Machine learning applications require timely access to fresh data from primary–backup databases to ensure accurate inference. Existing log replay strategies treat all updates equally and adhere to log-order dependencies, or only prioritize frequently accessed tables, resulting in high latency for prediction queries that usually access a small subset of attributes. Allowing immediate query execution can reduce latency but risks substantial accuracy degradation, as prediction models exhibit varying sensitivity even to minor data staleness. In this paper, we propose AALR, an accuracy-aware log replay strategy that accelerates data visibility for prediction queries while preserving inference accuracy. AALR prioritizes replay at the attribute level, enabling fine-grained replay aligned with query access patterns to avoid unnecessary delay. It leverages a learning-based model to quantify the relationship between data freshness and prediction accuracy, supporting adaptive replay decisions under diverse workloads. Furthermore, AALR introduces an epoch-based two-step replay mechanism, combining column-level parallel classification with row-level latest transaction retention to improve parallelism and resource utilization. Extensive experiments on multiple real-world datasets demonstrate that AALR significantly reduces data visibility latency for prediction queries while maintaining high prediction accuracy, outperforming state-of-the-art log replay strategies.