Abstract
Catastrophic forgetting remains the central obstacle in continual learning (CL): parameters shared across tasks interfere with one another, and existing regularization methods such as EWC and SI apply uniform penalties without awareness of which input region a parameter serves. We propose KAN-CL, a continual learning framework that exploits the compact-support spline parameterization of Kolmogorov-Arnold Networks (KANs) to perform importance-weighted anchoring at per-knot granularity. Deployed as a classification head on a convolutional backbone with standard EWC regularization on the backbone (bbEWC) KAN-CL achieves forgetting reductions of 88% and 93% over a head-only KAN baseline on Split-CIFAR-10/5T and Split-CIFAR-100/10T respectively, while matching or exceeding the accuracy of all baselines on both benchmarks. We further provide a Neural Tangent Kernel (NTK) analysis showing that KAN's spline locality induces a structural rank deficit in the cross-task NTK, yielding a forgetting bound that holds even in the feature-learning regime. These results establish that combining an architecture with natural parameter locality (KAN head) with a complementary backbone regularizer (bbEWC) yields a compositional and principled approach to catastrophic forgetting.
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Jun 16, 2026cs.LG
Catastrophic forgetting in continual adaptation is usually studied through parameter drift, replay, or distillation, but these views do not identify which output-space directions are vulnerable. We give a function-space account in the NTK regime: new-task training induces old-task prediction drift through the cross-task kernel, yielding a closed-form predictor for the forgetting vector before any new-task gradient step. In frozen-backbone linear-head PEFT-CL, where the model is linear in the trainable parameters, the predictor is exact up to numerical precision; for nonlinear adapters/full fine-tuning, it is a local NTK approximation. The same expression reveals that forgetting concentrates in a small number of old-task NTK eigenmodes and under frozen linear heads gives a Kronecker scaling rule for the vulnerable rank. These results clarify the relation to prior NTK-overlap theory, explain why parameter-space regularizers can miss output-space interference, and motivate a targeted spectral regularizer.
Ido Nitzan Hidekel, Dan Raviv
Aug 1, 2026cs.LG
Achieving continual learning (CL) with deep neural networks requires balancing stability and plasticity while enabling knowledge transfer. In this work, we focus on offline learning algorithms under the constraints: (I) no access to training data from prior tasks (II) no access to task-id at inference time. We introduce a novel measure, the relative parameter-importance, which measures the relative importance of each parameter with respect to both the current and past tasks. Parameters with high relative importance are interpreted as more important for maintaining past-task stability and thus heavily regularised, whereas parameters with low relative-importance are allowed to be more freely updated. Unlike existing methods, our approach allows the update of parameters with high past-task importance when they have low relative-importance, thus enabling backward knowledge transfer in addition to tackling the stability-plasticity trade-off. We demonstrate improvements against state-of-the-art CL methods on both class-incremental and domain-incremental learning text classification problems and provide insights for extending our method to text generation problems. Code available at: https://github.com/itsmemala/LACL
Malavika Suresh, Ikechukwu Nkisi-Orji, Nirmalie Wiratunga
Jun 1, 2026cs.LG
Catastrophic forgetting is often framed as a representational problem: after sequential training, a model appears to lose the features that supported performance on earlier tasks. We challenge the stronger form of this view. Across controlled continual-learning settings, we find that a significant portion of apparent forgetting can be attributed to interface drift between internal stages rather than permanent erasure of task-relevant computation. We study this phenomenon through a stitched evaluation protocol that combines early computation from a post-update network with late computation from its predecessor, optionally mediated by a compact, task-specific transport key. We describe transport keys at a systems level as compact interface-alignment operators estimated from a small set of paired anchor activations and evaluated through model stitching. On split CIFAR-100 with a ResNet-style network, transport keys recover most of the original Task A performance after sequential training on Task B. On a compact vision transformer, we observe a similar recovery pattern. These results suggest that continual learning may require better mechanisms for indexing and re-accessing latent computations, not only methods that prevent weight change.
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