In explainable AI, DNN gradients are used to interpret the prediction; in safety-critical control systems, gradients could encode safety constraints; in scientific-computing applications, gradients could encode physical invariants. While recent work on provable editing of DNNs has focused on input-output constraints, the problem of enforcing hard constraints on DNN gradients remains unaddressed. We present ProGrad, the first efficient approach for editing the parameters of a DNN to provably enforce hard constraints on the DNN gradients. Given a DNN $\mathcal{N}$ with parameters $\theta$, and a set $\mathcal{S}$ of pairs $(\mathrm{x}, \mathrm{Q})$ of input $\mathrm{x}$ and corresponding linear gradient constraints $\mathrm{Q}$, ProGrad finds new parameters $\theta'$ such that $\bigwedge_{(\mathrm{x}, \mathrm{Q}) \in \mathcal{S}} \frac{\partial}{\partial \mathrm{x}}\mathcal{N}(\mathrm{x}; \theta') \in \mathrm{Q}$ while minimizing the changes $\lVert\theta' - \theta\rVert$. The key contribution is a novel *conditional variable gradient* of DNNs, which relaxes the NP-hard provable gradient editing problem to a linear program (LP), enabling ProGrad to use an LP solver to efficiently and effectively enforce the gradient constraints. We experimentally evaluated ProGrad via enforcing (i) hard Grad-CAM constraints on ImageNet ResNet DNNs; (ii) hard Integrated Gradients constraints on Llama 3 and Qwen 3 LLMs; (iii) hard gradient constraints in training a DNN to approximate a target function as a proxy for safety constraints in control systems and physical invariants in scientific applications. The results highlight the unique capability of ProGrad in enforcing hard constraints on DNN gradients.

Abstract Practical adoption of static analysis often requires trading precision for performance. This paper focuses on improving the memory efficiency of abstract interpretation without sacrificing precision or time efficiency. Computationally, abstract interpretation reduces the problem of inferring program invariants to computing a fixpoint of a set of equations. This paper presents a method to minimize the memory footprint in Bourdoncle’s iteration strategy, a widely-used technique for fixpoint computation. Our technique is agnostic to the abstract domain used. We prove that our technique is optimal (i.e., it results in minimum memory footprint) for Bourdoncle’s iteration strategy while computing the same result. We evaluate the efficacy of our technique by implementing it in a tool called $$\textsc {Mikos}$$ M I K O S , which extends the state-of-the-art abstract interpreter $$\text {IKOS}$$ IKOS . On average $$\textsc {Mikos}$$ M I K O S demonstrated a $$24.57\times $$ 24.57 × and $$2.29\times $$ 2.29 × reduction in peak-memory usage compared to $$\text {IKOS}$$ IKOS when verifying user-provided assertions and performing interprocedural buffer-overflow analysis, respectively.

Abstract This paper presents a new approach to improve static program analysis using Large Language Models (LLMs). The approach interleaves calls to the static analyzer and queries to the LLM. The query to the LLM is constructed based on intermediate results from the static analysis, and subsequent static analysis uses the results from the LLM query. We apply our approach to the problem of error-specification inference : given systems code written in C, infer the set of values that each function can return on error. Such error specifications aid in program understanding and can be used to find error-handling bugs. We implemented our approach by incorporating LLMs into EESI, the state-of-the-art static analysis for error-specification inference. Compared to EESI, our approach achieves higher recall (from an average of 52.55% to 77.83%) and higher F1-score (from an average of 0.612 to 0.804) while maintaining precision (from an average of 86.67% to 85.12%) on real-world benchmarks such as Apache HTTPD and MbedTLS. We also conducted experiments to understand the sources of imprecision in our LLM-assisted analysis as well as the impact of LLM nondeterminism on the analysis results.

