iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compression
It is nontrivial to store rapidly growing big data nowadays, which demands high-performance lossless compression techniques. Likelihood-based generative models have witnessed their success on lossless compression, where flow based models are desirable in allowing exact data likelihood optimisation with bijective mappings. However, common continuous flows are in contradiction with the discreteness of coding schemes, which requires either 1) imposing strict constraints on flow models that degrades the performance or 2) coding numerous bijective mapping errors which reduces the efficiency. In this paper, we investigate volume preserving flows for lossless compression and show that a bijective mapping without error is possible. We propose Numerical Invertible Volume Preserving Flow (iVPF) which is derived from the general volume preserving flows. By introducing novel computation algorithms on flow models, an exact bijective mapping is achieved without any numerical error. We also propose a lossless compression algorithm based on iVPF. Experiments on various datasets show that the algorithm based on iVPF achieves state-of-the-art compression ratio over lightweight compression algorithms.
Code (4)
Similar Papers 제목 키워드 기반
iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compression
It is nontrivial to store rapidly growing big data nowadays, which demands high-performance lossless compression techniques. Likelihood-based generative models have witnessed their success on lossless compression, where …
Locally-symplectic neural networks for learning volume-preserving dynamics
We propose locally-symplectic neural networks LocSympNets for learning the flow of phase volume-preserving dynamics. The construction of LocSympNets stems from the theorem of the local Hamiltonian description of the dive…
Deep Neural Networks with Symplectic Preservation Properties
We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used…
Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equations
Many conservative physical systems can be described using the Hamiltonian formalism. A notable example is the Vlasov-Poisson equations, a set of partial differential equations that govern the time evolution of a phase-sp…
Analytic Bijections for Smooth and Interpretable Normalizing Flows
A key challenge in normalizing flows is finding expressive invertible scalar bijections. Existing approaches face trade-offs: affine transformations are smooth and analytically invertible but lack expressivity; monotonic…