Networked systems, from power grids to traffic networks and cloud clusters, carry loads across nodes with limited capacity. A node whose load exceeds its capacity fails and sheds its load onto its neighbors, which can trigger a system-wide cascade. We study how to allocate a fixed capacity budget across nodes to resist these cascades under local load redistribution. The problem is difficult because no optimal allocation is known, and the fail-or-survive objective is non-differentiable and piecewise constant, so exact and gradient-based optimization methods do not directly apply. We introduce TANGCO (Topology-Aware Neural Graph-Guided Capacity Optimization), which uses a graph neural network policy trained through the cascade simulator with policy-gradient learning and a heuristic anchor. We evaluate TANGCO on five synthetic graph families and five real networks spanning power, road, air, and Internet topologies. The learned policy improves on the best of four hand-designed heuristics in all 450 synthetic instances and in 40 of 45 real-network conditions, with robustness gains ranging from 1.6% to 246%. The learned policies transfer to unseen graphs within a family and partially across related topologies, and TANGCO$^{pre}$, pre-trained on synthetic graphs, matches per-network training on unseen real networks. Training scales near-linearly with graph size, and TANGCO$^{pre}$ allocates on a new network with no per-target training, matching the deployment cost of a hand-designed heuristic. Free-vector variants without the GNN, stay close to the heuristics, so the graph representation carries the gain beyond numerical search. Finally, analysis of the learned allocations identifies when local risk is sufficient, leads to an improved closed-form heuristic, and reveals the regimes where a topology-aware learned policy remains necessary.
We study how to share a single conserved capacity budget across many locations and two service classes when demand is uneven, time-varying, and can exceed supply. The shape recurs: an origin's request-rate cap split across its edge locations, a licensed throughput cap across premium and standard tenants, or an egress budget between latency-critical and batch workloads. We present a two-level algorithm. The first level redistributes capacity within a class across locations by proportional deficit and excess redistribution; the second lends capacity elastically between classes when one has surplus and the other deficit. We prove it conserves the budget exactly, preserves non-negativity, and reaches a stable allocation in one iteration under stationary demand because it carries no per-cycle state, at O(KN) cost per cycle for K classes and N locations. We evaluate it defending a CDN's per-domain budget under volumetric attack, where the classes are confirmed-legitimate and not-yet-cleared traffic; across 8 contention scenarios on a 22-location topology it serves 66-93% of high-priority demand, competitive with a single-class linear-programming optimum, while never leaving capacity idle or over-committing whenever aggregate demand meets or exceeds the budget (the contention regime these scenarios evaluate). Two findings carry beyond the application. First, a throughput-maximizing objective is wrong under contention: a two-class LP maximizing total served load serves less high-priority load than our demand-proportional, reservation-respecting allocator in most scenarios, because it cannot tell that some load it serves is the contention. Second, inter-class borrowing earns its complexity under bursty load, improving high-priority service by 1.5 points (isolated by ablation), and is neutral under stationary demand. A 5-location prototype with real HTTP traffic validates the pipeline.
Sub-model federated learning lets resource-constrained clients train width-reduced versions of a global model, but existing methods allocate capacity by device resources alone. A natural next step, allocating capacity by each client's data heterogeneity as estimated from the updates the server already observes, has been repeatedly suggested. We ask whether that step is possible, using HAS-FL, an adaptive capacity-allocation framework, as a test case. Our findings are threefold. First, validated against ground-truth label-distribution divergence on reproducible partitions, update-divergence estimates of client heterogeneity are dominated by capacity rather than data: across two corrected estimators, multiple datasets, and all seeds, the estimates correlate strongly and negatively with device capacity, and no data signal remains once capacity is controlled for. This previously undocumented confound affects any method estimating client statistics from sub-model updates. Second, adaptive allocation has a hidden failure mode: when every client is capped below full width, the uncovered parameters stay at random initialization and progressively corrupt the global model. A simple coverage guarantee removes the failure and explains why uniform allocation collapses. Third, a matched-budget control settles what adaptivity contributes: random allocation to the same average budget performs no differently on both image benchmarks, and on the naturally partitioned text benchmark the adaptive policy is the weakest of the three strategies while consuming the most capacity. Sub-model training remains valuable because it admits constrained clients at quadratically reduced cost, but what protects accuracy is parameter coverage rather than allocation intelligence. Its apparent benefits come from capacity budgeting and coverage, and future designs need heterogeneity signals separable from capacity effects.
Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.