arXiv:2607.01381 2026 Memory 1 ideas extracted · analyzed Aug 30, 2026
The paper combines hierarchical Tucker low-rank representations with a projection step that preserves selected macroscopic moments before truncation. The transferable asset is not the Vlasov discretization itself, but the pattern of compressing a high-dimensional tensor while enforcing exact preservation of task-relevant linear statistics. This suggests a moment-preserving tensorized neural layer or recurrent-state compressor: perform ordinary low-rank or HT compression, then correct the compressed tensor in a small constraint subspace so sums, coordinate-weighted sums, and quadratic energy-like statistics are unchanged. The approach is most relevant to tensorized models and learned physical simulators, where compression errors that violate invariants can destabilize long rollouts.
Add a conservative correction after low-rank tensor compression so selected linear moments of an activation or learned state are exactly preserved. This can reduce tensor rank and memory without allowing compression error to accumulate in physically meaningful global quantities.