SATNet is an award-winning MAXSAT solver that can be used to infer logical
rules and integrated as a differentiable layer in a deep neural network. It had
been shown to solve Sudoku puzzles visually from examples of puzzle digit
images, and was heralded as an impressive achievement towards the longstanding
AI goal of combining pattern recognition with logical reasoning. In this paper,
we clarify SATNet's capabilities by showing that in the absence of intermediate
labels that identify individual Sudoku digit images with their logical
representations, SATNet completely fails at visual Sudoku (0% test accuracy).
More generally, the failure can be pinpointed to its inability to learn to
assign symbols to perceptual phenomena, also known as the symbol grounding
problem, which has long been thought to be a prerequisite for intelligent
agents to perform real-world logical reasoning. We propose an MNIST based test
as an easy instance of the symbol grounding problem that can serve as a sanity
check for differentiable symbolic solvers in general. Naive applications of
SATNet on this test lead to performance worse than that of models without
logical reasoning capabilities. We report on the causes of SATNet's failure and
how to prevent them.

SATNet 是一个奖 - winning 的 MAXSAT 求解器，可以用来推断逻辑规则并作为深度神经网络中的可微分层。本文通过展示，在缺乏标识个别数独数字图像及其逻辑表示的中间标签的情况下，SATNet 在视觉数独上彻底失败（0％的测试准确性），澄清了 SATNet 的能力。一般来说，这个失败可以归因于 SATNet 无法学会将符号分配给感知现象，也就是所谓的符号基础问题，这被认为是智能代理执行真实世界逻辑推理的先决条件。我们提出了基于 MNIST 的测试，作为符号基础问题的简单实例，可以作为可微分符号求解器的健全性检查。对于这个测试的 SATNet 的朴素应用导致性能比没有逻辑推理能力的模型更差。我们报告了 SATNet 失败的原因以及如何防止它们。

评估 SATNet 解决符号基础问题的能力

Assessing SATNet's Ability to Solve the Symbol Grounding Problem

In this paper, we describe how we can effectively exploit alternative
parameter configurations to a MaxSAT solver. We describe how these
configurations can be computed in the context of MaxSAT. In particular, we
experimentally show how to easily combine configurations of a non-competitive
solver to obtain a better solving approach.

本篇论文探讨了如何利用 MaxSAT solver 的不同参数配置并进行实验，特别地，我们将多种非竞争性求解器配置相结合以获得更好的解决方案。

利用 MaxSAT 求解器的配置

Exploiting Configurations of MaxSAT Solvers

We are interested in computing $k$ most preferred models of a given d-DNNF
circuit $C$, where the preference relation is based on an algebraic structure
called a monotone, totally ordered, semigroup $(K, \otimes, <)$. In our
setting, every literal in $C$ has a value in $K$ and the value of an assignment
is an element of $K$ obtained by aggregating using $\otimes$ the values of the
corresponding literals. We present an algorithm that computes $k$ models of $C$
among those having the largest values w.r.t. $<$, and show that this algorithm
runs in time polynomial in $k$ and in the size of $C$. We also present a pseudo
polynomial-time algorithm for deriving the top-$k$ values that can be reached,
provided that an additional (but not very demanding) requirement on the
semigroup is satisfied. Under the same assumption, we present a pseudo
polynomial-time algorithm that transforms $C$ into a d-DNNF circuit $C'$
satisfied exactly by the models of $C$ having a value among the top-$k$ ones.
Finally, focusing on the semigroup $(\mathbb{N}, +, <)$, we compare on a large
number of instances the performances of our compilation-based algorithm for
computing $k$ top solutions with those of an algorithm tackling the same
problem, but based on a partial weighted MaxSAT solver.

提出一种基于代数结构的算法来计算具有最大价值最佳解的 DNNF 电路中的 k 个最优模型，并且 与 基于部分加权 MaxSAT 求解器的算法进行比较。

d-DNNF 电路的伪多项式时间 Top-k 算法

Pseudo Polynomial-Time Top-k Algorithms for d-DNNF Circuits

Integrating logical reasoning within deep learning architectures has been a
major goal of modern AI systems. In this paper, we propose a new direction
toward this goal by introducing a differentiable (smoothed) maximum
satisfiability (MAXSAT) solver that can be integrated into the loop of larger
deep learning systems. Our (approximate) solver is based upon a fast coordinate
descent approach to solving the semidefinite program (SDP) associated with the
MAXSAT problem. We show how to analytically differentiate through the solution
to this SDP and efficiently solve the associated backward pass. We demonstrate
that by integrating this solver into end-to-end learning systems, we can learn
the logical structure of challenging problems in a minimally supervised
fashion. In particular, we show that we can learn the parity function using
single-bit supervision (a traditionally hard task for deep networks) and learn
how to play 9x9 Sudoku solely from examples. We also solve a "visual Sudok"
problem that maps images of Sudoku puzzles to their associated logical
solutions by combining our MAXSAT solver with a traditional convolutional
architecture. Our approach thus shows promise in integrating logical structures
within deep learning.

本文提出了一种新的路线，即通过引入可微（平滑）的最大可满足性（MAXSAT）求解器，将逻辑推理纳入更大的深度学习系统的循环中，从而在端到端学习系统中学习有挑战性的问题的逻辑结构，表现出集成逻辑结构于深度学习的潜力。