No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural Networks

Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, it acts as a sophisticated designer of task-based neurons. In this study, we address the following question: since the human brain is a task-based neuron user, can the artificial network design go from the task-based architecture design to the task-based neuron design? Since methodologically there are no one-size-fits-all neurons, given the same structure, task-based neurons can enhance the feature representation ability relative to the existing universal neurons due to the intrinsic inductive bias for the task. Specifically, we propose a two-step framework for prototyping task-based neurons. First, symbolic regression is used to identify optimal formulas that fit input data by utilizing base functions such as logarithmic, trigonometric, and exponential functions. We introduce vectorized symbolic regression that stacks all variables in a vector and regularizes each input variable to perform the same computation, which can expedite the regression speed, facilitate parallel computation, and avoid overfitting. Second, we parameterize the acquired elementary formula to make parameters learnable, which serves as the aggregation function of the neuron. The activation functions such as ReLU and the sigmoidal functions remain the same because they have proven to be good. Empirically, experimental results on synthetic data, classic benchmarks, and real-world applications show that the proposed task-based neuron design is not only feasible but also delivers competitive performance over other state-of-the-art models.