Continual-learning rules shape representational drift

Abstract: Lifelong learning requires acquiring new knowledge without erasing the old. Yet neural population codes for familiar stimuli and behaviors change over days and weeks. This coexistence of stable memory and changing internal codes may depend on how a learning system prevents forgetting. We therefore tested whether different continual-learning mechanisms produce distinct patterns of representational drift. We trained convolutional networks on sequential image classification tasks and recurrent networks on sequences of cognitive tasks, tracking fixed probe representations across learning. Experience replay preserved earlier tasks in both architectures while representations drifted progressively with the number of intervening tasks. Drift was structured: later visual-processing stages and recurrent units' temporal tuning were especially labile, whereas coarse class organization and task-relevant temporal structure persisted. In contrast, algorithm that strongly anchored weights nearly froze representations. Directly anchoring an old representation during replay likewise suppressed drift and impaired acquisition of subsequent tasks. Together, these results link representational drift to the stability--plasticity trade-off: its magnitude is shaped by the mechanism that protects old knowledge, and suppressing it can restrict future learning. Drift may therefore provide an observable signature of the constraints that enable continual learning in brains and machines.

• The paper shows that experience replay preserves task performance while allowing gradual, structured representational drift, whereas strong parameter or activity anchoring largely freezes internal codes.
• The paper finds that drift is organized rather than random: deeper visual layers and precise recurrent tuning change faster, while class geometry, mean activity, and task-related temporal structure remain comparatively stable.
• The paper demonstrates that increasing representation anchoring reduces drift but also harms forward learning, directly linking internal-code flexibility to the stability–plasticity trade-off in continual learning.

Overview and motivation

Representational drift—the gradual change in neural population codes for stable stimuli and behaviors over days to weeks—has been documented across hippocampus, parietal, visual, auditory, and piriform cortex. A central unresolved question is which learning processes generate such change while preserving memory and behavior. Si and Qin address this by asking whether the specific mechanism a system uses for continual learning leaves a distinguishable signature in the magnitude and organization of drift. Their hypothesis is that parameter-anchoring methods (e.g., elastic weight consolidation, EWC) should suppress drift, whereas experience replay, which constrains performance on stored examples without anchoring weights, should permit it.

The study uses two architectures: ResNet-18 trained on 20 sequential five-class ImageNet tasks under naive sequential training, EWC, Learning without Forgetting (LwF), and experience replay; and a 256-unit continuous-time RNN trained on 18 cognitive tasks from the Yang et al. suite under naive training and replay. After each task, a fixed held-out probe set from task 1 is passed through each checkpoint, and representational change is quantified with cosine similarity, population-vector correlations, and centered kernel alignment (CKA). All conditions use 10 independently initialized networks; BatchNorm is replaced with GroupNorm plus weight standardization so that stored normalization statistics cannot confound drift measurements—a methodological detail that strengthens the interpretability of the results.

Drift in hierarchical visual representations

The four continual-learning methods occupy distinct positions on the retention–plasticity–stability trade-off. Naive sequential training exhibits catastrophic forgetting; EWC at $\lambda = 5\times10^5$ keeps checkpoint representations nearly frozen but adapts poorly to later tasks; LwF is intermediate; replay achieves the strongest overall retention while learning across the sequence. Critically, replay's retention does not require a fixed code: pairwise checkpoint similarity declines smoothly with task separation even as task-1 accuracy remains high, satisfying the defining condition for representational drift. Later residual stages drift faster than earlier ones, consistent with greater lability of task-specific features.

The drift is structured rather than diffuse. UMAP embeddings of layer-4 activations show that task-1 classes remain clustered at every checkpoint under replay even as cluster locations move. Quantitatively, CKA analysis of sample-similarity matrices shows that relational geometry is far more stable than individual activation vectors: adjacent-checkpoint CKA at stages 2–4 is 0.87–0.97, declining only to approximately 0.68–0.80 after 19 intervening tasks, while sample-level population-vector correlations fall substantially more. Much of the drift therefore corresponds to transformations that approximately preserve the pairwise geometry underlying class readout. Stage 1 is an exception, with low (~0.64) and highly variable CKA even between adjacent checkpoints.

