论文标题
非平滑区分编程的分发理论语义
Distribution Theoretic Semantics for Non-Smooth Differentiable Programming
论文作者
论文摘要
随着深度学习和梯度下降启发的优化算法的广泛传播，可区分的编程已获得了吸引力。如今，它也在许多不同领域找到了应用程序，例如科学计算，机器人技术，计算机图形和其他领域。它臭名昭著的困难问题之一是解释各处无可分割的程序。 在这项工作中，我们定义了$λ_δ$，这是一种用于非平滑差异程序的核心演算，并使用分布理论中的概念来定义其语义，该概念是一个良好的功能分析领域。我们还展示了$λ_δ$如何比其他现有语义提出更好的方程性能，并使用我们的语义来推理简化的射线跟踪算法。此外，我们通过提供与其他现有的可区分语义模型的翻译来将语义与现有的不同语言联系起来。最后，我们在本文的新结构中提供了概念概念的实施。
With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing, robotics, computer graphics and others. One of its notoriously difficult problems consists in interpreting programs that are not differentiable everywhere. In this work we define $λ_δ$, a core calculus for non-smooth differentiable programs and define its semantics using concepts from distribution theory, a well-established area of functional analysis. We also show how $λ_δ$ presents better equational properties than other existing semantics and use our semantics to reason about a simplified ray tracing algorithm. Further, we relate our semantics to existing differentiable languages by providing translations to and from other existing differentiable semantic models. Finally, we provide a proof-of-concept implementation in PyTorch of the novel constructions in this paper.
