784 research outputs found
Can -Learning with Graph Networks Learn a Generalizable Branching Heuristic for a SAT Solver?
We present Graph--SAT, a branching heuristic for a Boolean SAT solver
trained with value-based reinforcement learning (RL) using Graph Neural
Networks for function approximation. Solvers using Graph--SAT are complete
SAT solvers that either provide a satisfying assignment or proof of
unsatisfiability, which is required for many SAT applications. The branching
heuristics commonly used in SAT solvers make poor decisions during their
warm-up period, whereas Graph--SAT is trained to examine the structure of
the particular problem instance to make better decisions early in the search.
Training Graph--SAT is data efficient and does not require elaborate dataset
preparation or feature engineering. We train Graph--SAT using RL interfacing
with MiniSat solver and show that Graph--SAT can reduce the number of
iterations required to solve SAT problems by 2-3X. Furthermore, it generalizes
to unsatisfiable SAT instances, as well as to problems with 5X more variables
than it was trained on. We show that for larger problems, reductions in the
number of iterations lead to wall clock time reductions, the ultimate goal when
designing heuristics. We also show positive zero-shot transfer behavior when
testing Graph--SAT on a task family different from that used for training.
While more work is needed to apply Graph--SAT to reduce wall clock time in
modern SAT solving settings, it is a compelling proof-of-concept showing that
RL equipped with Graph Neural Networks can learn a generalizable branching
heuristic for SAT search.Comment: Camera-ready for NeurIPS 202
UpMax: User Partitioning for MaxSAT
It has been shown that Maximum Satisfiability (MaxSAT) problem instances can be effectively solved by partitioning the set of soft clauses into several disjoint sets. The partitioning methods can be based on clause weights (e.g., stratification) or based on graph representations of the formula. Afterwards, a merge procedure is applied to guarantee that an optimal solution is found.
This paper proposes a new framework called UpMax that decouples the partitioning procedure from the MaxSAT solving algorithms. As a result, new partitioning procedures can be defined independently of the MaxSAT algorithm to be used. Moreover, this decoupling also allows users that build new MaxSAT formulas to propose partition schemes based on knowledge of the problem to be solved. We illustrate this approach using several problems and show that partitioning has a large impact on the performance of unsatisfiability-based MaxSAT algorithms
A Unified View of Piecewise Linear Neural Network Verification
The success of Deep Learning and its potential use in many safety-critical
applications has motivated research on formal verification of Neural Network
(NN) models. Despite the reputation of learned NN models to behave as black
boxes and the theoretical hardness of proving their properties, researchers
have been successful in verifying some classes of models by exploiting their
piecewise linear structure and taking insights from formal methods such as
Satisifiability Modulo Theory. These methods are however still far from scaling
to realistic neural networks. To facilitate progress on this crucial area, we
make two key contributions. First, we present a unified framework that
encompasses previous methods. This analysis results in the identification of
new methods that combine the strengths of multiple existing approaches,
accomplishing a speedup of two orders of magnitude compared to the previous
state of the art. Second, we propose a new data set of benchmarks which
includes a collection of previously released testcases. We use the benchmark to
provide the first experimental comparison of existing algorithms and identify
the factors impacting the hardness of verification problems.Comment: Updated version of "Piecewise Linear Neural Network verification: A
comparative study
SMT for Polynomial Constraints on Real Numbers
AbstractThis paper preliminarily reports an SMT for solving polynomial inequalities over real numbers. Our approach is a combination of interval arithmetic (over-approximation, aiming to decide unsatisfiability) and testing (under-approximation, aiming to decide satisfiability) to sandwich precise results. In addition to existing interval arithmetic, such as classical intervals and affine intervals, we newly design Chebyshev Approximation Intervals, focusing on multiplications of the same variables, like Taylor expansions. When testing cannot find a satisfiable instance, this framework is designed to start a refinement loop by splitting input ranges into smaller ones (although this refinement loop implementation is left to future work). Preliminary experiments on small benchmarks from SMT-LIB are also shown
Hyperspectral Super-Resolution with Coupled Tucker Approximation: Recoverability and SVD-based algorithms
We propose a novel approach for hyperspectral super-resolution, that is based
on low-rank tensor approximation for a coupled low-rank multilinear (Tucker)
model. We show that the correct recovery holds for a wide range of multilinear
ranks. For coupled tensor approximation, we propose two SVD-based algorithms
that are simple and fast, but with a performance comparable to the
state-of-the-art methods. The approach is applicable to the case of unknown
spatial degradation and to the pansharpening problem.Comment: IEEE Transactions on Signal Processing, Institute of Electrical and
Electronics Engineers, in Pres
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