Mixture of Complementary Agents for Robust LLM Ensemble

Large language models (LLMs) are increasingly deployed in enterprise settings, yet individual models remain bounded by model-specific capability limitations. These heterogeneous boundaries pose a deployment challenge, but also create an opportunity: strategically coordinating multiple LLMs may unlock collective intelligence exceeding any single model. Existing approaches fix how models are combined in advance, overlooking the dynamic, state-dependent role of complementarity in complex problem solving. Drawing on the wisdom-of-crowds paradigm, we reconceptualize collective LLM intelligence as relay-style complementarity: a sequential process in which each successor model is selected to address the specific bottleneck identified in its predecessor's output. To operationalize this, we propose WILC (Wisdom Integration of LLM Crowds), a framework grounded in two design principles. First, iterative reflection-and-refinement establishes a state-preserving workflow through which models diagnose and refine prior outputs. Second, complementarity-driven model selection governs transitions via a dual-gate mechanism: prospective complementarity fit (PCF) identifies the worker most suited to the current bottleneck, while posterior complementarity gain (PCG) evaluates whether the selected transition improves the evolving solution. Experiments across four diverse benchmarks show that WILC outperforms existing approaches, including single-model self-refinement, ensemble methods, and query-routing methods. Under standardized pricing assumptions, WILC matches the average benchmark performance of GPT-5.2 at roughly 7 times lower estimated per-query cost, while facilitating data sovereignty through self-hosted deployment. This study extends wisdom-of-crowds theory from static aggregation to sequential AI complementarity and provides transferable design principles for multi-AI coordination.

Large Language Models (LLMs) explore problems through chain-of-thought, but this exploration is buried in unstructured prose. On high-stakes tasks, users cannot tell which steps are well-supported, which alternatives were seriously considered, or how the final conclusion compares to those the model discarded. We propose a framework that ensembles the reasoning structure, not just the answers, of multiple LLMs by weighted merging of Directed Acyclic Graphs (DAGs) extracted from reasoning chains. We weight each step by how many traces independently attest to it, to return "Consensus Reasoning". Across six benchmarks spanning statutory interpretation, graduate-level science, narrative multi-hop reasoning, and first-order logic, our ensemble outperforms a matched-budget majority-vote baseline, with a maximum accuracy gain of 3.1% on MuSR-MM (narrative multi-hop reasoning). On a single model, the framework matches or exceeds self-consistency at the same trace budget while additionally exposing an inspectable consensus reasoning graph. Ensemble weights correlate with LLM-judge rankings of reasoning quality at Spearman $ρ= 0.30$-$0.51$, and consensus subgraphs are preferred over alternatives leading to the majority-vote answer in 54.4-65.4% of head-to-head comparisons across five of six datasets. We observe that our framework can also be used to analyze diverse reasoning perspectives for a problem.

Model ensembling is a well-established technique for improving the performance of machine learning models. Conventionally, this involves averaging the output distributions of multiple models and selecting the most probable label. This idea has been naturally extended to large language models (LLMs), yielding improved performance but incurring substantial computational cost. This inefficiency stems from directly applying conventional ensemble implementation to LLMs, which require a separate forward pass for each model to explicitly compute the ensemble distribution. In this paper, we propose the Mixture-model-like Ensemble (ME). By reinterpreting the ensemble as a mixture model, ME stochastically selects a single model at each step to generate the next token, thereby avoiding the need to explicitly compute the full ensemble distribution. ME is mathematically equivalent to sampling from the ensemble distribution, but requires invoking only one model, making it 1.78x-2.68x faster than conventional ensembling. Furthermore, this perspective connects LLM ensembling and token-level routing methods, suggesting that LLM ensembling is a special case of routing methods. Our findings open new avenues for efficient LLM ensembling and motivate further exploration of token-level routing strategies for LLMs. Our code is available at https://github.com/Kamichanw/Mixture-model-like-Ensemble.