计数数据的随机流映射
Stochastic Flow Map for Count Data
- Center for Computational Neuroscience（计算神经科学中心）
- Flatiron Institute（熨斗研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出计数流映射（Count Flow Map），一种直接在计数空间学习有限时间随机转移的生成模型，通过泊松出生与二项死亡保持非负整数，实现一步或几步高质量生成，并成功应用于药物扰动预测和神经群体预测。
AI中文摘要：
高维计数数据在科学应用中普遍存在，但大多数扩散模型和流模型是为连续或分类数据设计的，且生成过程通常需要多次顺序模型评估。我们提出计数流映射（Count Flow Map），一种直接在计数空间中学习有限时间转移的生成模型，用于一步或几步生成。该模型直接学习有限时间区间内的随机转移，利用泊松出生和二项死亡过程来保持非负整数计数，无需预设最大值。这些转移模型经过训练，以匹配底层的局部出生-死亡动力学，并保持跨步长的一致性。我们刻画了局部动力学与有限时间转移一致性之间的联系，并推导了生成误差的界。在多个模拟中验证计数流映射后，包括高维、高计数设置，我们将其应用于单细胞药物扰动预测和神经群体预测，在这些任务中，它仅需一次或几次模型评估即可捕捉扰动响应并支持高活性事件的预测。这些实验共同表明，计数流映射能够在推理预算范围内（从一步到几步生成）直接实现计数空间中的高质量生成，且仅需一个训练好的模型。
英文摘要：
High-dimensional count data are common in scientific applications, but most diffusion and flow models are designed for continuous or categorical data, and generation often requires many sequential model evaluations. We propose Count Flow Map, a generative model that learns finite-time transitions directly in count space for one- or few-step generation. Our model directly learns stochastic transitions over finite time intervals, using Poisson births and Binomial deaths to preserve nonnegative integer counts without a predefined maximum. These transition models are trained to match the underlying local birth--death dynamics and to maintain consistency across step sizes. We characterize the connection between local dynamics and finite-time transition consistency and derive a bound on the generation error. After validating Count Flow Map in several simulations, including a high-dimensional, high-count setting, we apply it to single-cell drug perturbation prediction and neural population forecasting, where it captures perturbation responses and supports forecasts of high-activity events with only one or a few model evaluations. Together, these experiments demonstrate that Count Flow Map enables high-quality generation directly in count space across inference budgets, from one-step to few-step generation, using a single trained model.