Ensuring that a DNN satisfies a desired property is critical when deploying DNNs in safety-critical applications. There are efficient methods that can verify whether a DNN satisfies a property, as seen in the annual DNN verification competition (VNN-COMP). However, the problem of provably editing a DNN to satisfy a property remains challenging. We present PREPARED, the first efficient technique for provable editing of DNNs. Given a DNN $\mathcal{N}$ with parameters $\theta$, input polytope $P$, and output polytope $Q$, PREPARED finds new parameters $\theta'$ such that $\forall \mathrm{x} \in P . \mathcal{N}(\mathrm{x}; \theta') \in Q$ while minimizing the changes $\lVert{\theta' - \theta}\rVert$. Given a DNN and a property it violates from the VNN-COMP benchmarks, PREPARED is able to provably edit the DNN to satisfy this property within 45 seconds. PREPARED is efficient because it relaxes the NP-hard provable editing problem to solving a linear program. The key contribution is the novel notion of Parametric Linear Relaxation, which enables PREPARED to construct tight output bounds of the DNN that are parameterized by the new parameters $\theta'$. We demonstrate that PREPARED is more efficient and effective compared to prior DNN editing approaches i) using the VNN-COMP benchmarks, ii) by editing CIFAR10 and TinyImageNet image-recognition DNNs, and BERT sentiment-classification DNNs for local robustness, and iii) by training a DNN to model a geodynamics process and satisfy physics constraints.

Deep neural networks (DNNs) are becoming increasingly important components of software, and are considered the state-of-the-art solution for a number of problems, such as image recognition. However, DNNs are far from infallible, and incorrect behavior of DNNs can have disastrous real-world consequences. This paper addresses the problem of architecture-preserving V-polytope provable repair of DNNs. A V-polytope defines a convex bounded polytope using its vertex representation. V-polytope provable repair guarantees that the repaired DNN satisfies the given specification on the infinite set of points in the given V-polytope. An architecture-preserving repair only modifies the parameters of the DNN, without modifying its architecture. The repair has the flexibility to modify multiple layers of the DNN, and runs in polynomial time. It supports DNNs with activation functions that have some linear pieces, as well as fully-connected, convolutional, pooling and residual layers. To the best our knowledge, this is the first provable repair approach that has all of these features. We implement our approach in a tool called APRNN. Using MNIST, ImageNet, and ACAS Xu DNNs, we show that it has better efficiency, scalability, and generalization compared to PRDNN and REASSURE, prior provable repair methods that are not architecture preserving.

Deep Neural Networks (DNNs) have grown in popularity over the past decade and are now being used in safety-critical domains such as aircraft collision avoidance. This has motivated a large number of techniques for finding unsafe behavior in DNNs. In contrast, this paper tackles the problem of correcting a DNN once unsafe behavior is found. We introduce the provable repair problem, which is the problem of repairing a network N to construct a new network N′ that satisfies a given specification. If the safety specification is over a finite set of points, our Provable Point Repair algorithm can find a provably minimal repair satisfying the specification, regardless of the activation functions used. For safety specifications addressing convex polytopes containing infinitely many points, our Provable Polytope Repair algorithm can find a provably minimal repair satisfying the specification for DNNs using piecewise-linear activation functions. The key insight behind both of these algorithms is the introduction of a Decoupled DNN architecture, which allows us to reduce provable repair to a linear programming problem. Our experimental results demonstrate the efficiency and effectiveness of our Provable Repair algorithms on a variety of challenging tasks.

Abstract Deep Neural Networks (DNNs) are rapidly gaining popularity in a variety of important domains. Formally, DNNs are complicated vector-valued functions which come in a variety of sizes and applications. Unfortunately, modern DNNs have been shown to be vulnerable to a variety of attacks and buggy behavior. This has motivated recent work in formally analyzing the properties of such DNNs. This paper introduces SyReNN, a tool for understanding and analyzing a DNN by computing its symbolic representation. The key insight is to decompose the DNN into linear functions. Our tool is designed for analyses using low-dimensional subsets of the input space, a unique design point in the space of DNN analysis tools. We describe the tool and the underlying theory, then evaluate its use and performance on three case studies: computing Integrated Gradients, visualizing a DNN’s decision boundaries, and patching a DNN.

Abstract interpretation is a general framework for expressing static program analyses. It reduces the problem of extracting properties of a program to computing an approximation of the least fixpoint of a system of equations. The de facto approach for computing this approximation uses a sequential algorithm based on weak topological order (WTO). This paper presents a deterministic parallel algorithm for fixpoint computation by introducing the notion of weak partial order (WPO). We present an algorithm for constructing a WPO in almost-linear time. Finally, we describe Pikos, our deterministic parallel abstract interpreter, which extends the sequential abstract interpreter IKOS. We evaluate the performance and scalability of Pikos on a suite of 1017 C programs. When using 4 cores, Pikos achieves an average speedup of 2.06x over IKOS, with a maximum speedup of 3.63x. When using 16 cores, Pikos achieves a maximum speedup of 10.97x.

