SEER Model for Code Generation

• SEER is a decision-process framework that models chain-of-thought code generation as a Markov decision process with integrated MCTS, addressing exploration and quality assessment challenges.
• It employs diverse reasoning path exploration and dual-model training with policy and value networks to dynamically guide generation and mitigate unnecessary overthinking.
• Empirical evaluations reveal substantial improvements in accuracy and efficiency across benchmarks like MBPP, HumanEval, and LiveCodeBench, highlighting SEER’s practical impact.

SEER (Self-Exploring Deep Reasoning) is a decision-process-based framework for enhancing chain-of-thought (CoT) code generation with LLMs. It is designed to address three longstanding limitations of CoT code generation methods for code: limited exploration of diverse reasoning paths (which constrains generalization), absence of quality assessment for intermediate steps (leading to unreliable plans and code), and the negative impact of overthinking (unnecessary complexity for simple problems). SEER achieves substantial gains in accuracy, efficiency, and adaptivity by framing code generation as a Markov decision process, integrating Monte Carlo Tree Search (MCTS), value-guided dual model training, and an adaptive inference mechanism.

1. Markov Decision Process Formulation for Code Reasoning

SEER models CoT code generation as a Markov Decision Process (MDP) with the following elements:

• States ($\mathbf{s}_t$): The current sequence comprising the problem prompt and all previous reasoning steps.
• Actions ($\mathbf{a}_t$): Generation of the next reasoning step by the policy model.
• Transition: Concatenation of each generated step to advance the reasoning state.
• Reward: Binary (+1 if generated code passes all test cases, −1 if any test fails) for terminal states; intermediate steps are assigned expected value based on downstream correctness.

The agent (LLM) is thus trained to maximize the probability that its reasoning trajectory yields correct, executable programs.

2. Diverse Reasoning Path Exploration and Datasets

SEER employs a customized MCTS to systematically explore multiple reasoning chains for each input. The search tree is constructed as follows:

• Nodes: Partial reasoning sequences, from prompt up to the current step.
• Expansion: At each node, candidate reasoning steps are sampled from the LLM, explicitly delimited (XML-like delimiters are used for clarity and compatibility with parsing).
• Selection: Expansion uses the PUCT formula:

$$\mathbf{a}_t = \arg\max_{\mathbf{a} \in \mathcal{T}_k} \left[ \hat{Q}(\mathbf{s}_t, \mathbf{a}) + c_{\mathrm{puct}} \pi_{\theta_k}(\mathbf{a} | \mathbf{s}_t) \sqrt{ \frac{N_{\mathrm{parent}(\mathbf{a})}}{1 + N(\mathbf{s}_t, \mathbf{a})}} \right]$$

where $\hat{Q}$ is mean value estimate, $\pi$ is the policy probability, and $N$ denotes visit counts.

• Evaluation and Backpropagation: At leaves, candidate code is synthesized and tested. Rewards propagate backward, with value estimation at each step reflecting the empirically observed probability of correctness.
• Path Perturbation and Refinement: To address cases where MCTS yields only correct (or only incorrect) paths, SEER perturbs prompts/steps to synthesize negative examples and leverages reflection-based prompting for positive path refinement using the ground-truth solution.

As a result, SEER constructs a step-annotated dataset $D_{train}$ containing both correct and incorrect trajectories with detailed intermediate quality labels, all without relying on manual annotation or proprietary models.

3. Reasoning Quality-Aware Dual Model Training

SEER uses a dual-model structure:

• Policy Model ($\pi_\theta$): Predicts the next reasoning step, trained on correct paths via maximum likelihood (for correct examples) and reinforced by fine-grained exploration.
• Value Model ($V_\phi$): Predicts the expected correctness of current partial reasoning trajectories, training via regression to stepwise ground-truth values from both correct and incorrect paths.

The multi-task loss is: $$\min_{\theta, \phi} \sum_{\mathbf{x} \in X^+} -\log \pi_\theta(\mathbf{x} | \mathbf{q}) + \beta \sum_{\mathbf{x} \in X^+ \cup X^-} \sum_{t=1}^{T(\mathbf{x})} | V_\phi(\mathbf{s}_t) - \mathbf{v}_t |^2$$ where $X^+$ is the set of correct paths, $X^-$ the incorrect paths, and $\mathbf{v}_t$ the ground-truth value per step.

The value head is implemented as an auxiliary MLP atop the transformer backbone, differing only in output projection/activation.

4. Adaptive Chain-of-Thought Reasoning for Overthinking Mitigation

SEER addresses overthinking—unnecessary reasoning for simple or well-known problems—via an adaptive inference scheme:

• Both direct generation and CoT reasoning are attempted for each problem. In the first beam search step, both strategies are considered; subsequent expansions proceed only for stepwise reasoning.
• All candidates are scored by the value model, and the highest-value path is selected for output.
• During training, direct outputs are incorporated alongside CoT, with their values (+1/−1) determined by test set correctness. To prevent catastrophic forgetting, the training includes KL divergence regularization ensuring the adapted model does not deviate excessively from its pre-adaptivity baseline.

The final training objective in this phase becomes: $$\min_{\theta, \phi} \sum_{\mathbf{x} \in X^+} KL\Big( \pi_\theta(\mathbf{x} | \mathbf{q}), \pi_{old}(\mathbf{x} | \mathbf{q}) \Big) + \beta \sum_{\mathbf{x} \in X^+ \cup X^-} \sum_{t=1}^{T(\mathbf{x})} | V_\phi(\mathbf{s}_t) - \mathbf{v}_t |^2$$

5. Empirical Evaluation and Ablation

SEER was evaluated using DeepSeek-Coder-6.7B-Instruct and Qwen2.5-Coder-7B-Instruct as base models across MBPP, HumanEval, and LiveCodeBench. It consistently outperformed all baselines, including reinforcement learning-based methods, with observed absolute improvements of +4.2%–9.3% (MBPP pass@1), +1.9%–9.1% (HumanEval), and +3.5%–5.3% (LiveCodeBench). In favorable cases, SEER-augmented 7B-parameter models surpassed the performance of Llama3-70B, indicating marked data and parameter efficiency.

Notably, SEER reduces inference time by avoiding unnecessary multi-step reasoning when the value estimator predicts high probability of correctness for direct code generation.

Ablations verified that removing path diversity, the value model, or adaptive inference each led to measurable degradation in both accuracy and efficiency, confirming the additive value of each system component.

6. Contributions and Component Table

Component	Role	Addressed Limitation
MCTS + Path Perturb/Refine	Diverse, high-quality trajectory discovery	Overfitting; no alt. paths
Policy Model	Stepwise generation of next CoT action	–
Value Model	Intermediate, dynamic quality assessment	No stepwise quality checks
Adaptive Reasoning using Value Model	Switch between direct and stepwise generation	Overthinking; efficiency

This architecture advances prior art by removing reliance on GPT-4/path distillation, enabling self-supervision on diverse annotations, and providing dynamic, step-level plan assessment.

7. Implications and Practical Considerations

SEER’s process is computationally efficient compared to exhaustive expert annotation or proprietary distillation, as it uses open LLMs for both path generation and evaluation. The dual-model architecture is compact, as the value head is a lightweight extension. The adaptive control mechanism eliminates redundant computation on easy problems and selectively invokes CoT only where necessary, thus optimizing inference cost.

A plausible implication is that SEER can be integrated into real-world code assistants or automated programming agents to provide highly reliable code synthesis, particularly in settings where test or deployment stakes demand plan traceability and correctness guarantees. The framework is open-sourced for reproducibility and extensibility in future code generation research.