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Mayur Naik

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23 papers
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23

ICML Conference 2025 Conference Paper

DOLPHIN: A Programmable Framework for Scalable Neurosymbolic Learning

  • Aaditya Naik
  • Jason Liu
  • Claire Wang
  • Amish Sethi
  • Saikat Dutta 0001
  • Mayur Naik
  • Eric Wong 0001

Neurosymbolic learning enables the integration of symbolic reasoning with deep learning but faces significant challenges in scaling to complex symbolic programs, large datasets, or both. We introduce DOLPHIN, a framework that tackles these challenges by supporting neurosymbolic programs in Python, executing complex symbolic reasoning on the CPU while vectorizing probabilistic computations and gradient propagation on the GPU. Across 13 benchmarks spanning tasks over text, image, and video data, with symbolic reasoning features like recursion and blackbox functions, DOLPHIN converges to state-of-the-art accuracies on the more complex benchmarks while existing frameworks such as Scallop, ISED, and IndeCateR+ fail to converge within the time limit. On simpler benchmarks, DOLPHIN matches their performance, while achieving these results 1. 71x to 62x faster than the baselines. Overall, DOLPHIN advances the scalability of neurosymbolic frameworks, achieving state-of-the-art efficiency and convergence on difficult benchmarks where existing frameworks struggle. The code is published at https: //github. com/Dolphin-NeSy/Dolphin.

NeurIPS Conference 2025 Conference Paper

ESCA: Contextualizing Embodied Agents via Scene-Graph Generation

  • Jiani Huang
  • Amish Sethi
  • Matthew Kuo
  • Mayank Keoliya
  • Neelay Velingker
  • JungHo Jung
  • Ser Nam Lim
  • Ziyang Li

Multi-modal large language models (MLLMs) are making rapid progress toward general-purpose embodied agents. However, existing MLLMs do not reliably capture fine-grained links between low-level visual features and high-level textual semantics, leading to weak grounding and inaccurate perception. To overcome this challenge, we propose ESCA, a framework that contextualizes embodied agents by grounding their perception in spatial-temporal scene graphs. At its core is SGCLIP, a novel, open-domain, promptable foundation model for generating scene graphs that is based on CLIP. SGCLIP is trained on 87K+ open-domain videos using a neurosymbolic pipeline that aligns automatically generated captions with scene graphs produced by the model itself, eliminating the need for human-labeled annotations. We demonstrate that SGCLIP excels in both prompt-based inference and task-specific fine-tuning, achieving state-of-the-art results on scene graph generation and action localization benchmarks. ESCA with SGCLIP improves perception for embodied agents based on both open-source and commercial MLLMs, achieving state of-the-art performance across two embodied environments. Notably, ESCA significantly reduces agent perception errors and enables open-source models to surpass proprietary baselines. We release the source code for SGCLIP model training at https: //github. com/video-fm/LASER and for the embodied agent at https: //github. com/video-fm/ESCA.

ICLR Conference 2025 Conference Paper

IRIS: LLM-Assisted Static Analysis for Detecting Security Vulnerabilities

  • Ziyang Li 0002
  • Saikat Dutta 0001
  • Mayur Naik

Software is prone to security vulnerabilities. Program analysis tools to detect them have limited effectiveness in practice due to their reliance on human labeled specifications. Large language models (or LLMs) have shown impressive code generation capabilities but they cannot do complex reasoning over code to detect such vulnerabilities especially since this task requires whole-repository analysis. We propose IRIS, a neuro-symbolic approach that systematically combines LLMs with static analysis to perform whole-repository reasoning for security vulnerability detection. Specifically, IRIS leverages LLMs to infer taint specifications and perform contextual analysis, alleviating needs for human specifications and inspection. For evaluation, we curate a new dataset, CWE-Bench-Java, comprising 120 manually validated security vulnerabilities in real-world Java projects. A state-of-the-art static analysis tool CodeQL detects only 27 of these vulnerabilities whereas IRIS with GPT-4 detects 55 (+28) and improves upon CodeQL's average false discovery rate by 5% points. Furthermore, IRIS identifies 4 previously unknown vulnerabilities which cannot be found by existing tools. IRIS is available publicly at https://github.com/iris-sast/iris.

