Efficient FPGA realization of neural network activation functions using adaptive piecewise polynomial approximations with Chebyshev nodes

• Chebyshev-based, adaptive piecewise polynomial approximation enables highly efficient FPGA implementation of neural network activation functions. • Proposed framework achieves low approximation error at competitive operating frequencies on Xilinx Virtex UltraScale+ FPGA. • Quadratic and cubic polynomial designs offer configurable trade-offs between accuracy, hardware resource utilization, and latency. • Hardware-friendly approach delivers robust, real-time neural network activation for edge-AI and DSP applications. • Experimental results show significant improvements over prior methods, with up to 397 × lower MSE and 900,000 × faster Gaussian function evaluation. Efficient implementation of activation functions is critical for deploying neural networks on hardware platforms such as FPGAs, where resource constraints and real-time performance requirements dominate design considerations. This paper presents a unified framework for approximating three widely used nonlinear activation functions namely, sigmoid, hyperbolic tangent (tanh), and symmetric Gaussian using adaptive piecewise polynomial interpolation optimized for FPGA deployment. Leveraging Chebyshev nodes and curvature-based subinterval selection derived from higher-order derivatives, we develop both quadratic and cubic polynomial models that achieve high approximation accuracy while minimizing computational overhead. The proposed designs are implemented in SystemVerilog using Q32.32 fixed-point arithmetic and synthesized on a Xilinx Virtex UltraScale+ FPGA. Experimental results demonstrate that increasing the number of segments significantly reduces approximation error while maintaining competitive latency and resource efficiency. Compared to existing methods, our proposed approach achieves lower mean squared error (MSE) and higher operating frequencies with moderate hardware complexity, making it suitable for real-time and edge AI applications. Moreover, the proposed work provides a scalable and accurate hardware-friendly solution for activation function approximation in neural network accelerators.