Modular Adaptable Output Decomposition (MAOD)

• Modular Adaptable Output Decomposition (MAOD) is a method that segments LLM outputs into modular, independently editable, and semantically coherent components.
• It employs a six-stage algorithmic workflow—parse, segment, classify, link, validate, and export—to ensure structured, error-free decomposition.
• MAOD underpins component-based architectures, enabling user-driven editing, dynamic recomposition, and improved collaboration in research and code development.

Modular Adaptable Output Decomposition (MAOD) is a formal method for transforming monolithic outputs from LLMs into sets of modular, independently editable, and semantically coherent components. MAOD enables granular manipulation, recomposition, and reuse of generated text or code, and serves as the core of the componentization paradigm, which seeks to move beyond passive text consumption toward active, component-level collaboration and workflow integration (Lingo et al., 10 Sep 2025).

1. Formal Definition and Theoretical Foundation

MAOD is formally defined as a function $f_{maod}: \Sigma^* \rightarrow D$, where $\Sigma^*$ denotes the set of all finite strings, and $D$ is a DecomposedResponse that segments the monolithic response $R \in \Sigma^*$ into a set of $n$ components: $D = f_{maod}(R) = \{c_1, c_2, \ldots, c_n\}$ Each component $c_i$ is a tuple: $$c_i = (\mathrm{id}_i, \mathrm{type}_i, \mathrm{content}_i, \mathrm{meta}_i, \mathrm{includes}_i, \mathrm{links}_i)$$ with:

• $\mathrm{id}_i \in \text{String}$: stable identifier,
• $\mathrm{type}_i \in \mathbb{T}$: semantic class (e.g., Paragraph, Code, Step),
• $\Sigma^*$0: literal text/code span,
• $\Sigma^*$1: metadata (nesting, style),
• $\Sigma^*$2: inclusion flag,
• $\Sigma^*$3: directed inter-component relations.

Valid decompositions must satisfy coverage and disjointness (spans cover $\Sigma^*$4 with no overlap), semantic coherence (each $\Sigma^*$5 forms a rhetorical or functional unit), and acyclic linking (the directed graph $\Sigma^*$6 is acyclic). Segmentations are optimized using a semantic score $\Sigma^*$7 that scores potential boundaries by coherence cues.

2. Algorithmic Workflow for Semantic Segmentation

The MAOD algorithm implements a six-stage state-machine decomposition:

1. PARSE: Detect structural blocks in $\Sigma^*$8 (code, lists, headings, paragraphs).
2. SEGMENT: Divide each block into candidate spans using rhetorical cues.
3. CLASSIFY: Assign semantic types, stable IDs, and extract metadata for each span.
4. LINK: Infer hierarchical and ordering relations among components (parent/child, sequencing).
5. VALIDATE: Remove empties and resolve cycles to enforce constraints.
6. EXPORT: Mark all components as included by default.

The canonical workflow for MAOD:

$\Sigma^*$9

Following decomposition, the system supports fine-grained inline editing, toggling of inclusion, and regeneration (by rerunning MAOD or re-prompting the LLM on a component's content). This allows recomposition of the output as the ordered concatenation of segments marked $D$0, respecting any explicit component links for nesting or order.

3. Component-Based Response Architecture (CBRA)

CBRA provides a practical software architecture for MAOD and live component manipulation, based on three core principles:

• Principle I: Modular Decomposition (MAOD) – Implements the six-stage MAOD pipeline.
• Principle II: User-Driven Manipulation – Each component is editable, include/exclude toggled, or subject to regeneration.
• Principle III: Dynamic Recomposition – Final responses are live-recomposed from selected components, ordered and nested per inter-component links.

CBRA adopts a microservices layout:

Service Layer	Responsibilities	Technologies
Frontend	Four-column UI: Prompt, Response, Components, Recompose	Flask, vanilla JS
Backend	Session orchestration, persistence, model abstraction	FastAPI, PostgreSQL
MAOD Agent	Six-stage decomposition as state machine, REST A2A API	FastAPI, LangGraph
Database	DecomposedResponse and conversation state storage	PostgreSQL
Proxy	TLS termination, load balancing	Caddy

The workflow proceeds from LLM inference, through A2A-based decomposition, to interactive frontend manipulation with live recomposition and regeneration.

4. MAODchat Prototype Implementation

MAODchat demonstrates a full-stack SOA implementation of CBRA and MAOD:

• Frontend: Flask, HTML/CSS/JS, four-column drag-and-drop UI supporting inline edit and markdown support.
• Backend: FastAPI, conversation management (LangGraph), and vendor-agnostic model factory (extensible to GPT-3.5, Claude, etc.) using a centralized VendorMetadata mapping.
• MAOD Agent: FastAPI and LangGraph, implements the state machine decomposition and uses Pydantic models for DecomposedResponse.
• Persistence and Proxy: PostgreSQL for state, Caddy for routing.

Innovations include an Agent-to-Agent (A2A) protocol with strictly typed JSON messages, real-time recomposition in the frontend, and seamless integration of new LLMs via a pluggable model abstraction layer. Components within the UI retain inclusion and edit state and are concatenated for the live recomposed result.

5. Empirical User Study and Observed Workflows

A formative user study (n=4; academic researcher, HCI-trained PM, and two engineers) investigated the practical value and usability of MAODchat:

• Decomposition Utility: Segmenting outlines to sections proved beneficial for academic writing; code refactoring workflows validated isolation of functions for iterative development.
• Fluff Removal: Enabled selective exclusion of non-essential content (intros/conclusions).
• UI/Interaction Issues: Terminological mismatches (“Edit” vs. “Regenerate”) and unfamiliarity with the four-column paradigm caused confusion.
• Performance and Fidelity Concerns: Large responses (e.g., Docker Compose→Helm) exposed context window limitations; markdown formatting was occasionally degraded.
• Collaboration Affordances: Participants envisioned collaborative workflows including per-section assignments and “GitHub for papers”.

Design implications suggest aligning UI terms with established chat metaphors, preserving markdown fidelity, introducing progressive feature disclosure, and clarifying decomposition and context boundaries.

6. Agent-to-Agent Protocols for Automated Decomposition

MAOD operates over A2A protocols mediating decomposition requests and responses. The protocol is defined in JSON or a type-safe DSL:

JSON Example – Decomposition Exchange

$D$1 The protocol ensures clear semantics for decomposition actions, component inclusion, and linkages, facilitating seamless integration across agents and user interfaces.

7. Significance and Future Directions

MAOD formalizes componentization, enabling decomposed manipulation and collaborative editing across knowledge work, code review, and academic authoring. Early empirical results indicate alignment with common workflows and suggest potential for larger-scale, team-based document-centric collaboration. Opportunities remain for refining usability, improving semantic segmentation fidelity (especially for complex structures such as markdown lists), and scaling to larger outputs constrained by LLM context windows. The MAOD and CBRA paradigm offers a foundation for automated workflow tools, selective regeneration, and agent orchestration in document-centric LLM applications (Lingo et al., 10 Sep 2025).