Complex Networks

Dynamic expansion methods for class-incremental learning (CIL) protect task-specific knowledge by growing dedicated tokens or subnetworks, yet our analyses suggest that classification supervision alone does not sufficiently preserve task-agnostic shared backbone representations over long incremental sequences. We identify two intertwined challenges: cross-task confusion from sequential training on predominantly current-task data, which biases decision boundaries toward recent tasks; and under-optimized shared representations in the backbone that cap long-term discriminability as tasks accumulate. We propose the Decoupled Representation Dynamic Network (DRDN), which addresses these challenges via two orthogonal mechanisms. For shared backbone representations, DRDN continuously applies masked image modeling (MIM) at every incremental step, with reconstruction gradients routed exclusively through the backbone, encouraging it to retain general visual structure beyond class-discriminative cues. For task-specific discrimination, DRDN employs hierarchical task token expansion across all transformer layers, with a modified per-task attention rule that reduces inter-task interference. We support this design with accuracy degradation analysis and cross-task confusion rate measurements. In the from-scratch ViT CIL setting (no external pretraining), DRDN consistently improves over strong token-expansion baselines with comparable backbone scale. On CIFAR100-B0 (10 steps), DRDN achieves 77.19% average accuracy, outperforming DKT by 1.36 points and DyTox by 3.53 points, with an advantage that grows at longer incremental sequences. Multi-seed validation confirms stability (+/-0.31%). The MIM decoder is active only during training, adding no inference-time parameters or computation.

Reconstructing complex network topologies from data is a fundamental challenge in cybernetics and graph signal processing, with applications in neuroscience, sensor, and social networks. In practice, target-domain samples are scarce while heterogeneous source-domain data are abundant. Fusing these sources is challenging: Euclidean averaging works for homogeneous sources but degrades sharply as inter-source divergence grows, collapsing distinct geometries into an inflated, biased consensus. We exploit the Wasserstein metric's distribution-preserving properties to counter heterogeneity while preserving each source's intrinsic geometry. We propose MS-WDRO, a multi-source Wasserstein distributionally robust graph learning framework that fuses heterogeneous sources via their weighted Wasserstein barycenter, a geometrically principled nominal distribution, then builds an ambiguity ball around it to hedge residual uncertainty. Minimizing worst-case risk yields a tractable regularized Laplacian estimator solved efficiently via a provably convergent ADMM scheme. We establish non-asymptotic guarantees: a finite-sample concentration bound for the empirical barycenter, a pooling bias lower bound proving naive aggregation is suboptimal, and an out-of-sample excess risk bound decaying at a parametric rate with only logarithmic dependence on source count. To calibrate hyperparameters governing robustness, sparsity, and source fusion, we unroll the solver into a differentiable architecture trained end-to-end, achieving data-adaptive calibration beyond cross-validation while retaining interpretability. Experiments on synthetic benchmarks and the multi-site ABIDE~I neuroimaging dataset show MS-WDRO consistently outperforms seven baselines in graph recovery, sample efficiency, and downstream diagnostic utility, with the largest gains in the sample-scarce regime.