We consider a science network that runs applications requiring data transfers to be completed within a given deadline. The underlying network is a software defined network (SDN) that supports fine grain real-time network telemetry. Deadline-aware data transfer requests are made to a centralized network controller that schedules the flows by setting pacing rates of the deadline flows and metering the background traffic at the ingress routers. The goal of the scheduling algorithm is to maximize the number of flows that meet the deadline while maximizing the network utilization. In this paper, we develop a Reinforcement Learning (RL) agent based network controller and compare its performance with well-known heuristics. For a network consisting of a single bottleneck link, we show that the RL-agent based network controller performs as well as Earliest Deadline First (EDF), which is known to be optimal. We also show that the RL-agent performs significantly better than an idealized TCP protocol in which the bottleneck link capacity is equally shared among the competing flows. We also study the sensitivity of the RL-agent controller for different parameter settings and reward functions.

A linear restriction of a function is the same function with its domain restricted to points on a given line. This paper addresses the problem of computing a succinct representation for a linear restriction of a piecewise-linear neural network. This primitive, which we call ExactLine, allows us to exactly characterize the result of applying the network to all of the infinitely many points on a line. In particular, ExactLine computes a partitioning of the given input line segment such that the network is affine on each partition. We present an efficient algorithm for computing ExactLine for networks that use ReLU, MaxPool, batch normalization, fully-connected, convolutional, and other layers, along with several applications. First, we show how to exactly determine decision boundaries of an ACAS Xu neural network, providing significantly improved confidence in the results compared to prior work that sampled finitely many points in the input space. Next, we demonstrate how to exactly compute integrated gradients, which are commonly used for neural network attributions, allowing us to show that the prior heuristic-based methods had relative errors of 25-45% and show that a better sampling method can achieve higher accuracy with less computation. Finally, we use ExactLine to empirically falsify the core assumption behind a well-known hypothesis about adversarial examples, and in the process identify interesting properties of adversarially-trained networks.

Error-handling code responds to the occurrence of runtime errors. Failure to correctly handle errors can lead to security vulnerabilities and data loss. This paper deals with error handling in software written in C that uses the return-code idiom: the presence and type of error is encoded in the return value of a function. This paper describes EESI, a static analysis that infers the set of values that a function can return on error. Such a function error-specification can then be used to identify bugs related to incorrect error handling. The key insight of EESI is to bootstrap the analysis with domain knowledge related to error handling provided by a developer. EESI uses a combination of intraprocedural, flow-sensitive analysis and interprocedural, context-insensitive analysis to ensure precision and scalability. We built a tool ECC to demonstrate how the function error-specifications inferred by EESI can be used to automatically find bugs related to incorrect error handling. ECC detected 246 bugs across 9 programs, of which 110 have been confirmed. ECC detected 220 previously unknown bugs, of which 99 are confirmed. Two patches have already been merged into OpenSSL.

Identifying relationships among program elements is useful for program understanding, debugging, and analysis. One such kind of relationship is synonymy. Function synonyms are functions that play a similar role in code; examples include functions that perform initialization for different device drivers, and functions that implement different symmetric-key encryption schemes. Function synonyms are not necessarily semantically equivalent and can be syntactically dissimilar; consequently, approaches for identifying code clones or functional equivalence cannot be used to identify them. This paper presents Func2 vec , a technique that learns an embedding mapping each function to a vector in a continuous vector space such that vectors for function synonyms are in close proximity. We compute the function embedding by training a neural network on sentences generated using random walks over the interprocedural control-flow graph. We show the effectiveness of Func2 vec at identifying function synonyms in the Linux kernel. Finally, we apply Func2 vec to the problem of mining error-handling specifications in Linux file systems and drivers. We show that the function synonyms identified by Func2 vec result in error-handling specifications with high support.

