Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Agentic Reinforcement Learning (RL) shows promise for complex tasks, but Text-to-SQL remains mostly restricted to single-turn paradigms. A primary bottleneck is the credit assignment problem. In traditional paradigms, rewards are determined solely by the final-turn feedback, which ignores the intermediate process and leads to ambiguous credit evaluation. To address this, we propose Agentic SQL, a framework featuring a universal two-tiered reward mechanism designed to provide effective trajectory-level evaluation and dense step-level signals. First, we introduce Aggregated Trajectory Reward (ATR) to resolve multi-turn credit assignment. Using an asymmetric transition matrix, ATR aggregates process-oriented scores to incentivize continuous improvement. Leveraging Lyapunov stability theory, we prove ATR acts as an energy dissipation operator, guaranteeing a cycle-free policy and monotonic convergence. Second, Column-Set Matching Reward (CSMR) provides immediate step-level rewards to mitigate sparsity. By executing queries at each turn, CSMR converts binary (0/1) feedback into dense [0,1] signals based on partial correctness. Evaluations on BIRD show a 5% gain over binary-reward GRPO. Notably, our approach outperforms SOTA Arctic-Text2SQL-R1-7B on BIRD and Spider 2.0 using identical models, propelling Text-to-SQL toward a robust multi-turn agent paradigm.

While Chain-of-Thought (CoT) reasoning enhances code generation in Large Language Models (LLMs), it introduces a critical challenge in uncertainty estimation: Confidence Saturation. Existing calibration methods, such as Self-Consistency, rely on the assumption that consensus implies correctness. This assumption fails under systematic errors, where models confidently repeat flawed logic, leading to miscalibrated high-confidence predictions. To address this, we introduce NeuroSym-Cal, a hierarchical calibration framework. We posit that reliable confidence requires interrogating the model at two complementary levels: the extrinsic consensus of its symbolic outputs and the intrinsic sensitivity of its latent reasoning. Specifically, we propose Reasoning Sensitivity Analysis to measure the local curvature of the deductive process via latent perturbation, providing a fine-grained signal that persists even when output consensus saturates. These orthogonal features are fused by a Contextual Calibration Network to predict correctness. Experiments across state-of-the-art reasoning models (e.g., DeepSeek-R1) demonstrate that NeuroSym-Cal effectively de-saturates overconfident errors, achieving state-of-the-art Expected Calibration Error (ECE) and superior selective generation performance on Out-Of-Domain (OOD) benchmarks.