Neural networks that can grow or both grow and shrink during learning, referred to as growing neural networks and elastic neural networks, respectively, have recently been explored in offline continual learning with a particular focus on catastrophic forgetting. Driven by the observations that 1) online continual learning closely resembles how animals learn; 2) loss of plasticity---the progressive decline in a learning network's ability to learn---is another crucial challenge facing continual learning; and 3) incremental introduction of randomly initialized hidden units was recently shown to help preserve plasticity, in this paper, we study the plasticity of several foundational growing and elastic networks in online continual learning. Our experiments in supervised learning settings show that adaptive growing networks, which incrementally incorporate new, randomly initialized units to the network while keeping all existing connections adaptive, can maintain high prediction accuracy without losing plasticity despite the continuous increase in the dead hidden unit proportion. Furthermore, we demonstrate that adaptive elastic networks, which in addition to progressively adding new hidden units also prune estimated dead hidden units at the beginning of each new task, can achieve excellent accuracy without loss of plasticity while simultaneously maintaining a near-constant, compact size. Our results suggest that growing and elastic networks, which exhibit the ability to adapt its structure to the relevant learning objectives, can be a promising class of algorithms also for preserving high plasticity in online continual learning.
Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program. We formalize Exact Network Surgery: the in-place insertion of a residual block into a live computational graph such that (i) the network function is preserved -- bit-exactly under explicit floating-point hypotheses -- and (ii) inserted parameters remain trainable immediately after insertion. We prove an identity-morphism theorem for gated residual blocks, a structural-locality theorem showing that a reactive invalidation engine recomputes exactly the downstream cone of the insertion point, leaving every other node's value and optimizer state untouched, and an escape-from-initialization proposition showing that the Gradient Shadowing gate alpha, initialized at zero over a randomly initialized branch, receives a generically non-zero gradient at insertion time. We identify a degenerate configuration -- zero-initialized output projections combined with a zero gate -- that is an exact saddle point gradient descent cannot escape. Every claim is validated on the reference implementation in NeuroDSL, a reactive graph engine in Julia: grafting is bit-exact on every logit tested (0 mismatches out of 1600); the gate escapes zero at the first optimizer step and unlocks branch gradients at the second, exactly as predicted; the degenerate configuration exhibits gradients identically zero for the entire 600-step run; surgery cost tracks downstream cone size with r = 0.9992 while graft-plus-invalidation bookkeeping is constant (about 0.75 ms) across insertion depths; and training resumes bit-identically across a real process restart. A flagged preliminary appendix reports first single-seed observations on post-insertion gate dynamics.