologies like vessel trees and organ shapes.