The attention mechanism is a pivotal element within the Transformer architecture, making a substantial contribution to its exceptional performance. Within this attention mechanism, Softmax is an imperative component that enables the model to assess the degree of correlation between various segments of the input. Yet, prior research has shown that Softmax operations can significantly increase processing latency and energy consumption in the Transformer network due to their internal nonlinear operations and data dependencies. In this work, we proposed~\textit{Hyft}, a hardware efficient floating point Softmax accelerator for both training and inference. Hyft aims to reduce the implementation cost of different nonlinear arithmetic operations by adaptively converting intermediate results into the most suitable numeric format for each specific operation, leading to reconfigurable accelerator with hybrid numeric format. The evaluation results highlight that Hyft achieves a remarkable $15\times$ reduction in hardware resource utilization and a $20 \times$ reduction in processing latency, all while maintaining a negligible impact on Transformer accuracy.
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