Algorithms are ways of mapping problems to solutions. An algorithm is
invertible precisely when this mapping is injective, such that the initial
problem can be uniquely inferred from its solution.
While invertible algorithms can be described in general-purpose languages, no
guarantees are generally made by such languages as regards invertibility, so
ensuring invertibility requires additional (and often non-trivial) proof. On
the other hand, while reversible programming languages guarantee that their
programs are invertible by restricting the permissible operations to those
which are locally invertible, writing programs in the reversible style can be
cumbersome, and may differ significantly from conventional implementations even
when the implemented algorithm is, in fact, invertible.
In this paper we introduce Jeopardy, a functional programming language that
guarantees program invertibility without imposing local reversibility. In
particular, Jeopardy allows the limited use of uninvertible -- and even
nondeterministic! -- operations, provided that they are used in a way that can
be statically determined to be invertible. To this end, we outline an
\emph{implicitly available arguments analysis} and three further approaches
that can give a partial static guarantee to the (generally difficult) problem
of guaranteeing invertibility.

本文介绍了一种名为 Jeopardy 的函数式编程语言，它可以在不实施局部可逆的限制下保证程序可逆性，并且通过一系列方法来解决保证可逆性的通常困难问题，其中一个方法是隐含可用参数分析。

Jeopardy: 可逆的函数式编程语言

Jeopardy: An Invertible Functional Programming Language

We show that standard ResNet architectures can be made invertible, allowing
the same model to be used for classification, density estimation, and
generation. Typically, enforcing invertibility requires partitioning dimensions
or restricting network architectures. In contrast, our approach only requires
adding a simple normalization step during training, already available in
standard frameworks. Invertible ResNets define a generative model which can be
trained by maximum likelihood on unlabeled data. To compute likelihoods, we
introduce a tractable approximation to the Jacobian log-determinant of a
residual block. Our empirical evaluation shows that invertible ResNets perform
competitively with both state-of-the-art image classifiers and flow-based
generative models, something that has not been previously achieved with a
single architecture.

本研究展示了传统的 ResNet 模型可以被做成可逆的，这意味着同一个模型可以同时用于分类、密度估计和生成。令人惊讶的是，我们的方法只需要在训练时增加一个简单的归一化步骤，而不需要将维度分割或限制网络结构。作为一种生成模型，可逆的 ResNet 可以通过无标签数据的最大似然估计进行训练。为了计算似然，我们引入了一个可计算的对余块 Jacobian 行列式对数的近似值。实验证明，可逆 ResNet 在严格意义下表现出色，达到了同一个架构内同时具有现有最先进图像分类器和流式生成模型的性能。