Miguel Ángel Lagunas

Marc Martinez-Gost, Ana Pérez-Neira, Miguel Ángel Lagunas

The expressiveness of neural networks highly depends on the nature of the activation function, although these are usually assumed predefined and fixed during the training stage. Under a signal processing perspective, in this paper we present Expressive Neural Network (ENN), a novel model in which the non-linear activation functions are modeled using the Discrete Cosine Transform (DCT) and adapted using backpropagation during training. This parametrization keeps the number of trainable parameters low, is appropriate for gradient-based schemes, and adapts to different learning tasks. This is the first non-linear model for activation functions that relies on a signal processing perspective, providing high flexibility and expressiveness to the network. We contribute with insights in the explainability of the network at convergence by recovering the concept of bump, this is, the response of each activation function in the output space. Finally, through exhaustive experiments we show that the model can adapt to classification and regression tasks. The performance of ENN outperforms state of the art benchmarks, providing above a 40% gap in accuracy in some scenarios.

Marc Martinez-Gost, Sara Pepe, Ana Pérez-Neira et al.

In this paper, we extend our previous work on the Expressive Neural Network (ENN), a multilayer perceptron with adaptive activation functions parametrized using the Discrete Cosine Transform (DCT). Building upon previous work that demonstrated the strong expressiveness of ENNs with compact architectures, we now emphasize their efficiency, interpretability and pruning capabilities. The DCT-based parameterization provides a structured and decorrelated representation that reveals the functional role of each neuron and allows direct identification of redundant components. Leveraging this property, we propose an efficient pruning strategy that removes unnecessary DCT coefficients with negligible or no loss in performance. Experimental results across classification and implicit neural representation tasks confirm that ENNs achieve state-of-the-art accuracy while maintaining a low number of parameters. Furthermore, up to 40% of the activation coefficients can be safely pruned, thanks to the orthogonality and bounded nature of the DCT basis. Overall, these findings demonstrate that the ENN framework offers a principled integration of signal processing concepts into neural network design, achieving a balanced trade-off between expressiveness, compactness, and interpretability.

Marc Martinez-Gost, Ana Pérez-Neira, Miguel Ángel Lagunas

This paper utilizes the properties of type-based multiple access (TBMA) to investigate its effectiveness as a robust approach for over-the-air computation (AirComp) in the presence of Byzantine attacks, this is, adversarial strategies where malicious nodes intentionally distort their transmissions to corrupt the aggregated result. Unlike classical direct aggregation (DA) AirComp, which aggregates data in the amplitude of the signals and are highly vulnerable to attacks, TBMA distributes data over multiple radio resources, enabling the receiver to construct a histogram representation of the transmitted data. This structure allows the integration of classical robust estimators and supports the computation of diverse functions beyond the arithmetic mean, which is not feasible with DA. Through extensive simulations, we demonstrate that robust TBMA significantly outperforms DA, maintaining high accuracy even under adversarial conditions, and showcases its applicability in federated learning (FEEL) scenarios. Additionally, TBMA reduces channel state information (CSI) requirements, lowers energy consumption, and enhances resiliency by leveraging the diversity of the transmitted data. These results establish TBMA as a scalable and robust solution for AirComp, paving the way for secure and efficient aggregation in next-generation networks.

Ana I. Pérez-Neira, Marc Martinez-Gost, Miguel Ángel Lagunas

This paper studies the cosine as basis function for the approximation of univariate and continuous functions without memory. This work studies a supervised learning to obtain the approximation coefficients, instead of using the Discrete Cosine Transform (DCT). Due to the finite dynamics and orthogonality of the cosine basis functions, simple gradient algorithms, such as the Normalized Least Mean Squares (NLMS), can benefit from it and present a controlled and predictable convergence time and error misadjustment. Due to its simplicity, the proposed technique ranks as the best in terms of learning quality versus complexity, and it is presented as an attractive technique to be used in more complex supervised learning systems. Simulations illustrate the performance of the approach. This paper celebrates the 50th anniversary of the publication of the DCT by Nasir Ahmed in 1973.