Approximate multipliers can reduce hardware area and energy consumption in Deep Neural Network (DNN) inference; however, they introduce computational errors. Assessing the accuracy of numerous approximate multiplier designs across diverse DNN models and large-scale datasets remains challenging due to prohibitive evaluation times. This overhead primarily stems from the slow emulation of approximate multiplier behavior using look-up tables (LUTs) on CPU and GPU platforms. Moreover, the resulting accuracy degradation must be carefully quantified and, if necessary, mitigated (e.g., through retraining), further increasing the overall evaluation cost. To address these challenges, we propose FAME, an FPGA-based platform for evaluating approximate multipliers. The platform exploits the reconfigurable logic of Field-Programmable Gate Arrays (FPGAs) to implement approximate multipliers directly in hardware, eliminating the need for LUT-based emulation on CPU/GPU platforms and thereby enabling efficient DNN inference while significantly reducing evaluation time on large datasets. Furthermore, we introduce a pattern-guided DNN retraining technique to mitigate accuracy degradation induced by approximate multipliers. Specifically, retraining is guided by multiplier-specific patterns to effectively recover potential accuracy losses. We evaluate FAME using two DNN models, ResNet-18 and MobileNetV2, on the ImageNet dataset across 27 approximate multipliers. During inference, our approach achieves up to a 3.47x speedup in approximate multiplier evaluation compared to prior LUT-based emulation methods. Furthermore, the proposed retraining technique improves accuracy by up to 65.5% over existing retraining approaches for the evaluated multipliers. The code is publicly available at: https://github.com/gicLAB/FAME
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