ICLR Conference 2025 Conference Paper

LASER: A Neuro-Symbolic Framework for Learning Spatio-Temporal Scene Graphs with Weak Supervision

  • Jiani Huang
  • Ziyang Li 0002
  • Mayur Naik
  • Ser-Nam Lim

Supervised approaches for learning spatio-temporal scene graphs (STSG) from video are greatly hindered due to their reliance on STSG-annotated videos, which are labor-intensive to construct at scale. Is it feasible to instead use readily available video captions as weak supervision? To address this question, we propose LASER, a neuro-symbolic framework to enable training STSG generators using only video captions. LASER employs large language models to first extract logical specifications with rich spatio-temporal semantic information from video captions. LASER then trains the underlying STSG generator to align the predicted STSG with the specification. The alignment algorithm overcomes the challenges of weak supervision by leveraging a differentiable symbolic reasoner and using a combination of contrastive, temporal, and semantics losses. The overall approach efficiently trains low-level perception models to extract a fine-grained STSG that conforms to the video caption. In doing so, it enables a novel methodology for learning STSGs without tedious annotations. We evaluate our method on three video datasets: OpenPVSG, 20BN, and MUGEN. Our approach demonstrates substantial improvements over fully-supervised baselines, achieving a unary predicate prediction accuracy of 27.78% (+12.65%) and a binary recall@5 of 0.42 (+0.22) on OpenPVSG. Additionally, LASER exceeds baselines by 7% on 20BN and 5.2% on MUGEN in terms of overall predicate prediction accuracy.

NeurIPS Conference 2025 Conference Paper

Once Upon an Input: Reasoning via Per-Instance Program Synthesis

  • Adam Stein
  • Neelay Velingker
  • Mayur Naik
  • Eric Wong

Large language models (LLMs) excel at zero-shot inference but continue to struggle with complex, multi-step reasoning. Recent methods that augment LLMs with intermediate reasoning steps such as Chain of Thought (CoT) and Program of Thought (PoT) improve performance but often produce undesirable solutions, especially in algorithmic domains. We introduce Per-Instance Program Synthesis (PIPS), a method that generates and refines programs at the instance level using structural feedback without relying on task-specific guidance or explicit test cases. To further improve performance, PIPS incorporates a confidence metric that dynamically chooses between direct inference and program synthesis on a per-instance basis. Experiments across three frontier LLMs and 30 benchmarks including all tasks of Big Bench Extra Hard (BBEH), visual question answering tasks, relational reasoning tasks, and mathematical reasoning tasks show that PIPS improves the absolute harmonic mean accuracy by up to 8. 6\% and 9. 4\% compared to PoT and CoT respectively, and reduces undesirable program generations by 65. 1\% on the algorithmic tasks compared to PoT with Gemini-2. 0-Flash.

NeurIPS Conference 2024 Conference Paper

Data-Efficient Learning with Neural Programs

  • Alaia Solko-Breslin
  • Seewon Choi
  • Ziyang Li
  • Neelay Velingker
  • Rajeev Alur
  • Mayur Naik
  • Eric Wong

Many computational tasks can be naturally expressed as a composition of a DNN followed by a program written in a traditional programming language or an API call to an LLM. We call such composites "neural programs" and focus on the problem of learning the DNN parameters when the training data consist of end-to-end input-output labels for the composite. When the program is written in a differentiable logic programming language, techniques from neurosymbolic learning are applicable, but in general, the learning for neural programs requires estimating the gradients of black-box components. We present an algorithm for learning neural programs, called ISED, that only relies on input-output samples of black-box components. For evaluation, we introduce new benchmarks that involve calls to modern LLMs such as GPT-4 and also consider benchmarks from the neurosymbolic learning literature. Our evaluation shows that for the latter benchmarks, ISED has comparable performance to state-of-the-art neurosymbolic frameworks. For the former, we use adaptations of prior work on gradient approximations of black-box components as a baseline, and show that ISED achieves comparable accuracy but in a more data- and sample-efficient manner.

