Abduction-Based Explanations for Machine Learning Models

The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers to understand. Most earlier work on computing explanations is based on heuristic approaches, providing no guarantees of quality, in terms of how close such solutions are from cardinality- or subset-minimal explanations. This paper develops a constraint-agnostic solution for computing explanations for any ML model. The proposed solution exploits abductive reasoning, and imposes the requirement that the ML model can be represented as sets of constraints using some target constraint reasoning system for which the decision problem can be answered with some oracle. The experimental results, obtained on well-known datasets, validate the scalability of the proposed approach as well as the quality of the computed solutions

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

Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions

We present a technique for neural network verification using mixed-integer programming (MIP) formulations. We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions. Additionally, as in general, these formulations may require an exponential number of inequalities, we also derive a separation procedure that runs in super-linear time in the input dimension. We first introduce and develop our technique on the class of \emph{staircase} functions, which generalizes the ReLU, binarized, and quantized activation functions. We then use results for staircase activation functions to obtain a separation method for general piecewise linear activation functions. Empirically, using our strong formulation and separation technique, we can reduce the computational time in exact verification settings based on MIP and improve the false negative rate for inexact verifiers relying on the relaxation of the MIP formulation