Abstract
Trainable activation functions, whose parameters are optimized alongside network weights, offer increased expressivity compared to fixed activation functions. Specifically, trainable activation functions defined as ratios of polynomials (rational functions) have been proposed to enhance plasticity in reinforcement learning. However, their impact on training stability remains unclear. In this work, we study trainable rational activations in both reinforcement and continual learning settings. We find that while their flexibility enhances adaptability, it can also introduce instability, leading to overestimation in RL and feature collapse in longer continual learning scenarios. Our main result is demonstrating a trade-off between expressivity and plasticity in rational activations. To address this, we propose a constrained variant that structurally limits excessive output scaling while preserving adaptability. Experiments across MetaWorld and DeepMind Control Suite (DMC) environments show