FRACTAL: A Self-Similar Multi-Agent Orchestration Architecture with Formal Communication, Convergence, and Depth Bounds

Ohad Dan; Abhinav Taliyan

cs.AIOct 15, 2026

FRACTAL: A Self-Similar Multi-Agent Orchestration Architecture with Formal Communication, Convergence, and Depth Bounds

Authors: Ohad Dan, Abhinav Taliyan

Abstract

We present FRACTAL, a self-similar multi-agent architecture for recursive goal decomposition, in which the same five-component organizational pattern -- Orchestrator, Ensemble, Knowledge Ledger, Decision Maker, Meta-Observer -- recurs at every level of a decomposition tree. We make four formal contributions: (1) a communication bound showing intra-node cost is linear in ensemble size and round count (O(kr)) under a two-phase blind-proposal/stress-test protocol, versus quadratic cost for free-form debate, with an explicit, stated assumption on fixed evaluator count; (2) a two-mode orchestration criterion separating generative and evaluative phases via a measurable diversity-saturation threshold; (3) a supermajority convergence guarantee with explicit probability bounds at stated agreement levels, and a formal depth bound under an operationalized goal-complexity measure; (4) a Bayesian inter-layer escalation mechanism unifying hysteresis and contract-breach signaling under one posterior update. We illustrate the architecture's execution qualitatively on a worked example and a multi-layer case study; we do not report quantitative performance claims in this paper, and we explicitly discuss the formal and inductive-bias limitations of the model, including an unimplemented but architecture-compatible direction toward bounded self-improvement. We use "fractal" as an architectural metaphor for self-similarity, not a measured mathematical property. Empirical validation of the architecture's comparative performance is left to future work.

Figures & tables

Figure 1: FRACTAL’s formal node structure (Definition 1), shown schematically — a diagram of the model, not a measured system. Self-similar recursive tree where every node (regardless of depth) instantiates the same 5-component structure: Orchestrator (O), Ensemble (E), Knowledge Ledger (L), Decision Maker (D), Meta-Observer (M). Downward arrows carry immutable Execution Contracts; upward dashed arrows indicate CONCERN escalation. Sibling isolation (no lateral communication) is enforced by construction.

$k$	$C_{2P}$ (Eq. 1)	$C_{debate}$ (Eq. 2)	$C_{2P}/C_{debate}$	Reduction
3	$3{,}500+1{,}800+500=6{,}800$	$4{,}500+2{,}700=7{,}200$	$0.944$	$1.06\times$
4	$6{,}000+1{,}800+500=8{,}300$	$6{,}000+5{,}400=11{,}400$	$0.728$	$1.37\times$
5	$7{,}500+1{,}800+500=9{,}800$	$7{,}500+9{,}000=16{,}500$	$0.594$	$1.68\times$

Table 1: Worked numeric example under one self-consistent, explicitly stated set of token constants (illustrative, not measured). FRACTAL is cheaper than debate across the entire stated range

k\in[3,5]

under these constants.

Figure 2: Communication cost as predicted by Theorem 6’s formula (Equation 1 vs. Equation 2) under the token constants stated in the worked numeric example (

T_{p}=T_{turn}=500

T_{s}=T_{resp}=300

T_{synth}=500

c=3

m=2

r=3

), not measured experimentally. FRACTAL is cheaper than free-form debate for all

k\in[3,5]

under these constants; see Theorem 6 for the general

O(kr)

vs.

O(k^{2}r)

comparison.

Figure 3: Two-mode dynamics as predicted by the model in Definition 9 and Proposition 10 under illustrative parameter values, not measured from any run. Top: proposal diversity grows logistically in Divergent mode; convergence follows in Convergent mode. Bottom: mode switch triggered when marginal diversity gain drops below

\tau_{sat}

, subject to minimum dwell time

r_{dwell}\geq 2

Figure 4: Supermajority convergence probability as predicted by Theorem 12’s formula, plotted across illustrative agreement probabilities

p

; not measured experimentally. At

p=0.7

: 89.5% within 3 rounds; at the higher illustrative calibration point

p=0.85

: 99.6%.

Figure 5: An illustrative trajectory of the concern accumulator (Definition 15) under example evidence

e(t)

, not data from any run. The concern accumulator smooths noisy evidence into a continuous signal, crossing categorical thresholds for CONCERN and BREACH emission.

Paradigm	System	FRACTAL analogue
Inference-time refinement	Self-Refine ( Madaan et al., 2023 )	Within-node convergent phase
Episodic memory	Reflexion ( Shinn et al., 2023 )	Knowledge Ledger persistence
Meta-agent search	ADAS ( Hu et al., 2024 )	Possible future direction ∗
Evolutionary generation	EvoAgent ( Yuan et al., 2025 )	Ensemble persona selection
Skill accumulation	Voyager ( Wang et al., 2023 )	Ledger of validated strategies
Program search	FunSearch ( Romera-Paredes et al., 2024 )	Falsification-guided refinement

Table 2: Self-improvement paradigms and FRACTAL’s architectural analogues (compatibility, not implementation). ∗ These two rows describe directions the architecture is compatible with extending toward, not a mechanism implemented in this paper; see the discussion below.

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PANDA: A Decentralized Architecture with Flexible Orchestration for Scalable, Fault-Tolerant Multi-Agent Systems

Matthew D. Laws, Cristina Nita-Rotaru

Khoury College of Computer Sciences Northeastern University

Multi-Agent LLM Systems Multi-Agent Orchestration Multi-Agent Systems AI Agent Governance

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Existing architectures for LLM-based multi-agent systems (MAS) cannot reliably and efficiently solve multi-step tasks at scale: they struggle to support large numbers of agents and concurrent tasks, tolerate failures, govern agent interactions, and accommodate the diverse planning and execution patterns different tasks require. We present PANDA, a decentralized architecture that connects a large collective of heterogeneous, independently administered agents, letting them discover each other's capabilities and self-organize into small specialized teams per task. PANDA scales by decoupling collective communication from team communication, allowing agents to participate in multiple teams simultaneously, load-balancing tasks across the collective, and scheduling concurrent work within each agent. PANDA further separates the underlying architecture from the orchestration strategy, supporting three planning and execution patterns (star, chain, and mesh) that can be selected according to the structure and requirements of each task. PANDA detects infrastructure and orchestration failures and recovers affected tasks by dynamically replanning around failed components. Finally, to provide governance without a centralized service that would limit scalability, PANDA uses a web-of-trust model to constrain agent interactions to established trust relationships. We evaluate PANDA on the HotPotQA benchmark, demonstrating that it scales to thousands of agents, assembles teams in milliseconds, matches state-of-the-art accuracy at up to 8x the efficiency, and sustains 100% task completion under faults where existing systems fail.

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