Yueqi Zhang

Xinglin Wang, Shaoxiong Feng, Yiwei Li et al.

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants, Adaptive self-consistency (ASC) and Early-stopping self-consistency (ESC), dynamically adjust the number of samples based on the posterior distribution of a set of pre-samples, reducing the cost of SC with minimal impact on performance. Both methods, however, do not exploit the prior information about question difficulty. It often results in unnecessary repeated sampling for easy questions that could be accurately answered with just one attempt, wasting resources. To tackle this problem, we propose Difficulty-Adaptive Self-Consistency (DSC), which leverages the difficulty information of batch queries from both prior and posterior perspectives to adaptively allocate inference resources, further reducing the overall cost of SC. To demonstrate the effectiveness of DSC, we conduct extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning on six benchmarks. The empirical results show that DSC consistently surpasses the strong baseline ASC and ESC in terms of costs by a significant margin, while attaining comparable performances.

Yiwei Li, Ji Zhang, Shaoxiong Feng et al.

Self-consistency improves reasoning by aggregating diverse stochastic samples, yet the dynamics behind its efficacy remain underexplored. We reframe self-consistency as a dynamic distributional alignment problem, revealing that decoding temperature not only governs sampling randomness but also actively shapes the latent answer distribution. Given that high temperatures require prohibitively large sample sizes to stabilize, while low temperatures risk amplifying biases, we propose a confidence-driven mechanism that dynamically calibrates temperature: sharpening the sampling distribution under uncertainty to align with high-probability modes, and promoting exploration when confidence is high. Experiments on mathematical reasoning tasks show this approach outperforms fixed-diversity baselines under limited samples, improving both average and best-case performance across varying initial temperatures without additional data or modules. This establishes self-consistency as a synchronization challenge between sampling dynamics and evolving answer distributions.

Chuyi Tan, Peiwen Yuan, Xinglin Wang et al.

Reinforcement learning with verifiable rewards (RLVR) scales the reasoning ability of large language models (LLMs) but remains bottlenecked by limited labeled samples for continued data scaling. Reinforcement learning with intrinsic rewards (RLIR), where the policy model assigns rewards to its own rollouts, enables sustainable scaling in unlabeled settings, yet its performance and stability lag behind RLVR. We trace this gap to a system bias: the model tends to overestimate its high-confidence rollouts, leading to biased and unstable reward estimation. This bias accumulates as training progresses, with deviations from the oracle drifting toward over-reward, causing unstable training. We characterize this bias using three metrics: $ρ_{\text{noise}}$, $ρ_{\text{selfbias}}$, and $ρ_{\text{symbias}}$. We find that $ρ_{\text{noise}}$ and $ρ_{\text{symbias}}$ impact convergence, while $ρ_{\text{selfbias}}$ amplifies both correct and incorrect updates, leading to instability. To mitigate this, we propose reinforcement learning with ensembled rewards (RLER), which aggregates diverse models and adapts reward interpolation and rollout selection. Extensive experiments show that RLER improves by +13.6% over RLIR and is only 3.6% below RLVR, achieving stable scaling on unlabeled samples, making it highly applicable.