MemCo: Memory-Centric Collaboration for Generalizing LLM Agents to Unseen Environments

# 1Introduction
Source: [https://arxiv.org/html/2610.07376](https://arxiv.org/html/2610.07376)
![[Uncaptioned image]](https://arxiv.org/html/2610.07376v1/ubc-logo-2018-crest-blue-cmyk.png)![[Uncaptioned image]](https://arxiv.org/html/2610.07376v1/logo/Vector-Logo-FullColour_Vertical.png)![[Uncaptioned image]](https://arxiv.org/html/2610.07376v1/logo/nvidia-logo-vert-blk.png)

MemCo:Memory\-Centric Collaboration for Generalizing LLM Agents to Unseen Environments

Xinting Liao1,2,†\\dagger, Siyan Liu1,†\\dagger, Rabab K\. Ward1, Holger R\. Roth3,\*, Xiaoxiao Li1,2,\*

1The University of British Columbia, Vancouver, BC, Canada

2Vector Institute, Toronto, ON, Canada

3NVIDIA, Santa Clara, CA, USA

†\\daggerEqual contribution\.

###### Abstract

Large language model \(LLM\) agents increasingly operate in interactive environments, where they need to make sequential decisions through observation, action, and feedback\. Although memory can help agents reuse experience, existing work designs memory in isolation, where collecting enough trajectories to populate it is expensive\. Existing shared\-memory approaches mitigate isolated experience by pooling episodic memories across tasks and environments\. However, retrieving shared memory is challenged by the granularity, where retrieved memories can be either too specific to preserve current grounding or too coarse to support the next action\. In this work, we proposeMemCo, a memory\-centric collaboration framework for generalizing LLM agents to unseen interactive environments\. It maintains complementary local and global memory spaces, preserving environment\-specific details locally while promoting transferable workflows induced from local trajectories to global memory\. During online interaction,MemCoroutes relevant local and global memories in terms of the agent’s current state and decision phase, enabling agents to reuse the experience of other agents without blindly transferring environment\-specific details\. Experiments on interactive decision\-making benchmarks show thatMemCoimproves task success and reduces redundant exploration compared with isolate\-memory and shared\-memory baselines\. Our codes are available at[https://github\.com/SYannL/nvdamas](https://github.com/SYannL/nvdamas)\.

## 1Introduction

Large language model \(LLM\) agents are increasingly applied to interact with environments, where they make decisions based on the current state and execute actions toward the task goal\. Retrieving episodic memories allows agents to reuse interaction experience at inference time\([Cao et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib5);[Fang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib4);[Liang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib6)\)\. Methods such as Reflexion\([Shinn et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib18)\), MemRL\([Zhang et al\., 2026b](https://arxiv.org/html/2610.07376#bib.bib11)\), and A\-Mem\([Xu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib33)\)improve how individual agents organize and reuse prior experience\. However, each agent still needs to collect useful trajectories through its own interactions, while limited experience may provide incomplete or unreliable guidance\([Kwon et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib15)\)\.

When multiple agents operate independently in different environments, experience acquired by one agent provides a natural reference for others\. As illustrated in Fig\.[1](https://arxiv.org/html/2610.07376#S1.F1)\(a\), agents can preserve experience from their own environments while sharing reusable experience that may support other agents, including those executing tasks in unseen environments, i\.e\., environments they have not previously interacted with\. This motivates us to ask:how can one agent’s experience help other agents and vice versa?Existing methods such as G\-Memory\([Zhang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib12)\), PlugMem\([Yang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib26)\), and MCMA\([Liang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib6)\)organize or transfer interaction experience across tasks or agents, demonstrating the potential of sharing experience\. As shown in Fig\.[1](https://arxiv.org/html/2610.07376#S1.F1)\(b,c\), G\-Memory improves over in\-context learning \(ICL\) and agents with isolated memory, yet still leaves room for improving task success and interaction efficiency, particularly on held\-out layouts\. Yet shared experience is not inherently useful across environments or decision contexts\. This raises a crucial challenge:how can shared experience be organized into useful memory and effectively used to support another agent’s current decision?

To address this challenge, we proposeMemCo, aMemory\-centricCollaboration framework with complementary local and global memory spaces\. As shown in Fig\.[2](https://arxiv.org/html/2610.07376#S3.F2),MemCocontains three main modules\. In each agent,local memory constructionconverts interaction trajectories into a local memory graph, preserving environment\-specific context while extracting experience patterns, actionable knowledge, and failure reflections\. To form useful shared memory,progressive global memory collaborationabstracts selected local records while retaining their applicability conditions, aggregates evidence across agents, and promotes sufficiently supported records to global memory\. To translate memory into effective decision guidance,query\-guided memory supportretrieves local and global memories according to the current decision context, filters incompatible guidance, and grounds shared experience in the current environment before composing memory support for the next decision\. Thus,MemCoenables agents to benefit from experience accumulated by others without blindly transferring source\-environment\-specific information, while preserving the local grounding required for task execution in unseen environments\.

![Refer to caption](https://arxiv.org/html/2610.07376v1/alfworld_performance_with_backbone_comparison.png)Figure 1:\(a\) Memory\-centric collaboration among independently acting agents: each agent preserves environment\-specific local experience while contributing reusable experience to global memory for use across environments\. \(b\) and \(c\) ALFWorld performance on familiar and held\-out layouts, respectively, with Qwen3\-32B\. Markers and error bars denote the mean and standard deviation\.Our main contributions are: \(1\) We introduce memory\-centric collaboration for agents interacting with environments, where experience accumulated across different environments can be shared to reduce repeated exploration and support task execution in unseen environments\. \(2\) We developMemCowith complementary local and global memory, turning shared experience into useful memory through evidence\-aware global promotion and into decision guidance related to execution state\. \(3\) Experiments across four benchmarks \(ALFWorld, PDDL, FEVER, and ScienceWorld\) and multiple LLM backbones show improved task performance with generally fewer interaction steps\.

## 2Related Work

Individual Experience and Agent Memory\.Early agent paradigms such as ReAct\([Yao et al\., 2022](https://arxiv.org/html/2610.07376#bib.bib16)\)rely on the current interaction context without persistent experience across trials\. Long\-term memory systems subsequently support persistent storage and retrieval across interactions\([Park et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib20);[Packer et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib23);[Zhong et al\., 2024](https://arxiv.org/html/2610.07376#bib.bib27);[Chhikara et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib22);[Wang and Chen, 2025](https://arxiv.org/html/2610.07376#bib.bib31);[Kwon et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib15)\)\. For interactive agents, prior work further turns trajectories into reflections, skills, procedural knowledge, or adaptive memory\([Shinn et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib18);[Wang et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib29);[Zhu et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib30);[Ding et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib17);[Fang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib4);[Cao et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib5);[Wu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib24);[Xu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib33);[Nan et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib25);[Zhang et al\., 2026b](https://arxiv.org/html/2610.07376#bib.bib11);[Zhang et al\., 2026a](https://arxiv.org/html/2610.07376#bib.bib13)\)\. These methods mainly improve how experience accumulated within an individual agent or memory system is represented and reused\.

Agent Collaboration through Shared Experience\.Beyond communication, agent selection, or execution\-time orchestration\([Wu et al\., 2024](https://arxiv.org/html/2610.07376#bib.bib14);[Jia et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib28)\), agents can collaborate by reusing experience acquired in prior interactions\. G\-Memory\([Zhang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib12)\)organizes cross\-trial collaboration memory within multi\-agent systems, while MATM\([Kim et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib38)\)supports population\-level sharing of producer\-agent trajectories\. Agent KB\([Tang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib39)\)enables structured experience reuse across heterogeneous agent frameworks, whereas MemCollab\([Chang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib40)\)and FedAgentKE\([Li et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib41)\)construct shared knowledge across different models or agent frameworks\. Collectively, these works demonstrate the value of sharing agent experience\. For agents interacting with different environments, however, shared experience is not uniformly useful: its value can depend on the receiving environment and current decision\.MemCoaddresses this setting by preserving local grounding while sharing reusable experience across agents\.

Constructing and Using Shared Memory\.Prior work studies how reusable experience can be represented as transferable skills, rules, workflows, or structured memories\([Ding et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib17);[Fang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib4);[Cao et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib5);[Wu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib24);[Xiang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib32);[Yang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib26);[Liang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib6);[Xia et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib3)\), as well as how stored memory can be selectively used at inference time\([Liu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib1);[Zhao et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib2)\)\.MemCojointly addresses both stages through evidence\-aware global promotion and query\-guided local and global memory use, while retaining the local grounding needed for execution\. A more comprehensive discussion is provided in Appendix[A](https://arxiv.org/html/2610.07376#A1)\.

## 3Methodology

### 3\.1Problem Formulation

![Refer to caption](https://arxiv.org/html/2610.07376v1/framework.png)Figure 2:Overview ofMemCo\.Local memory constructionorganizes environment\-specific interaction experience and extracts reusable records\.Progressive global memory collaborationaggregates evidence across agents and promotes supported reusable records to global memory\.Query\-guided memory supportgrounds and composes local and global memory for the current decision\.AmongNNagents, each agentiiindependently interacts with an environment using an LLM\-based policy modelπθ\\pi\_\{\\theta\}\. At steptt, the agent receives a task goal𝒈\\bm\{g\}, a state observation𝒙t\\bm\{x\}\_\{t\}, and an available action set𝒜t\\mathcal\{A\}\_\{t\}\. It selects an action𝒂t∈𝒜t\\bm\{a\}\_\{t\}\\in\\mathcal\{A\}\_\{t\}, and the environment returns feedback𝒇t\\bm\{f\}\_\{t\}indicating state progress, pause, failure, or success\. An episode trajectory isτ=\{\(𝒙t,𝒂t,𝒇t,𝒙t\+1\)\}t=1T\\tau=\\\{\(\\bm\{x\}\_\{t\},\\bm\{a\}\_\{t\},\\bm\{f\}\_\{t\},\\bm\{x\}\_\{t\+1\}\)\\\}\_\{t=1\}^\{T\}\. Agentiiaccumulates experience from environments it has interacted with, but is expected to execute tasks in*unseen environments*, i\.e\., environments it has not interacted with before evaluation\. The next action is selected using context𝒞t\\mathcal\{C\}\_\{t\}composed from memory available to the agent:

𝒂t∼πθ​\(𝒂t∣𝒈,𝒙t,𝒜t,𝒞t\)\.\\bm\{a\}\_\{t\}\\sim\\pi\_\{\\theta\}\(\\bm\{a\}\_\{t\}\\mid\\bm\{g\},\\bm\{x\}\_\{t\},\\mathcal\{A\}\_\{t\},\\mathcal\{C\}\_\{t\}\)\.\(1\)
We aim to organize experience accumulated across agents into reusable memory and selectively use it to support independent task execution in seen and unseen environments\.

### 3\.2Framework Overview

As in Fig\.[2](https://arxiv.org/html/2610.07376#S3.F2),MemComaintains local memoryℳil\\mathcal\{M\}\_\{i\}^\{l\}for environment\-specific experience and global memoryℳg\\mathcal\{M\}^\{g\}for reusable experience shared across agents\. The framework addresses two stages: constructing memory from accumulated experience and using it for the current decision\. For memory construction,local memory constructionorganizes each agent’s episodes into a graph and extracts patterns, actionable knowledge, and reflections, whileprogressive global memory collaborationabstracts selected shareable records, aggregates evidence across agents, and promotes supported records to global memory\. For decision\-time use,query\-guided memory supportselectively retrieves and composes relevant local and global memories into context𝒞t\\mathcal\{C\}\_\{t\}for the current decision\.

At steptt, agentiiselects an action according to Eq\.[1](https://arxiv.org/html/2610.07376#S3.E1)and uses environment feedback to form the next query, repeating this process until the episode terminates\. During memory acquisition, completed episodes update local memory and provide selected records and evidence for global promotion\. Subsequent queries can access the updated memories, enabling agents to benefit from one another’s experience while executing their own tasks independently\. The algorithm details are in Appendix[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)\.

### 3\.3Local Memory Construction

Local memory construction organizes an agent’s interaction episodes into a graph that connects related state–action transitions and their feedback across episodes\. The graph preserves the context in which individual experiences occur and exposes recurring structures across episodes, from whichMemCoinduces shareable records together with their supporting evidence\. This provides environment\-specific memory for the agent itself and candidate records for cross\-agent sharing\.

For each episodeτn\\tau\_\{n\}of agentii,MemCoconstructs an episodic graphGτn=\(Vτn,Eτn\)G\_\{\\tau\_\{n\}\}=\(V\_\{\\tau\_\{n\}\},E\_\{\\tau\_\{n\}\}\)whose nodesvtxv\_\{t\}^\{x\},vtav\_\{t\}^\{a\}, andvtfv\_\{t\}^\{f\}store normalized observations, parsed operations, and environment feedback, respectively\. Directed edges connect them as temporal transitions:vtx→vta→vtf→vt\+1xv\_\{t\}^\{x\}\\rightarrow v\_\{t\}^\{a\}\\rightarrow v\_\{t\}^\{f\}\\rightarrow v\_\{t\+1\}^\{x\}\. AcrossNiN\_\{i\}episodes of the same agent, nodes are matched when their types and normalized contents agree, and edges are matched when their relations and endpoints agree\. Merging these elements gives local memory graphGil←LocalMerge⁡\(\{Gτn\}n=1Ni\)G\_\{i\}^\{l\}\\leftarrow\\operatorname\{LocalMerge\}\(\\\{G\_\{\\tau\_\{n\}\}\\\}\_\{n=1\}^\{N\_\{i\}\}\)as detailed in Algo\.[B\.2\.2](https://arxiv.org/html/2610.07376#A2.SS2.SSS2)\. The graph and the record sets𝒫il,ℰil,\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},andℛil\\mathcal\{R\}\_\{i\}^\{l\}derived from the interaction episodes together form the local memory:

ℳil=\[Gil,𝒫il,ℰil,ℛil\],\\mathcal\{M\}\_\{i\}^\{l\}=\\left\[G\_\{i\}^\{l\},\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},\\mathcal\{R\}\_\{i\}^\{l\}\\right\],\(2\)where𝒫il\\mathcal\{P\}\_\{i\}^\{l\}contains pattern records of workflows, action preconditions, repairs, and failures,ℰil\\mathcal\{E\}\_\{i\}^\{l\}contains actionable\-knowledge records, andℛil\\mathcal\{R\}\_\{i\}^\{l\}contains concrete cases and reflection records\. We consolidate records of the same type and normalized content, retaining occurrence\-level statistics locally and per\-episode annotations for promotion\.

A local record is shareable whenp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}\. For each such recordpp,MemCorecords supporting, contradicting, and no\-progress evidence from its observed occurrences\. Before global promotion, annotations associated with the same record, source scope, and episode are deterministically reduced to at most one signed vote\. The resultingni\+​\(p\)n\_\{i\}^\{\+\}\(p\)andni−​\(p\)n\_\{i\}^\{\-\}\(p\)are the episode\-reduced supporting and contradicting counts used for promotion, whileni0​\(p\)n\_\{i\}^\{0\}\(p\)records episode\-level stall markers and is kept separate from the signed Wilson sample\. Detailed evidence assignment and reduction rules are provided in Appendix[B\.2](https://arxiv.org/html/2610.07376#A2.SS2)\.

MemCoupdates the graph after each completed episodeτnew\\tau\_\{\\mathrm\{new\}\}asGil←LocalMerge⁡\(\{Gil,Gτnew\}\)G\_\{i\}^\{l\}\\leftarrow\\operatorname\{LocalMerge\}\(\\\{G\_\{i\}^\{l\},G\_\{\\tau\_\{\\mathrm\{new\}\}\}\\\}\)and merges the newly extracted records and evidence into the existing𝒫il\\mathcal\{P\}\_\{i\}^\{l\},ℰil\\mathcal\{E\}\_\{i\}^\{l\}, andℛil\\mathcal\{R\}\_\{i\}^\{l\}\. BothGilG\_\{i\}^\{l\}andℛil\\mathcal\{R\}\_\{i\}^\{l\}remain local because they retain environment\-specific context\. Selected shareable records from𝒫il\\mathcal\{P\}\_\{i\}^\{l\}andℰil\\mathcal\{E\}\_\{i\}^\{l\}, together with their episode\-reduced promotion counts, are shared as they become available\.

### 3\.4Progressive Global Memory Collaboration

Progressive global memory collaboration turns selected local experience into reusable memory shared across agents\. Each agent abstracts and shares selected local records with their episode\-reduced promotion counts, while keeping fine\-grained trajectories, local memory graphs, and instance\-specific reflections local\.MemCoaggregates evidence across agents and promotes supported abstract records into global memory for subsequent queries\.

For a shareable local recordp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\},MemCoconstructs its abstract formp¯=Abstract⁡\(p\)\\bar\{p\}=\\operatorname\{Abstract\}\(p\)by replacing concrete entities where supported by the benchmark\-specific task\-role mapping and removing episode\- and scene\-specific anchors \(Algo\.[B\.3\.1](https://arxiv.org/html/2610.07376#A2.SS3.SSS1.Px1)\)\. This preserves the record type, applicability conditions, action sequence or relation, and outcome\. Records without removable environment\-specific anchors can retain their structured form, while records without a transferable global form remain local\. For example, a kettle’s current location remains local, while a fill\-then\-heat procedure can be shared using object and tool roles\.

Abstract records across agents share the same abstract key when their record types, applicability conditions, action sequences or relations, and outcomes match exactly \(Appendix[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)\)\. This key determines which local records contribute to the same abstract record\. The episode\-reduced counts of local records mapping to the same abstract record are aggregated as

nω\(p¯\)=∑i∈\[N\],p′:Abstract⁡\(p′\)=p¯niω\(p′\),ω∈\{\+,−\}\.n^\{\\omega\}\(\\bar\{p\}\)=\\sum\_\{\\begin\{subarray\}\{c\}i\\in\[N\],p^\{\\prime\}:\\operatorname\{Abstract\}\(p^\{\\prime\}\)=\\bar\{p\}\\end\{subarray\}\}n\_\{i\}^\{\\omega\}\(p^\{\\prime\}\),\\qquad\\omega\\in\\\{\+,\-\\\}\.\(3\)
Before promotion, fixed type\-specific filters exclude incomplete or uninformative abstract records\. Promotion further depends on how consistently the aggregated evidence supports each retained record\. Lets⁡\(p¯\)=n\+​\(p¯\)\+n−​\(p¯\)s\(\\bar\{p\}\)=n^\{\+\}\(\\bar\{p\}\)\+n^\{\-\}\(\\bar\{p\}\)denote the signed episode\-level evidence size andρ\+​\(p¯\)=n\+​\(p¯\)/max⁡\{s⁡\(p¯\),1\}\\rho^\{\+\}\(\\bar\{p\}\)=\\nicefrac\{\{n^\{\+\}\(\\bar\{p\}\)\}\}\{\{\\max\\\{s\(\\bar\{p\}\),1\\\}\}\}its empirical supporting rate for promotion\.

However, finite trajectories may provide sparse evidence, so a high empirical supporting rate can arise from only a few episode\-level votes\. We therefore use the one\-sided Wilson lower confidence bound ofρ\+​\(p¯\)\\rho^\{\+\}\(\\bar\{p\}\), i\.e\.,W⁡\(p¯\)W\(\\bar\{p\}\), as a finite\-evidence promotion score that accounts for both the empirical supporting rate and evidence size\([Wilson, 1927](https://arxiv.org/html/2610.07376#bib.bib34);[Brown et al\., 2001](https://arxiv.org/html/2610.07376#bib.bib35)\)\. Its statistical interpretation and assumptions are discussed in Appendix[D\.1](https://arxiv.org/html/2610.07376#A4.SS1)\. Letz=Φ−1​\(1−α\)z=\\Phi^\{\-1\}\(1\-\\alpha\), whereα∈\(0,1/2\)\\alpha\\in\(0,1/2\)is the one\-sided tail probability andΦ\\Phiis the standard normal cumulative distribution function\. We setW⁡\(p¯\)=0W\(\\bar\{p\}\)=0ifs⁡\(p¯\)=0s\(\\bar\{p\}\)=0; otherwise,

W⁡\(p¯\)=s⁡\(p¯\)​ρ\+​\(p¯\)\+z22−z​s⁡\(p¯\)​ρ\+​\(p¯\)​\(1−ρ\+​\(p¯\)\)\+z24s⁡\(p¯\)\+z2\.W\(\\bar\{p\}\)=\\frac\{s\(\\bar\{p\}\)\\rho^\{\+\}\(\\bar\{p\}\)\+\\frac\{z^\{2\}\}\{2\}\-z\\sqrt\{s\(\\bar\{p\}\)\\rho^\{\+\}\(\\bar\{p\}\)\(1\-\\rho^\{\+\}\(\\bar\{p\}\)\)\+\\frac\{z^\{2\}\}\{4\}\}\}\{s\(\\bar\{p\}\)\+z^\{2\}\}\.\(4\)
The following result characterizes the finite\-evidence correction\.

