DIANOIA: Diagnostic Decomposition and Joint Optimization for Multi-Agent Reasoning

Multi-agent LLM systems consistently outperform single-agent baselines, yet practitioners still cannot predict which design works for a new task or diagnose why one fails. We argue this gap persists largely because the field lacks a diagnostic framework with measurable primitives and testable predictions. We introduce DIANOIA, a three-channel decomposition of multi-agent reasoning gain into coverage, fidelity, and synthesis, each of which is empirically measurable. From this decomposition, we derive a diagnostic protocol that identifies the bottleneck channels for any given task. We instantiate the protocol as a multi-agent system whose three components mirror the channels: role-diverse proposers for coverage, execution-grounded verification for fidelity, and iterative synthesis. On GSM8K, AIME-2025, MBPP, and BFCL-SP, our method outperforms strong multi-agent baselines under matched token budgets, dominating the Pareto frontier on MBPP at ~5× token savings and reaching +4.6pp at matched cost. On every benchmark, the protocol picks the right bottleneck channels; the system we built around it leads across models. We release code, adapters, diagnostic metrics, and a Claude Code skill at https://anonymous.4open.science/r/DIANOIA4MAS. DIANOIA reframes multi-agent design as channel-aware resource allocation: diagnose which channel is the bottleneck for your task, then invest tokens accordingly.