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Existing FPGA-based DNN accelerators typically fall into two design paradigms. Either they adopt a generic reusable architecture to support different DNN networks but leave some performance and efficiency on the table because of the sacrifice of design specificity. Or they apply a layer-wise tailor-made architecture to optimize layer-specific demands for computation and resources but loose the scalability of adaptation to a wide range of DNN networks. To overcome these drawbacks, this paper proposes a novel FPGA-based DNN accelerator design paradigm and its automation tool, called DNNExplorer, to enable fast exploration of various accelerator designs under the proposed paradigm and deliver optimized accelerator architectures for existing and emerging DNN networks. Three key techniques are essential for DNNExplorer's improved performance, better specificity, and scalability, including (1) a unique accelerator design paradigm with both high-dimensional design space support and fine-grained adjustability, (2) a dynamic design space to accommodate different combinations of DNN workloads and targeted FPGAs, and (3) a design space exploration (DSE) engine to generate optimized accelerator architectures following the proposed paradigm by simultaneously considering both FPGAs' computation and memory resources and DNN networks' layer-wise characteristics and overall complexity. Experimental results show that, for the same FPGAs, accelerators generated by DNNExplorer can deliver up to 4.2x higher performances (GOP/s) than the state-of-the-art layer-wise pipelined solutions generated by DNNBuilder for VGG-like DNN with 38 CONV layers. Compared to accelerators with generic reusable computation units, DNNExplorer achieves up to 2.0x and 4.4x DSP efficiency improvement than a recently published accelerator design from academia (HybridDNN) and a commercial DNN accelerator IP (Xilinx DPU), respectively.