What Does Model Growth Really Add? Functional Capacity that Survives Continual Learning

Model growth adds parameters to a trained checkpoint and continues training, aiming to increase capacity while reusing the existing model instead of training from scratch. But does growing a trained model actually create new functional capacity that survives subsequent training? Parameter count alone cannot answer this question, and “capacity” is itself ambiguous; it can refer to parameter count, effective dimensionality, or the ability to represent new functions. We measure it directly, as the number of new, functionally independent directions a growth step adds, formalized as the rank increment of the model's functional Jacobian and estimated matrix-free at scale. For zero-gated function-preserving growth, this increment is exactly $K$ under a transversality condition, i.e. $\mathrm{rank}(J_{\mathrm{grown}})=\mathrm{rank}(J_{\mathrm{old}})+K$. Continually training a Transformer grown from $253\mathrm{M}$ to $857\mathrm{M}$ parameters across three domains, we find these added directions persist, with all $K=36$ remaining independent after continual learning, even when the model catastrophically forgets (perplexity $28\to 481$) or we deliberately destroy the old function ($25.9\to 127$). Geometric capacity and retained function are therefore decoupled. The functional capacity introduced by growth persists, while the previously learned function is not retained. A second, geometrically distinct mechanism, Net2Net, reaches the same $K$-dimensional capacity from directions that are dormant at initialization ($0\to K$) and then retains it, so the decoupling is not specific to the zero-gate parameterization. The implication is precise. Catastrophic forgetting need not reflect a loss of functional capacity, and preserving dimensionality alone is insufficient to preserve the learned function.