Gated Target Propagation for Compositional Generalization in Continual Learning

Continual learning commonly relies on post-hoc mechanisms such as replay, elastic regularization, or distillation. This work argues that forgetting should instead be modeled directly as interference between tasks. In the frozen-feature regime, forgetting from learning a new task is exactly the interference energy induced on the old task. In deep networks, the same quantity is recovered through path-averaged curvature with minimal additional forward passes. When task supports are disjoint, forgetting can be eliminated structurally and when task supports overlap in conflicting directions, a non-zero distortion floor is unavoidable. The same geometry optimally merges models through task-aware orthogonalization. From this analysis we derive Interference-Gated Functional Allocation (IGFA), a replay-free, Fisher-free method that shares directions when tasks align and protects them when they conflict. Across benchmarks, IGFA achieves lossless retention when tasks are structurally separable and moves unavoidable cost from irreversible forgetting into deferred but recoverable plasticity when they are not. It matches the strongest replay-free structural baselines on dissimilar-task streams and improves on unconditional projection when similarity makes transfer worth preserving.

Catastrophic forgetting is a major problem in task-incremental learning, where neural networks tend to overwrite previously learned knowledge when trained on new tasks. A number of architecture-based approaches have been proposed to address this problem. However, the architecture-based approaches suffer from another problem related to network capacity when the networks learn long task sequences: As a network is trained on an increasing number of new tasks in a long task sequence, a growing proportion of active parameters becomes static to prevent forgetting of previously learned knowledge. In this paper, we propose Adaptive Hard Attention to the Task (AdaHAT) with an adaptive attention mechanism which allows adaptive updates to static parameters by taking into account the information about previous tasks on both the importance of these parameters to previous tasks and the current network capacity. Based on this idea, we develop a new neural network architecture incorporating our proposed AdaHAT mechanism. AdaHAT extends an existing architecture-based approach, Hard Attention to the Task (HAT), to better support task-incremental learning over long task sequences. We conduct experiments on a number of datasets and compare AdaHAT with task-incremental learning baselines including HAT. Our experimental results show that AdaHAT achieves better average performance across tasks than these baselines, especially on long task sequences, demonstrating the benefits from balancing the trade-off between stability and plasticity of a network when learning such sequences of tasks, alleviating the network capacity problem. Our code is available at pengxiang-wang.com/projects/continual-learning-arena.

Block-sequential continual learning demands that a single model both protect prior solutions from catastrophic forgetting and efficiently infer at inference time which prior solution matches the current input without task labels. We present Functional Task Networks (FTN), a parameter-isolation method inspired by structural and dynamical motifs found in the mammalian neocortex. Similar to mixture-of-experts, this method uses a high dimensional, self-organizing binary mask over a large population of small but deep networks, inspired by dendritic models of pyramidal neurons. The mask is produced by a three-stage procedure: (1) gradient descent on a continuous mask identifies task-relevant neurons, (2) a smoothing kernel biases the result toward spatial contiguity, (3) and k-winner-take-all binarizes the resulting group at a fixed capacity budget. Like mixture-of-experts, each neuron is an independent deep network, so disjoint masks give exactly disjoint gradient updates, providing structural guarantees against catastrophic forgetting. This three-stage procedure recovers the sub-network of a previously-trained task in a single gradient step, providing unsupervised task segmentation at inference time. We test it on three continual-learning benchmarks: (1) a synthetic multi-task classification/regression generator, (2) MNIST with shuffled class labels (pure concept shift), and (3) Permuted MNIST (domain shift). On all three, FTN with fine grained smoothing (FTN-Slow) results in nearly zero forgetting. FTN with a large kernel and only 2 iterations of smoothing (FTN-Fast) trades off some retention for increased speed. We show that the spatial organization mechanism reduces the effective mask search from the combinatorial top-k subset problem in O(C(H,K)) to the complexity of a near-linear scan in O(H) over compact cortical neighborhoods, which is parallelized by the gradient-based update.