# Action Conditioned Bisimulation For GUI Agent Memory

arXiv: https://arxiv.org/abs/2609.38778 · HTML: https://mlsanity.com/paper/2609.38778/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Agent memory systems, one of 16 directions in LLM agents and tool use.
- Builds on 14 of its 17 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Placed in

- LLM agents and tool use / [Agent memory systems](https://mlsanity.com/agents/agent-memory-systems/)

## Builds on (most cited first, 14 of 14)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023)
- [ExpeL: LLM Agents Are Experiential Learners](https://mlsanity.com/paper/2308.10144/) (2023)
- [UI-TARS: Pioneering Automated GUI Interaction with Native Agents](https://mlsanity.com/paper/2501.12326/) (2025)
- [Learning Invariant Representations for Reinforcement Learning without Reconstruction](https://mlsanity.com/paper/2006.10742/) (2020)
- [Agent Workflow Memory](https://mlsanity.com/paper/2409.07429/) (2024)
- [Reinforcement Learning on Web Interfaces Using Workflow-Guided Exploration](https://mlsanity.com/paper/1802.08802/) (2018)
- [Synapse: Trajectory-as-Exemplar Prompting with Memory for Computer Control](https://mlsanity.com/paper/2306.07863/) (2023)
- [The BrowserGym Ecosystem for Web Agent Research](https://mlsanity.com/paper/2412.05467/) (2024)
- [Scalable methods for computing state similarity in deterministic Markov Decision Processes](https://mlsanity.com/paper/1911.09291/) (2019)
- [AgentOccam: A Simple Yet Strong Baseline for LLM-Based Web Agents](https://mlsanity.com/paper/2410.13825/) (2024)
- [AutoGuide: Automated Generation and Selection of Context-Aware Guidelines for Large Language Model Agents](https://mlsanity.com/paper/2403.08978/) (2024)
- [Understanding Behavioral Metric Learning: A Large-Scale Study on Distracting Reinforcement Learning Environments](https://mlsanity.com/paper/2506.00563/) (2025)
- [Revisiting Bisimulation Metric for Robust Representations in Reinforcement Learning](https://mlsanity.com/paper/2507.18519/) (2025)

## Abstract (arXiv)

An agent that remembers what it did on a web page must decide when two pages count as the same. Memories built on observation similarity merge pages that look alike but behave differently, and GUIs are full of such pages: two tabs of one widget or two rows of one menu answer the same click differently. We define the merge rule as an action-conditioned bisimulation over the empirical predictive state graph a frozen agent fills as it acts. Two states merge only when their shared actions lead to agreeing outcomes and successor blocks under an affordance label. Observation similarity never enters the rule, and nothing is trained. It replaces the merge rule of an existing outcome-value memory, so a closed-loop comparison isolates it. On MiniWoB++ it raises success rate over a memoryless agent, while a control taking identical exploratory detours, the prior successor-representation merge, and the same criterion without action conditioning change nothing.