Developing a code optimizer is challenging, especially for new, idiosyncratic ISAs. Superoptimization can, in principle, discover machine-specific optimizations automatically by searching the space of all instruction sequences. If we can increase the size of code fragments a superoptimizer can optimize, we will be able to discover more optimizations. We develop LENS, a search algorithm that increases the size of code a superoptimizer can synthesize by rapidly pruning away invalid candidate programs. Pruning is achieved by selectively refining the abstraction under which candidates are considered equivalent, only in the promising part of the candidate space. LENS also uses a bidirectional search strategy to prune the candidate space from both forward and backward directions. These pruning strategies allow LENS to solve twice as many benchmarks as existing enumerative search algorithms, while LENS is about 11-times faster.

Developing an optimizing compiler backend remains a laborious process, especially for nontraditional ISAs that have been appearing recently. Superoptimization sidesteps the need for many code transformations by searching for the most optimal instruction sequence semantically equivalent to the original code fragment. Even though superoptimization discovers the best machine-specific code optimizations, it has yet to become widely-used. We propose GreenThumb, an extensible framework that reduces the cost of constructing superoptimizers and provides a fast search algorithm that can be reused for any ISA, exploiting the unique strengths of enumerative, stochastic, and symbolic (SAT-solver-based) search algorithms. To extend GreenThumb to a new ISA, it is only necessary to implement an emulator for the ISA and provide some ISA-specific search utility functions.

Separation logic is an expressive logic for reasoning about heap structures in programs. This paper presents a semi-decision procedure for checking unsatisfiability of formulas in a fragment of separation logic that includes points-to assertions (x |-> y), acyclic-list-segment assertions (ls(x,y)), logical-and, logical-or, separating conjunction, and septraction (the DeMorgan-dual of separating implication). The fragment that we consider allows negation at leaves, and includes formulas that lie outside other separation-logic fragments considered in the literature.

Fixing concurrency bugs (or crugs) is critical in modern software systems. Static analyses to find crugs such as data races and atomicity violations scale poorly, while dynamic approaches incur high run-time overheads. Crugs manifest only under specific execution interleavings that may not arise during in-house testing, thereby demanding a lightweight program monitoring technique that can be used post-deployment. We present Cooperative Crug Isolation (CCI), a lowoverhead instrumentation framework to diagnose productionrun failures caused by crugs. CCI tracks specific thread interleavings at run-time, and uses statistical models to identify strong failure predictors among these. We offer a varied suite of predicates that represent different trade-offs between complexity and fault isolation capability. We also develop variant random sampling strategies that suit different types of predicates and help keep the run-time overhead low. Experiments with 9 real-world bugs in 6 non-trivial C applications show that these schemes span a wide spectrum of performance and diagnosis capabilities, each suitable for different usage scenarios.

We present an algorithm DASH to check if a program P satisfies a safety property φ. The unique feature of this algorithm is that it uses only test generation operations, and it refines and maintains a sound program abstraction as a consequence of failed test generation operations. Thus, each iteration of the algorithm is inexpensive, and can be implemented without any global may-alias information. In particular, we introduce a new refinement operator WPαthat uses only the alias information obtained by symbolically executing a test to refine abstractions in a sound manner. We present a full exposition of the DASH algorithm and its theoretical properties. We have implemented DASH in a tool called YOGI that plugs into Microsoft's Static Driver Verifier framework. We have used this framework to run YOGI on 69 Windows Vista drivers with 85 properties and find that YOGI scales much better than SLAM, the current engine driving Microsoft's Static Driver Verifier.

Data-flow analysis is an integral part of any aggressive optimizing compiler. We propose a framework for improving the precision of data-flow analysis in the presence of complex control-flow. We initially perform data-flow analysis to determine those control-flow merges which cause the loss in data-flow analysis precision. The control-flow graph of the program is then restructured such that performing data-flow analysis on the resulting restructured graph gives more precise results. The proposed framework is both simple, involving the familiar notion of product automata, and also general, since it is applicable to any forward data-flow analysis. Apart from proving that our restructuring process is correct, we also show that restructuring is effective in that it necessarily leads to more optimization opportunities. Furthermore, the framework handles the trade-off between the increase in data-flow precision and the code size increase inherent in the restructuring. We show that determining an optimal restructuring is NP-hard, and propose and evaluate a greedy strategy. The framework has been implemented in the Scale research compiler, and instantiated for the specific problem of Constant Propagation. On the SPECINT 2000 benchmark suite we observe an average speedup of 4% in the running times over Wegman-Zadeck conditional constant propagation algorithm and 2% over a purely path profile guided approach.