Rethinking the stability–plasticity dilemma in continual learning through functional equivalence

Continual learning requires models to acquire new knowledge without disrupting previously learned capabilities, creating a fundamental tension between stability and plasticity. Stability, however, is often imposed without distinguishing which internal changes are actually detrimental to retention. This paper reconceptualizes continual learning through functional equivalence: internal states that realize the same function are treated as equivalent, thereby leaving functionally invariant degrees of freedom available for adaptation. In multiclass softmax classification, this equivalence admits an exact decomposition of logits into relative class scores that determine class probabilities within a task and common score shifts that leave them unchanged. Building on this structure, we instantiate the principle in continual learning through FEAST (Functional Equivalence–guided Allocation of STability and Plasticity). FEAST yields strong Class-IL and Task-IL performance compared with methods that do not retain an additional full teacher network. We further provide a mechanistic account of how these gains arise: stability is concentrated on function-defining coordinates, while functionally invariant freedom provides an alternative path for adaptation. This division of labor improves acquisition while reducing function-defining output change and forgetting. Together, these results recast the stability–plasticity dilemma in terms of the functional consequences of change rather than change itself.