OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding $10^4$ dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

Neural operator learning for collision-aware trajectory planning of spacecraft swarms

Autonomous spacecraft swarms must plan fuel-efficient, collision-free maneuvers in increasingly congested orbits, yet classical trajectory optimization scales poorly as pairwise safety constraints multiply with swarm size, and learning-based planners rarely transfer across swarm sizes or debris densities. Here we introduce a permutation-equivariant neural operator that maps distributions of spacecraft, targets and debris to collision-aware trajectories for an entire swarm in a single forward pass, paired with a batched Gauss-Newton finish that enforces exact orbital dynamics. The operator is trained without optimal-trajectory labels, combining self-supervised physics objectives with adversarial threats generated against its own rollouts. Trained on ten spacecraft, it generalizes zero-shot to swarms of 1,000 amid more than 11,000 catalogued objects, matching a per-agent optimal-control solver's accuracy, evading worst-case threats that a debris-blind baseline cannot, and reducing proximity within the swarm several-fold. Physics-grounded operator learning thus offers a fast, scalable alternative to optimal control for crowded orbits.

Stability of Flow Models for Graph Signals

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.