Pyramid MoA: A Probabilistic Framework for Cost-Optimized Anytime Inference

Mixture-of-Agents (MoA) architectures improve inference-time scaling by organizing multiple LLM agents into layered reasoning pipelines. However, existing MoA variants fail to sustain gains as depth increases, exhibiting degradation, early plateauing, or saturation. We propose ReM-MoA, a memory-augmented MoA framework that sustains scaling through two mechanisms: (1) a Ranked Reasoning Memory that persistently stores and ranks reasoning traces from all layers using a comparative Reviewer Agent, and (2) a Curated Diversified Memory Routing scheme that exposes different agents to distinct combinations of successful and failed traces, preserving exploration diversity while propagating high-quality reasoning. We further introduce an optional multi-domain Reviewer distillation pipeline that improves ranking quality through frontier-model supervision. Across five reasoning benchmarks spanning math, formal logic, code, knowledge, and commonsense, ReM-MoA consistently outperforms prior MoA variants across both depth and width scaling, and its advantage widens with depth, establishing structured cross-layer reasoning memory as a key missing mechanism for scalable multi-agent inference.

Large language model (LLM) cascades answer easy requests with a small model and escalate selected requests to a larger model. Most routers prioritize examples on which the small model appears uncertain or likely to be wrong. This proxy ignores a decisive fact: escalation is useful only when the large model corrects the small model, and it is harmful when the large model replaces a correct answer with an incorrect one. We introduce Signed Rescue Routing (SRR), a budgeted routing method that predicts these two events separately and ranks requests by their difference. We show that this signed conditional gain is the Bayes-optimal routing score under a fixed escalation budget. SRR requires only the small model's output statistics at deployment and adds a lightweight two-head router. We evaluate SRR with Qwen3-4B and Qwen3-8B on TBD examples from MMLU, HellaSwag, and ARC-Challenge. Across the accuracy-compute curve, SRR reaches an area of TBD, compared with TBD for a learned small-model error predictor and TBD for entropy routing. These results show that predicting incremental value, rather than model uncertainty, is a simple and effective objective for efficient LLM cascades.

The growing ecosystem of large language models (LLMs) offers huge potential to optimize performance-cost trade-offs. However, their heterogeneous capabilities and inference costs make efficiently routing queries a significant challenge. Existing paradigms are inflexible: one-shot routers commit before observing responses, whereas conventional cascades stop adaptively but follow a fixed model order. Cascade routing removes both restrictions by reconsidering whether to stop or invoke another model after each response. Current methods use a predict-then-optimize pipeline estimating response quality and future model utility. However, prediction loss for quality or utility is not equivalent to routing-decision loss. A lower prediction error does not necessarily yield a better action; a small boundary-crossing error can reverse a stop'' or model-selection decision. Therefore, we propose RLCascadeRouter, a quality-estimator-free framework that formulates cascade routing as a Markov decision process with actions comprising stop'' and model selection. It uses trajectory returns and advantages to directly optimize the performance-cost objective. Its Cascade Policy Network models candidate complementarity for model selection and remaining-action value for stopping, eliminating independent post-hoc response-quality estimators. Evaluated across ten LLMRouterBench benchmarks with thirteen LLMs, RLCascadeRouter outperforms strong baselines and achieves superior performance-cost trade-offs. It incorporates unseen models without retraining, and ablation studies validate both policy components.