###### Theorem 3\.1\(Wilson finite\-evidence correction\)\.

Fors⁡\(p¯\)\>0s\(\\bar\{p\}\)\>0and fixedz\>0z\>0, the correctionϵW​\(p¯\)=ρ\+​\(p¯\)−W⁡\(p¯\)\\epsilon\_\{W\}\(\\bar\{p\}\)=\\rho^\{\+\}\(\\bar\{p\}\)\-W\(\\bar\{p\}\)satisfies

0≤ϵW​\(p¯\)=z​W​\(p¯\)​\(1−W​\(p¯\)\)s⁡\(p¯\)≤z2​s⁡\(p¯\)\.0\\leq\\epsilon\_\{W\}\(\\bar\{p\}\)=z\\sqrt\{\\frac\{W\(\\bar\{p\}\)\(1\-W\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\}\\leq\\frac\{z\}\{2\\sqrt\{s\(\\bar\{p\}\)\}\}\.\(5\)Thus, Wilson promotion discounts empirical support under finite evidence, with the maximal correction vanishing uniformly asO\(s\(p¯\)−1/2\)O\(s\(\\bar\{p\}\)^\{\-1/2\}\)\.

The proof and exact threshold and sample\-size implications are given in Appendix[D](https://arxiv.org/html/2610.07376#A4)\.

After the fixed type\-specific filters above, global memory is initialized asℳg=∅\\mathcal\{M\}^\{g\}=\\varnothingand updated by merging abstract records whose Wilson score passes thresholdλ\\lambda:

ℳg←GlobalMerge⁡\(ℳg,\{p¯:W⁡\(p¯\)≥λ\}\),0<λ<1\.\\mathcal\{M\}^\{g\}\\leftarrow\\operatorname\{GlobalMerge\}\\left\(\\mathcal\{M\}^\{g\},\\\{\\bar\{p\}:W\(\\bar\{p\}\)\\geq\\lambda\\\}\\right\),\\quad 0<\\lambda<1\.\(6\)GlobalMerge⁡\(⋅\)\\operatorname\{GlobalMerge\}\(\\cdot\)maintains one global record per abstract key, inserting new records or replacing the stored evidence with the latest aggregated counts \(Algo\.[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)\)\. New local records or updated evidence trigger reaggregation and reassessment of the affected abstract records\. Existing global records that no longer satisfy the preceding filters or threshold are removed\. These updates become available to subsequent queries, allowing each agent to use experience contributed by other agents while executing its own task independently\.

### 3\.5Query\-guided Memory Support

To translate stored experience into support for the next decision,MemCocombines environment\-specific local memory with reusable global memory accumulated across agents\. The selected memory must be relevant to the current decision and grounded in the environment the agent is currently interacting with\. At steptt, the query𝒒t=𝒬⁡\(𝒈,𝒙t,𝒜t,τ<t\)\\bm\{q\}\_\{t\}=\\mathcal\{Q\}\(\\bm\{g\},\\bm\{x\}\_\{t\},\\mathcal\{A\}\_\{t\},\\tau\_\{<t\}\)captures the goal, current observation, available actions, and task progress inferred from the preceding interaction historyτ<t\\tau\_\{<t\}\. This query guides both memory selection and composition\.

We retrieve two sets of memory entries from local and global sources separately:

𝒮tl=ℝ⁡\(𝒒t,ℳil,kl\),𝒮tg=ℝ⁡\(𝒒t,ℳg,kg\),\\mathcal\{S\}\_\{t\}^\{l\}=\\mathbb\{R\}\\left\(\\bm\{q\}\_\{t\},\\mathcal\{M\}\_\{i\}^\{l\},k^\{l\}\\right\),\\qquad\\mathcal\{S\}\_\{t\}^\{g\}=\\mathbb\{R\}\\left\(\\bm\{q\}\_\{t\},\\mathcal\{M\}^\{g\},k^\{g\}\\right\),\(7\)whereℝ⁡\(⋅\)\\mathbb\{R\}\(\\cdot\)is specified in Algo\.[B\.4\.3](https://arxiv.org/html/2610.07376#A2.SS4.SSS3)\. The local output𝒮tl\\mathcal\{S\}\_\{t\}^\{l\}is selected from records in𝒫il\\mathcal\{P\}\_\{i\}^\{l\},ℰil\\mathcal\{E\}\_\{i\}^\{l\}, andℛil\\mathcal\{R\}\_\{i\}^\{l\}, together with bounded transition entries from query\-matched states inGilG\_\{i\}^\{l\}\. These entries provide bounded local structural context for assessing workflow or rule applicability\. The global output𝒮tg\\mathcal\{S\}\_\{t\}^\{g\}is selected from the promoted records inℳg\\mathcal\{M\}^\{g\}\. Both outputs obey their respective cardinality caps\.

Before selection, each memory entrymmin the source\-specific retrieval pool is scored along three complementary dimensions: state, task phase, and goal:

r⁡\(m,𝒒t\)=rx​\(m,𝒒t\)\+rp​\(m,𝒒t\)\+rg​\(m,𝒒t\),r\(m,\\bm\{q\}\_\{t\}\)=r\_\{x\}\(m,\\bm\{q\}\_\{t\}\)\+r\_\{p\}\(m,\\bm\{q\}\_\{t\}\)\+r\_\{g\}\(m,\\bm\{q\}\_\{t\}\),\(8\)whererxr\_\{x\}measures consistency with the current state and available actions,rpr\_\{p\}measures compatibility with task progress, andrgr\_\{g\}measures the alignment of object, destination, or tool roles with the goal\.

Selection distinguishes applicability constraints from ranking preferences\. Entries are filtered when their required conditions contradict the current state or their actions cannot be matched to𝒜t\\mathcal\{A\}\_\{t\}when such matching is required\. The remaining entries are ranked using joint relevance, stored evidence, and action compatibility\. We reduce priority when stale local information and other soft conflicts occur\. Selection retains at mostklk^\{l\}local andkgk^\{g\}global entries\. When a retrieval pool exceeds its budget, strong matches along individual relevance dimensions are retained before the remaining positions are filled by rank, preserving complementary support within the limit \(Algo\.[B\.4\.3](https://arxiv.org/html/2610.07376#A2.SS4.SSS3)\)\.

Composition connects shared knowledge to its local use by grounding global records against𝒙t\\bm\{x\}\_\{t\}and𝒜t\\mathcal\{A\}\_\{t\}, with local evidence supplying environment\-specific context where available\. For example, a shared clean\-before\-place workflow specifies action order, while local evidence identifies a usable basin for cleaning the current object \(Appendix[B\.4\.5](https://arxiv.org/html/2610.07376#A2.SS4.SSS5)\)\. The selected entries are organized by their roles in the current decision:groundingprovides evidence for interpreting the current state, graph relations, and concrete action references;workflow guidanceprovides plans, procedures, and preconditions; andreflectionprovides failure patterns, repairs, and blocked actions\. For each support usage roleh∈ℋ=\{ground,workflow,reflection\}h\\in\\mathcal\{H\}=\\\{\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\\\}, let𝒰th\\mathcal\{U\}\_\{t\}^\{h\}contain the entries assigned to that role\. Role\-aware composition and query\-guided textual rendering produce the final memory context:

\{𝒰th\}h∈ℋ\\displaystyle\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}=Compose\(𝒮tl,𝒮tg∣𝒒t,𝒜t\),\\displaystyle=\\operatorname\{Compose\}\(\\mathcal\{S\}\_\{t\}^\{l\},\\mathcal\{S\}\_\{t\}^\{g\}\\mid\\bm\{q\}\_\{t\},\\mathcal\{A\}\_\{t\}\),\(9\)𝒞t\\displaystyle\\mathcal\{C\}\_\{t\}=Render⁡\(𝒒t,\{𝒰th\}h∈ℋ\)=\[ctground,ctworkflow,ctreflection\],\\displaystyle=\\operatorname\{Render\}\(\\bm\{q\}\_\{t\},\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\)=\[c\_\{t\}^\{\\mathrm\{ground\}\},c\_\{t\}^\{\\mathrm\{workflow\}\},c\_\{t\}^\{\\mathrm\{reflection\}\}\],\(10\)wherecthc\_\{t\}^\{h\}is the final textual context, functionsRender⁡\(⋅\)\\operatorname\{Render\}\(\\cdot\)andCompose⁡\(⋅\)\\operatorname\{Compose\}\(\\cdot\)are defined in Algo\.[B\.4\.4](https://arxiv.org/html/2610.07376#A2.SS4.SSS4)\-[B\.4\.4](https://arxiv.org/html/2610.07376#A2.SS4.SSS4)\. The resulting𝒞t\\mathcal\{C\}\_\{t\}conditions next\-action prediction in Eq\.[1](https://arxiv.org/html/2610.07376#S3.E1)\. After each action, new observations and feedback update the history and the next query, allowing memory support to follow task progress\.

## 4Experiments

Benchmarks\.We evaluateMemCoon four benchmarks that necessitate multi\-step decision\-making across episodes: \(1\)ALFWorld[Shridhar et al\. \(2020\)](https://arxiv.org/html/2610.07376#bib.bib7)aligns high\-level language instructions with low\-level robotic actions, challenging agents to reason and act within simulated environments; \(2\)PDDL[Ma et al\. \(2024\)](https://arxiv.org/html/2610.07376#bib.bib9)evaluates symbolic planning by requiring agents to generate valid action sequences that achieve specified goals under domain constraints; \(3\)FEVER[Thorne et al\. \(2018\)](https://arxiv.org/html/2610.07376#bib.bib10)evaluates large\-scale fact verification, requiring agents to retrieve and reason over external evidence to classify claims asSupports,Refutes, orNot Enough Info\(NEI\); and \(4\)ScienceWorld[Wang et al\. \(2022\)](https://arxiv.org/html/2610.07376#bib.bib8)is a comprehensive interactive benchmark for elementary science experiments\.

Baselines\.We compareMemCoagainst several representative baselines: \(1\)In\-Context Learning\(ICL\), using direct in\-context prompting without a persistent memory bank; \(2\)A\-Mem[Xu et al\. \(2025\)](https://arxiv.org/html/2610.07376#bib.bib33), a specialized long\-term memory architecture; \(3\)MemRL[Zhang et al\. \(2026b\)](https://arxiv.org/html/2610.07376#bib.bib11), which utilizes reinforcement learning to enable self\-evolution via a value\-based decision process; \(4\)MemSkill[Zhang et al\. \(2026a\)](https://arxiv.org/html/2610.07376#bib.bib13), which reframes memory management as a set of learnable natural\-language skills; and \(5\)G\-Memory[Zhang et al\. \(2025\)](https://arxiv.org/html/2610.07376#bib.bib12), a hierarchical graph\-based memory for multi\-agent systems that incorporates interactions and insights\.

Implementation Details\.We implementMemCousing AutoGen[Wu et al\. \(2024\)](https://arxiv.org/html/2610.07376#bib.bib14)and evaluate open\- and closed\-source models\. We useα=0\.05\\alpha=0\.05andλ=0\.35\\lambda=0\.35for promotion across all benchmarks\. Open\-source model inference is conducted on a single NVIDIA RTX PRO 6000 Blackwell GPU\. Both local and global retrievers use deterministic bounded selection with facet coverage and rank\-based filling, i\.e\.,kℓ=kg=5k^\{\\ell\}=k^\{g\}=5\. Unless otherwise specified, we report accuracy \(Acc\., %\) and the average number of interaction steps during evaluation\. For each benchmark, memory is constructed from designated source partitions and evaluated on disjoint tasks, with no evaluation trajectories used for memory construction\. We use one agent per source domain: four agents for ALFWorld and PDDL, two for FEVER, and ten for ScienceWorld\. Each agent is evaluated on the merged test set using its own frozen local memory and the shared global memory, covering both its acquisition domain and other environments\. ALFWorld’s Familiar and Held\-out splits additionally assess layout generalization\. Full partitioning and construction details are in Appendix[F](https://arxiv.org/html/2610.07376#A6)\.

### 4\.1Experimental Analysis

Table 1:Main results on FEVER, PDDL, and ALFWorld \(mean±\\pmstandard deviation over three runs\)\.Boldandunderlinedindicate the best and second\-best results within each backbone, respectively\.Overall Results\.Tab\.[1](https://arxiv.org/html/2610.07376#S4.T1)presents the main comparison across three benchmarks and three LLM backbones\. For ALFWorld, Familiar and Held\-out denote the officialvalid\_seenandvalid\_unseenlayout splits, respectively\. Counting FEVER, PDDL, and ALFWorld for each backbone,MemCoachieves the highest accuracy in 10 out of the 12 evaluation settings and requires the fewest interaction steps in 9 of them\. The performance gains are frequently accompanied by shorter trajectories, indicating thatMemCoimproves task outcomes without relying on additional environment exploration\.

The largest gains occur on ALFWorld: with Qwen3\-4B,MemCoimproves held\-out layout accuracy by 43\.47% and reduces interaction steps by 32\.10% relative to the runner\-up baseline \(MemSkill\)\. Gains with Qwen3\-32B show that benefits extend beyond weaker policy models\. Held\-out results further support transfer across layouts under this cross\-environment evaluation protocol\.MemCoalso leads FEVER in both accuracy and interaction efficiency under all three backbones\. With GPT\-4o\-mini, it improves accuracy by 12\.54% and reduces steps by 58\.45% relative to the runner\-up baseline\. It also improves PDDL accuracy with both Qwen models\. These PDDL gains do not always coincide with the fewest interaction steps, showing that success and interaction efficiency are not always aligned\. GPT\-4o\-mini reveals model dependence, butMemCostill achieves the best held\-out\-layout accuracy and shortest ALFWorld trajectories\. Furthermore, exact two\-sided Wilcoxon signed\-rank tests on the 12 matched configuration means indicate improvements over each baseline in accuracy and steps after Holm correction, under the stated block\-level assumptions\. Full statistics and effect sizes appear in Appendix[H](https://arxiv.org/html/2610.07376#A8)\.

Robustness across Additional LLM Backbones\.Tab\.[4](https://arxiv.org/html/2610.07376#S4.T4)examines whether the improvements persist across additional LLM families\. Across them,MemCoconsistently achieves the highest FEVER accuracy, improving over the runner\-up baseline by 10\.81%, 32\.82%, and 6\.98%, respectively\. These gains generally coincide with shorter trajectories\. On DeepSeek\-v4\-flash,MemCoimproves accuracy while requiring nearly the same number of steps as ICL\. However, G\-Memory did not complete successfully in this setting\. Together with Tab\.[1](https://arxiv.org/html/2610.07376#S4.T1), these results indicate that the benefit ofMemCogeneralizes across model families rather than depending on a particular backbone or model scale\.

\\captionsetup

skip=3pt

Table 2:Generalization across LLM backbones and to more complex tasks\.\\captionsetup

\[subtable\] font=scriptsize, labelfont=bf, textfont=bf, skip=1\.5pt

\{subtable\}

\[t\]0\.58

Table 3:FEVER across different LLM backbones\.\{subtable\}

\[t\]0\.40

Table 4:ScienceWorld with Qwen3\-32B\.Generalization to a More Complex Interactive Environment\.On ScienceWorld, Tab\.[4](https://arxiv.org/html/2610.07376#S4.T4)shows thatMemCoachieves the highest final success and score, and the auxiliary metrics further reveal a distinction between intermediate exploration and successful task completion\. G\-Memory achieves higher intermediate progress, while MemRL terminates in fewer steps, yet neither converts these advantages into comparable final success\. These results show that intermediate progress and fewer steps alone do not ensure successful completion, e\.g\.,MemCoachieves better final outcomes with a step count close to G\-Memory’s\.

### 4\.2Mechanism and Sensitivity Analysis

Following the memory lifecycle introduced in Section[3](https://arxiv.org/html/2610.07376#S3), we conduct controlled studies ofMemCo’s complementary memory scopes, evidence\-aware promotion, and query\-guided memory use\. Unless otherwise specified, all variants use the same frozen local\-memory snapshot and differ only in the component under evaluation\. These results represent controlled within\-snapshot comparisons rather than independent repetitions of the main experiments\.

Complementary Local and Global Memory\.Fig\.[4](https://arxiv.org/html/2610.07376#S4.F4)\(c\)\-\(d\) shows that Local\-only performs well on familiar layouts but degrades on held\-out layouts, whereas Global\-only narrows this gap\. Held\-out accuracy increases from89\.64%89\.64\\%with Local\-only to97\.14%97\.14\\%with Global\-only and97\.86%97\.86\\%with the full system\. Retaining local evidence also improves familiar\-layout accuracy over Global\-only, from96\.10%96\.10\\%to97\.40%97\.40\\%\. Their adaptive combination achieves the highest overall accuracy with shorter trajectories than either isolated scope, supporting complementary roles for local grounding and transferable global guidance with abstract rules and workflows\.

Figure 3:Memory efficiency and interaction\-budget sensitivity on ALFWorld with Qwen3\-32B\.Panels \(a\)–\(c\) report the global\-memory size, average retrieved memory entries, and memory\-prompt tokens per retrieval call\. Panel \(d\) comparesMemCoand ICL under different interaction budgets\.Figure 4:Sensitivity and component ablations on ALFWorld with Qwen3\-32B\.Panels \(a\)–\(b\) report familiar\-layout and held\-out\-layout performance under different Wilson promotion thresholdsλ\\lambda; bubble area represents the number of promoted global\-memory records\. Panels \(c\)–\(d\) compare memory\-scope, fixed\-concatenation, empirical\-promotion, and fullMemCovariants\.Finite\-Evidence\-Aware Progressive Collaboration\.We replace the Wilson lower confidence bound promotion ruleW⁡\(p¯\)W\(\\bar\{p\}\)with its counterpartρ\+​\(p¯\)\\rho^\{\+\}\(\\bar\{p\}\)while keepingλ=0\.35\\lambda=0\.35and the frozen local evidence fixed\. As shown in Fig\.[3](https://arxiv.org/html/2610.07376#S4.F3)\(a\)\-\(c\) and Fig\.[4](https://arxiv.org/html/2610.07376#S4.F4)\(c\)\-\(d\), Wilson promotion reduces the global bank from 736 to 426 records and improves familiar\- and held\-out\-layout accuracy by 2\.27 and 1\.43 percentage points, respectively, with fewer interaction steps\. Because the two variants inject nearly the same number of entries per decision, the difference is not due to prompt size alone\. This result is consistent with Wilson calibration favoring candidates supported by more reliable finite evidence\.

Efficiency under Restricted Interaction Budgets\.As shown in Fig\.[3](https://arxiv.org/html/2610.07376#S4.F3)\(d\),MemCoimproves when the interaction budget increases from 10 to 30 steps, but gains only marginally from 30 to 50 steps on both splits\. This early saturation suggests that a 30\-step budget is largely sufficient in this setting forMemCoto exploit its retrieved experience effectively\. In comparison, ICL improves more gradually as the budget increases and requires more interaction opportunities to approachMemCo’s performance\. By varying step limits,MemCoat 30 steps already exceeds ICL at 50 steps on both splits, supporting improved task completion under smaller execution budgets\.

