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Conversion represents an effective approach for obtaining low-power models by transforming Artificial Neural Networks (ANNs) into event-driven Spiking Neural Networks (SNNs) without additional training. However, existing training-free conversion methods often incur substantial conversion errors. Here, we first reveal that these conversion errors primarily arise from a distributional mismatch, as the activation distributions of ANNs exhibit channel-wise shifts and scaling, whereas spike rates lack corresponding channel-specific characteristics. To address this limitation, we propose Adaptive Integrate-and-Fire (AIF) neurons with channel-specific thresholds and membrane-potential offsets that dynamically adjust spike rates. These parameters are optimized to jointly minimize conversion errors and maximize information entropy, enabling AIF neurons to capture the activation distribution characteristics of the original ANN. Moreover, AIF neurons can be seamlessly integrated into Transformer architectures with only negligible additional computational cost. Our method achieves state-of-the-art results on multiple vision and natural language processing benchmarks, in particular attaining a notable top-1 accuracy of 85.52% on ImageNet-1K.