This paper analyzes the impact of data freshness on remote inference systems, where a pre-trained neural network infers a time-varying target based on features observed at a sensing node. The study shows that inference error is a function of Age of Information (AoI), which may be non-monotonic. A new "selection-from-buffer" model is proposed for sending features, which is more general than the "generate-at-will" model used in previous studies. Low-complexity scheduling policies are designed to improve inference performance. For single-source, single-channel systems, an optimal scheduling policy is provided. In multi-source, multi-channel systems, the scheduling problem becomes a multi-action restless multi-armed bandit problem. A new scheduling policy is designed by integrating Whittle index-based source selection and duality-based feature selection-from-buffer algorithms. This policy is proven to be asymptotically optimal. These results hold for minimizing general AoI functions (monotonic or non-monotonic). Data-driven evaluations demonstrate the significant advantages of the proposed scheduling policies. The paper also introduces an information-theoretic framework for remote inference to analyze when fresher data is better and when it is not. The results show that the inference error can be non-monotonic with respect to AoI, and that the optimal scheduling policy can be expressed as an index-based threshold policy. The paper also discusses the relationship between information freshness and real-world applications, and provides theoretical interpretations of the experimental results. The results show that the training and inference errors can be non-monotonic with respect to AoI, and that the optimal scheduling policy can be expressed as an index-based threshold policy. The paper also discusses the relationship between information freshness and real-world applications, and provides theoretical interpretations of the experimental results.This paper analyzes the impact of data freshness on remote inference systems, where a pre-trained neural network infers a time-varying target based on features observed at a sensing node. The study shows that inference error is a function of Age of Information (AoI), which may be non-monotonic. A new "selection-from-buffer" model is proposed for sending features, which is more general than the "generate-at-will" model used in previous studies. Low-complexity scheduling policies are designed to improve inference performance. For single-source, single-channel systems, an optimal scheduling policy is provided. In multi-source, multi-channel systems, the scheduling problem becomes a multi-action restless multi-armed bandit problem. A new scheduling policy is designed by integrating Whittle index-based source selection and duality-based feature selection-from-buffer algorithms. This policy is proven to be asymptotically optimal. These results hold for minimizing general AoI functions (monotonic or non-monotonic). Data-driven evaluations demonstrate the significant advantages of the proposed scheduling policies. The paper also introduces an information-theoretic framework for remote inference to analyze when fresher data is better and when it is not. The results show that the inference error can be non-monotonic with respect to AoI, and that the optimal scheduling policy can be expressed as an index-based threshold policy. The paper also discusses the relationship between information freshness and real-world applications, and provides theoretical interpretations of the experimental results. The results show that the training and inference errors can be non-monotonic with respect to AoI, and that the optimal scheduling policy can be expressed as an index-based threshold policy. The paper also discusses the relationship between information freshness and real-world applications, and provides theoretical interpretations of the experimental results.