Sensitivity to the Promotion Threshold\.Fig\.[4](https://arxiv.org/html/2610.07376#S4.F4)\(a\)\-\(b\) evaluates the robustness of the promotion threshold by varyingλ\\lambdawhile keeping the same frozen local\-memory snapshot and reconstructing only the global memory\. Increasingλ\\lambdareduces the global memory from 735 to 294 records, while accuracy and trajectory length remain insensitive\. Thresholdλ=0\.35\\lambda=0\.35reduces the number of global memory records by 42\.0% compared withλ=0\.25\\lambda=0\.25, while maintaining similar accuracy and interaction steps\.

Query\-Guided Memory Support\.The fixed\-concatenation variants in Fig\.[4](https://arxiv.org/html/2610.07376#S4.F4)\(c\)–\(d\) test whetherMemCobenefits merely from exposing the policy model to more stored experience\. As shown in Fig\.[4](https://arxiv.org/html/2610.07376#S4.F4)\(c\)–\(d\) and Fig\.[3](https://arxiv.org/html/2610.07376#S4.F3)\(b\)–\(c\), the results show the opposite: L5\+G5 trails fullMemCoby 10\.71 and 16\.07 percentage points on the Familiar and Held\-out Layout splits, respectively, despite injecting more memory\. These results indicate that the way retrieved records are selected and composed matters; simply concatenating more records does not recover the benefit of adaptive composition\. The full system uses less context while achieving higher accuracy and shorter trajectories\. This is consistent with less targeted memory leading irrelevant guidance into state\-specific decision making\.

Fig\.[5](https://arxiv.org/html/2610.07376#S4.F5)\(a\) examines the state, phase, and goal relevance facets\. Removing any one facet or retaining only a single facet lowers accuracy and increases interaction steps on both splits\. The all\-zero relevance control in Appendix[C](https://arxiv.org/html/2610.07376#A3)also underperforms the full method\. These within\-snapshot comparisons support the complementary, incremental contributions of the three facets to memory selection\. Fig\.[5](https://arxiv.org/html/2610.07376#S4.F5)\(b\) examines an orthogonal design choice: how memory relevance is scored\. It replacesMemCo’s explicit state, phase, and goal matching with cosine similarity or BM25\. Both alternatives underperform the full method in accuracy and efficiency, and neither consistently dominates across splits\. These comparisons support explicit state, phase, and goal matching over generic semantic or lexical similarity for selecting memory entries in the evaluated setting\.

Figure 5:Ablation of relevance scoring and retrieval on ALFWorld with Qwen3\-32B\.Bars show changes from fullMemCo, withΔ\\DeltaAcc\. measured in percentage points andΔ\\DeltaSteps in interactions\. In \(a\), for each relevance facetd∈\{x,p,g\}d\\in\\\{x,p,g\\\},−rd\-r\_\{d\}removes termrdr\_\{d\}, whereasrdr\_\{d\}retains only that term\. Panel \(b\) replacesMemCo’s retrieval strategy with cosine similarity or BM25\.Qualitative trajectory analysis in Appendix[I](https://arxiv.org/html/2610.07376#A9)further illustrates how this mechanism combines transferable global workflows with environment\-specific local grounding, while excluding incompatible source\-environment guidance in the shown cross\-environment trajectories\.

## 5Case Study: Adaptive Memory Support and Cross\-Environment Generalization

![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/casestudy4.png)Figure 6:Case study showcasing adaptive memory support and cross\-environment generalization\.\(a\) In the shown G\-Memory trajectory, the agent attempts placement before satisfying the cleanliness requirement\. \(b\)MemCouses local actionable knowledge to avoid the invalid placement in the same environment\. \(c\) In an unseen environment,MemCocombines a reusable global workflow with current\-environment grounding\.Figure[6](https://arxiv.org/html/2610.07376#S5.F6)illustrates how local situational grounding and global procedural workflows interact during online decision making\. For the task “Put a clean cloth in countertop”, G\-Memory attempts placement before satisfying the cleanliness requirement, whileMemCoretrieves the clean\-before\-store ordering together with local actionable knowledge and avoids the invalid move\. In the unseen bathroom environment, query\-guided selection excludes incompatible kitchen\-specific guidance and grounds the transferable workflow in the available basin and vanity, completing the task in six steps\.

## 6Conclusion

In this work, we introduced MemCo, a memory\-centric collaboration framework for generalizing LLM agents to unseen interactive environments\.MemCoconstructs local memory from each agent’s interaction trajectories, progressively promotes reusable abstract records to shared global memory, and adaptively selects and composes local and global evidence into a decision\-relevant memory context during online interaction\. Experiments across four heterogeneous benchmarks show thatMemCoimproves task success and generally reduces redundant exploration compared with memory\-free, isolated\-memory, and shared\-memory baselines\.

## Limitations

First, our framework relies on initial interaction traces to bootstrap the global workflow memory\. While a complete lack of early experience limits global guidance, this cold\-start characteristic is common to all retrieval\-based experience sharing systems\. Second, we evaluateMemCoexclusively on text\-based and symbolic interactive benchmarks\. Extending this hierarchical memory architecture to multimodal environments with visual observations remains an open direction for future work\.

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## Appendix Contents

## Appendix AExtended Related Work

Individual Experience and Agent Memory\.Generative Agents\([Park et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib20)\)stores observation streams and derives higher\-level reflections, while MemGPT\([Packer et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib23)\)manages information beyond the immediate context window\. MemoryBank\([Zhong et al\., 2024](https://arxiv.org/html/2610.07376#bib.bib27)\), Mem0\([Chhikara et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib22)\), and MIRIX\([Wang and Chen, 2025](https://arxiv.org/html/2610.07376#bib.bib31)\)study long\-term memory for conversational, personalized, or multimodal interactions, while MEMENTO\([Kwon et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib15)\)evaluates memory utilization for personalized embodied assistance\. Long contexts themselves do not guarantee effective reuse, since relevant information may become difficult to access and irrelevant context can distract reasoning\([Liu et al\., 2024](https://arxiv.org/html/2610.07376#bib.bib19);[Shi et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib21)\), motivating explicit storage and retrieval of decision\-relevant experience\. For interactive agents, a closely related line of work turns environment interaction into reusable decision support\. Reflexion\([Shinn et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib18)\)stores verbal reflections from previous trials; Voyager\([Wang et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib29)\)and GITM\([Zhu et al\., 2023](https://arxiv.org/html/2610.07376#bib.bib30)\)accumulate reusable skills or knowledge for open\-world interaction; and SkillGen\([Ding et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib17)\)extracts domain skills for sequential decision making\. Memp\([Fang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib4)\)studies procedural\-memory construction, retrieval, and update, while ReMe\([Cao et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib5)\)distills and refines procedural experience\. Meta\-Policy Reflexion\([Wu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib24)\)consolidates reflections into reusable rules, whereas A\-Mem\([Xu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib33)\), Nemori\([Nan et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib25)\), MemRL\([Zhang et al\., 2026b](https://arxiv.org/html/2610.07376#bib.bib11)\), and MemSkill\([Zhang et al\., 2026a](https://arxiv.org/html/2610.07376#bib.bib13)\)improve memory organization, episodic reuse, or memory\-management policies\. These methods primarily improve how experience accumulated within an individual agent or memory system is represented and reused\. When multiple agents interact with different environments, a complementary question is how experience acquired by one agent can become useful to others\.

Agent Collaboration through Shared Experience\.Multi\-agent collaboration is commonly realized through communication, agent selection, or execution\-time orchestration, e\.g\., AutoGen\([Wu et al\., 2024](https://arxiv.org/html/2610.07376#bib.bib14)\)and AgentStore\([Jia et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib28)\)\. Experience sharing provides a complementary form of collaboration in which experience acquired in prior interactions can support other agents later\. Recent work realizes such sharing through different representations\. G\-Memory\([Zhang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib12)\)organizes prior collaboration within a multi\-agent system through hierarchical interaction, query, and insight memory\. MATM\([Kim et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib38)\)supports population\-level storage and retrieval of producer\-agent trajectories for later use by consumer agents\. Agent KB\([Tang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib39)\)aggregates trajectories from heterogeneous agent frameworks into a structured knowledge base for cross\-domain planning and feedback\. MemCollab\([Chang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib40)\)distills shared constraints from trajectories generated by different backbone models, while FedAgentKE\([Li et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib41)\)evolves transferable semantic knowledge across heterogeneous agents through federated distillation and aggregation\. Collectively, these works demonstrate that experience can be reused beyond its original interaction and, in different settings, across agents, models, or agent frameworks\.MemCobuilds on this direction for independently acting agents that accumulate experience in different environments\. It keeps environment\-specific experience local while sharing reusable records across agents, so that cross\-agent experience can be used without collapsing the context in which it was acquired\.

Constructing and Using Shared Memory\.A first question is how reusable experience should be represented and retained\. Procedural\-memory methods show that trajectories can be distilled into more compact skills, scripts, rules, or workflows\([Ding et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib17);[Fang et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib4);[Cao et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib5);[Wu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib24)\)\. FlowSearcher\([Xiang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib32)\)synthesizes memory\-guided workflows from historical experience, while PlugMem\([Yang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib26)\)organizes episodic experience into a knowledge\-centric memory graph\. MCMA\([Liang et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib6)\)learns memory structures at different abstraction levels for selective transfer under distribution shift, and Memora\([Xia et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib3)\)explicitly balances abstraction against specificity\. Together, these studies highlight that transferable memory benefits from capturing reusable structure while retaining information needed for later application\. A second question is how stored memory should be used for the current decision\. RCR\-Router\([Liu et al\., 2025](https://arxiv.org/html/2610.07376#bib.bib1)\)dynamically selects structured memory subsets according to agent role and task stage, while ShardMemo\([Zhao et al\., 2026](https://arxiv.org/html/2610.07376#bib.bib2)\)uses masked mixture\-of\-experts routing over sharded memory\. These works highlight that the utility of stored memory also depends on context\-aware selection at inference time\.MemCoconnects these two stages in a single memory\-centric collaboration process: environment\-specific evidence is retained locally, reusable records are promoted using evidence accumulated across agents, and local and global memory are selected and grounded according to the receiving agent’s current state, progress, goal, and available actions\. These mechanisms jointly define the proposed collaboration framework rather than treating shared\-memory construction and decision\-time use as separate problems\.

## Appendix BAlgorithms and Implementation

### B\.1Algorithmic Overview

To improve reproducibility, this section summarizes the concrete procedures used byMemCo\. Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)constructs local graph memory and extracts pattern records from interaction trajectories\. Algorithm[B\.2\.2](https://arxiv.org/html/2610.07376#A2.SS2.SSS2)specifies the structural merge used to consolidate one agent’s episodic graphs\. Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)abstracts the shareable pattern and actionable records in𝒫il∪ℰil\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}, aggregates their evidence across agents, and rebuilds the Wilson\-promoted global snapshot\. Algorithm[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)separately specifies the exact\-key update of promoted records in global memory\. Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)retrieves and composes local and global memory according to the current decision context\.

Following the main text, local memory isℳil=\(Gil,𝒫il,ℰil,ℛil\)\\mathcal\{M\}\_\{i\}^\{l\}=\(G\_\{i\}^\{l\},\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},\\mathcal\{R\}\_\{i\}^\{l\}\)\. Herep∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}denotes a shareable local pattern or actionable record andp¯=Abstract⁡\(p\)\\bar\{p\}=\\operatorname\{Abstract\}\(p\)its abstract form\. The local graphGilG\_\{i\}^\{l\}and concrete cases and reflectionsℛil\\mathcal\{R\}\_\{i\}^\{l\}remain local\. At decision time,mmdenotes a memory entry, including a record or a bounded transition entry derived fromGilG\_\{i\}^\{l\}\. We useNNfor the number of agents andNiN\_\{i\}for agentii’s episodes\. The countersciω​\(p\)c\_\{i\}^\{\\omega\}\(p\)andniω​\(p\)n\_\{i\}^\{\\omega\}\(p\)denote occurrence\-level and episode\-reduced evidence, respectively;cthc\_\{t\}^\{h\}denotes rendered text for support rolehh\.

Table[15](https://arxiv.org/html/2610.07376#A5.T15)provides a unified reference for the memory components, their record types, local examples, and possible global counterparts\. Appendix[E](https://arxiv.org/html/2610.07376#A5)distinguishes these stored types from the support roles used during retrieval and composition\.

\{algorithm\*\}

\[\!htbp\]Local Memory Construction\{algorithmic\}\[1\]\\STATEInput:Agentii’s interaction trajectories\{τn\}n=1Ni\\\{\\tau\_\{n\}\\\}\_\{n=1\}^\{N\_\{i\}\}, whereτn=\{\(𝒙t,𝒂t,𝒇t,𝒙t\+1\)\}t=1Tn\\tau\_\{n\}=\\\{\(\\bm\{x\}\_\{t\},\\bm\{a\}\_\{t\},\\bm\{f\}\_\{t\},\\bm\{x\}\_\{t\+1\}\)\\\}\_\{t=1\}^\{T\_\{n\}\}\\STATEReturn:Local memoryℳil=\(Gil,𝒫il,ℰil,ℛil\)\\mathcal\{M\}\_\{i\}^\{l\}=\(G\_\{i\}^\{l\},\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},\\mathcal\{R\}\_\{i\}^\{l\}\)

\\FOR

each trajectoryτn\\tau\_\{n\}\\STATEInitialize an episodic graphGτn=\(Vτn,Eτn\)G\_\{\\tau\_\{n\}\}=\(V\_\{\\tau\_\{n\}\},E\_\{\\tau\_\{n\}\}\)\.\\FOReach transition\(𝒙t,𝒂t,𝒇t,𝒙t\+1\)∈τn\(\\bm\{x\}\_\{t\},\\bm\{a\}\_\{t\},\\bm\{f\}\_\{t\},\\bm\{x\}\_\{t\+1\}\)\\in\\tau\_\{n\}\\STATEAt the method level, associate state nodesvtx,vt\+1xv\_\{t\}^\{x\},v\_\{t\+1\}^\{x\}, action nodevtav\_\{t\}^\{a\}, and feedback nodevtfv\_\{t\}^\{f\}with the normalized observation, parsed operation, and observed outcome\.\\STATERepresent the interaction asvtx→vta→vtf→vt\+1xv\_\{t\}^\{x\}\\rightarrow v\_\{t\}^\{a\}\\rightarrow v\_\{t\}^\{f\}\\rightarrow v\_\{t\+1\}^\{x\}\. In the serialized graph, materialize thevtx→vta→vt\+1xv\_\{t\}^\{x\}\\rightarrow v\_\{t\}^\{a\}\\rightarrow v\_\{t\+1\}^\{x\}backbone and attach the information represented byvtfv\_\{t\}^\{f\}to the corresponding transition\.\\STATEStore the attached feedback through transition statistics and, when present, typed state\-delta, subgoal, and failure relations together with the record evidence ledger\.\\ENDFOR\\ENDFOR

\\STATE

Preserve the observed transition order within each episodic graph so that record induction follows the executed trajectory, while the merged graph accumulates recurring structure across episodes\.\\STATEConstruct the local graph asGil←LocalMerge⁡\(\{Gτn\}n=1Ni\)G\_\{i\}^\{l\}\\leftarrow\\operatorname\{LocalMerge\}\(\\\{G\_\{\\tau\_\{n\}\}\\\}\_\{n=1\}^\{N\_\{i\}\}\)using Algorithm[B\.2\.2](https://arxiv.org/html/2610.07376#A2.SS2.SSS2)\.\\STATEInitialize𝒫il←∅\\mathcal\{P\}\_\{i\}^\{l\}\\leftarrow\\emptyset,ℰil←∅\\mathcal\{E\}\_\{i\}^\{l\}\\leftarrow\\emptyset, andℛil←∅\\mathcal\{R\}\_\{i\}^\{l\}\\leftarrow\\emptyset\.

\\FOR

each trajectoryτn\\tau\_\{n\}and its episodic graphGτnG\_\{\\tau\_\{n\}\}\\STATEInduce workflows, preconditions, repairs, and failure\-pattern records from the observed episode structure and add them to𝒫il\\mathcal\{P\}\_\{i\}^\{l\}\.\\STATEExtract state–action–outcome relations intoℰil\\mathcal\{E\}\_\{i\}^\{l\}, and retain concrete examples, failure diagnoses, and recoveries inℛil\\mathcal\{R\}\_\{i\}^\{l\}\.\\ENDFOR

\\STATE

Within𝒫il\\mathcal\{P\}\_\{i\}^\{l\}andℰil\\mathcal\{E\}\_\{i\}^\{l\}, consolidate records with the same local record key and union their occurrence references\.

\\FOR

each shareable local recordp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}\\STATEInitialize occurrence countersci\+​\(p\),ci−​\(p\),ci0​\(p\)c\_\{i\}^\{\+\}\(p\),c\_\{i\}^\{\-\}\(p\),c\_\{i\}^\{0\}\(p\)to zero and an episode ledger𝒥i​\(p\)←∅\\mathcal\{J\}\_\{i\}\(p\)\\leftarrow\\emptyset\.\\FOReach observed occurrencejjofpp\\STATEAssign signed evidenceej​\(p\)∈\{\+,−\}e\_\{j\}\(p\)\\in\\\{\+,\-\\\}according to whether the observed feedback and transition support or contradict the relation encoded bypp\.\\IFej\(p\)=\+e\_\{j\}\(p\)=\+\\STATEci\+​\(p\)←ci\+​\(p\)\+1c\_\{i\}^\{\+\}\(p\)\\leftarrow c\_\{i\}^\{\+\}\(p\)\+1\.\\ELSE\\STATEci−​\(p\)←ci−​\(p\)\+1c\_\{i\}^\{\-\}\(p\)\\leftarrow c\_\{i\}^\{\-\}\(p\)\+1\.\\ENDIF\\IFoccurrencejjhas no observable state or task progress\\STATEci0​\(p\)←ci0​\(p\)\+1c\_\{i\}^\{0\}\(p\)\\leftarrow c\_\{i\}^\{0\}\(p\)\+1\.\\ENDIF\\STATEAdd the signed annotation and optional stall marker to𝒥i​\(p\)​\[scope⁡\(j\),episode⁡\(j\)\]\\mathcal\{J\}\_\{i\}\(p\)\[\\operatorname\{scope\}\(j\),\\operatorname\{episode\}\(j\)\]\.\\ENDFOR\\STATEReduce each annotated episode once: contradiction takes precedence for ordinary relations, while a stall marker supports an anti\-pattern\. Store the resulting promotion counts asni\+​\(p\),ni−​\(p\),ni0​\(p\)n\_\{i\}^\{\+\}\(p\),n\_\{i\}^\{\-\}\(p\),n\_\{i\}^\{0\}\(p\)\.\\ENDFOR

\\STATE

Returnℳil=\(Gil,𝒫il,ℰil,ℛil\)\\mathcal\{M\}\_\{i\}^\{l\}=\(G\_\{i\}^\{l\},\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},\\mathcal\{R\}\_\{i\}^\{l\}\)according to Eq\.[2](https://arxiv.org/html/2610.07376#S3.E2)\.\{algorithm\*\}\[\!htbp\]Progressive Memory Collaboration and Global Promotion\{algorithmic\}\[1\]\\STATEInput:Shareable local records\{𝒫il∪ℰil\}i=1N\\\{\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}\\\}\_\{i=1\}^\{N\}, promotion thresholdλ\\lambda, and one\-sided tail probabilityα\\alpha\\STATEReturn:Rebuilt global memoryℳg\\mathcal\{M\}^\{g\}\\STATEInitialize an empty global memoryℳg←∅\\mathcal\{M\}^\{g\}\\leftarrow\\emptyset\.\\FOReachp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}from each agentii\\STATEConstruct its abstract formp¯←Abstract⁡\(p\)\\bar\{p\}\\leftarrow\\operatorname\{Abstract\}\(p\)using Algorithm[B\.3\.1](https://arxiv.org/html/2610.07376#A2.SS3.SSS1.Px1); keeppplocal if no transferable abstract form is defined\.\\STATECompute its deterministic global record keyκg​\(p¯\)\\kappa\_\{g\}\(\\bar\{p\}\)\.\\STATEMergeppinto the aggregate forκg​\(p¯\)\\kappa\_\{g\}\(\\bar\{p\}\): sum its occurrence statistics, union its source provenance, and register its episode\-reduced countsni\+​\(p\)n\_\{i\}^\{\+\}\(p\),ni−​\(p\)n\_\{i\}^\{\-\}\(p\), andni0​\(p\)n\_\{i\}^\{0\}\(p\)\.\\ENDFOR\\FOReach abstract\-record aggregatep¯κ\\bar\{p\}\_\{\\kappa\}\\STATEAggregate the episode\-reduced counts according to Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)to obtainn\+​\(p¯κ\)n^\{\+\}\(\\bar\{p\}\_\{\\kappa\}\),n−​\(p¯κ\)n^\{\-\}\(\\bar\{p\}\_\{\\kappa\}\), and diagnosticn0​\(p¯κ\)n^\{0\}\(\\bar\{p\}\_\{\\kappa\}\); occurrence\-level counters are not used in the Wilson sample\.\\STATECompute the signed evidence sizes←n\+​\(p¯κ\)\+n−​\(p¯κ\)s\\leftarrow n^\{\+\}\(\\bar\{p\}\_\{\\kappa\}\)\+n^\{\-\}\(\\bar\{p\}\_\{\\kappa\}\)andρ\+←n\+​\(p¯κ\)/max⁡\(s,1\)\\rho^\{\+\}\\leftarrow n^\{\+\}\(\\bar\{p\}\_\{\\kappa\}\)/\\max\(s,1\)\.\\STATESetz←Φ−1​\(1−α\)z\\leftarrow\\Phi^\{\-1\}\(1\-\\alpha\)and setW←0W\\leftarrow 0ifs=0s=0; otherwise compute the one\-sided Wilson lower bound using Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)\.\\IFp¯κ\\bar\{p\}\_\{\\kappa\}passes its record\-type structural check, passes the applicable low\-information check, andW≥λW\\geq\\lambda\\STATEUpdate the rebuilt global memory asℳg←GlobalMerge⁡\(ℳg,\{p¯κ\}\)\\mathcal\{M\}^\{g\}\\leftarrow\\operatorname\{GlobalMerge\}\(\\mathcal\{M\}^\{g\},\\\{\\bar\{p\}\_\{\\kappa\}\\\}\)using Algorithm[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)\.\\ENDIF\\ENDFOR\\STATEAtomically publish the complete rebuilt snapshot for subsequent queries; do not change the memory context of a decision already in progress\.\\STATEReturnℳg\\mathcal\{M\}^\{g\}\.

