Towards Permutation Invariant Learning with High-Dimensional Particle Filters

Sequential learning in deep models often suffers from challenges such as catastrophic forgetting and loss of plasticity. This effect is largely due to the permutation dependence of gradient-based algorithms, where the order of training data affects the learning outcome. In this work, we introduce a novel learning framework based on high-dimensional particle filters that yields approximately permutation-invariant results. We theoretically demonstrate that particle filters are approximately invariant to the sequential ordering of training minibatches or tasks, offering a principled solution to mitigate catastrophic forgetting and loss-of-plasticity. Next, we develop an efficient particle filter for optimizing high-dimensional models, combining the strengths of Bayesian methods with gradient-based optimization. Finally, through extensive experiments on continual supervised and reinforcement learning benchmarks, including SplitMNIST, SplitCIFAR100, and ProcGen, we empirically demonstrate that our method consistently improves performance, while reducing variance compared to standard baselines.