This solution presents a fully integrated LLM-based mathematical reasoning system designed to solve AIMO3 olympiad-level problems through a combination of:
\nRather than relying on single-pass generation, the system transforms the model into a search-based reasoning engine that explores multiple solution paths per problem and aggregates results using uncertainty-informed voting.
\nWe deploy a large transformer model served via vLLM OpenAI-compatible API server, enabling high-throughput streaming inference.
\nKey optimizations include:
\nTo reduce cold-start latency, model weights are preloaded into OS page cache prior to inference.
\nEach problem is solved using a structured reasoning protocol:
\nThe model is explicitly instructed to:
\n\\boxed{} format within range [0, 99999]For each problem, the system performs multiple independent reasoning attempts (default: 8), each with different random seeds.
\nThis converts deterministic inference into a stochastic reasoning search process, increasing coverage of possible solution paths.
\nWe implement a persistent Jupyter-based sandbox for code execution. Each sandbox:
\nThis enables:
\nThe LLM can invoke Python execution dynamically during reasoning. Tool outputs are fed back into the conversation, enabling a closed-loop reasoning cycle between:
\n\n\nlanguage reasoning ↔ executable computation
\n
To evaluate reasoning quality, we compute mean entropy over token-level log probabilities.
\nThis metric is used later for weighted answer aggregation.
\nFinal answers are extracted using robust pattern matching from:
\n\\boxed{answer} formatAll extracted values are validated to ensure they fall within the required range [0, 99999].
\nIf multiple attempts converge to the same answer (default threshold ≥ 4), inference is stopped early to reduce computation cost.
\nFinal answer selection is performed using a weighted voting scheme:
\nThis ensures that more confident reasoning paths have higher influence on the final decision.
\nThe system dynamically allocates computation time per problem based on:
\nThis ensures balanced compute distribution across the full evaluation set.
\nTo support parallel reasoning, we maintain a pool of persistent Jupyter kernels:
\nThis avoids repeated kernel initialization overhead and ensures scalability across multiple inference threads.
\nFor each problem:
\nInput is formatted with system + tool prompts
Multiple reasoning attempts are launched in parallel
Each attempt performs:
\nResults are aggregated using entropy-weighted voting
Final answer is selected and returned
The system is deployed via Kaggle inference API:
\n{id, answer}Memory cleanup is performed after each inference to ensure stability under sequential evaluation.
\nThis solution introduces a unified framework combining:
\nThe proposed system transforms a large language model into a search-driven mathematical reasoning engine, capable of exploring multiple solution trajectories, verifying results via executable computation, and selecting final answers through uncertainty-weighted consensus.
\nThis design improves robustness over single-pass inference by combining:
\n\n\nreasoning diversity + tool execution + probabilistic aggregation
\n
This solution presents a fully integrated LLM-based mathematical reasoning system designed to solve AIMO3 olympiad-level problems through a combination of:
\nRather than relying on single-pass generation, the system transforms the model into a search-based reasoning engine that explores multiple solution paths per problem and aggregates results using uncertainty-informed voting.
\nWe deploy a large transformer model served via vLLM OpenAI-compatible API server, enabling high-throughput streaming inference.
\nKey optimizations include:
\nTo reduce cold-start latency, model weights are preloaded into OS page cache prior to inference.
\nEach problem is solved using a structured reasoning protocol:
\nThe model is explicitly instructed to:
\n\\boxed{} format within range [0, 99999]For each problem, the system performs multiple independent reasoning attempts (default: 8), each with different random seeds.
\nThis converts deterministic inference into a stochastic reasoning search process, increasing coverage of possible solution paths.
\nWe implement a persistent Jupyter-based sandbox for code execution. Each sandbox:
\nThis enables:
\nThe LLM can invoke Python execution dynamically during reasoning. Tool outputs are fed back into the conversation, enabling a closed-loop reasoning cycle between:
\n\n\nlanguage reasoning ↔ executable computation
\n
To evaluate reasoning quality, we compute mean entropy over token-level log probabilities.
\nThis metric is used later for weighted answer aggregation.
\nFinal answers are extracted using robust pattern matching from:
\n\\boxed{answer} formatAll extracted values are validated to ensure they fall within the required range [0, 99999].
\nIf multiple attempts converge to the same answer (default threshold ≥ 4), inference is stopped early to reduce computation cost.
\nFinal answer selection is performed using a weighted voting scheme:
\nThis ensures that more confident reasoning paths have higher influence on the final decision.
\nThe system dynamically allocates computation time per problem based on:
\nThis ensures balanced compute distribution across the full evaluation set.
\nTo support parallel reasoning, we maintain a pool of persistent Jupyter kernels:
\nThis avoids repeated kernel initialization overhead and ensures scalability across multiple inference threads.
\nFor each problem:
\nInput is formatted with system + tool prompts
Multiple reasoning attempts are launched in parallel
Each attempt performs:
\nResults are aggregated using entropy-weighted voting
Final answer is selected and returned
The system is deployed via Kaggle inference API:
\n{id, answer}Memory cleanup is performed after each inference to ensure stability under sequential evaluation.
\nThis solution introduces a unified framework combining:
\nThe proposed system transforms a large language model into a search-driven mathematical reasoning engine, capable of exploring multiple solution trajectories, verifying results via executable computation, and selecting final answers through uncertainty-weighted consensus.
\nThis design improves robustness over single-pass inference by combining:
\n\n\nreasoning diversity + tool execution + probabilistic aggregation
\n