\{algorithm\*\}

\[\!htbp\]Query\-guided Local–Global Memory Support\{algorithmic\}\[1\]\\STATEInput:Task goal𝒈\\bm\{g\}, observation𝒙t\\bm\{x\}\_\{t\}, available actions𝒜t\\mathcal\{A\}\_\{t\}, interaction historyτ<t\\tau\_\{<t\}, local memoryℳil\\mathcal\{M\}\_\{i\}^\{l\}, global memoryℳg\\mathcal\{M\}^\{g\}, and retrieval capskl,kgk^\{l\},k^\{g\}\\STATEReturn:Memory context𝒞t=\[ctground,ctworkflow,ctreflection\]\\mathcal\{C\}\_\{t\}=\[c\_\{t\}^\{\\mathrm\{ground\}\},c\_\{t\}^\{\\mathrm\{workflow\}\},c\_\{t\}^\{\\mathrm\{reflection\}\}\]

\\STATE

Construct the current decision query𝒒t←𝒬⁡\(𝒈,𝒙t,𝒜t,τ<t\)\\bm\{q\}\_\{t\}\\leftarrow\\mathcal\{Q\}\(\\bm\{g\},\\bm\{x\}\_\{t\},\\mathcal\{A\}\_\{t\},\\tau\_\{<t\}\)following the query definition in Section[3\.5](https://arxiv.org/html/2610.07376#S3.SS5)\.

\\STATE

Retrieve local memory using𝒮tl←ℝ⁡\(𝒒t,ℳil,kl\)\\mathcal\{S\}\_\{t\}^\{l\}\\leftarrow\\mathbb\{R\}\(\\bm\{q\}\_\{t\},\\mathcal\{M\}\_\{i\}^\{l\},k^\{l\}\)\.

\\STATE

Retrieve global memory using the same function:𝒮tg←ℝ⁡\(𝒒t,ℳg,kg\)\\mathcal\{S\}\_\{t\}^\{g\}\\leftarrow\\mathbb\{R\}\(\\bm\{q\}\_\{t\},\\mathcal\{M\}^\{g\},k^\{g\}\)\.

\\STATE

Use Algorithm[B\.4\.3](https://arxiv.org/html/2610.07376#A2.SS4.SSS3)for both retrieval calls, consistent with Eq\.[7](https://arxiv.org/html/2610.07376#S3.E7)\.

\\STATE

Defineℋ=\{ground,workflow,reflection\}\\mathcal\{H\}=\\\{\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\\\}\.

\\STATE

Compose role\-specific support as\{𝒰th\}h∈ℋ←Compose\(𝒮tl,𝒮tg∣𝒒t,𝒜t\)\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\\leftarrow\\operatorname\{Compose\}\\\!\\left\(\\mathcal\{S\}\_\{t\}^\{l\},\\mathcal\{S\}\_\{t\}^\{g\}\\mid\\bm\{q\}\_\{t\},\\mathcal\{A\}\_\{t\}\\right\)using Algorithm[B\.4\.4](https://arxiv.org/html/2610.07376#A2.SS4.SSS4)\.

\\STATE

Render the selected support as𝒞t←Render⁡\(𝒒t,\{𝒰th\}h∈ℋ\)\\mathcal\{C\}\_\{t\}\\leftarrow\\operatorname\{Render\}\\\!\\left\(\\bm\{q\}\_\{t\},\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\\right\)using Algorithm[B\.4\.4](https://arxiv.org/html/2610.07376#A2.SS4.SSS4)\.

\\STATE

Return𝒞t\\mathcal\{C\}\_\{t\}\.

### B\.2Local Graph Representation and Record Evidence

#### B\.2\.1Trajectory and Episodic Graph Representation

Given an interaction episode

τ=\{\(𝒙t,𝒂t,𝒇t,𝒙t\+1\)\}t=1T,\\tau=\\\{\(\\bm\{x\}\_\{t\},\\bm\{a\}\_\{t\},\\bm\{f\}\_\{t\},\\bm\{x\}\_\{t\+1\}\)\\\}\_\{t=1\}^\{T\},\(11\)MemConormalizes the interaction records and constructs an episodic graph

Gτ=\(Vτ,Eτ\)\.G\_\{\\tau\}=\(V\_\{\\tau\},E\_\{\\tau\}\)\.\(12\)
At the method level, state nodesvtxv\_\{t\}^\{x\}, action nodesvtav\_\{t\}^\{a\}, and feedback nodesvtfv\_\{t\}^\{f\}represent the normalized observation, parsed operation, and environment feedback, respectively\. Directed edges connect them according to the temporal interaction:vtx→vta→vtf→vt\+1xv\_\{t\}^\{x\}\\rightarrow v\_\{t\}^\{a\}\\rightarrow v\_\{t\}^\{f\}\\rightarrow v\_\{t\+1\}^\{x\}\. The feedback node records the observed outcome associated with the executed action, including state progress, failure, or task completion information\.

In the serialized implementation,vtfv\_\{t\}^\{f\}is not materialized as a separate stored node for every transition\. Instead, its information is attached to the corresponding transition through edge statistics and, when present, typed state\-delta, subgoal, and failure relations together with the record evidence ledger\. The stored graph backbone is thereforevtx→vta→vt\+1xv\_\{t\}^\{x\}\\rightarrow v\_\{t\}^\{a\}\\rightarrow v\_\{t\+1\}^\{x\}, while preserving the feedback information represented byvtfv\_\{t\}^\{f\}in the paper\-level episodic graph\. The structural merge below operates on this stored realization of the same episodic graph; we retain the notationGτG\_\{\\tau\}because the feedback semantics above are preserved in its attached transition fields\.

Record induction remains anchored to the observed order of each completed episode and its temporary episodic graph\. The persistent merged graph described next is a structural index: it does not retain per\-edge episode membership and is not used to reconstruct an episode\-consistent trajectory after merging\.

#### B\.2\.2Structural Matching and Local Graph Merge

To connect related experience across episodes,MemCocompares graph elements using structural equality after their contents have been normalized\. Two nodes are considered equivalent only when both their node types and normalized contents match, while two edges are equivalent only when they share the same relation and equivalent endpoints\. Matched elements accumulate their statistics\. In the serialized representation, normalized feedback associated with a transition is compared through its attached transition payload and typed relations rather than through a separately stored feedback node\. The local memory records the completed episode identifiers at store level, but not a membership list on every merged node or edge\. For each agentii, equivalent graph elements across its episodic trajectories are aligned to construct

Gil=LocalMerge⁡\(\{Gτn\}n=1Ni\)\.G\_\{i\}^\{l\}=\\operatorname\{LocalMerge\}\\left\(\\\{G\_\{\\tau\_\{n\}\}\\\}\_\{n=1\}^\{N\_\{i\}\}\\right\)\.\(13\)The resulting graph therefore provides a connected aggregate structural index across trajectories rather than a collection of isolated action records\. An adjacent path in this merged index is not asserted to be a newly observed single\-episode trajectory\. This operation acts on graph nodes and edges before abstraction; it is not the global exact\-key record update in Algorithm[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)\.

\{algorithm\*\}

\[\!htbp\]LocalMerge\\operatorname\{LocalMerge\}: Structural Merge of Episodic Graphs\{algorithmic\}\[1\]\\STATEInput:Episodic graphs\{Gτn=\(Vτn,Eτn\)\}n=1Ni\\\{G\_\{\\tau\_\{n\}\}=\(V\_\{\\tau\_\{n\}\},E\_\{\\tau\_\{n\}\}\)\\\}\_\{n=1\}^\{N\_\{i\}\}for agentii\\STATEReturn:Merged local graphGil=\(V⁡\(Gil\),E⁡\(Gil\)\)G\_\{i\}^\{l\}=\(V\(G\_\{i\}^\{l\}\),E\(G\_\{i\}^\{l\}\)\)\\STATEInitializeV⁡\(Gil\)←∅V\(G\_\{i\}^\{l\}\)\\leftarrow\\emptyset,E⁡\(Gil\)←∅E\(G\_\{i\}^\{l\}\)\\leftarrow\\emptyset, and an empty map from episodic node identifiers to matching local nodes\.\\FOReach episodic graphGτnG\_\{\\tau\_\{n\}\}\\FOReach nodev∈Vτnv\\in V\_\{\\tau\_\{n\}\}\\STATEForm the local node keyκv​\(v\)=\(type⁡\(v\),Normalize⁡\(content⁡\(v\)\)\)\\kappa\_\{v\}\(v\)=\(\\operatorname\{type\}\(v\),\\operatorname\{Normalize\}\(\\operatorname\{content\}\(v\)\)\)\.\\IFno node inV⁡\(Gil\)V\(G\_\{i\}^\{l\}\)has keyκv​\(v\)\\kappa\_\{v\}\(v\)\\STATEInsert a local copy ofvvintoV⁡\(Gil\)V\(G\_\{i\}^\{l\}\)\.\\ELSE\\STATEReuse the matching local node and accumulate node statistics\.\\ENDIF\\STATEMap the episodic identifier ofvvto that local node\.\\ENDFOR\\FOReach edgee=\(u,η,v\)∈Eτne=\(u,\\eta,v\)\\in E\_\{\\tau\_\{n\}\}\\STATEResolveuuandvvto their matching local nodes and formκe​\(e\)=\(κv​\(u\),η,κv​\(v\)\)\\kappa\_\{e\}\(e\)=\(\\kappa\_\{v\}\(u\),\\eta,\\kappa\_\{v\}\(v\)\)\.\\IFno edge inE⁡\(Gil\)E\(G\_\{i\}^\{l\}\)has keyκe​\(e\)\\kappa\_\{e\}\(e\)\\STATEInsert a local edge with relationη\\etaintoE⁡\(Gil\)E\(G\_\{i\}^\{l\}\)\.\\ELSE\\STATEReuse the matching edge and accumulate edge statistics; retain the payload of the stored signature entry\.\\ENDIF\\ENDFOR\\ENDFOR\\STATEReturnGil=\(V⁡\(Gil\),E⁡\(Gil\)\)G\_\{i\}^\{l\}=\(V\(G\_\{i\}^\{l\}\),E\(G\_\{i\}^\{l\}\)\)\.

#### B\.2\.3Type\-Specific Record Extraction

The local graph exposes recurring structures across episodes, from whichMemCoinduces reusable records\. Record induction remains anchored to the observed order of the contributing episodes, so it does not mine arbitrary synthetic paths from the merged graph\. Recurring records with the same normalized content are consolidated so that repeated observations contribute evidence to the same local entry\.

Specifically, aworkflowpattern captures an ordered sequence of progress phases and associated operations; apreconditionpattern records a temporal transition associated with successful progress; arepairpattern records a successful action that resolves an observed failure; and afailurepattern records an action associated with a failure or no\-progress outcome\. Here, a precondition is an experience\-derived condition for progress, not a claim that a logically necessary or sufficient operator precondition has been proved\.

The other local components in Eq\.[2](https://arxiv.org/html/2610.07376#S3.E2)retain complementary information\. The graphGilG\_\{i\}^\{l\}preserves connected state–action–feedback experience across episodes\. Actionable knowledgeℰil\\mathcal\{E\}\_\{i\}^\{l\}stores state–action–outcome relations that can ground an executable action, while concrete cases and reflectionsℛil\\mathcal\{R\}\_\{i\}^\{l\}retain episode\-specific examples, failure diagnoses, and recoveries\. These components may describe related transitions but serve different purposes: patterns summarize recurring structure, actionable knowledge supports a concrete decision, andℛil\\mathcal\{R\}\_\{i\}^\{l\}keeps instance\-level context\.

Extracted records with the same record type and normalized content are consolidated into a single entry in𝒫il\\mathcal\{P\}\_\{i\}^\{l\}; actionable records inℰil\\mathcal\{E\}\_\{i\}^\{l\}are consolidated analogously by their local normalized keys\. This record consolidation is distinct from graph\-element merging and from global promotion\. Only selected records in𝒫il∪ℰil\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}are considered for sharing;GilG\_\{i\}^\{l\}andℛil\\mathcal\{R\}\_\{i\}^\{l\}remain local\. Table[15](https://arxiv.org/html/2610.07376#A5.T15)summarizes the corresponding memory types and sharing scope\.

#### B\.2\.4Record Evidence and Local Counts

Evidence is defined relative to the relation encoded by each shareable recordp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}\. A record may be observed multiple times within one episode or across different episodes\. For itsjj\-th occurrence, we assign a signed evidence label

ej​\(p\)∈\{\+,−\},e\_\{j\}\(p\)\\in\\\{\+,\-\\\},\(14\)whereej\(p\)=\+e\_\{j\}\(p\)=\+means that the observed transition supports the relation encoded bypp, andej\(p\)=−e\_\{j\}\(p\)=\-means that it contradicts that relation\.

##### Occurrence\-level counters\.

The occurrence counters summarize all matched observations of the local record:

ciω\(p\)=∑j𝕀\[ej\(p\)=ω\],ω∈\{\+,−\}\.c\_\{i\}^\{\\omega\}\(p\)=\\sum\_\{j\}\\mathbb\{I\}\[e\_\{j\}\(p\)=\\omega\],\\qquad\\omega\\in\\\{\+,\-\\\}\.\(15\)No\-progress behavior is tracked as an auxiliary, potentially overlapping statistic,

ci0​\(p\)=∑j𝕀⁡\[NoProgress⁡\(j,p\)\]\.c\_\{i\}^\{0\}\(p\)=\\sum\_\{j\}\\mathbb\{I\}\[\\operatorname\{NoProgress\}\(j,p\)\]\.\(16\)A no\-progress occurrence does not by itself determine the signej​\(p\)e\_\{j\}\(p\): the same observed outcome can contradict a workflow that claims progress while supporting a failure or anti\-pattern whose relation predicts no progress\. The countersci\+​\(p\)c\_\{i\}^\{\+\}\(p\),ci−​\(p\)c\_\{i\}^\{\-\}\(p\), andci0​\(p\)c\_\{i\}^\{0\}\(p\)are retained as occurrence\-level evidence for local record statistics and retrieval\-side ranking\. They are*not*the sample counts used by the Wilson promotion rule\.

##### Episode\-reduced promotion counters\.

For global promotion, repeated occurrences of the same local record within one episode are first reduced to at most one signed vote\. Let𝒥i​\(p\)\\mathcal\{J\}\_\{i\}\(p\)be the evidence ledger keyed by the local record’s source scope and episode identifier\. A deterministic, relation\-aware reducer maps the annotations under each episode keyξ\\xitoe~ξ​\(p\)∈\{\+,−\}\\widetilde\{e\}\_\{\\xi\}\(p\)\\in\\\{\+,\-\\\}or to no vote\. For ordinary progress relations, a contradiction takes precedence over support within the same episode\. For a failure/no\-progress relation, an observed stall supports the asserted anti\-pattern rather than being treated as successful execution\. An unannotated episode contributes no signed vote\. The promotion counters are

niω\(p\)=∑ξ∈𝒥i​\(p\)𝕀\[e~ξ\(p\)=ω\],ω∈\{\+,−\}\.n\_\{i\}^\{\\omega\}\(p\)=\\sum\_\{\\xi\\in\\mathcal\{J\}\_\{i\}\(p\)\}\\mathbb\{I\}\[\\widetilde\{e\}\_\{\\xi\}\(p\)=\\omega\],\\qquad\\omega\\in\\\{\+,\-\\\}\.\(17\)The diagnostic stall count is

ni0\(p\)=∑ξ∈𝒥i​\(p\)𝕀\[zξ\(p\)=1\],n\_\{i\}^\{0\}\(p\)=\\sum\_\{\\xi\\in\\mathcal\{J\}\_\{i\}\(p\)\}\\mathbb\{I\}\[z\_\{\\xi\}\(p\)=1\],\(18\)wherezξ​\(p\)z\_\{\\xi\}\(p\)indicates that episode keyξ\\xicontains a no\-progress marker\. Likeci0​\(p\)c\_\{i\}^\{0\}\(p\),ni0​\(p\)n\_\{i\}^\{0\}\(p\)may overlap the signed counts\. It is never added to the Wilson sample size\.

The two levels therefore have distinct roles:

\{ej​\(p\),NoProgress⁡\(j,p\)\}j→\(ci\+,ci−,ci0,𝒥i\)→\(ni\+,ni−,ni0\)→\(n\+​\(p¯\),n−​\(p¯\)\)→ρ\+​\(p¯\),W⁡\(p¯\)\.\\\{e\_\{j\}\(p\),\\operatorname\{NoProgress\}\(j,p\)\\\}\_\{j\}\\;\\rightarrow\\;\(c\_\{i\}^\{\+\},c\_\{i\}^\{\-\},c\_\{i\}^\{0\},\\mathcal\{J\}\_\{i\}\)\\;\\rightarrow\\;\(n\_\{i\}^\{\+\},n\_\{i\}^\{\-\},n\_\{i\}^\{0\}\)\\;\\rightarrow\\;\(n^\{\+\}\(\\bar\{p\}\),n^\{\-\}\(\\bar\{p\}\)\)\\;\\rightarrow\\;\\rho^\{\+\}\(\\bar\{p\}\),\\,W\(\\bar\{p\}\)\.The first counters summarize occurrences and may affect retrieval ranking\. For promotion, annotations associated with the same local record, source scope, and episode are first reduced to at most one signed vote, producingni\+​\(p\)n\_\{i\}^\{\+\}\(p\)andni−​\(p\)n\_\{i\}^\{\-\}\(p\)\. Equation[3](https://arxiv.org/html/2610.07376#S3.E3)then aggregates these episode\-reduced counts over local records that map to the same abstract record\. Wilson uses onlys⁡\(p¯\)=n\+​\(p¯\)\+n−​\(p¯\)s\(\\bar\{p\}\)=n^\{\+\}\(\\bar\{p\}\)\+n^\{\-\}\(\\bar\{p\}\)andρ\+​\(p¯\)=n\+​\(p¯\)/max⁡\{s⁡\(p¯\),1\}\\rho^\{\+\}\(\\bar\{p\}\)=n^\{\+\}\(\\bar\{p\}\)/\\max\\\{s\(\\bar\{p\}\),1\\\}\. Neither the occurrence countersciωc\_\{i\}^\{\\omega\}nor the diagnostic countn0n^\{0\}enterss⁡\(p¯\)s\(\\bar\{p\}\)or the Wilson formula\. Consequently, repeated occurrences of the same local record within one episode do not directly multiply the Wilson evidence\.

