AlphaApollo: Orchestrating Foundation Models and Professional Tools into a Self-Evolving System for Deep Agentic Reasoning

TL;DR

AlphaApollo presents a self-evolving agentic reasoning system that overcomes two fundamental bottlenecks in foundation models by integrating a Python-based computation module and a retrieval module into a rollout framework. It enables multi-round, multi-model solution evolution via a shared state map and demonstrates consistent gains on AIME 2024/2025 across diverse models, with tool usage improving correctness and performance. The work highlights the practical potential of tool-augmented reasoning to raise the capability ceiling of large FMs and sets the stage for broader multi-model collaboration, test-time scaling, and open-source dissemination. Overall, AlphaApollo advances trustworthy, verifiable reasoning by grounding model outputs in exact computation and external knowledge, while enabling parallel, iterative refinement across models and tools.

Abstract

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

Figures (27)

• Figure 1: The Apollo Program mobilized more than 400,000 people over the span of a decade, from Apollo 1 to Apollo 17, to develop the mission systems that enabled humanity’s first moon landings. As a tribute to this historic achievement, we name our project AlphaApollo. The two projects share common principles despite their different domains: (1) reliance on advanced tools—the Apollo mission system and, in our case, Python code with retrieval systems; (2) collaboration among many participants—people or models; and (3) iterations across a series of missions or solutions.
• Figure 2: A comparison of three reasoning paradigms.
• Figure 3: Test-time evolving with multiple models.
• Figure 4: Schematic illustrating the tool-calling process of the rollout framework. The example shown demonstrates computational tool calls, while the dashed path indicates retrieval tool calls.
• Figure 5: The pipeline of the computational module in processing code with or without errors. The light-blue components (Code checking, Result checking) correspond to Client 1, while the purple components correspond to the Computational Server.