Continual Learning of Feedback-based Molecular Communication

Synaptic plasticity is metabolically expensive, yet animals continuously update their internal models without exhausting energy reserves. However, when artificial neural networks are trained, the network parameters are typically updated on every sample that is presented, even if the sample was classified correctly. Inspired by the human negativity bias and error-related negativity, we propose 'memorized mistake-gated learning' -- a biologically plausible plasticity rule where synaptic updates are strictly gated by current and past classification errors. This reduces the number of updates the network needs to make by $50\%\sim80\%$. Mistake gating is particularly well suited in two cases: 1) For incremental learning where new knowledge is acquired on a background of pre-existing knowledge, 2) For online learning scenarios when data needs to be stored for later replay, as mistake-gating reduces storage buffer requirements. The algorithm can be implemented in a few lines of code, adds no hyper-parameters, and comes at negligible computational overhead. Learning on mistakes is an energy efficient and biologically relevant modification to commonly used learning rules that is well suited for continual learning.

Continual learning with Low-Rank Adapters (LoRA) typically mitigates forgetting by penalizing the overlap between a new update and the accumulated past weights, which discourages certain update directions without controlling how an update distributes its energy over the ones that remain. We ask whether that restriction has to be task-aware, or whether a generic one supplied by the optimizer is enough. We train a plain incremental LoRA (IncLoRA) with Muon, which orthogonalizes each update, and compare it against O-LoRA and ELLA over five seeds and three task orders on the Standard CL Benchmark and three seeds on TRACE. IncLoRA+Muon reaches the accuracy band of the dedicated methods on Standard CL and improves on every AdamW configuration on TRACE. One update-constraining mechanism is enough, whether it comes from the loss or from the optimizer; on Standard CL a second one does not help, and for the most restrictive method it costs 8.4 points of accuracy and the plasticity to fit each task. What separates the two optimizers is not the size of the update, which under Muon is 0.91 to 2.06 times that under AdamW, but how it is distributed. AdamW confines it to between 1.4 and 1.8 effective singular directions, Muon spreads it over 7.0, and the two do not overlap in any tracked run. Part of the advantage usually attributed to dedicated CL methods may therefore be explained by the geometry of the optimizer's updates.

Continual learning (CL) studies how models acquire tasks sequentially while retaining previously learned knowledge. Despite substantial progress in benchmarking CL methods, comparative evaluations typically keep the fine-tuning regime fixed. In this paper, we argue that the fine-tuning regime, defined by the trainable parameter subspace, is itself a key evaluation variable. We formalize adaptation regimes as projected optimization over fixed trainable subspaces, showing that changing the trainable depth alters the effective update signal through which both current task fitting and knowledge preservation operate. This analysis motivates the hypothesis that method comparisons need not be invariant across regimes. We test this hypothesis in task incremental CL, five trainable depth regimes, and four standard methods: online EWC, LwF, SI, and GEM. Across five benchmark datasets, namely MNIST, Fashion MNIST, KMNIST, QMNIST, and CIFAR-100, and across 11 task orders per dataset, we find that the relative ranking of methods is not consistently preserved across regimes. We further show that deeper adaptation regimes are associated with larger update magnitudes, higher forgetting, and a stronger relationship between the two. These results show that comparative conclusions in CL can depend strongly on the chosen fine-tuning regime, motivating regime-aware evaluation protocols that treat trainable depth as an explicit experimental factor.