Table 5:Record\-level evidence used before episode reduction\. Evidence is assigned relative to the relation encoded by the record; the same environment outcome can therefore support one relation while contradicting another\.

#### B\.2\.5Deterministic Evidence Assignment

Evidence signs are assigned from normalized interaction signals rather than by an additional LLM call\. Each environment interface maps its native observations and outcomes to the common information required by the method, including action admissibility, state or task progress, failure, and terminal success\. These normalized signals are interpreted relative to the relation encoded by the record to produceej​\(p\)e\_\{j\}\(p\)and the optional no\-progress marker\. The evidence semantics, episode reduction, aggregation, and Wilson promotion rule are shared across evaluation environments; only the interface that exposes the normalized state, action, and feedback fields depends on the environment\.

### B\.3Progressive Memory Collaboration Details

#### B\.3\.1Role\-Level Abstraction

Before global aggregation,MemCoapplies Algorithm[B\.3\.1](https://arxiv.org/html/2610.07376#A2.SS3.SSS1.Px1)only to selected recordsp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}\. The abstraction preserves the relation that makes a record useful—its type, applicability conditions, action order or state–action relation, and outcome—while removing details that identify only the source episode or scene\. When a concrete entity has a supported semantic role in the task representation, the stored entity can be replaced by that role; otherwise it remains an applicability constraint that must be matched before use\. Records for which no transferable abstract form can be constructed remain local\. NeitherGilG\_\{i\}^\{l\}norℛil\\mathcal\{R\}\_\{i\}^\{l\}is promoted as a global copy\.

##### Type preservation and shared\-record fields\.

Global memory is therefore a collection of promoted abstractions of𝒫il\\mathcal\{P\}\_\{i\}^\{l\}andℰil\\mathcal\{E\}\_\{i\}^\{l\}, not a duplicate of the complete local memory\. For a selected recordpp,p¯=Abstract⁡\(p\)\\bar\{p\}=\\operatorname\{Abstract\}\(p\)retains the fields that define the transferable relation, while source\-episode and scene\-specific anchors are removed\. A promoted entry additionally carries its aggregated evidence, promotion score, and source provenance as specified in Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)\. Abstraction preserves operational conditions rather than turning a conditional relation into an unconditional rule\. Consequently, a shared record is still checked and grounded against the receiving agent’s current decision context before it is used\.

Each abstracted pattern or actionable record is assigned the deterministic global key

κg​\(p¯\)=StoredRecordID⁡\(type⁡\(p¯\),sig⁡\(relation⁡\(p¯\)\)\),\\kappa\_\{g\}\(\\bar\{p\}\)=\\operatorname\{StoredRecordID\}\\bigl\(\\operatorname\{type\}\(\\bar\{p\}\),\\operatorname\{sig\}\(\\operatorname\{relation\}\(\\bar\{p\}\)\)\\bigr\),\(19\)whererelation⁡\(p¯\)\\operatorname\{relation\}\(\\bar\{p\}\)denotes the retained applicability condition, ordered actions or state–action relation, and outcome fields for the record\. Evidence counts, display\-only summaries, source sets, and removed local anchors do not participate in the identifier\. Thus records are merged only when their transferable relation matches exactly after abstraction\.

Consider a schematic household episode in which an agent takes a kettle from a counter, fills it at a sink, and heats it on a stove burner\. The local trajectory is first converted into a workflow record and is then abstracted into a role\-level representation before promotion\. Table[6](https://arxiv.org/html/2610.07376#A2.T6)shows which information is retained and which local anchors are removed\.

Table 6:Schematic household abstraction example\. The action strings illustrate the existing abstraction fields rather than a verbatim benchmark rollout\. Concrete entities are removed, while the workflow type, abstract condition, action order, and outcome relation are retained\.\{algorithm\*\}

\[\!htbp\]Abstract\\operatorname\{Abstract\}: Role\-Level Abstraction\{algorithmic\}\[1\]\\STATEInput:Shareable local recordp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}and its record\-type abstraction schema\\STATEReturn:Abstract formp¯\\bar\{p\}with attached occurrence and episode evidence, or∅\\varnothingwhenppremains local\\STATEInitializep¯\\bar\{p\}from the transferable pattern or actionable relation fields ofpp\.\\IFno transferable abstract form is defined forpp\\STATEReturn∅\\varnothing\.\\ENDIF\\STATEPreserve the record type, applicability condition, action order, and outcome relation defined bypp\.\\STATEReplace a stored entity by a task role when the task representation supports that mapping; otherwise retain it as an applicability constraint\.\\STATERemove the designated episode, scene, layout, raw\-observation, and local graph\-reference fields for this record type\.\\STATEPreserve the retained operational relation, action order, occurrence statistics, source sets, and source\-scoped episode ledger\.\\STATEComputeκg​\(p¯\)\\kappa\_\{g\}\(\\bar\{p\}\)using Eq\.[19](https://arxiv.org/html/2610.07376#A2.E19)\.\\STATEReturnp¯\\bar\{p\}\.

#### B\.3\.2Pre\-Promotion Record Checks

The Wilson test is applied only to records that first pass two deterministic checks\. LetAstr​\(p¯\)A\_\{\\mathrm\{str\}\}\(\\bar\{p\}\)denote structural completeness andAinfo​\(p¯\)A\_\{\\mathrm\{info\}\}\(\\bar\{p\}\)denote the low\-information check\. A record proceeds to Wilson scoring only whenAstr=Ainfo=1A\_\{\\mathrm\{str\}\}=A\_\{\\mathrm\{info\}\}=1; all shareable record types then use the same Wilson formula and thresholdλ\\lambda\.

Table 7:Structural completeness checks applied before Wilson promotion\. The checks retain only records with sufficient transferable content; incomplete, source\-bound, or uninformative records remain local\.The low\-information check removes records whose abstract form contains no usable condition, relation, or outcome beyond generic interaction advice\. These checks operate before evidence calibration and do not change the Wilson score or threshold\. Source provenance and retrieval relevance are retained for later aggregation or decision\-time use rather than used as alternative promotion thresholds\.

#### B\.3\.3Global Exact\-Key Merge of Promoted Records

Global construction does not use embedding similarity or an LLM to decide whether two records are equivalent\. It first constructs the applicable abstract form for each selectedp∈𝒫il∪ℰilp\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}and then groups the resulting pattern and actionable representations by the key in Eq\.[19](https://arxiv.org/html/2610.07376#A2.E19)\. Evidence counts do not participate in identifier matching\. The Wilson implementation rebuilds each snapshot from all current local memories, so occurrence statistics and source sets are recomputed from those local records rather than cumulatively added to an earlier global report\. Episode reduction is completed before global aggregation, and Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)then sums the resulting episode\-reduced signed counts for records with the same exact abstract key\. Occurrence counts are therefore never substituted for the promotion counts\. The accompanying diagnostic is aggregated as

n0\(κ\)=∑i∈\[N\],p∈𝒫il∪ℰil:κg​\(Abstract⁡\(p\)\)=κni0\(p\),n^\{0\}\(\\kappa\)=\\sum\_\{\\begin\{subarray\}\{c\}i\\in\[N\],\\,p\\in\\mathcal\{P\}\_\{i\}^\{l\}\\cup\\mathcal\{E\}\_\{i\}^\{l\}:\\kappa\_\{g\}\(\\operatorname\{Abstract\}\(p\)\)=\\kappa\\end\{subarray\}\}n\_\{i\}^\{0\}\(p\),\(20\)whereκ\\kappais the global record key\. Onlyn\+​\(κ\)\+n−​\(κ\)n^\{\+\}\(\\kappa\)\+n^\{\-\}\(\\kappa\)enters the Wilson sample size\. This is the same episode\-reduction\-then\-aggregation order specified by Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)\.

After aggregation, each record is evaluated by the structural, low\-information, and Wilson gates\. Because every rebuild starts from an empty global memory, a record that no longer passes is absent from the new snapshot; every retained global record therefore satisfies the promotion rule under the current local evidence\.

The exact\-record\-key rule prevents overly broad merging\. A filling workflow and a cleaning workflow may both mention a water source, but they are not the same pattern entry\. Tables[8](https://arxiv.org/html/2610.07376#A2.T8)and[9](https://arxiv.org/html/2610.07376#A2.T9)retain concrete and global examples for readability and illustrate normalized workflow\-identifier matching rather than surface semantic overlap\.

Merge decision\.Merged as one promoted workflow record inℳg\\mathcal\{M\}^\{g\}\. The two𝒫il\\mathcal\{P\}\_\{i\}^\{l\}records have the sameκg\\kappa\_\{g\}after induction\-time role normalization\. Snapshot construction recomputes the source set and evidence totals from all current local records\.

Table 8:Positive merge example\. Different local objects can map to the same global workflow when the record fields match exactly\.Merge decision\.Not merged\. The entries share the phrasewater source, but their normalized workflow identifiers differ because their action sequences and outcomes differ\.

Table 9:Negative merge example\. Surface overlap is insufficient for merging\.Algorithm[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)implementsGlobalMerge\\operatorname\{GlobalMerge\}in Eq\.[6](https://arxiv.org/html/2610.07376#S3.E6)\. Evidence is aggregated before promotion; this update stores the current totals under the appropriate global record key\. In contrast,LocalMerge\\operatorname\{LocalMerge\}acts on graph elements \(Algorithm[B\.2\.2](https://arxiv.org/html/2610.07376#A2.SS2.SSS2)\)\.\{algorithm\*\}\[\!htbp\]GlobalMerge\\operatorname\{GlobalMerge\}: Exact\-Key Update of Promoted Global Records\{algorithmic\}\[1\]\\STATEInput:Global memoryℳg\\mathcal\{M\}^\{g\}and abstract aggregatesp¯\\bar\{p\}that pass the pre\-promotion checks and satisfyW⁡\(p¯\)≥λW\(\\bar\{p\}\)\\geq\\lambda, carrying the aggregated evidence from Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)\\STATEReturn:Updated global memoryℳg\\mathcal\{M\}^\{g\}\\FOReach promoted aggregatep¯\\bar\{p\}\\STATECompute its global record keyκg​\(p¯\)\\kappa\_\{g\}\(\\bar\{p\}\)using Eq\.[19](https://arxiv.org/html/2610.07376#A2.E19)\.\\IFno stored record has keyκg​\(p¯\)\\kappa\_\{g\}\(\\bar\{p\}\)\\STATEInsertp¯\\bar\{p\}, its current source set, promotion score, and aggregated evidence intoℳg\\mathcal\{M\}^\{g\}\.\\ELSE\\STATEKeep one record for the matching global key and replace its mutable fields with the current source set, promotion score, occurrence statistics, and episode\-reduced countsn\+​\(p¯\)n^\{\+\}\(\\bar\{p\}\),n−​\(p¯\)n^\{\-\}\(\\bar\{p\}\), andn0​\(p¯\)n^\{0\}\(\\bar\{p\}\)\.\\ENDIF\\ENDFOR\\STATEReturnℳg\\mathcal\{M\}^\{g\}\.

##### Snapshot realization\.

Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)constructs the global snapshot from the current local memories by reducing episode evidence, grouping records by the exact global keyκg\\kappa\_\{g\}, and applying the pre\-promotion and Wilson checks\. A complete rebuilt snapshot is then made available to subsequent decisions\. The acquisition and evaluation lifecycle is summarized in Appendix[F\.5](https://arxiv.org/html/2610.07376#A6.SS5)\.

### B\.4Query\-Guided Memory Support Details

#### B\.4\.1Local Graph Query Anchoring

The local graph is queried as a bounded structural index\. State anchors are matched to the current query using normalized state content together with location, visible or held entities, task progress, and goal\-related cues when available\. From each retained anchor, retrieval follows only a bounded local neighborhood of the observed state–action–feedback–next\-state transition\. In the serialized graph, this is the corresponding state–action–next\-state backbone together with its attached feedback fields\. The resulting transition entries summarize concrete local evidence that can support the current decision; retrieval does not search arbitrary paths or construct a new long workflow from the merged graph\.

Graph\-derived entries and records from𝒫il\\mathcal\{P\}\_\{i\}^\{l\},ℰil\\mathcal\{E\}\_\{i\}^\{l\}, andℛil\\mathcal\{R\}\_\{i\}^\{l\}enter the same bounded local selection stage\. Their graph provenance can strengthen a record when the retrieved state, action, or outcome matches the current query, while incompatible or stale context lowers its priority\. All such entries remain subject to the common state, progress, goal, and action\-compatibility checks below\.

#### B\.4\.2Memory Entry Construction, Matching, and Ranking

At each decision step,MemCoconstructs the query defined in Section[3\.5](https://arxiv.org/html/2610.07376#S3.SS5)from the current goal, observation, available actions, and interaction history\. The same retrieval functionℝ\\mathbb\{R\}is called independently on local and global memory according to Eq\.[7](https://arxiv.org/html/2610.07376#S3.E7)\. Local retrieval draws from the local records and bounded graph neighborhoods described above, whereas global retrieval draws from promoted abstract records inℳg\\mathcal\{M\}^\{g\}\.

Candidate entries are evaluated through the three complementary relevance facets in Eq\.[8](https://arxiv.org/html/2610.07376#S3.E8):

r⁡\(m,𝒒t\)=rx​\(m,𝒒t\)\+rp​\(m,𝒒t\)\+rg​\(m,𝒒t\)\.r\(m,\\bm\{q\}\_\{t\}\)=r\_\{x\}\(m,\\bm\{q\}\_\{t\}\)\+r\_\{p\}\(m,\\bm\{q\}\_\{t\}\)\+r\_\{g\}\(m,\\bm\{q\}\_\{t\}\)\.Hererxr\_\{x\}measures consistency with the current state and available actions,rpr\_\{p\}measures compatibility with task progress, andrgr\_\{g\}measures alignment with the goal and its functional roles\. These facets score the same memory entry from complementary views; they are not independent pass/fail gates\. Each facet is computed by deterministic comparisons over the normalized fields available to the entry: compatible matches contribute positively, explicit mismatches reduce the score, and unavailable optional fields contribute no update\. The reported outer weights of the three facets are one\. These comparisons use the common normalized representation rather than a benchmark\-specific retrieval objective\.

Applicability constraints are handled before ranking: an entry is removed when a required condition contradicts the current state or when a required action cannot be matched to𝒜t\\mathcal\{A\}\_\{t\}\. These hard compatibility checks are distinct from the soft preferences used to rank the remaining entries\.

The joint relevance score is then combined with stored evidence, current action binding, source\-specific context, and soft conflict penalties to obtain the full rank used for bounded selection:

srank​\(m,𝒒t\)=r⁡\(m,𝒒t\)\+Δev​\(m\)\+Δbind​\(m,𝒒t\)\+Δsrc​\(m,𝒒t\)−psoft​\(m,𝒒t\)\.s\_\{\\mathrm\{rank\}\}\(m,\\bm\{q\}\_\{t\}\)=r\(m,\\bm\{q\}\_\{t\}\)\+\\Delta\_\{\\mathrm\{ev\}\}\(m\)\+\\Delta\_\{\\mathrm\{bind\}\}\(m,\\bm\{q\}\_\{t\}\)\+\\Delta\_\{\\mathrm\{src\}\}\(m,\\bm\{q\}\_\{t\}\)\-p\_\{\\mathrm\{soft\}\}\(m,\\bm\{q\}\_\{t\}\)\.HereΔev\\Delta\_\{\\mathrm\{ev\}\}summarizes the occurrence\-level evidence retained with the entry,Δbind\\Delta\_\{\\mathrm\{bind\}\}reflects compatibility between the stored operation or semantic roles and the currently available actions,Δsrc\\Delta\_\{\\mathrm\{src\}\}incorporates source\-specific supporting context \(such as query\-matched local graph context for local entries or retained applicability and role context for global entries\), andpsoftp\_\{\\mathrm\{soft\}\}collects non\-disqualifying conflicts such as stale or weakly mismatched guidance\. These terms are deterministic adjustments over the same normalized fields used by the common retrieval interface\. Occurrence\-level statistics can contribute to retrieval ranking, whereas the episode\-reduced countsn\+,n−n^\{\+\},n^\{\-\}are reserved for Wilson promotion\. The Wilson score therefore controls membership in global memory rather than being added directly to the online relevance score\.

#### B\.4\.3Bounded Selection

Algorithm[B\.4\.3](https://arxiv.org/html/2610.07376#A2.SS4.SSS3)combines source\-aware pool construction, compatibility filtering, joint relevance, and bounded selection\. The capsklk^\{l\}andkgk^\{g\}bound the retrieved sets\. Before rank\-based filling, selection preserves at most one strongest supporting match for each relevance facet, when such a match is available, so that one dominant score does not remove complementary state\-, progress\-, or goal\-related support\. A supporting facet match is one withrd​\(m,𝒒t\)\>0r\_\{d\}\(m,\\bm\{q\}\_\{t\}\)\>0ford∈\{x,p,g\}d\\in\\\{x,p,g\\\}\. Remaining positions are filled by decreasing full rank\. Composition may subsequently reject or deduplicate selected entries after current\-environment grounding\.

\{algorithm\*\}

\[\!htbp\]ℝ\\mathbb\{R\}: Source\-Aware Retrieval, Filtering, and Bounded Selection\{algorithmic\}\[1\]\\STATEInput:Query𝒒t\\bm\{q\}\_\{t\}, one memoryℳ∈\{ℳil,ℳg\}\\mathcal\{M\}\\in\\\{\\mathcal\{M\}\_\{i\}^\{l\},\\mathcal\{M\}^\{g\}\\\}, and a nonnegative capkk\\STATEReturn:Selected memory entries𝒮\\mathcal\{S\}\\STATEInitialize the retrieval poolℬ←∅\\mathcal\{B\}\\leftarrow\\emptyset\.\\IFℳ=ℳil=\(Gil,𝒫il,ℰil,ℛil\)\\mathcal\{M\}=\\mathcal\{M\}\_\{i\}^\{l\}=\(G\_\{i\}^\{l\},\\mathcal\{P\}\_\{i\}^\{l\},\\mathcal\{E\}\_\{i\}^\{l\},\\mathcal\{R\}\_\{i\}^\{l\}\)\\STATEAdd records from𝒫il\\mathcal\{P\}\_\{i\}^\{l\},ℰil\\mathcal\{E\}\_\{i\}^\{l\}, andℛil\\mathcal\{R\}\_\{i\}^\{l\}toℬ\\mathcal\{B\}\.\\STATEAdd bounded transition entries from query\-matched neighborhoods ofGilG\_\{i\}^\{l\}, preserving the paper\-level state–action–feedback–next\-state semantics and the attached serialized feedback\.\\ELSE\\STATEAdd the promoted abstract records inℳg\\mathcal\{M\}^\{g\}toℬ\\mathcal\{B\}\.\\ENDIF\\STATEInitialize the eligible scored pool𝒱←∅\\mathcal\{V\}\\leftarrow\\emptyset\.\\FOReach memory entrym∈ℬm\\in\\mathcal\{B\}\\STATEComputerx​\(m,𝒒t\)r\_\{x\}\(m,\\bm\{q\}\_\{t\}\),rp​\(m,𝒒t\)r\_\{p\}\(m,\\bm\{q\}\_\{t\}\), andrg​\(m,𝒒t\)r\_\{g\}\(m,\\bm\{q\}\_\{t\}\)\.\\IFmmcontradicts a required current condition or a required action cannot be matched to𝒜t\\mathcal\{A\}\_\{t\}\\STATEExcludemmfrom𝒱\\mathcal\{V\}\.\\ELSE\\STATECompute the full rank from joint relevance, stored evidence, current action binding, source context, and soft conflicts\.\\STATEAddmmand its facet scores, full rank, provenance, and available action/graph evidence to𝒱\\mathcal\{V\}\.\\ENDIF\\ENDFOR\\STATEDeduplicate equivalent entries in𝒱\\mathcal\{V\}, keeping the higher\-ranked applicable entry, and sort by decreasing full rank\.\\IF\|𝒱\|≤k\|\\mathcal\{V\}\|\\leq k\\STATEReturn𝒱\\mathcal\{V\}\.\\ENDIF\\STATEInitialize𝒮←\[\]\\mathcal\{S\}\\leftarrow\[\\,\]\.\\FOReach relevance facetd∈\{x,p,g\}d\\in\\\{x,p,g\\\}\\IF\|𝒮\|<k\|\\mathcal\{S\}\|<kand an unselected entry satisfiesrd​\(m,𝒒t\)\>0r\_\{d\}\(m,\\bm\{q\}\_\{t\}\)\>0\\STATEAppend the unselected entry with the largestrdr\_\{d\}, breaking ties by full rank\.\\ENDIF\\ENDFOR\\FOReach remaining entry in decreasing full\-rank order\\IF\|𝒮\|<k\|\\mathcal\{S\}\|<k\\STATEAppend the entry to𝒮\\mathcal\{S\}without duplication\.\\ENDIF\\ENDFOR\\STATERetain provenance, facet scores, full rank, and action/graph evidence for composition\.\\STATEReturn𝒮\\mathcal\{S\}\.

