NSNet: A General Neural Probabilistic Framework for Satisfiability Problems

We present the Neural Satisfiability Network (NSNet), a general neural framework that models satisfiability problems as probabilistic inference and meanwhile exhibits proper explainability. Inspired by the Belief Propagation (BP), NSNet uses a novel graph neural network (GNN) to parameterize BP in the latent space, where its hidden representations maintain the same probabilistic interpretation as BP. NSNet can be flexibly configured to solve both SAT and #SAT problems by applying different learning objectives. For SAT, instead of directly predicting a satisfying assignment, NSNet performs marginal inference among all satisfying solutions, which we empirically find is more feasible for neural networks to learn. With the estimated marginals, a satisfying assignment can be efficiently generated by rounding and executing a stochastic local search. For #SAT, NSNet performs approximate model counting by learning the Bethe approximation of the partition function. Our evaluations show that NSNet achieves competitive results in terms of inference accuracy and time efficiency on multiple SAT and #SAT datasets

Chronosymbolic Learning: Efficient CHC Solving with Symbolic Reasoning and Inductive Learning

Solving Constrained Horn Clauses (CHCs) is a fundamental challenge behind a wide range of verification and analysis tasks. Data-driven approaches show great promise in improving CHC solving without the painstaking manual effort of creating and tuning various heuristics. However, a large performance gap exists between data-driven CHC solvers and symbolic reasoning-based solvers. In this work, we develop a simple but effective framework, "Chronosymbolic Learning", which unifies symbolic information and numerical data points to solve a CHC system efficiently. We also present a simple instance of Chronosymbolic Learning with a data-driven learner and a BMC-styled reasoner. Despite its great simplicity, experimental results show the efficacy and robustness of our tool. It outperforms state-of-the-art CHC solvers on a dataset consisting of 288 benchmarks, including many instances with non-linear integer arithmetics

TorchProbe: Fuzzing Dynamic Deep Learning Compilers

Static and dynamic computational graphs represent two distinct approaches to constructing deep learning frameworks. The former prioritizes compiler-based optimizations, while the latter focuses on programmability and user-friendliness. The recent release of PyTorch 2.0, which supports compiling arbitrary deep learning programs in Python, signifies a new direction in the evolution of deep learning infrastructure to incorporate compiler techniques in a more dynamic manner and support more dynamic language features like dynamic control flows and closures. Given PyTorch's seamless integration with Python, its compiler aims to support arbitrary deep learning code written in Python. However, the inherent dynamism of Python poses challenges to the completeness and robustness of the compiler. While recent research has introduced fuzzing to test deep learning compilers, there is still a lack of comprehensive analysis on how to test dynamic features. To address this issue, we propose several code transformations to generate test cases involving dynamic features. These transformations preserve the program's semantics, ensuring that any discrepancy between the transformed and original programs indicates the presence of a bug. Through our approach, we have successfully identified twenty previously unknown bugs in the PyTorch compiler and its underlying tensor compiler Triton

Scalar Invariant Networks with Zero Bias

Just like weights, bias terms are the learnable parameters of many popular machine learning models, including neural networks. Biases are thought to enhance the representational power of neural networks, enabling them to solve a variety of tasks in computer vision. However, we argue that biases can be disregarded for some image-related tasks such as image classification, by considering the intrinsic distribution of images in the input space and desired model properties from first principles. Our findings suggest that zero-bias neural networks can perform comparably to biased networks for practical image classification tasks. We demonstrate that zero-bias neural networks possess a valuable property called scalar (multiplication) invariance. This means that the prediction of the network remains unchanged when the contrast of the input image is altered. We extend scalar invariance to more general cases, enabling formal verification of certain convex regions of the input space. Additionally, we prove that zero-bias neural networks are fair in predicting the zero image. Unlike state-of-the-art models that may exhibit bias toward certain labels, zero-bias networks have uniform belief in all labels. We believe dropping bias terms can be considered as a geometric prior in designing neural network architecture for image classification, which shares the spirit of adapting convolutions as the transnational invariance prior. The robustness and fairness advantages of zero-bias neural networks may also indicate a promising path towards trustworthy and ethical AI.Comment: 22 pages, 8 figure

