In conventional paradigms of machine learning (ML) and deep learning (DL), models are trained as ’black boxes’ on task-specific datasets prior to deployment. This poses various challenges to the application of AI for spectral adaptation. First, we cannot ensure the reliability of the model, since we do not know how they correlate signal features with their recognition target. We need a method to explain the final stage of decision-making. To address the first challenge, we propose a zero-bias neural network where we replace the penultimate layer of a specific DNN or CNN model with an extended Cosine Similarity Matching layer, called the zero-bias dense layer. This adaptation has been proven not to affect the learning and inferential capabilities of AI models. In this research study, we used the zero-bias neural network (ZBNN) for spectral sensing on the RADIOML 2016.10A dataset, which consists of 11 different modulation types, consisting of both analog and digital signals having varying Signal-to-noise ratio (SNR). To compare the ZBNN accuracy, we used the CNN model having identical hyperparameters. The proposed ZBNN for spectral sensing has the potential to become the fundamental building block for explainable AI, especially in remote spectral sensing.

The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids, this limits the efficiency of such neural operators when applied to problems where the input and output functions need to be processed on general non-equispaced point distributions. Leveraging the observation that a limited set of Fourier (Spectral) modes suffice to provide the required expressivity of a neural operator, we propose a simple method, based on the efficient direct evaluation of the underlying spectral transformation, to extend neural operators to arbitrary domains. An efficient implementation of such direct spectral evaluations is coupled with existing neural operator models to allow the processing of data on arbitrary non-equispaced distributions of points. With extensive empirical evaluation, we demonstrate that the proposed method allows us to extend neural operators to arbitrary point distributions with significant gains in training speed over baselines, while retaining or improving the accuracy of Fourier neural operators (FNOs) and related neural operators.