#### B\.4\.4Composition and Rendering

Retrieval and composition serve different roles\. Retrieval selects relevant entries within each memory source, whereas composition determines how the selected local and global entries should be used in the current decision\. Withℋ=\{ground,workflow,reflection\}\\mathcal\{H\}=\\\{\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\\\}, grounding uses current\-state facts and graph relations; workflow support uses plans, procedures, and preconditions; and reflection uses failure patterns, repairs, and blocked actions\. Entries whose content is incompatible with the current role or decision context are removed\.

For a global record, composition first binds its abstract object, destination, tool, and action roles to the current query and available actions\. A global record is not emitted when a required binding cannot be established\. Local state constraints and concrete local grounding take precedence over an incompatible abstract recommendation\. The remaining support is deduplicated, organized by role, and kept within a bounded context budget before rendering\. This stage therefore converts shared knowledge into current\-environment support rather than directly copying a stored global record into the prompt\.

The renderer serializes the admitted support into the three memory\-bearing fields in Eq\.[10](https://arxiv.org/html/2610.07376#S3.E10)\. It keeps only information needed for the current decision and uses the current bindings for grounded global records rather than source\-environment anchors\. The full prompt template is shown in Appendix[G](https://arxiv.org/html/2610.07376#A7)\.

\{algorithm\*\}

\[\!htbp\]Compose\\operatorname\{Compose\}: Query\-Conditioned Local–Global Support Composition\{algorithmic\}\[1\]\\STATEInput:Selected memory entries𝒮tl,𝒮tg\\mathcal\{S\}\_\{t\}^\{l\},\\mathcal\{S\}\_\{t\}^\{g\}, query𝒒t\\bm\{q\}\_\{t\}, actions𝒜t\\mathcal\{A\}\_\{t\}, rolesℋ=\{ground,workflow,reflection\}\\mathcal\{H\}=\\\{\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\\\}, and the configured context budget\\STATEReturn:Role\-specific supports\{𝒰th\}h∈ℋ\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\\STATEInitialize𝒰th←\[\]\\mathcal\{U\}\_\{t\}^\{h\}\\leftarrow\[\\,\]for everyh∈ℋh\\in\\mathcal\{H\}\.\\FOReach memory entrym∈𝒮tl∪𝒮tgm\\in\\mathcal\{S\}\_\{t\}^\{l\}\\cup\\mathcal\{S\}\_\{t\}^\{g\}in retained full\-rank order\\STATEPreserve the source, full rank, facet scores, and available action/graph evidence attached tomm\.\\IFmmis an abstract global record\\STATEBind its object, destination, tool, and action roles against𝒒t\\bm\{q\}\_\{t\}and𝒜t\\mathcal\{A\}\_\{t\}\.\\IFa required role cannot be grounded or its required action is unavailable\\STATEExcludemmfrom the current composition\.\\ENDIF\\ENDIF\\IFmmremains eligible after binding and compatibility checks\\STATEDetermine the compatible role setℋm⊆ℋ\\mathcal\{H\}\_\{m\}\\subseteq\\mathcal\{H\}from the record type and its current contextual trigger\.\\STATEAssign current\-state facts and graph relations toground\\mathrm\{ground\}; plans, procedures, and preconditions toworkflow\\mathrm\{workflow\}; and failures, repairs, and blocked actions toreflection\\mathrm\{reflection\}whenever the corresponding role is inℋm\\mathcal\{H\}\_\{m\}\.\\ENDIF\\ENDFOR\\STATERemove duplicate support items within each role while retaining the higher\-ranked applicable item and its provenance\.\\STATEResolve action conflicts by discarding unavailable actions and by letting current\-state constraints and concrete local grounding override an incompatible abstract recommendation\.\\STATEApply the fixed context budget to the remaining support in deterministic full\-rank order\.\\STATERetain the admitted memory\-bearing support in the corresponding𝒰th\\mathcal\{U\}\_\{t\}^\{h\}in deterministic rank order\.\\STATEReturn\{𝒰th\}h∈ℋ\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\.

\{algorithm\*\}

\[\!htbp\]Render\\operatorname\{Render\}: Role\-Specific Memory Context Rendering\{algorithmic\}\[1\]\\STATEInput:Query𝒒t\\bm\{q\}\_\{t\}and composed supports\{𝒰th\}h∈ℋ\\\{\\mathcal\{U\}\_\{t\}^\{h\}\\\}\_\{h\\in\\mathcal\{H\}\}\\STATEReturn:Memory context𝒞t=\[ctground,ctworkflow,ctreflection\]\\mathcal\{C\}\_\{t\}=\[c\_\{t\}^\{\\mathrm\{ground\}\},c\_\{t\}^\{\\mathrm\{workflow\}\},c\_\{t\}^\{\\mathrm\{reflection\}\}\]\\FOReach support roleh∈\(ground,workflow,reflection\)h\\in\(\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\)\\STATEOrder𝒰th\\mathcal\{U\}\_\{t\}^\{h\}by the deterministic composition order\.\\STATEConvert each selected memory entry into a concise instruction using only fields relevant to𝒒t\\bm\{q\}\_\{t\}and rolehh\.\\STATEFor grounded global records, emit the current concrete bindings rather than removed scene\-specific anchors\.\\STATEDeduplicate equivalent instructions and retain the highest\-priority applicable instruction for each emitted memory line\.\\STATEStore the resulting text incthc\_\{t\}^\{h\}; setcthc\_\{t\}^\{h\}to the empty string when𝒰th\\mathcal\{U\}\_\{t\}^\{h\}is empty after composition\.\\ENDFOR\\STATEIf all three rendered fields are empty, return an empty memory context\.\\STATESet𝒞t←\[ctground,ctworkflow,ctreflection\]\\mathcal\{C\}\_\{t\}\\leftarrow\[c\_\{t\}^\{\\mathrm\{ground\}\},c\_\{t\}^\{\\mathrm\{workflow\}\},c\_\{t\}^\{\\mathrm\{reflection\}\}\]\.\\STATEReturn𝒞t\\mathcal\{C\}\_\{t\}\.

#### B\.4\.5Concrete Retrieval Example

Suppose the current task is to clean a bar of soap and place it in a vanity\. The current observation mentions a bathroom basin, and the environment exposes an admissible action for cleaning the soap with the basin\. The local record in this illustrative example is actionable knowledge inℰil\\mathcal\{E\}\_\{i\}^\{l\}; the shared record is a promoted workflow fromℳg\\mathcal\{M\}^\{g\}\. They support the same decision in different ways: the local relation grounds an executable cleaning action, while the global workflow supplies the clean\-before\-place ordering\. The global roles are bound to the current soap, basin, and vanity before use\. The rejected kitchen\-specific instruction illustrates a grounding conflict, not an additional observed record in the global snapshot\.

Table 10:Schematic typed retrieval and composition example\. Local actionable knowledge supplies executable grounding, while a global workflow supplies action order\. Source, record type, and support role are shown separately\.

### B\.5Reported Configuration and Scope of the Details

The reported configuration usesα=0\.05\\alpha=0\.05,λ=0\.35\\lambda=0\.35, retrieval capskl=kg=5k^\{l\}=k^\{g\}=5, and unit outer weights for the three relevance facets\. These are the paper\-level parameters governing promotion and bounded retrieval\. Across the evaluated benchmarks, the same paper\-level pipeline is used for local memory construction, abstraction and promotion, query\-guided retrieval, and composition\. Environment interfaces provide the normalized state, action, feedback, goal, progress, and supported task\-role fields consumed by this pipeline; benchmark\-specific serialization details are not additional components of the method\. The paper\-level memory context is the three\-role𝒞t\\mathcal\{C\}\_\{t\}in Eq\.[10](https://arxiv.org/html/2610.07376#S3.E10); surrounding task\-wrapper context shown in Appendix[G](https://arxiv.org/html/2610.07376#A7)is kept separate from this local/global retrieval interface\.

## Appendix CExtended Experimental Results

This section provides the numerical results underlying the mechanism and sensitivity analyses in Figs\.[3](https://arxiv.org/html/2610.07376#S4.F3),[4](https://arxiv.org/html/2610.07376#S4.F4), and[5](https://arxiv.org/html/2610.07376#S4.F5)\. Table[11](https://arxiv.org/html/2610.07376#A3.T11)reports the Wilson\-threshold sweep, Table[12](https://arxiv.org/html/2610.07376#A3.T12)combines the memory\-scope, promotion, composition, and memory\-cost results, Table[13](https://arxiv.org/html/2610.07376#A3.T13)reports interaction\-budget sensitivity, and Table[14](https://arxiv.org/html/2610.07376#A3.T14)gives the absolute relevance\-scoring and retrieval results\.

Unless otherwise specified, the component, promotion, and retrieval variants reuse the same frozen local\-memory snapshot and differ only in the evaluated component\. These are controlled within\-snapshot comparisons rather than independent repetitions of the main experiments\. The interaction\-budget sweep follows the budget\-specific evaluation protocol used in Fig\.[3](https://arxiv.org/html/2610.07376#S4.F3)\(d\)\. Accuracy and success rates are reported in percent, and Steps denotes the average number of environment interactions\. Familiar and Held\-out refer to ALFWorld’s officialvalid\_seenandvalid\_unseenlayout splits, respectively\. Collectively, the controlled studies examine the three mechanisms emphasized by the method: complementary local/global memory scope, evidence\-aware global promotion, and query\-guided use of memory for the current decision\.

### C\.1Experimental Reproduction Boundaries

The main results and the controlled component studies serve different purposes\. Table[1](https://arxiv.org/html/2610.07376#S4.T1)reports mean±\\pmstandard deviation over three runs\. The component, promotion, and retrieval studies in this appendix instead reuse a fixed local\-memory snapshot so that the evaluated mechanism can be changed without recollecting experience\. For threshold sensitivity, only the promoted global snapshot is reconstructed from the same local evidence; for retrieval and composition studies, the underlying memories remain fixed\.

The main experiments use the shared settingλ=0\.35\\lambda=0\.35across benchmarks, while Table[11](https://arxiv.org/html/2610.07376#A3.T11)reports a controlled sensitivity sweep around this operating point\. The cross\-setting significance analysis in Appendix[H](https://arxiv.org/html/2610.07376#A8)uses the displayed main\-result means as matched backbone–task blocks; it does not treat the repeated runs as additional independent blocks\.

### C\.2Sensitivity to the Wilson Promotion Threshold

Table[11](https://arxiv.org/html/2610.07376#A3.T11)reconstructs global memory at each threshold while reusing the same local evidence\. Increasingλ\\lambdafrom0\.250\.25to0\.500\.50reduces the global bank from 735 to 294 records\. Over this range, familiar\-layout accuracy remains between96\.10%96\.10\\%and97\.40%97\.40\\%, and held\-out\-layout accuracy between97\.50%97\.50\\%and97\.86%97\.86\\%\. The reported settingλ=0\.35\\lambda=0\.35uses 426 records,42\.0%42\.0\\%fewer thanλ=0\.25\\lambda=0\.25, while attaining the highest familiar\-layout accuracy and tying the highest held\-out\-layout accuracy\. The lower threshold nevertheless has the fewest steps on both splits\. The table therefore characterizes the accuracy–compactness–efficiency trade\-off rather than establishing that one threshold optimizes every metric\.

Table 11:Sensitivity to the Wilson promotion threshold on ALFWorld with Qwen3\-32B\. All thresholds use the same frozen local\-memory snapshot; only global memory is reconstructed\.
### C\.3Memory Scope, Promotion, and Query\-Guided Composition

Table[12](https://arxiv.org/html/2610.07376#A3.T12)separates the roles of the two memory sources, the promotion criterion, and the way retrieved records are used\. Local\-only retains strong familiar\-layout accuracy but has a larger familiar–held\-out layout gap; Global\-only improves held\-out\-layout accuracy from89\.64%89\.64\\%to97\.14%97\.14\\%relative to Local\-only\. The complete system improves on both isolated sources and uses fewer steps on both splits\. Simply concatenating local and global records does not recover this benefit: relative to fixed L5\+G5, the full method gains 10\.71 and 16\.07 percentage points on familiar\- and held\-out\-layout accuracy, respectively\.

The empirical\-promotion row changes the admission score fromW⁡\(p¯\)W\(\\bar\{p\}\)toρ\+​\(p¯\)\\rho^\{\+\}\(\\bar\{p\}\)at the sameλ=0\.35\\lambda=0\.35, leaving the structural eligibility checks and query\-guided retrieval policy unchanged\. Wilson promotion improves accuracy by 2\.27 and 1\.43 percentage points and reduces steps by 0\.82 and 0\.54 on the familiar\-layout and held\-out\-layout splits, respectively\. Together with Figure[3](https://arxiv.org/html/2610.07376#S4.F3), this comparison separates the quality of the promoted bank from merely retrieving more records\. These within\-snapshot results support the contribution of each component without attributing every change to a single underlying cause\.

Table 12:Ablation of memory organization, global promotion, and query\-guided composition on ALFWorld with Qwen3\-32B\.All variants use the same frozen local\-memory snapshot\. “Global records” denotes the size of promoted global memory\. “Avg\. \#Mem” and “Avg\. Mem\. Tok\.” denote the average number of entries and memory\-prompt tokens injected per retrieval call, respectively, averaged over the Familiar and Held\-out splits\. A dash indicates that no global memory is used\.
### C\.4Interaction\-Budget Sensitivity

Table[13](https://arxiv.org/html/2610.07376#A3.T13)reports the exact success rates underlying Fig\.[3](https://arxiv.org/html/2610.07376#S4.F3)\(d\)\. This experiment varies only the maximum interaction budget under its budget\-specific evaluation protocol\.

Table 13:Sensitivity to the maximum interaction budget on ALFWorld with Qwen3\-32B\.Success rates are reported for the Familiar and Held\-out layout splits\.
### C\.5Relevance Scoring and Retrieval

Table[14](https://arxiv.org/html/2610.07376#A3.T14)reports the absolute results underlying Fig\.[5](https://arxiv.org/html/2610.07376#S4.F5)\. The main\-text figure visualizes signed changes from the full MemCo row, whereas the table reports the corresponding absolute accuracy and trajectory length\.

Table 14:Absolute results for relevance\-scoring and retrieval ablations on ALFWorld with Qwen3\-32B\.In the component rows,−ri\-r\_\{i\}removes termrir\_\{i\}, whereas an isolatedrir\_\{i\}retains only that term\. The all\-zero control is included for completeness but omitted from the main\-text visualization\.

## Appendix DTheoretical Analysis

This section analyzes two properties ofMemCo’s global promotion mechanism\. We first prove the finite\-evidence correction stated in Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)and derive sharper asymptotic and threshold implications\. We then characterize the stability of the episode\-level evidence aggregation used before Wilson promotion\. Throughout this section,n\+n^\{\+\}andn−n^\{\-\}denote the episode\-reduced promotion counts defined in Appendix[B\.2\.4](https://arxiv.org/html/2610.07376#A2.SS2.SSS4), rather than the occurrence\-level statistics used for retrieval\. Wilson promotion uses only these signed episode\-reduced counts throughs=n\+\+n−s=n^\{\+\}\+n^\{\-\}andρ\+=n\+/s\\rho^\{\+\}=n^\{\+\}/swhens\>0s\>0; neithercωc^\{\\omega\}nor the diagnosticn0n^\{0\}enters the Wilson score\.

### D\.1Wilson Finite\-Evidence Correction

###### Proof of Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)\.

For brevity, lets=s⁡\(p¯\)s=s\(\\bar\{p\}\),ρ=ρ\+​\(p¯\)\\rho=\\rho^\{\+\}\(\\bar\{p\}\), andW=W⁡\(p¯\)W=W\(\\bar\{p\}\)\. The Wilson lower bound in Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)is equivalently the smaller root of

\(s\+z2\)​W2−\(2​s​ρ\+z2\)​W\+s​ρ2=0\.\(s\+z^\{2\}\)W^\{2\}\-\(2s\\rho\+z^\{2\}\)W\+s\\rho^\{2\}=0\.\(21\)Indeed, solving Eq\.[21](https://arxiv.org/html/2610.07376#A4.E21)forWWrecovers exactly the closed form in Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)\.

Rearranging Eq\.[21](https://arxiv.org/html/2610.07376#A4.E21)gives

s​\(ρ−W\)2=z2​W​\(1−W\)\.s\(\\rho\-W\)^\{2\}=z^\{2\}W\(1\-W\)\.\(22\)SinceWWis the lower endpoint and thereforeW≤ρW\\leq\\rho,

ϵW​\(p¯\)=ρ\+​\(p¯\)−W⁡\(p¯\)=z​W​\(p¯\)​\(1−W​\(p¯\)\)s⁡\(p¯\)\.\\epsilon\_\{W\}\(\\bar\{p\}\)=\\rho^\{\+\}\(\\bar\{p\}\)\-W\(\\bar\{p\}\)=z\\sqrt\{\\frac\{W\(\\bar\{p\}\)\(1\-W\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\}\.\(23\)Forρ\+​\(p¯\)=0\\rho^\{\+\}\(\\bar\{p\}\)=0, Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)givesW⁡\(p¯\)=0W\(\\bar\{p\}\)=0, so the same identity holds trivially\.