Novice Type Error Diagnosis with Natural Language Models

Strong static type systems help programmers eliminate many errors without much burden of supplying type annotations. However, this flexibility makes it highly non-trivial to diagnose ill-typed programs, especially for novice programmers. Compared to classic constraint solving and optimization-based approaches, the data-driven approach has shown great promise in identifying the root causes of type errors with higher accuracy. Instead of relying on hand-engineered features, this work explores natural language models for type error localization, which can be trained in an end-to-end fashion without requiring any features. We demonstrate that, for novice type error diagnosis, the language model-based approach significantly outperforms the previous state-of-the-art data-driven approach. Specifically, our model could predict type errors correctly 62% of the time, outperforming the state-of-the-art Nate's data-driven model by 11%, in a more rigorous accuracy metric. Furthermore, we also apply structural probes to explain the performance difference between different language models.Comment: 17 pages, 8 figure

Effective Interactive Resolution of Static Analysis Alarms

We propose an interactive approach to resolve static analysis alarms. Our approach synergistically combines a sound but imprecise analysis with precise but unsound heuristics, through user interaction. In each iteration, it solves an optimization problem to find a set of questions for the user such that the expected payoff is maximized. We have implemented our approach in a tool, Ursa, that enables interactive alarm resolution for any analysis specified in the declarative logic programming language Datalog. We demonstrate the effectiveness of Ursa on a state-of-the-art static datarace analysis using a suite of 8 Java programs comprising 41-194 KLOC each. Ursa is able to eliminate 74% of the false alarms per benchmark with an average payoff of 12 per question. Moreover, Ursa prioritizes user effort effectively by posing questions that yield high payoffs earlier

Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and ({\delta}-)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI^2 , Reluplex, and Reluval

Learning-Aided Program Synthesis and Verification

The enormous rise in the scale, scope, and complexity of software projects has created a thriving marketplace for program reasoning tools. Despite broad adoption by industry, developing such tools remains challenging. For each project, specialized heuristics or analysis rules have to be carefully designed and customized, which requires non-trivial expertise. Recently machine learning, especially deep learning, achieved remarkable successes in many challenging areas such as image recognition and strategy game playing. Inspired by these successes, this thesis is concerned with the following question: can program reasoning be effectively learned and automatically improved over time? This thesis demonstrates that learning-based techniques can be a new driving force for tackling fundamental program reasoning challenges, particularly, program synthesis and program verification. First, this thesis presents a scalable inductive logic programming (ILP) framework, Difflog, which can synthesize a rich set of logical rules used in various important domains like program analysis, relational query and knowledge discovery. Unlike classic program synthesis techniques, which heavily rely on manually designed heuristics or symbolic constraint solvers, Difflog leverages efficient gradient-based approaches, which is possible due to a novel numerical relaxation of logical rules. Second, this thesis presents an end-to-end deep learning framework for program verification, Code2Inv, which directly maps a piece of source code to its related proof without requiring any annotations from human experts. Code2Inv is inspired by the recent AI breakthrough, AlphaGo; however, unlike the two-dimensional game board, programs have sophisticated structures and correct proofs are extremely rare, posing unique challenges on representation learning and reinforcement learning. To address these challenges, we leverage advances of graph neural networks and develop a counterexample-based smooth reward mechanism. Code2Inv outperforms state-of-the-art approaches that are based on manually designed heuristics or decision tree learning, and the learned policy by Code2Inv can generalize to unseen programs. Furthermore, Code2Inv can be flexibly customized as a Constrained Horn Clause (CHC) solver as well as a meta-solver for syntax-guided program synthesis tasks