Process Reward Models (PRMs), which assign fine-grained scores to intermediate reasoning steps within a solution trajectory, have emerged as a promising approach to enhance the reasoning quality of Large Language Models (LLMs).However, most existing PRMs rely on a unidirectional left-to-right (L2R) evaluation scheme, which restricts their utilization of global context.In light of this challenge, we propose a novel bidirectional evaluation paradigm, named Bidirectional Process Reward Model (BiPRM).BiPRM incorporates a parallel right-to-left (R2L) evaluation stream, implemented via prompt reversal, alongside the conventional L2R flow.Then a gating mechanism is introduced to adaptively fuse the reward scores from both streams to yield a holistic quality assessment.Remarkably, compared to the original PRM, BiPRM introduces only a 0.3% parameter increase for the gating module, and the parallel execution of two streams incurs merely 5% inference time latency.Our extensive empirical evaluations spanning diverse benchmarks, LLM backbones, PRM objectives and sampling policies demonstrate that BiPRM consistently surpasses unidirectional baselines, achieving an average relative gain of 10.6% over 54 solution-level configurations and 37.7% in 12 step-level error detection scenarios.Generally, our results highlight the effectiveness, robustness and general applicability of BiPRM, offering a promising new direction for processbased reward modeling.1

Music recommendation systems aim to suggest tracks that users may enjoy. However, the accuracy of recommendation results is affected by popularity bias. Previous studies have focused on mitigating the direct effect of single-item popularity in video, news, or e-commerce recommendations, but have overlooked the multisource popularity biases in music recommendations. This article proposes a causal inference-based method to reduce the influence of both track and artist popularity. First, we construct a causal graph that encompasses users, tracks, and artists within the context of music recommendations. Next, we employ matrix factorization in conjunction with counterfactual inference theory to mitigate the popularity effects of artists and tracks, taking into account both the natural direct and indirect effects of these entities on music recommendations. Experimental results evaluated on four music recommendation datasets indicate that our method outperforms other baselines and effectively alleviates the popularity bias of both tracks and artists.