Abstract:The energy and latency costs of deep neural network inference are increasingly driven by deployment rather than training, motivating hardware-specialized alternatives to arithmetic-heavy models. Field-Programmable Gate Arrays (FPGAs) provide an attractive substrate for such specialization, yet existing FPGA-based neural approaches are fragmented and difficult to compare. We present BitLogic, a fully gradient-based, end-to-end trainable framework for FPGA-native neural networks built around Lookup Table (LUT) computation. BitLogic replaces multiply-accumulate operations with differentiable LUT nodes that map directly to FPGA primitives, enabling native binary computation, sparse connectivity, and efficient hardware realization. The framework offers a modular functional API supporting diverse architectures, along with learned encoders, hardware-aware heads, and multiple boundary-consistent LUT relaxations. An automated Register Transfer Level (RTL) export pipeline translates trained PyTorch models into synthesizable HDL, ensuring equivalence between software and hardware inference. Experiments across standard vision benchmarks and heterogeneous hardware platforms demonstrate competitive accuracy and substantial gains in FPGA efficiency, including 72.3% test accuracy on CIFAR-10 achieved with fewer than 0.3M logic gates, while attaining sub-20 ns single-sample inference using only LUT resources.