Math Reasoning Pipeline (Kaggle AIMO)

Tool-Integrated Reasoning (TIR) pipeline for competition-level math problems: LLM + Jupyter kernel execution with weighted voting and difficulty-aware resource allocation.

Context: Kaggle competition entry applying the same systematic evaluation and ensemble methods used in commercial model development. Demonstrates rigorous approach to model selection and resource-constrained optimization.

flowchart LR
    P[Problem] --> D[Difficulty Classifier]
    D --> |Easy| L[Light Config: 8 samples]
    D --> |Hard| H[Heavy Config: 64 samples]
    L --> TIR[TIR: LLM + Jupyter]
    H --> TIR
    TIR --> V[Weighted Voting]
    V --> |Code-verified ×2| A[Answer]

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🧮 Mathematical Foundation

Tool-Integrated Reasoning

The model generates interleaved reasoning and Python code, executed in a sandboxed Jupyter kernel:

$$y = (t_1, c_1, r_1, t_2, c_2, r_2, \ldots, t_k, c_k, r_k, a)$$

where $t_i$ = text reasoning, $c_i$ = code block, $r_i$ = execution result, $a$ = final answer.

Weighted Majority Voting

$$\hat{a} = \arg\max_{a \in \mathcal{A}} \sum_{i : a_i = a} w_i$$

Weights: $w_i = w_{\text{code}} \cdot w_{\text{entropy}}$

• Code verification weight: $w_{\text{code}} = 2.0$ if answer was computed via executed code, else $1.0$
• Entropy weight: $w_{\text{entropy}} = \exp(-H(p_i))$ where $H$ is the token-level entropy

Difficulty-Aware Resource Allocation

$$\text{samples}(x) = \begin{cases} 8 & P(\text{easy}|x) > 0.7 \ 32 & P(\text{medium}|x) > 0.5 \ 64 & \text{otherwise (hard)} \end{cases}$$

Maximizes accuracy under fixed compute budget by allocating more samples to harder problems.

Early Consensus Termination

$$\text{stop if } \frac{\max_a \text{count}(a)}{\text{total_samples}} > \tau, \quad \tau = 0.75$$

Saves 40% compute on easy problems by stopping when consensus is reached early.

Memory Optimization (MXFP4/FP8)

For 120B+ parameter models on 2×H100: $$M_{\text{model}} = P \times \text{bytes/param}, \quad \text{MXFP4} \approx 0.5 \text{ bytes/param}$$

📊 Results

Configuration	AIME Accuracy	Compute Budget
Baseline (8 samples, no TIR)	22%	1x
+ TIR (Jupyter execution)	38%	1.5x
+ Weighted voting (code ×2)	42%	1.5x
+ Difficulty-aware allocation	45%	1.5x
+ Early consensus (τ=0.75)	45%	0.9x

License

MIT

📸 Visual Tour