将AlphaFold的结构预测机制重新解释为贝叶斯更新的数学框架。
AlphaFold's Bayesian Roots in Probability Kinematics
- 用概率动力学重构AlphaFold，使其成为可解释的贝叶斯模型。
- 在合成模型中验证了角度随机游走与距离证据的联合更新机制。
- 为下一代生成式蛋白结构模型提供理论基础，适合研究者参考。
AlphaFold在蛋白质结构预测中的突破性进展依赖于由深度模型参数化的学习势能函数，而其后续版本AlphaFold2和AlphaFold3则缺乏显式的概率解释。尽管早期的势能函数基于物理平均力势的启发式类比，我们证明其可被严格视为概率动力学（PK）——即杰弗里条件化——的一个实例，是贝叶斯更新的推广。这一重释表明，AlphaFold本质上是一个广义贝叶斯模型，明确定义了结构上的后验分布，从而更深刻地解释其成功，并为未来模型设计提供理论基础。为精确演示该框架，我们引入一个可解析的合成模型：以角度随机游走为先验，通过距离证据进行概率动力学更新，直接复现AlphaFold的机制。该设定使我们能清晰、可解释地探索AlphaFold的概率根基。本工作将这一蛋白质结构预测的里程碑与更广泛的组合式深度生成模型联系起来，揭示了严谨概率方法的新机遇。
原文摘要 · Abstract (English)
The seminal breakthrough of AlphaFold in protein structure prediction relied on a learned potential energy function parameterized by deep models, in contrast to its successors AlphaFold2 and AlphaFold3, which lack an explicit probabilistic interpretation. While AlphaFold's potential was originally justified by heuristic analogy to physical potentials of mean force, we show that it can instead be understood as a principled instance of probability kinematics (PK), also known as Jeffrey conditioning, a generalization of Bayesian updating. This reinterpretation reveals that AlphaFold is a generalized Bayesian model that explicitly defines a posterior distribution over structures, providing a deeper explanation of its success and a foundation for future model design. To demonstrate this framework with precision, we introduce a tractable synthetic model in which an angular random walk prior is updated with distance-based evidence via PK, directly mirroring AlphaFold's mechanism. This setting allows us to explore the probabilistic foundations of AlphaFold in a clear and interpretable way. Our work connects a landmark in protein structure prediction to a broader class of compositional deep generative models and points to new opportunities for principled probabilistic approaches.
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