The most consequential intervention is a representation-anchor penalty added to replay: cached task-1 probe activations at stages 3–4 are penalized for displacement during subsequent learning. Increasing anchor strength progressively suppresses final drift while preserving task-1 accuracy—but reduces forward accuracy on newly introduced tasks, and across anchor strengths larger final drift correlates with higher forward accuracy. This directly demonstrates a trade-off between representational stability and continued plasticity within a single replay regime. The authors are careful to note this does not establish that drift is universally beneficial: the penalty changes the optimization problem, and an anchoring scheme with smaller cost is not excluded.

Drift in recurrent cognitive dynamics

The RNN experiments extend the dissociation from static feature vectors to temporally extended trajectories. Naive sequential training produces catastrophic interference, with off-diagonal task accuracies near chance. Replay yields near-perfect retention—almost all task-by-checkpoint accuracies exceed 0.95—with only transient interference between task families (e.g., Go tasks tested immediately after Anti-task introduction).

Stable behavior again coexists with systematic drift. Spatiotemporal population-vector (STPV) similarity between checkpoints decreases monotonically with task gap, reaching 0.59 at maximum separation. The four representation summaries drift at different rates, with a consistent ordering: ensemble rate vector (ERV) most stable (~0.63 at gap 17), then STPV, then population vector (PV), with tuning curve vectors (TCV) most labile (~0.43). Mean unit activity is thus better preserved than precise temporal tuning—a dynamic analogue of the depth-dependent drift in the CNN. Cross-checkpoint, cross-time correlation matrices further show that under replay, trial epochs remain internally organized even as their population states shift gradually, whereas naive training destroys cross-checkpoint correlations entirely.

Implications for theories of drift and biological learning

Three implications follow directly from these results. First, accuracy alone is an insufficient metric for evaluating continual-learning algorithms: methods with comparable retention can differ substantially in how they reorganize internal codes. Second, gradual structured drift can emerge from ordinary task-driven multi-task learning without explicitly imposed synaptic volatility, extending single-task accounts based on implicit regularization or stochastic synaptic change into the regime where old knowledge is actively maintained. Third, the replay-generated drift profile—change accumulating with intervening learning, component-specific rates, preserved coarse structure—is qualitatively compatible with cortical observations and with complementary-learning-systems theories in which reactivation supports consolidation. The authors emphasize this is algorithmic compatibility, not biological mechanism: artificial replay is not a model of hippocampal replay, and the simulations do not identify the microscopic source of biological drift.

On the origin-versus-function question, the paper is appropriately cautious. The anchoring result links representational flexibility to subsequent learning but is equally consistent with drift being an inseparable consequence of the parameter movement required for new learning rather than an adaptive feature. Distinguishing these requires interventions that vary drift while matching retention, new-task performance, and parameter displacement.

Limitations and open questions

The authors state several limitations plainly. The protocol is task-incremental (task identity available at evaluation); class-incremental learning may yield different drift profiles. The strongly regularized EWC condition learned later tasks poorly, making it a freezing reference rather than a performance-matched control. EWC and LwF did not achieve reliable continual-learning performance in the RNN, so whether the CNN method ordering generalizes to recurrent systems remains unknown. Task order was not varied, and comparisons with biological data must account for differences in task structure, timescale, and recording statistics. The method comparison is also explicitly qualitative rather than a ranking, since methods were not matched for retention, plasticity, or total parameter movement.

Conclusion

This paper establishes continual-learning rules as a testable source of variation in representational drift. Experience replay permits progressive, structured drift compatible with stable memory; functional distillation yields intermediate drift; strong parameter or representation anchoring approaches freezing at the cost of future plasticity. The central empirical contribution is the demonstration, via direct intervention, that suppressing drift within replay impairs acquisition of later tasks—linking the stability–plasticity trade-off to an observable signature in internal codes. The key open question left by the work is whether matched comparisons among parameter-, function-, and activity-constraining methods, combined with quantitative alignment to longitudinal neural recordings, can determine when drift is merely tolerated versus when it actively enables lifelong learning.