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

Arindam Khaled · Feb 23, 2026 · Citations: 0

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Coverage: Stale

Use this page to decide whether the paper is strong enough to influence an eval design. If the signals below are thin, treat it as background context and compare it against the stronger hub pages before making protocol choices.

Paper metadata checked

Mar 13, 2026, 1:46 AM

Stale

Protocol signals checked

Mar 13, 2026, 1:46 AM

Stale

Signal strength

Moderate

Model confidence 0.55

Abstract

Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability. While "Oracle" models (e.g., Llama-3.3-70B) achieve state-of-the-art accuracy, they are prohibitively expensive for high-volume deployment. Smaller models (e.g., 7-9B parameters) are cost-effective but struggle with complex tasks. We observe that the emerging practice of LLM cascading and routing implicitly solves an anytime computation problem -- a class of algorithms, well-studied in classical AI, that produce valid solutions immediately and improve them as additional computation is allocated. In this work, we formalize this connection and propose "Pyramid MoA", a hierarchical Mixture-of-Agents architecture governed by a decision-theoretic router that dynamically escalates queries only when necessary. We establish a Probabilistic Anytime Property, proving that expected solution quality is monotonically non-decreasing with computational depth under identifiable conditions on router precision. We derive a generalized escalation rule from Value of Computation theory that accounts for imperfect oracles, extending the classical monitoring framework of Hansen and Zilberstein to stochastic LLM inference. On the MBPP code generation benchmark, the Consensus Router intercepts 81.6% of bugs. On the GSM8K/MMLU mathematical reasoning benchmark, the system matches the Oracle baseline of 68.1% accuracy while enabling up to 18.4% compute savings at a balanced operating point. Crucially, the router transfers zero-shot to unseen benchmarks: on HumanEval it achieves 81.1% accuracy (matching the Oracle) with 62.7% cost savings in economy mode, and on the highly complex MATH 500 benchmark it preserves the 58.0% Oracle ceiling. The framework acts dynamically: serving as an aggressive cost-cutter for low-entropy tasks and a strict safety net for high-entropy tasks.

Use caution before copying this protocol

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A benchmark-and-metrics comparison anchor.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

15/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

HFEPX Fit

Adjacent candidate

Extraction confidence: Moderate

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Reliably Extract

Each protocol field below shows whether the signal looked explicit, partial, or missing in the available metadata. Use this to judge what is safe to trust directly and what still needs full-paper validation.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Evaluation Modes

strong

Automatic Metrics

Confidence: Moderate Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Quality Controls

strong

Calibration

Confidence: Moderate Source: Persisted extraction evidenced

Calibration/adjudication style controls detected.

Evidence snippet: Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Benchmarks / Datasets

strong

GSM8K

Confidence: Moderate Source: Persisted extraction evidenced

Useful for quick benchmark comparison.

Evidence snippet: On the GSM8K/MMLU mathematical reasoning benchmark, the system matches the Oracle baseline of 68.1% accuracy while enabling up to 18.4% compute savings at a balanced operating point.

Reported Metrics

strong

Accuracy, Precision, Latency, Cost, Inference cost

Confidence: Moderate Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Rater Population

missing

Unknown

Confidence: Low Source: Persisted extraction missing

Rater source not explicitly reported.

Evidence snippet: Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: Math
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Calibration
  • Confidence: 0.55
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

GSM8K

Reported Metrics

accuracyprecisionlatencycostinference cost

Research Brief

Deterministic synthesis

Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.

Generated Mar 13, 2026, 1:46 AM · Grounded in abstract + metadata only

Key Takeaways

  • Large Language Models (LLMs) face a persistent trade-off between inference cost and reasoning capability.
  • While "Oracle" models (e.g., Llama-3.3-70B) achieve state-of-the-art accuracy, they are prohibitively expensive for high-volume deployment.
  • Smaller models (e.g., 7-9B parameters) are cost-effective but struggle with complex tasks.

Researcher Actions

  • Compare this paper against others mentioning MMLU and GSM8K.
  • Validate inferred eval signals (Automatic metrics) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

MMLU GSM8K Accuracy

Research Summary

Contribution Summary

  • 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.
  • 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.

Why It Matters For Eval

  • 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.
  • On the GSM8K benchmark, our system achieves 93.0% accuracy, effectively matching the Oracle baseline (98.0%) while reducing compute costs by 61%.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Pass: Quality control reporting appears

    Detected: Calibration

  • Pass: Benchmark or dataset anchors are present

    Detected: GSM8K

  • Pass: Metric reporting is present

    Detected: accuracy, precision, latency, cost

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Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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