# Beyond Weighted Summation: Learnable Nonlinear Aggregation Functions for Robust Artificial Neurons

arXiv: https://arxiv.org/abs/2603.19344 · HTML: https://mlsanity.com/paper/2603.19344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Reliable Graph Neural Networks via Robust Aggregation](https://mlsanity.com/paper/2010.15651/) (2020)
- [Learned-Norm Pooling for Deep Feedforward and Recurrent Neural Networks](https://mlsanity.com/paper/1311.1780/) (2013)
- [Learning Aggregation Functions](https://mlsanity.com/paper/2012.08482/) (2020)
- [Towards NeuroAI: Introducing Neuronal Diversity into Artificial Neural Networks](https://mlsanity.com/paper/2301.09245/) (2023)
- [Deep Learning: a new definition of artificial neuron with double weight](https://mlsanity.com/paper/1905.04545/) (2019)
- [Finite Gaussian Neurons: Defending against adversarial attacks by making neural networks say "I don't know"](https://mlsanity.com/paper/2306.07796/) (2023)

## Abstract (arXiv)

Weighted summation has remained the default input aggregation mechanism in artificial neurons since the earliest neural network models. While computationally efficient, this design implicitly behaves like a mean-based estimator and is therefore sensitive to noisy or extreme inputs. This paper investigates whether replacing fixed linear aggregation with learnable nonlinear alternatives can improve neural network robustness without sacrificing trainability. Two differentiable aggregation mechanisms are introduced: an F-Mean neuron based on a learnable power-weighted aggregation rule, and a Gaussian Support neuron based on distance-aware affinity weighting. To preserve the optimisation stability of standard neurons, hybrid neurons are proposed that interpolate between linear and nonlinear aggregation through a learnable blending parameter. Evaluated in multilayer perceptrons and convolutional neural networks on CIFAR-10 and a noisy CIFAR-10 variant with additive Gaussian corruption, hybrid neurons consistently improve robustness under noise while F-Mean hybrids also yield modest gains on clean data. The three-way hybrid achieves robustness scores of up to 0.991 compared to 0.890 for the standard baseline, and learned parameters converge consistently to sub-linear aggregation (p ≈ 0.43--0.50) and high novelty utilisation (α ≈ 0.69--0.79). These findings suggest that neuron-level aggregation is a meaningful and underexplored design dimension for building more noise-tolerant neural networks.