Finally, since0≤W⁡\(p¯\)≤10\\leq W\(\\bar\{p\}\)\\leq 1andW⁡\(p¯\)​\(1−W⁡\(p¯\)\)≤1/4W\(\\bar\{p\}\)\(1\-W\(\\bar\{p\}\)\)\\leq 1/4,

0≤ϵW​\(p¯\)≤z2​s⁡\(p¯\)\.0\\leq\\epsilon\_\{W\}\(\\bar\{p\}\)\\leq\\frac\{z\}\{2\\sqrt\{s\(\\bar\{p\}\)\}\}\.\(24\)The bound is independent ofρ\+​\(p¯\)\\rho^\{\+\}\(\\bar\{p\}\), establishing the uniformO\(s\(p¯\)−1/2\)O\(s\(\\bar\{p\}\)^\{\-1/2\}\)correction stated in Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)\. ∎

###### Corollary D\.1\(Exact promotion threshold and required evidence\)\.

Fors=s⁡\(p¯\)\>0s=s\(\\bar\{p\}\)\>0,z\>0z\>0, and0<λ<10<\\lambda<1, the Wilson gate satisfies

W\(p¯\)≥λ⟺ρ\+\(p¯\)≥λ\+zλ⁡\(1−λ\)s⁡\(p¯\)\.W\(\\bar\{p\}\)\\geq\\lambda\\quad\\Longleftrightarrow\\quad\\rho^\{\+\}\(\\bar\{p\}\)\\geq\\lambda\+z\\sqrt\{\\frac\{\\lambda\(1\-\\lambda\)\}\{s\(\\bar\{p\}\)\}\}\.\(25\)Equivalently, for integer signed evidence counts,

n\+​\(p¯\)≥⌈s⁡\(p¯\)​λ\+z​s⁡\(p¯\)​λ​\(1−λ\)⌉\.n^\{\+\}\(\\bar\{p\}\)\\geq\\left\\lceil s\(\\bar\{p\}\)\\lambda\+z\\sqrt\{s\(\\bar\{p\}\)\\lambda\(1\-\\lambda\)\}\\right\\rceil\.\(26\)For a fixed empirical rateρ\+​\(p¯\)\>λ\\rho^\{\+\}\(\\bar\{p\}\)\>\\lambda, this is equivalent to

s⁡\(p¯\)≥z2​λ​\(1−λ\)\(ρ\+​\(p¯\)−λ\)2\.s\(\\bar\{p\}\)\\geq\\frac\{z^\{2\}\\lambda\(1\-\\lambda\)\}\{\(\\rho^\{\+\}\(\\bar\{p\}\)\-\\lambda\)^\{2\}\}\.\(27\)No finite positive evidence size passes whenρ\+​\(p¯\)≤λ\\rho^\{\+\}\(\\bar\{p\}\)\\leq\\lambda\. At the all\-supporting boundaryn−​\(p¯\)=0n^\{\-\}\(\\bar\{p\}\)=0, the minimum integer evidence size is

smin=⌈z2​λ1−λ⌉\.s\_\{\\min\}=\\left\\lceil\\frac\{z^\{2\}\\lambda\}\{1\-\\lambda\}\\right\\rceil\.\(28\)Below this size, no supporting rate can pass the Wilson gate\. These conditions concern the Wilson gate only; structural and information eligibility are still required for global promotion\.

###### Proof\.

Writeρ=ρ\+​\(p¯\)\\rho=\\rho^\{\+\}\(\\bar\{p\}\)and defineQρ​\(w\)=s​\(ρ−w\)2−z2​w​\(1−w\)Q\_\{\\rho\}\(w\)=s\(\\rho\-w\)^\{2\}\-z^\{2\}w\(1\-w\)\. By Eq\.[21](https://arxiv.org/html/2610.07376#A4.E21), its smaller root isWW\. For0<ρ<10<\\rho<1,Qρ​\(ρ\)<0Q\_\{\\rho\}\(\\rho\)<0, soρ\\rholies strictly between the two roots\. Consequently, whenλ≤ρ\\lambda\\leq\\rho, the conditionW≥λW\\geq\\lambdais equivalent toQρ​\(λ\)≥0Q\_\{\\rho\}\(\\lambda\)\\geq 0\. Taking the nonnegative square root givesρ−λ≥z​λ⁡\(1−λ\)/s\\rho\-\\lambda\\geq z\\sqrt\{\\lambda\(1\-\\lambda\)/s\}\. Whenλ\>ρ\\lambda\>\\rho, both sides of the claimed equivalence are false becauseW≤ρW\\leq\\rho\. The boundaryρ=0\\rho=0givesW=0W=0; atρ=1\\rho=1,W=s/\(s\+z2\)W=s/\(s\+z^\{2\}\)gives the same equivalence directly\. Multiplying byssand using integern\+n^\{\+\}proves Eq\.[26](https://arxiv.org/html/2610.07376#A4.E26); rearranging forρ\>λ\\rho\>\\lambdaproves Eq\.[27](https://arxiv.org/html/2610.07376#A4.E27)\. Finally, the right\-hand side of Eq\.[25](https://arxiv.org/html/2610.07376#A4.E25)must not exceed one\. This is equivalent tos≥z2​λ/\(1−λ\)s\\geq z^\{2\}\\lambda/\(1\-\\lambda\), which is attained when all votes are supporting\. ∎

##### Pointwise refinement\.

The uniform bound in Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)controls the largest possible finite\-evidence correction over supporting rates\. The dependence on a fixed supporting rate can be characterized more precisely\.

Substituting Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)intoϵW​\(p¯\)=ρ\+​\(p¯\)−W⁡\(p¯\)\\epsilon\_\{W\}\(\\bar\{p\}\)=\\rho^\{\+\}\(\\bar\{p\}\)\-W\(\\bar\{p\}\)gives the exact closed form

ϵW​\(p¯\)=\\displaystyle\\epsilon\_\{W\}\(\\bar\{p\}\)=\{\}11\+z2/s⁡\(p¯\)\[z2s⁡\(p¯\)\(ρ\+\(p¯\)−12\)\\displaystyle\\frac\{1\}\{1\+z^\{2\}/s\(\\bar\{p\}\)\}\\Biggl\[\\frac\{z^\{2\}\}\{s\(\\bar\{p\}\)\}\\left\(\\rho^\{\+\}\(\\bar\{p\}\)\-\\frac\{1\}\{2\}\\right\)\(29\)\+z\(ρ\+​\(p¯\)​\(1−ρ\+​\(p¯\)\)s⁡\(p¯\)\+z24​s​\(p¯\)2\)1/2\]\.\\displaystyle\+z\\left\(\\frac\{\\rho^\{\+\}\(\\bar\{p\}\)\(1\-\\rho^\{\+\}\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\+\\frac\{z^\{2\}\}\{4s\(\\bar\{p\}\)^\{2\}\}\\right\)^\{1/2\}\\Biggr\]\.
For a fixed0<ρ\+​\(p¯\)<10<\\rho^\{\+\}\(\\bar\{p\}\)<1and increasings⁡\(p¯\)s\(\\bar\{p\}\),

\[ρ\+​\(p¯\)​\(1−ρ\+​\(p¯\)\)s⁡\(p¯\)\+z24​s​\(p¯\)2\]1/2\\displaystyle\\left\[\\frac\{\\rho^\{\+\}\(\\bar\{p\}\)\(1\-\\rho^\{\+\}\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\+\\frac\{z^\{2\}\}\{4s\(\\bar\{p\}\)^\{2\}\}\\right\]^\{1/2\}\(30\)=\[ρ\+​\(p¯\)​\(1−ρ\+​\(p¯\)\)s⁡\(p¯\)\]1/2\+O\(s\(p¯\)−3/2\)\.\\displaystyle=\\left\[\\frac\{\\rho^\{\+\}\(\\bar\{p\}\)\(1\-\\rho^\{\+\}\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\\right\]^\{1/2\}\+O\\\!\\left\(s\(\\bar\{p\}\)^\{\-3/2\}\\right\)\.Substituting Eq\.[30](https://arxiv.org/html/2610.07376#A4.E30)into Eq\.[29](https://arxiv.org/html/2610.07376#A4.E29), together with

\(1\+z2s⁡\(p¯\)\)−1=1\+O⁡\(s​\(p¯\)−1\),\\left\(1\+\\frac\{z^\{2\}\}\{s\(\\bar\{p\}\)\}\\right\)^\{\-1\}=1\+O\\\!\\left\(s\(\\bar\{p\}\)^\{\-1\}\\right\),gives

ϵW​\(p¯\)=z​ρ\+​\(p¯\)​\(1−ρ\+​\(p¯\)\)s⁡\(p¯\)\+O⁡\(s​\(p¯\)−1\)\.\\epsilon\_\{W\}\(\\bar\{p\}\)=z\\sqrt\{\\frac\{\\rho^\{\+\}\(\\bar\{p\}\)\(1\-\\rho^\{\+\}\(\\bar\{p\}\)\)\}\{s\(\\bar\{p\}\)\}\}\+O\\\!\\left\(s\(\\bar\{p\}\)^\{\-1\}\\right\)\.\(31\)
At the all\-supporting boundaryρ\+​\(p¯\)=1\\rho^\{\+\}\(\\bar\{p\}\)=1, Eq\.[4](https://arxiv.org/html/2610.07376#S3.E4)reduces to

W⁡\(p¯\)=s⁡\(p¯\)s⁡\(p¯\)\+z2,ϵW​\(p¯\)=1−W⁡\(p¯\)=z2s⁡\(p¯\)\+z2\.W\(\\bar\{p\}\)=\\frac\{s\(\\bar\{p\}\)\}\{s\(\\bar\{p\}\)\+z^\{2\}\},\\qquad\\epsilon\_\{W\}\(\\bar\{p\}\)=1\-W\(\\bar\{p\}\)=\\frac\{z^\{2\}\}\{s\(\\bar\{p\}\)\+z^\{2\}\}\.\(32\)Thus, for fixed0<ρ\+​\(p¯\)<10<\\rho^\{\+\}\(\\bar\{p\}\)<1, the leading correction isO\(s\(p¯\)−1/2\)O\(s\(\\bar\{p\}\)^\{\-1/2\}\), whereas at the all\-supporting boundary it decreases asO⁡\(s​\(p¯\)−1\)O\(s\(\\bar\{p\}\)^\{\-1\}\)\. TheO\(s\(p¯\)−1/2\)O\(s\(\\bar\{p\}\)^\{\-1/2\}\)statement in Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)is therefore a uniform bound rather than a claim that every fixed supporting\-rate regime has the same asymptotic behavior\.

##### Interpretation and assumptions\.

Theorem[3\.1](https://arxiv.org/html/2610.07376#S3.Thmtheorem1)establishes an explicit finite\-evidence correction relative to the empirical supporting rate, while Corollary[D\.1](https://arxiv.org/html/2610.07376#A4.Thmtheorem1)gives its direct promotion interpretation: under a fixed threshold, records supported by less evidence require stronger empirical support\.

The identities and bounds above are algebraic properties of the Wilson score and do not themselves require independent observations\. The nominal one\-sided confidence interpretation additionally relies on the corresponding binomial sampling assumption\. Wilson coverage is an approximation under that model, not an exact finite\-sample coverage guarantee\. Episode\-level reduction prevents repeated annotations within one episode from directly multiplying the promotion evidence, but does not establish independence or identical distribution across episodes\.

### D\.2Stability of Episode\-Level Evidence Aggregation

The preceding analysis characterizes how Wilson promotion treats a fixed pair of aggregated signed counts\. We next consider the stability of the procedure that constructs those counts\.

###### Proposition D\.2\(Order and repetition invariance of episode\-reduced aggregation\)\.

Fix the current set of local records, their abstract keys, and the deterministic pre\-promotion checks\. Apply the episode reduction in Appendix[B\.2\.4](https://arxiv.org/html/2610.07376#A2.SS2.SSS4)separately to each record to obtainni\+​\(p\)n\_\{i\}^\{\+\}\(p\),ni−​\(p\)n\_\{i\}^\{\-\}\(p\), andni0​\(p\)n\_\{i\}^\{0\}\(p\), and then aggregate these counts by exact abstract key as in Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)\. The resulting\(n\+,n−,n0\)\(n^\{\+\},n^\{\-\},n^\{0\}\), Wilson score, and promotion decision are invariant to the processing order of this fixed input\. Repeating an annotation already present for the same record and episode does not change its episode\-reduced contribution\.

###### Proof\.

For a fixed record and episode, the relation\-aware reducer depends on the set of support, contradiction, and no\-progress annotations, not on their processing order\. Repeating an annotation that is already present therefore does not change the reduced signed count or its diagnostic stall marker\. The subsequent aggregation in Eq\.[3](https://arxiv.org/html/2610.07376#S3.E3)is a sum over the fixed episode\-reduced counts associated with each exact abstract key, and is therefore associative and commutative\. Since the abstract key and the pre\-promotion checks are also fixed, the Wilson score and promotion decision are unchanged\. ∎

##### Scope\.

Proposition[D\.2](https://arxiv.org/html/2610.07376#A4.Thmtheorem2)concerns a fixed set of current local records\. It does not make stale or out\-of\-order replacement safe in an asynchronous implementation; a streaming realization must separately ensure that the retained source state is current\. The evaluated snapshot\-rebuild specialization is described in Appendix[B\.3\.3](https://arxiv.org/html/2610.07376#A2.SS3.SSS3)\. Different intermediate snapshots may affect subsequent trajectories, so order\-dependent acquisition does not constitute fixed input evidence\.

Adding previously absent contradictory evidence or a no\-progress marker can legitimately change an episode\-reduced count\. The repetition guarantee does not apply to occurrence\-level retrieval counters\. Finally, neither exact\-key aggregation nor episode reduction establishes independence or identical distribution of the aggregated evidence; the nominal statistical interpretation of the Wilson bound therefore remains subject to the assumptions stated in Appendix[D](https://arxiv.org/html/2610.07376#A4)\.

## Appendix EMemory Types and Local–Global Examples

This section complements the implementation details with a unified account of what each memory component stores, what can be shared, and how the resulting records are used\. The four pattern types belong to𝒫il\\mathcal\{P\}\_\{i\}^\{l\}; together withGilG\_\{i\}^\{l\},ℰil\\mathcal\{E\}\_\{i\}^\{l\}, andℛil\\mathcal\{R\}\_\{i\}^\{l\}, they constitute the local memory in Eq\.[2](https://arxiv.org/html/2610.07376#S3.E2)\. Global memory stores promoted abstract records from the shareable components, not a duplicate of the entire local memory\.

### E\.1Type Definitions and Local–Global Correspondence

Table[15](https://arxiv.org/html/2610.07376#A5.T15)covers every component and pattern subtype\. The examples are schematic adaptations of the household and PDDL examples used in this appendix, not new benchmark rollouts or literal serialized dumps\. Role\-level examples assume that a concrete entity has a supported task\-role mapping; operational conditions are retained\. “Shareable” in the sharing column means eligible for consideration, not automatically admitted to global memory\. Concrete PDDL memory snapshots are shown separately in Appendix[J](https://arxiv.org/html/2610.07376#A10)\.

Table 15:Memory definitions, schematic examples, and sharing scope\. The global column shows possible abstract records, not guaranteed promotions\. Every shared record remains subject to type\-specific eligibility, aggregated evidence, and the Wilson threshold\. Applicability conditions and current action binding are still required when a promoted record is used\.
### E\.2From Local Records to Promoted Records

The global column in Table[15](https://arxiv.org/html/2610.07376#A5.T15)describes possible abstract counterparts, not automatic promotions or interchangeable copies of local records\. In particular, a supported failure pattern remains a conditioned failure relation rather than becoming a successful workflow\. Table[6](https://arxiv.org/html/2610.07376#A2.T6)gives the field\-level abstraction; Tables[8](https://arxiv.org/html/2610.07376#A2.T8)and[9](https://arxiv.org/html/2610.07376#A2.T9)illustrate exact\-key matching\. Evidence aggregation and admission are specified once in Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)\. Every admitted record must still be compatible with the receiving agent’s current state and action bindings\.

### E\.3Memory Source, Record Type, and Support Role

Three distinctions are important\.*Source*specifies whether an item comes fromℳil\\mathcal\{M\}\_\{i\}^\{l\}orℳg\\mathcal\{M\}^\{g\}\.*Record type*specifies the stored content, such as a workflow, repair, or actionable relation\.*Support role*specifies its query\-conditioned use inℋ=\{ground,workflow,reflection\}\\mathcal\{H\}=\\\{\\mathrm\{ground\},\\mathrm\{workflow\},\\mathrm\{reflection\}\\\}\. These are not three alternative classifications of the memory banks\.

In Table[10](https://arxiv.org/html/2610.07376#A2.T10), a local actionable record supplies grounding and a global workflow supplies action order\. A local workflow can also support procedural guidance, while an applicable global record can support grounding after role binding\. Local or promoted repair/failure records may supply reflection support when their conditions are triggered; this does not require sharing the concrete cases inℛil\\mathcal\{R\}\_\{i\}^\{l\}\. Selection and use remain governed by the current state, task phase, goal, and admissible actions, rather than by a fixed one\-to\-one assignment from local/global scope to a support role\. This separates reusable experience from the local context needed to execute it without treating all cross\-agent experience as directly applicable\.

## Appendix FBenchmark Domain Construction and Evaluation Scope

### F\.1ALFWorld Multi\-Domain Environment

To evaluate collaboration across environments, ALFWorld tasks are organized into four functional scene domains: Kitchen, Living Room, Bedroom, and Bathroom\. We sample 100 training tasks from each domain for experience acquisition\. Following the official protocol, evaluation uses both the*Familiar Layout*\(valid\_seen\) and*Held\-out Layout*\(valid\_unseen\) splits\. The resulting training/Familiar/Held\-out counts are Kitchen \(100/20/20100/20/20\), Living Room \(100/17/11100/17/11\), Bedroom \(100/20/20100/20/20\), and Bathroom \(100/20/19100/20/19\)\.

Following the problem formulation, an*unseen environment*is defined with respect to the evaluated agent: it is an environment in which that agent did not acquire experience before evaluation\. This agent\-specific notion and the official held\-out\-layout split provide complementary axes of generalization\. An environment may be unseen to one agent while experience from other agents is available through global memory; the Held\-out Layout split additionally changes layout familiarity\.

### F\.2PDDL Planning and Domain Partitioning

PDDL tasks are organized into the four planning domains Gripper, Barman, Blockworld, and Tyreworld\. The source sets contain 20, 20, 10, and 10 tasks, respectively, and evaluation uses a unified test set of 60 tasks\. Local memory is constructed independently for each source domain before cross\-agent global memory is formed\.

### F\.3FEVER Domain Partitioning

For FEVER, we construct two semantic source domains, Film/TV and Music, with 100 training examples in each domain\. As noted in the AI Use Statement, GPT\-4o\-mini is used only to assist the semantic domain labeling used for this partition construction; it is not an evaluation\-time memory component\. Evaluation uses 60 disjoint examples, 30 from each domain, with a balanced distribution over SUPPORTS, REFUTES, and NEI labels\. These partitions provide distinct sources of interaction experience while keeping the verification task and action interface unchanged\.

### F\.4ScienceWorld Task\-Family Partitioning

ScienceWorld tasks are organized by their official task families while preserving the official train/test variation split\. We sample up to 10 training variations per task template for local experience acquisition and up to 2 test variations for evaluation, yielding 60 held\-out evaluation variations in the merged test set\. Each local domain is evaluated with the same local\-plus\-global memory protocol\.

### F\.5Acquisition, Evaluation, and Controlled Comparisons

During acquisition, agents interact with their designated source environments, update their own local memories, and contribute selected shareable records to global promotion\. Global memory is constructed only from the completed local stores\. During evaluation, local and global memories are frozen: the evaluated agent refreshes its query and retrieved support at every decision step, but the test trajectory is not written back into either memory\.

For each source\-domain local memory, evaluation is performed on the common merged test set together with the shared global memory\. Consequently, the same evaluated agent encounters both tasks aligned with its own acquisition domain and tasks from environments in which it did not acquire local experience\. This operationalizes the agent\-specific unseen\-environment setting in the problem formulation while allowing the shared global memory to supply experience contributed by other agents\. In ALFWorld, Familiar and Held\-out additionally measure whether the layout itself was seen in the benchmark training split\.

The controlled ablations in Appendix[C](https://arxiv.org/html/2610.07376#A3)reuse the same frozen local\-memory snapshot\. Threshold sensitivity reconstructs only the global memory from the same evidence, while the other component studies change the evaluated memory scope, promotion rule, retrieval, or composition policy without recollecting source experience\.

## Appendix GMemCoPer\-Step Prompt Template

The displayedLocal memory,Global memory, andFailure memorylines are rendering labels for the grounding, workflow, and reflection fields of Eq\.[10](https://arxiv.org/html/2610.07376#S3.E10), respectively; they do not define three independently stored memory banks\. Record provenance is retained during composition, and an applicable global record may also contribute to grounding after current\-state role binding \(Appendix[E\.3](https://arxiv.org/html/2610.07376#A5.SS3)\)\. The displayed prompt also contains reference\-case, trajectory, and insight slots outside the Memory Decision Summary, but the formatter emits an optional slot only when its list is nonempty\. In the implementedMemCopayload,reference\_cases,insights,action\_constraints, andrepair\_hintsare empty\. TheMemCosummary is supplied as at most oneplanner\_notesentry after query\-guided composition and rendering\.execution\_patternsis an optional wrapper slot: it is empty for ALFWorld, PDDL, and FEVER, while in ScienceWorld it may contain at most two score\-improving fragments retrieved from committed local histories\. Separately, the task wrapper supplies benchmark\-authored few\-shot reference cases from the task configuration and currently truncates that list to its first case\. These surrounding wrapper slots are outside the three\-field Memory Decision Summary in Eq\.[10](https://arxiv.org/html/2610.07376#S3.E10)\.

