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

Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability. While "Oracle" models (e.g., Llama-3-70B) achieve state-of-the-art accuracy, they are prohibitively expensive for high-volume deployment. Smaller models (e.g., 8B parameters) are cost-effective but struggle with complex tasks. In this work, we propose "Pyramid MoA", a hierarchical Mixture-of-Agents architecture that uses a lightweight Router to dynamically escalate queries only when necessary. By leveraging semantic agreement and confidence calibration among an ensemble of small models, our Router identifies "hard" problems with high precision. On the GSM8K benchmark, our system achieves 93.0% accuracy, effectively matching the Oracle baseline (98.0%) while reducing compute costs by 61%. We demonstrate that the system introduces negligible latency overhead (+0.82s) and allows for a tunable trade-off between performance and budget.

Solving Limited-Memory Influence Diagrams Using Branch-and-Bound Search

A limited-memory influence diagram (LIMID) generalizes a traditional influence diagram by relaxing the assumptions of regularity and no-forgetting, allowing a wider range of decision problems to be modeled. Algorithms for solving traditional influence diagrams are not easily generalized to solve LIMIDs, however, and only recently have exact algorithms for solving LIMIDs been developed. In this paper, we introduce an exact algorithm for solving LIMIDs that is based on branch-and-bound search. Our approach is related to the approach of solving an influence diagram by converting it to an equivalent decision tree, with the difference that the LIMID is converted to a much smaller decision graph that can be searched more efficiently.