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Theoretical Analysis on MAD :

--- Ongoing

• Background：
  • The effectiveness of Multi-Agent Discussion (MAD) remains debate. Some studies endorse its utility [1], others argue that a sparse structure is superior [2], while some suggest prompt optimization as a more direct approach [3].
    • To date (2024/08/15), only one paper[6] has attempted to optimize MAD, focusing primarily on agent quantity reduction rather than structural optimization (Detailed comparison can be seen in the Appendix below).
  • There is a lack of a unified (theoretical) framework that comprehensively explains the roles of: 1. agent role, 2. agent quantity, and 3. agent connectivity within MAD. Through this framwork, we can design appropriate structures and communication strategies for factual reasoning.
• Objective：
  • Develop a unified (theoretical) framework to model MAD, explaining the interplay among the aspects mentioned above.
    • By modeling MAD (through rounds) as a Directed Acyclic Graph (DAG) [6], we expect that through paramter estimation under certain assumptions, our framework can directly recommend the optimal distribution of agents given the training set (Similar to the analysis in [7]).
    • The model should offer (qualitative) analysis for when to create new agents, discard existing ones or maintain existing agents, as inappropriate attempts may lead to non-convergent answers.
• Approach：(Outline)
  • We model the discussions as the in-context demonstrations, and the whole discussion can be seen as the Bayesian network (Similar to [4], where multiple Hidden Markov Models (HMMs) are used to represent the different roles of agents).
  • Further, given the Bayesian Network characterized above, we can model the MAD structure as a RNN-like network, applying techniques from [5] to optimize the graph (with gradients accumulated through exponential smoothing). For each sub-problem, the agents should be able to assess its complexity and distribute the appropriate number of agents and discussion structure to address it effectively.

References:

[1] ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate, 202308, Tsinghua

[2] Improving Multi-Agent Debate with Sparse Communication Topology, 202406, GoogleMind

[3] Should we be going MAD? A Look at Multi-Agent Debate Strategies for LLMs, 202311, InstaDeep

[4] An Explanation of In-context Learning as Implicit Bayesian Inference, 202111, Stanford

[5] GPTSwarm: Language Agents as Optimizable Graphs. 202402, KAUST

[6] Dynamic LLM-Agent Network: An LLM-agent Collaboration Framework with Agent Team Optimization, 202310, Stanford

[7] Are More LLM Calls All You Need? Towards Scaling Laws of Compound Inference Systems, 202403, Stanford

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Appendix (Related Works):

Efficacy (Within Same Hierarchical Level, Task Completion as Goal)：

Agent Framework	After allocation, is the number and role of agents dynamically adjusted in each round of communication?	After allocation, is the number and role of agents dynamically adjusted before generating the initial answer (i.e., information passing to output node)?	After allocation, is the connectivity between agents dynamically adjusted in each communication round?	After allocation, is the structure optimized further when generating the initial answer (i.e., information passing to output node)?	Additional Information from the Paper
AutoGen	×	×	×	×
Agentverse	×	√	×	×	Communication between agents is implemented through Debate.
Adaptive Team Building	×	√	×	×	Communication between agents is implemented through Debate.
GPT-Swarm	×	×	×	√	Flexibility in agent interactions is refined iteratively through a utility function, where agents may be removed during refinement (although the quantity and roles of agents are predefined).；
Trace	×	×	×	×	This approach optimizes all prompts simultaneously, rather than only local prompts.
DyLAN	×	×	√ (agents are only reduced in number, with no other dynamic adjustments)	√ (agents are only reduced in number, with no other dynamic adjustments)	1. There is no hierarchical structure (a fixed number of agents engage from start to finish); 2. Dynamic adjustment in quantity only reduces agents without adding or changing roles; 3. Dynamic connectivity adjustments are limited to reduction from full connectivity, with no additions.
Symbolic Learning	×	√	×	√	1. The paper remains incomplete, so specific implementation details are not available; 2. The framework aims to establish a unified agent network, enabling concurrent updates to agent quantity, prompts, and tools.

Efficiency (Communication)：

Agent Framework	Is each agent's prompt optimized?	Is there bidirectional communication between adjacent agents?	Do agents communicate with each other based on needs during each task execution round?
AutoGen	×	×	×
Agentverse	×	×	×
Adaptive Team Building	×	×	×
GPT-Swarm	√	×	×
Trace	√	×	×
DyLAN	×	—	—
Symbolic Learning	√	×	×

--- Edited on 2024/10/29

Contributors

Hua Tang

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