aiqbench analysis
KoopCell introduces a novel generative framework leveraging Koopman operator theory to model single-cell developmental dynamics from sparse, unpaired snapshots. By integrating non-Markovian memory mechanisms, the method effectively addresses branching trajectories and extrapolation limits that often hinder neural differential equation approaches. This work represents a significant theoretical advancement in applying linear latent dynamics to high-dimensional biological data distributions.
KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots
arXiv:2609.33350v1 Announce Type: new Abstract: Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.
Abstract:Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Quantitative Methods (q-bio.QM)
arXiv:2609.33350 [cs.LG]
(or arXiv:2609.33350v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.33350 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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