Continual Learning Activation Function

We propose the problem of designing a dynamic, continuously-adaptive activation function that embeds continual-learning inductive biases directly into neuron nonlinearity. The target activation should trade off plasticity versus stability so networks can incrementally integrate concepts from multiple domains without catastrophic forgetting, while remaining scalable (avoiding saturation/dead neurons) and self-stabilizing (preserving bounded mean/variance across layers). Crucially, this mechanism must not rely on predefined task counts, explicit task identities, or brittle masking hacks; instead it should fold related concepts into shared representations and enable layer-wise progressive knowledge integration and reuse so that higher-level abstractions and deductive reasoning can emerge.