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TUMIX: Multi-Agent Test-Time Scaling with Tool-Use Mixture

🕒 Published (v1): 2026-01-01 · Source: ICLR · Venue: ICLR 2026 · link

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Test-time scaling via mixed tool use (code and search) in LLM agents

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TL;DR

TUMIX is a multi-agent test-time scaling framework that runs heterogeneous tool-using agents (Code Interpreter, Search, CoT) in parallel and iteratively refines their answers across rounds. It outperforms prior test-time scaling methods by an average of +3.55% on HLE, GPQA Diamond, and AIME 24&25 at near-equal inference cost. An adaptive LLM-as-Judge termination strategy halves inference cost while preserving accuracy.

Problem

Existing test-time scaling methods (MoA, Self-MoA, Symbolic-MoE, DEI) do not integrate external tools like Code Interpreter and Search, leaving complementary reasoning modalities (symbolic computation, live retrieval) underexploited. Meanwhile, tool-augmented systems lack principled methods for combining text, code, and search strategies across diverse question types, and no prior work has studied how to scale heterogeneous tool-use agents at test time with adaptive cost control.

Method

TUMIX maintains a pool of \(K=15\) pre-designed agents with distinct tool-use strategies (Table 1): text-only CoT, Code Interpreter, WebSearch, combined Code+Search, and guided/hinted variants with three search sub-variants each. At each round \(r\), every agent generates a solution conditioned on the original question and all agents' previous-round outputs (concatenated as a joint prompt). Formally, the policy \(\pi\) jointly optimizes: $\(\max_\pi P\{\hat{a}^\pi = a^\star\} - \lambda \cdot \text{Cost}^\pi\)$ over agent selection, communication graph, stopping rule, and aggregation rule.

Iterative refinement: Responses from round \(r\) are appended to the prompt for round \(r+1\), acting as message-passing that raises average accuracy in early rounds but collapses diversity (coverage) in later rounds as agents converge.

Adaptive termination: An LLM judge is queried each round (with a minimum of 2 rounds enforced) to decide whether marginal gain \(\Delta_r = E[A_{r+1} - A_r]\) justifies another round. This halts refinement before over-convergence discards correct answers.

LLM-as-agent-designer: A separate LLM prompt is used to generate new agent configurations beyond the 15 human-designed ones, yielding +1.2% average gain at no additional inference cost.

Final answer selection: Majority voting over all agents' terminal-round responses, with Gemini-2.5-Pro used to normalize and compare answers.

Key Contributions

  • TUMIX framework: heterogeneous multi-agent test-time scaling integrating Code Interpreter and Search, achieving +3.55% average accuracy over best prior methods at equal inference cost.
  • Empirical finding that agent diversity beats high-temperature sampling from a single best agent in tool-augmented multi-agent scaling (contradicting Self-MoA's conclusion for text-only settings).
  • Characterization of the coverage–accuracy trade-off across refinement rounds: coverage monotonically declines while average accuracy peaks early then plateaus or degrades.
  • LLM-as-agent-designer: prompting an LLM to auto-generate new heterogeneous agents adds +1.2% without cost increase.
  • LLM-as-Judge adaptive termination: reduces inference cost to ~49% of fixed-round or majority-vote-consistency termination while preserving accuracy.
  • TUMIX+ (with higher inference budget) pushes Gemini-2.5-Pro HLE accuracy to 34.1%, surpassing Gemini-2.5-Pro Deep Research (26.9%).

Results

  • vs. no TTS baseline: +7.8% (Gemini-2.5-Pro) and +17.4% (Gemini-2.5-Flash) average accuracy across HLE, GPQA Diamond, AIME 24&25.
  • vs. best baseline (same inference cost): +3.55% average; +2.0% on Pro, +5.9% on Flash.
  • HLE (Gemini-2.5-Pro): TUMIX 28.7%, TUMIX+ 34.1%; best baseline (SciMaster*) 29.5%; Deep Research 26.9%.
  • GPQA Diamond (Pro): TUMIX 85.8%, TUMIX+ 88.3%; best baseline 86.9%.
  • AIME 24&25 (Pro): TUMIX 93.7%, TUMIX+ 96.7%; best baseline 95.0%.
  • Flash GPQA: TUMIX 77.3% vs. best baseline 67.9%.
  • Adaptive early termination achieves ~same accuracy as full-round TUMIX at 49% of inference cost.
  • LLM-auto-designed agents (TUMIX-EVO) add +1.2% average over TUMIX-FIXED with no cost increase.
  • Statistical significance: two-tailed paired t-tests show \(p < 0.05\) on nearly all benchmarks and models.

Limitations

  • Evaluation is confined to three benchmarks (HLE, GPQA Diamond, AIME); coverage of broader task types (long-form generation, open-ended reasoning) is absent.
  • Results are obtained on Gemini-2.5-Pro/Flash only; generalizability to open-source or other closed models is shown only in an appendix with limited detail.
  • SciMaster baseline comparison is potentially confounded by different (non-open-sourced) tool implementations.
  • Coverage on HLE reaches ≥65% (at least one correct answer exists among candidates), but final accuracy plateaus near 34%—the answer selection bottleneck remains unsolved.
  • LLM-as-agent-designer requires additional inference to generate new agent configurations, though the paper frames this as zero marginal cost at serving time.
  • 15 pre-designed agents involve significant human engineering; automated agent design is only an additive refinement, not a replacement.

Relevance to Agentic AI / LLM Agents

TUMIX directly addresses a core challenge in LLM agent design: how to compose heterogeneous tool-using agents (code execution, web retrieval, chain-of-thought) within a test-time compute budget. Its finding that agent diversity across tool-use strategies matters more than scale or temperature is a concrete empirical result that should inform multi-agent orchestration design beyond this specific framework. The LLM-as-judge termination and LLM-as-agent-designer components demonstrate that meta-level agent reasoning (agents reasoning about agents) can substantially improve both cost and accuracy, a pattern central to emerging agentic systems. The coverage–accuracy plateau analysis exposes a fundamental bottleneck in current multi-agent pipelines—generating diverse candidate solutions is achievable, but reliably selecting the correct one remains an open problem relevant to anyone building agentic reasoning systems.