cs.LGOct 3, 2026

Gated Target Propagation for Compositional Generalization in Continual Learning

Authors: Abdel Mfougouon Njupoun, Colin Bredenberg, Blake Aaron Richards, Guillaume Lajoie

Organizations: Université de Montr´eal Mila Quebec AI Institute · University of Oregon Mila Quebec AI Institute · McGill University Mila Quebec AI Institute

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Abstract

Continual learning is typically framed as acquiring new knowledge without catastrophically forgetting previous tasks. However, a flexible continual learner should also be able to reuse and recombine previously acquired knowledge to rapidly solve novel task compositions. We introduce Gated Target Propagation (GaTaP), a continual learning algorithm in which task-specific gating variables---learned through a closed-form inner loop update---selectively suppress or enhance network modules. Network parameters are learned in a slower timescale outer loop, using the same local difference target propagation error signal as is used for adapting gating variables. We provide tractable experiments on class-incremental learning scenarios for both multilayer perceptron and convolutional network architectures. We show strong performance retention on previously learned tasks, as well as compositional generalization to unseen tasks, achieved through few-shot gain adaptation at inference. We analyze learned gating patterns and find that related tasks exhibit similar gating patterns, suggesting that inferred gates capture meaningful, reusable task structure. Overall, GaTaP provides a powerful framework for jointly ameliorating catastrophic forgetting and enabling few-shot compositional generalization in neural network models.

Figures & tables

Figure 1: Parallel subnetworks with task-specific row-wise gating. (a) The transformed state Φi−1(hi−1)\Phi_{i-1}(h_{i-1}) is processed by nin_{i} parallel subnetworks with shared weight matrices Wi(k)W_{i}^{(k)} . Each task-specific gate vector Γi(k)\Gamma_{i}^{(k)} scales the rows of its corresponding weight matrix. The resulting branch outputs are summed, and additive noise ϵi\epsilon_{i} yields the next layer state hih_{i} . (b) Illustration of row-wise gating within one subnetwork: each gate entry multiplies every weight in the corresponding row. Values of 11 , 00 , and 0.40.4 respectively preserve, suppress, and attenuate that row, allowing task-dependent modulation of shared connectivity.
Figure 2: MNIST vs. CIFAR-10 comparison across methods. a) Average performance on tasks networks have already been exposed to during the training process, evaluated at the end of training. b) Average performance on unseen task combinations of data classes already seen during training, compared to performance on task combinations never seen during training. c) Same as (a), evaluated as networks are trained on an increasing number of tasks for MNIST (top) and CIFAR-10 (bottom). d) Average performance on unseen task combinations as a function of the number of support set examples provided per-class to train gates Γ\Gamma during evaluation, for MNIST (top) and CIFAR-10 (bottom).
Figure 3: Visualizing gain similarity across tasks. a) Cosine similarity of learned Γ\Gamma parameters across MNIST two-way classification tasks. “fewshot” indicates an unseen recombination of previously seen digits. b) Same as (a), for CIFAR-10 two-way classification tasks. c) Average cosine similarity of Γ\Gamma parameters for MNIST two-way classification tasks that share both digits, one digit, or no digits. d) Same as (c), for CIFAR-10 two-way classification tasks.
Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1: Two gating mechanisms for residual convolutional networks. Both variants combine parallel convolutional branches with task-specific gates and add the residual contribution Ri(hi−1)R_{i}(h_{i-1}) to the sum of the gated branch outputs. Left: Channel-wise gating assigns one scalar to each output channel, uniformly scaling its entire feature map. Right: Spatial gating assigns a separate gate value to each spatial location within each output channel, enabling selective modulation within a feature map. The lower panels illustrate how gate values preserve, suppress, or attenuate the corresponding activations.
Figure S2: Resplitting the support and query sets every epoch, as compared to a fixed split used across all epochs, as evaluated by a) average seen-task accuracy, b) compositional (unseen-combination) accuracy, and c) held-out-class accuracy.
Figure S3: Retention across sequential tasks with varying numbers of classes per-task. Networks are trained with GaTaP (green), EWC (orange), and standard backpropagation (blue). a) Models trained on MNIST, for two-way, three-way and five-way continual learning classification tasks. b) Models trained on CIFAR-10, for two-way, three-way, and five-way continual learning classification tasks. c) Models trained on CIFAR-100, for two-way, ten-way, and twenty-way continual learning classification tasks.
Figure S4: A comparison of seen- (left) and unseen-combination (right) task accuracy when using GaTaP in conjunction with spatial vs. channel gating for convolutional neural network models on a) CIFAR-10 and b) CIFAR-100.
HyperparameterValue
ArchitectureFeedforward MLP
Hidden layer sizes64, 128
Epochs per task10
Learning rate ( lrwlr_{w} )1×10−31\times 10^{-3}
OptimizerAdam
Random seed42
Appendix
Table 1: Shared training hyperparameters for MNIST (2-way, 3-way, and 5-way protocols). Values are identical across all three protocols and all three methods (GaTaP, EWC, Backprop) except where noted.
GaTaP
Number of subnetworks1
Sparsity coefficient ( α\alpha )10−510^{-5}
Gamma inference steps (train / test)10 / 10
Noise scale by layer ( σ\sigma )0.1, 0.1, 0.1
Support examples per class (train / test)32 / 64
Query batch size (train / test)128 / 256
Appendix
Table 2: Method-specific hyperparameters for MNIST. GaTaP columns apply identically across the 2-way, 3-way, and 5-way protocols.
HyperparameterValue
ArchitectureSimple ResNet (CNN)
Channel widths16, 32, 64, 128, 256, 512
Kernel size5
Epochs per task10
Learning rate ( lrwlr_{w} )1×10−31\times 10^{-3}
OptimizerAdam
Appendix
Table 3: Shared training hyperparameters for CIFAR-10 (2-way, 3-way, and 5-way protocols). Values are identical across all three protocols and all three methods (GaTaP, EWC, Backprop) except where noted.
GaTaP
Number of subnetworks1
Gamma modeSpatial
Sparsity coefficient ( α\alpha )10−510^{-5}
Gamma scale1.0
Gamma inference steps (train / test)10 / 10
Noise scale by layer ( σ\sigma )0.1 (all 7 layers)
Appendix
Table 4: Method-specific hyperparameters for CIFAR-10. GaTaP columns apply identically across the 2-way, 3-way, and 5-way protocols.
HyperparameterValue
ArchitectureSimple ResNet (CNN)
Channel widths16, 32, 64, 128, 256, 512
Kernel size5
Epochs per task20
Learning rate ( lrwlr_{w} )3×10−43\times 10^{-4}
OptimizerAdam
Appendix
Table 5: Shared training hyperparameters for CIFAR-100 (2-way, 10-way, and 20-way protocols). Values are identical across all three protocols and all three methods (GaTaP, EWC, Backprop) except where noted.
GaTaP
Number of subnetworks2
Gamma modeSpatial
Sparsity coefficient ( α\alpha )10−710^{-7}
Gamma scale1.0
Gamma inference steps (train / test)10 / 10
Noise scale by layer ( σ\sigma )0.1 (all 7 layers)
Appendix
Table 6: Method-specific hyperparameters for CIFAR-100. GaTaP columns apply identically across the 2-way, 10-way, and 20-way protocols.
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