Vision Transformers have reshaped computer vision by using self-attention to capture global context across image regions. This makes them attractive for edge visual inspection and monitoring in applications such as renewable-energy infrastructure, industrial quality control, medical imaging, and autonomous-system sensing. However, deploying ViTs on small FPGAs remains challenging because the softmax stage in self-attention requires exponential evaluation and normalization, which are costly in hardware. Existing implementations often rely on CORDIC pipelines or BRAM-based look-up tables, increasing area and power consumption. This paper presents a BRAM-free approximate attention-weighting unit for FPGA-based ViT inference. The proposed design approximates the natural exponential in softmax using a 16-segment piecewise-linear function implemented entirely with distributed LUT fabric. Unlike base-2 approximations, the natural-exponential formulation preserves the pre-trained attention temperature and avoids model-specific recalibration. Implemented on a Xilinx Zynq-7020, the complete attention-row core uses 1444 LUTs, 77 DSPs, and no BRAM, while hardware-accurate emulation shows accuracy within a \(0.20\%\) absolute top-1 difference from the exact-softmax reference on ViT-family models. These results demonstrate the potential of the proposed core for energy-efficient ViT inference on resource-constrained edge-AI platforms.

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