\{tcolorbox\}

\[skillbox,title=MemCoPer\-Step Prompt Template\]System Prompt \[ENVIRONMENT\-SPECIFIC SYSTEM PROMPT\] For example, the system prompt specifies the legal action space and output format for the current benchmark: ALFWorld household actions, PDDL operators, FEVER Search/Lookup/Finish actions, or ScienceWorld valid commands\.

User Prompt \#\# Successful Examples \(Reference Cases; optional, task\-configured\) Below are some examples of similar tasks that were successfully completed\. Please use these as references to guide your thinking and approach to the current task: \[FEW\-SHOT REFERENCE CASES\]

\#\# Your Own Past Successes \(Execution Patterns\) Here are examples of successful execution processes you’ve previously used on similar tasks\. Pay special attention to the step\-by\-step procedures and strategies, especially when encountering obstacles: \[RETRIEVED SUCCESSFUL TRAJECTORIES\]

\#\# Key Insights from Related Tasks \(empty in the MemCo payload\) The following are insights gathered during the execution of similar tasks\. You may refer to them during your task execution to improve problem\-solving accuracy\. \[RETRIEVED RULES / INSIGHTS\] \[PLANNER NOTES: AT MOST ONE MemCo SUMMARY\] \[ACTION CONSTRAINTS: EMPTY FOR MemCo \] \[REPAIR HINTS: EMPTY FOR MemCo \]

\#\# How to Use Your Intermediate Findings \[ENVIRONMENT\-SPECIFIC MEMORY\-USAGE INSTRUCTIONS\] For example, treat retrieved memories as planning hints rather than exact action sources; prefer currently valid actions; avoid copying stale object names, operator arguments, evidence labels, or unavailable commands; and do not repeat actions that failed or made no progress\.

\#\#\# MemCo Memory Decision Summary Current phase: \[PHASE\_LABEL\] Current state: \[STATE\_SUMMARY\] Local memory: \[LOCAL\_MEMORY\] Global memory: \[GLOBAL\_MEMORY\] Failure memory: \[FAILURE\_MEMORY\] Next priority: \[NEXT\_PRIORITY\] Confidence / caveat: \[CONFIDENCE\_CAVEAT\]

\#\# Your Turn: Take Action\! Use the above examples and insights as a foundation, and now work on the following task: \[TASK DESCRIPTION / QUERY\]

\[CURRENT OBSERVATION\] \[CURRENT VALID ACTIONS, IF PROVIDED\] \[RECENT ACTION\-OBSERVATION HISTORY\]

Output exactly one valid next action\.

## Appendix HCross\-Setting Statistical Significance Analysis

We conduct a complementary non\-parametric analysis to assess whether the performance improvements ofMemCoare consistent across backbone and task settings\. Following standard practice for comparing multiple learning methods across matched evaluation settings[Demšar \(2006\)](https://arxiv.org/html/2610.07376#bib.bib36), each backbone–task configuration is treated as one evaluation block\. The inputs are the method\-wise mean results in Table[1](https://arxiv.org/html/2610.07376#S4.T1)\. Table[16](https://arxiv.org/html/2610.07376#A8.T16)summarizes relative standing, Table[17](https://arxiv.org/html/2610.07376#A8.T17)tests the across\-method omnibus null, and Table[18](https://arxiv.org/html/2610.07376#A8.T18)reports the paired comparisons against each baseline\. These tables answer different questions and are not additional independent experimental runs\.

### H\.1Matched Evaluation Blocks and Average Ranks

##### Evaluation blocks\.

The analysis containsNblk=12N\_\{\\mathrm\{blk\}\}=12matched configurations, corresponding to three LLM backbones and four task settings: FEVER, PDDL, ALFWorld Familiar Layout, and ALFWorld Held\-out Layout\. Six methods are compared in every block: ICL, A\-Mem, MemSkill, MemRL, G\-Memory, andMemCo, givingKmeth=6K\_\{\\mathrm\{meth\}\}=6\.

Accuracy and interaction steps are analyzed separately\. This avoids treating the two metrics obtained from the same evaluation as independent blocks\. For accuracy, larger values indicate better performance; for interaction steps, smaller values indicate better performance\. Within each block, the best method receives rank 1, and tied methods receive their average rank\.

##### Average Ranks\.

Letranki​j\(μ\)\\operatorname\{rank\}\_\{ij\}^\{\(\\mu\)\}denote the rank of methodjjin blockiifor metricμ∈\{Acc,Steps\}\\mu\\in\\\{\\mathrm\{Acc\},\\mathrm\{Steps\}\\\}\. The average rank is

R¯j\(μ\)=1Nblk​∑i=1Nblkranki​j\(μ\)\.\\overline\{R\}\_\{j\}^\{\(\\mu\)\}=\\frac\{1\}\{N\_\{\\mathrm\{blk\}\}\}\\sum\_\{i=1\}^\{N\_\{\\mathrm\{blk\}\}\}\\operatorname\{rank\}\_\{ij\}^\{\(\\mu\)\}\.\(33\)
Table[16](https://arxiv.org/html/2610.07376#A8.T16)reports the resulting average ranks\.MemCoobtains the best average rank for both accuracy and interaction steps\. We additionally report the average over all 24 metric\-specific slices as a descriptive summary; this combined value is not used as the sample size of the inferential tests\. In particular, the combined column is the arithmetic mean of the two metric\-specific average ranks; it is not a new set of 24 independent evaluation blocks\.

Table 16:Average ranks across the matched backbone–task configurations\. Lower values are better\. The final column is descriptive only; statistical tests are conducted separately for accuracy and steps\.

### H\.2Omnibus Tests Across Methods

For each metric, the Friedman statistic is

χF,μ2=12​NblkKmeth​\(Kmeth\+1\)​\[∑j=1Kmeth\(R¯j\(μ\)\)2−Kmeth​\(Kmeth\+1\)24\]\.\\chi\_\{F,\\mu\}^\{2\}=\\frac\{12N\_\{\\mathrm\{blk\}\}\}\{K\_\{\\mathrm\{meth\}\}\(K\_\{\\mathrm\{meth\}\}\+1\)\}\\left\[\\sum\_\{j=1\}^\{K\_\{\\mathrm\{meth\}\}\}\\left\(\\overline\{R\}\_\{j\}^\{\(\\mu\)\}\\right\)^\{2\}\-\\frac\{K\_\{\\mathrm\{meth\}\}\(K\_\{\\mathrm\{meth\}\}\+1\)^\{2\}\}\{4\}\\right\]\.\(34\)
When tied ranks occur, we apply the standard correction

Cμ=1−∑i=1Nblk∑g\(ti​g3−ti​g\)Nblk​\(Kmeth3−Kmeth\),χ~F,μ2=χF,μ2Cμ,C\_\{\\mu\}=1\-\\frac\{\\sum\_\{i=1\}^\{N\_\{\\mathrm\{blk\}\}\}\\sum\_\{g\}\\left\(t\_\{ig\}^\{3\}\-t\_\{ig\}\\right\)\}\{N\_\{\\mathrm\{blk\}\}\(K\_\{\\mathrm\{meth\}\}^\{3\}\-K\_\{\\mathrm\{meth\}\}\)\},\\qquad\\widetilde\{\\chi\}\_\{F,\\mu\}^\{2\}=\\frac\{\\chi\_\{F,\\mu\}^\{2\}\}\{C\_\{\\mu\}\},\(35\)
whereti​gt\_\{ig\}denotes the number of tied methods in tie groupggof blockii\. Accuracy contains three pairwise ties, resulting inCAcc=0\.9929C\_\{\\mathrm\{Acc\}\}=0\.9929\. No ties occur for interaction steps, soCSteps=1C\_\{\\mathrm\{Steps\}\}=1\.

Because the classical Friedman statistic can be conservative, we use the Iman–Davenport correction:

FF,μ=\(Nblk−1\)​χ~F,μ2Nblk​\(Kmeth−1\)−χ~F,μ2\.F\_\{F,\\mu\}=\\frac\{\(N\_\{\\mathrm\{blk\}\}\-1\)\\widetilde\{\\chi\}\_\{F,\\mu\}^\{2\}\}\{N\_\{\\mathrm\{blk\}\}\(K\_\{\\mathrm\{meth\}\}\-1\)\-\\widetilde\{\\chi\}\_\{F,\\mu\}^\{2\}\}\.\(36\)
Under the omnibus null hypothesis, the Iman–Davenport statistic is compared with an approximateFFreference distribution withKmeth−1=5K\_\{\\mathrm\{meth\}\}\-1=5and\(Kmeth−1\)​\(Nblk−1\)=55\(K\_\{\\mathrm\{meth\}\}\-1\)\(N\_\{\\mathrm\{blk\}\}\-1\)=55degrees of freedom\.

As reported in Table[17](https://arxiv.org/html/2610.07376#A8.T17), the omnibus null hypothesis is rejected for both metrics under this testing model\. This omnibus result indicates an across\-method difference, but does not establish which individual baseline differs fromMemCo; those comparisons are reported next\.

Table 17:Friedman tests with the Iman–Davenport correction\. The reported Friedman statistics include the tie correction where applicable\.
### H\.3Paired Comparisons, Effect Sizes, and Interpretation

After rejecting the omnibus null hypotheses, we compareMemCowith each baseline using exact two\-sided Wilcoxon signed\-rank tests\. Unlike a comparison based only on average ranks, this paired test uses the direction and magnitude of the performance differences within each matched configuration\.

For baselinebb, we define the accuracy difference as

Δi,bAcc=Acci,MemCo−Acci,b,\\Delta\_\{i,b\}^\{\\mathrm\{Acc\}\}=\\mathrm\{Acc\}\_\{i,\\texttt\{MemCo\}\{\}\}\-\\mathrm\{Acc\}\_\{i,b\},\(37\)
and the interaction\-step difference as

Δi,bSteps=Stepsi,b−Stepsi,MemCo\.\\Delta\_\{i,b\}^\{\\mathrm\{Steps\}\}=\\mathrm\{Steps\}\_\{i,b\}\-\\mathrm\{Steps\}\_\{i,\\texttt\{MemCo\}\{\}\}\.\(38\)
Thus, positive differences favorMemCofor both metrics\. Zero differences are excluded from the signed\-rank statistic\. The remaining absolute differences are ranked, with average ranks assigned to ties\. LetTW\+T\_\{\\mathrm\{W\}\}^\{\+\}andTW−T\_\{\\mathrm\{W\}\}^\{\-\}be the sums of ranks associated with positive and negative differences, respectively\. The two\-sided test statistic is

TW=min⁡\{TW\+,TW−\}\.T\_\{\\mathrm\{W\}\}=\\min\\\{T\_\{\\mathrm\{W\}\}^\{\+\},T\_\{\\mathrm\{W\}\}^\{\-\}\\\}\.\(39\)
We calculate the conditional two\-sidedpp\-values by enumerating all sign assignments to the observed nonzero absolute\-difference ranks under the paired sign\-symmetry null\. HereTWT\_\{\\mathrm\{W\}\}denotes the signed\-rank statistic;W⁡\(p¯\)W\(\\bar\{p\}\)remains the Wilson promotion score\. The enumeration is exact for this sign\-assignment model, including averaged tied ranks; it does not itself establish that the evaluation blocks are independent\.

Because the analysis contains five control\-versus\-baseline comparisons for each of two metrics, we jointly correct allM=10M=10post\-hocpp\-values using Holm’s step\-down procedure[Holm \(1979\)](https://arxiv.org/html/2610.07376#bib.bib37)\. Given the ordered rawpp\-valuesp\(1\)≤⋯≤p\(M\)p\_\{\(1\)\}\\leq\\cdots\\leq p\_\{\(M\)\}, the adjusted values are

p~\(i\)=max1≤j≤i⁡\{min⁡\[1,\(M−j\+1\)​p\(j\)\]\}\.\\widetilde\{p\}\_\{\(i\)\}=\\max\_\{1\\leq j\\leq i\}\\left\\\{\\min\\left\[1,\(M\-j\+1\)p\_\{\(j\)\}\\right\]\\right\\\}\.\(40\)
This correction controls the family\-wise error rate across all reported method–metric comparisons\.

##### Effect Size\.

In addition to statistical significance, we report the matched\-pairs rank\-biserial correlation

rrb=TW\+−TW−TW\+\+TW−\.r\_\{\\mathrm\{rb\}\}=\\frac\{T\_\{\\mathrm\{W\}\}^\{\+\}\-T\_\{\\mathrm\{W\}\}^\{\-\}\}\{T\_\{\\mathrm\{W\}\}^\{\+\}\+T\_\{\\mathrm\{W\}\}^\{\-\}\}\.\(41\)
Positive values indicate an advantage forMemCo, with values closer to 1 indicating greater cross\-configuration consistency\.

Table[18](https://arxiv.org/html/2610.07376#A8.T18)reports the complete results\. The Win/Loss/Tie column counts the configurations in whichMemCois better, worse, or tied with the corresponding baseline\. For example, the G\-Memory comparisons give 10 wins and 2 losses for each metric, with positive rank\-biserial effects and Holm\-adjustedp=0\.0146p=0\.0146\. The win counts summarize direction, whereas the effect sizes and signed\-rank statistics also depend on the ranked magnitudes of the paired differences\.

Table 18:Exact two\-sided Wilcoxon signed\-rank comparisons betweenMemCoand each baseline across the 12 matched backbone–task configurations\. Holm correction is applied jointly to all ten comparisons\. All differences are defined such that positive values favorMemCo\.
##### Summary\.

Under the stated block\-level testing assumptions, all ten paired comparisons have Holm\-adjustedp<0\.05p<0\.05\. In particular, the improvements over G\-Memory remain significant for both accuracy \(pHolm=0\.0146p\_\{\\mathrm\{Holm\}\}=0\.0146\) and interaction steps \(pHolm=0\.0146p\_\{\\mathrm\{Holm\}\}=0\.0146\)\. The corresponding rank\-biserial correlations are 0\.846 and 0\.872, respectively, indicating that the differences are not only statistically significant but also directionally consistent across the evaluated configurations\.

The unit of analysis in these tests is the matched backbone–task configuration\. The two metrics are tested separately, and the analysis does not treat the three repeated runs or the two metrics from one configuration as additional independent evaluation blocks\. Accordingly, these results should be interpreted as evidence of consistent performance differences across the evaluated configurations rather than as a claim about all possible models and environments\. Configurations reuse backbones and task families, so dependence between blocks may limit that inferential interpretation; the reportedpp\-values are conditional on the block\-level assumptions and are not a substitute for independent task\- or seed\-level replication\. The average ranks and paired differences remain descriptive summaries of the evaluated configurations\.

## Appendix ICase Study: Adaptive Memory Support and Cross\-Environment Generalization

![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/casestudy4.png)Figure A\.1:Case study showcasing adaptive memory support and cross\-environment generalization\.\(a\) In the shown G\-Memory trajectory, the agent attempts placement before satisfying the cleanliness requirement\. \(b\)MemCouses local actionable knowledge to avoid the invalid placement in the same environment\. \(c\) In an unseen environment,MemCocombines a reusable global workflow with current\-environment grounding\.To qualitatively evaluateMemCo, we analyze the trajectories across heterogeneous settings to investigate how local situational grounding and global procedural workflows interact dynamically online\.

##### Exploration Efficiency\.

As shown in Fig\.[A\.1](https://arxiv.org/html/2610.07376#A9.F1)\(a\) and[A\.1](https://arxiv.org/html/2610.07376#A9.F1)\(b\), when facing the same task “Put a clean cloth in countertop”, the displayed G\-Memory trajectory attempts to place the cloth before satisfying the cleanliness requirement, resulting in redundant interactions\. In contrast,MemCoretrieves decision\-relevant support before placement: the reusable clean\-before\-store ordering is combined with local actionable knowledge for the current state\. The resulting trajectory avoids the invalid move and completes the task with fewer interaction steps\.

##### Unseen\-Environment Generalization\.

The comparison between Fig\.[A\.1](https://arxiv.org/html/2610.07376#A9.F1)\(b\) and[A\.1](https://arxiv.org/html/2610.07376#A9.F1)\(c\) illustrates how shared experience supports an agent in an unseen environment\. The task changes from cleaning a cloth in a kitchen to “Clean a bar of soap and put it in a vanity” in a bathroom\. A kitchen\-specific instruction can be irrelevant in the bathroom, whereas the clean\-before\-place ordering can remain useful under the corresponding applicability conditions\.

As illustrated in Fig\.[A\.1](https://arxiv.org/html/2610.07376#A9.F1)\(c\), query\-guided selection and composition exclude incompatible kitchen\-specific guidance, including the irrelevant “clothwasher trace”\. The shared workflow supplies the action order; the current observation and available actions ground its roles in the bathroom basin and vanity, with applicable local evidence providing further context\. This decision\-time grounding does not require writing new environment\-specific records into the frozen evaluation memory\. The shown trajectory completes the task in 6 steps, illustrating how shared procedural guidance can be transferred to an environment unseen by the evaluated agent while current\-environment grounding determines how that guidance is executed\.

## Appendix JVisualizations of PDDL Memory Structures

To present a clear and concrete view of our memory repository, we visualize the actual global and local memory structures generated during the PDDL symbolic planning tasks\. Because these structures are very wide, each visualization and its caption are rotated together and placed on a standalone figure page to use the page height and improve readability\.

### J\.1Global Memory Structure

Figure[A\.2](https://arxiv.org/html/2610.07376#A10.F2)shows the global memory snapshot assembled from contributions in gripper, blockworld, barman, and tyreworld\. The sharing interface in Algorithm[B\.1](https://arxiv.org/html/2610.07376#A2.SS1)receives selected reusable records and their evidence rather than complete local trajectories or graphs\. The visualization contains promoted workflows and precondition relations from different planning domains, illustrating how recurrent local structures are represented in the shared global bank\. The stored global records remain conditional and are checked against the current planning state before use\.

![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/pddl_gm3_real_global.png)Figure A\.2:Visualization of the final PDDL global memory structure\.The centralized server aggregates top\-promoted rules and preconditions across heterogeneous planning domains into a structured global bank\.
### J\.2Local Memory Graphs

Figures[A\.3](https://arxiv.org/html/2610.07376#A10.F3)through[A\.6](https://arxiv.org/html/2610.07376#A10.F6)display local\-memory snapshots across the four PDDL domains, including state and interaction structure, outcome\-annotated records, and sample artifacts\. The connected experience and concrete cases remain local; selected patterns and actionable relations may be shared through the separate sharing interface\.

Figure[A\.6](https://arxiv.org/html/2610.07376#A10.F6)provides examples of the stored local relations, including goal\-advancing conditions, failure\-triggered repairs, and failure\-avoidance guidance\. These entries illustrate the complementary roles of structured patterns, actionable knowledge, and concrete local context\. The visualization labels reflect the stored instances; the paper\-level memory components remain theGG–𝒫\\mathcal\{P\}–ℰ\\mathcal\{E\}–ℛ\\mathcal\{R\}decomposition in Eq\.[2](https://arxiv.org/html/2610.07376#S3.E2)\.

![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/pddl_gm3_real_local_tyreworld.png)Figure A\.3:Local memory structure for the tyreworld domain\.The graph captures real\-time planning states and local records for vehicle repair configurations\.![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/pddl_gm3_real_local_gripper.png)Figure A\.4:Local memory structure for the gripper domain\.The graph visualizes execution trajectories and goal\-advancing action links for robotic manipulation tasks\.![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/pddl_gm3_real_local_barman.png)Figure A\.5:Local memory structure for the barman domain\.The snapshot logs successful action combinations and filters out invalid interaction paths in a dense action space\.![Refer to caption](https://arxiv.org/html/2610.07376v1/fig/pddl_gm3_real_local_blockworld.png)Figure A\.6:Local memory structure for the blockworld domain\.The network represents temporal sequence steps and block rearrangement heuristics\.