# ACAR: Adaptive Complexity Routing for Multi-Model Ensembles with Auditable Decision Traces

arXiv: https://arxiv.org/abs/2602.21231 · HTML: https://mlsanity.com/paper/2602.21231/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 6 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [A Survey on Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2407.06204/) (2024)
- [The Shapley Value in Machine Learning](https://mlsanity.com/paper/2202.05594/) (2022)

## Built on by (most cited first, 1 of 1)

- [Optimizing the Cost-Quality Tradeoff of Agentic Theorem Provers in Lean](https://mlsanity.com/paper/2606.04883/) (2026)

## Abstract (arXiv)

We present ACAR (Adaptive Complexity and Attribution Routing), a measurement framework for studying multi-model orchestration under auditable conditions. ACAR uses self-consistency variance (sigma) computed from N=3 probe samples to route tasks across single-model, two-model, and three-model execution modes. The system is implemented on top of TEAMLLM, a deterministic execution substrate with immutable artifacts and complete decision traces. We evaluate ACAR on 1,510 tasks spanning four benchmarks: MathArena, Reasoning Gym, LiveCodeBench, and SuperGPQA, using Claude Sonnet 4, GPT-4o, and Gemini 2.0 Flash, producing more than 7,550 auditable runs. Results show that sigma-based routing achieves 55.6 percent accuracy, exceeding the two-model baseline of 54.4 percent while avoiding full ensembling on 54.2 percent of tasks. The routing mechanism is model-agnostic and requires no learned components. We also document negative results. First, retrieval augmentation reduced accuracy by 3.4 percentage points, as median retrieval similarity was only 0.167, demonstrating that experience injection without semantic alignment introduces noise rather than grounding. Second, when models agree on incorrect answers (sigma equals zero), no downstream ensemble can recover; this agreement-but-wrong failure mode is intrinsic to self-consistency and bounds achievable accuracy at approximately eight percentage points below full ensembling. Third, attribution estimates based on proxy signals such as response similarity and entropy showed weak correlation with ground-truth leave-one-out values, indicating that practical attribution requires explicit counterfactual computation. This work documents which assumptions fail in practice and provides falsifiable baselines for future research on routing, retrieval, and multi-model attribution.