# T2T-LA: A Topology-to-Topology LLM Agent for Graph Learning with Neither Feature Access nor Task Knowledge

arXiv: https://arxiv.org/abs/2512.08964 · HTML: https://mlsanity.com/paper/2512.08964/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 30 Nov 2025.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 17 of 17)

- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [GPT4Graph: Can Large Language Models Understand Graph Structured Data ? An Empirical Evaluation and Benchmarking](https://mlsanity.com/paper/2305.15066/) (2023)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Graph Chain-of-Thought: Augmenting Large Language Models by Reasoning on Graphs](https://mlsanity.com/paper/2404.07103/) (2024)
- [Graph Barlow Twins: A self-supervised representation learning framework for graphs](https://mlsanity.com/paper/2106.02466/) (2021)
- [GraphEdit: Large Language Models for Graph Structure Learning](https://mlsanity.com/paper/2402.15183/) (2024)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [GAugLLM: Improving Graph Contrastive Learning for Text-Attributed Graphs with Large Language Models](https://mlsanity.com/paper/2406.11945/) (2024)
- [HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering](https://mlsanity.com/paper/2210.14813/) (2022)
- [HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering](https://mlsanity.com/paper/2108.07901/) (2021)
- [Towards Scalable Spectral Clustering via Spectrum-Preserving Sparsification](https://mlsanity.com/paper/1710.04584/) (2017)
- [HyperEF 2.0: Spectral Hypergraph Coarsening via Krylov Subspace Expansion and Resistance-based Local Clustering](https://mlsanity.com/paper/2511.06600/) (2025)

## Abstract (arXiv)

Graph learning aims to convert data into graph representations, which are fundamental to many problems in machine learning for CAD, where circuits, layouts, designs, and optimization states are often modeled as graph-structured objects. Existing graph learning methods usually rely on carefully designed graph construction rules, extensive parameter tuning, and sophisticated mathematical theory; moreover, achieving good performance often requires task-specific graph construction tailored to the downstream objective. In this work, we study whether a large language model (LLM) can reason about graph structure and infer a useful topology without observing the feature matrix, without knowing the downstream task, and without relying on any carefully designed graph construction algorithm or parameter tuning process. To this end, we propose T2T-LA, a Topology-to-Topology LLM Agent that receives no input other than a set of previously failed topologies and the scores assigned to them by a private scorer. The agent is not told what task or algorithm produces the scores, how these topologies are generated, or what the scores mean. Since none of the observed topologies is satisfactory, T2T-LA cannot simply imitate a good example. Instead, it is forced to infer hidden relationships between graph connectivity patterns and the observed scores, a capability that is particularly relevant to CAD scenarios where useful design structures may be difficult to specify manually. Experimental results show that T2T-LA can generate, in one shot, a graph topology that enables the downstream algorithm to produce a sufficiently good solution, suggesting a new LLM-driven direction for topology reasoning and graph representation learning in ML-for-CAD workflows.