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Researchers use networks to model relational data from complex systems, and tools from network science to map them and understand their function. Flow communities capture the organization of various real-world systems such as social networks, protein-protein interactions, and species distributions, and are often overlapping. However, mapping overlapping flow-based communities requires higher-order data, which is not always available. To address this issue, we take inspiration from the representation-learning algorithm node2vec, and apply higher-order biased random walks on first-order networks to obtain higher-order data. But instead of explicitly simulating the walks, we model them with sparse memory networks and control the complexity of the higher-order model with an information-theoretic approach through a tunable information-loss parameter. Using the map equation framework, we partition the resulting higher-order networks into overlapping modules. We find that our method recovers planted overlapping partitions in synthetic benchmarks and identifies overlapping communities in real-world networks.