ICML Conference 2024 Conference Paper

DISCRET: Synthesizing Faithful Explanations For Treatment Effect Estimation

  • Yinjun Wu
  • Mayank Keoliya
  • Kan Chen
  • Neelay Velingker
  • Ziyang Li 0002
  • Emily J. Getzen
  • Qi Long
  • Mayur Naik

Designing faithful yet accurate AI models is challenging, particularly in the field of individual treatment effect estimation (ITE). ITE prediction models deployed in critical settings such as healthcare should ideally be (i) accurate, and (ii) provide faithful explanations. However, current solutions are inadequate: state-of-the-art black-box models do not supply explanations, post-hoc explainers for black-box models lack faithfulness guarantees, and self-interpretable models greatly compromise accuracy. To address these issues, we propose DISCRET, a self-interpretable ITE framework that synthesizes faithful, rule-based explanations for each sample. A key insight behind DISCRET is that explanations can serve dually as database queries to identify similar subgroups of samples. We provide a novel RL algorithm to efficiently synthesize these explanations from a large search space. We evaluate DISCRET on diverse tasks involving tabular, image, and text data. DISCRET outperforms the best self-interpretable models and has accuracy comparable to the best black-box models while providing faithful explanations. DISCRET is available at https: //github. com/wuyinjun-1993/DISCRET-ICML2024.

AAAI Conference 2024 Conference Paper

Relational Programming with Foundational Models

  • Ziyang Li
  • Jiani Huang
  • Jason Liu
  • Felix Zhu
  • Eric Zhao
  • William Dodds
  • Neelay Velingker
  • Rajeev Alur

Foundation models have vast potential to enable diverse AI applications. The powerful yet incomplete nature of these models has spurred a wide range of mechanisms to augment them with capabilities such as in-context learning, information retrieval, and code interpreting. We propose Vieira, a declarative framework that unifies these mechanisms in a general solution for programming with foundation models. Vieira follows a probabilistic relational paradigm and treats foundation models as stateless functions with relational inputs and outputs. It supports neuro-symbolic applications by enabling the seamless combination of such models with logic programs, as well as complex, multi-modal applications by streamlining the composition of diverse sub-models. We implement Vieira by extending the Scallop compiler with a foreign interface that supports foundation models as plugins. We implement plugins for 12 foundation models including GPT, CLIP, and SAM. We evaluate Vieira on 9 challenging tasks that span language, vision, and structured and vector databases. Our evaluation shows that programs in Vieira are concise, can incorporate modern foundation models, and have comparable or better accuracy than competitive baselines.

ICML Conference 2024 Conference Paper

Towards Compositionality in Concept Learning

  • Adam Stein
  • Aaditya Naik
  • Yinjun Wu
  • Mayur Naik
  • Eric Wong 0001

Concept-based interpretability methods offer a lens into the internals of foundation models by decomposing their embeddings into high-level concepts. These concept representations are most useful when they are compositional, meaning that the individual concepts compose to explain the full sample. We show that existing unsupervised concept extraction methods find concepts which are not compositional. To automatically discover compositional concept representations, we identify two salient properties of such representations, and propose Compositional Concept Extraction (CCE) for finding concepts which obey these properties. We evaluate CCE on five different datasets over image and text data. Our evaluation shows that CCE finds more compositional concept representations than baselines and yields better accuracy on four downstream classification tasks.

ICML Conference 2023 Conference Paper

Do Machine Learning Models Learn Statistical Rules Inferred from Data?

  • Aaditya Naik
  • Yinjun Wu
  • Mayur Naik
  • Eric Wong 0001

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to even formalize. We thereby seek to infer statistical rules from the data and quantify the extent to which a model has learned them. We propose a framework SQRL that integrates logic-based methods with statistical inference to derive these rules from a model’s training data without supervision. We further show how to adapt models at test time to reduce rule violations and produce more coherent predictions. SQRL generates up to 300K rules over datasets from vision, tabular, and language settings. We uncover up to 158K violations of those rules by state-of-the-art models for classification, object detection, and data imputation. Test-time adaptation reduces these violations by up to 68. 7% with relative performance improvement up to 32%. SQRL is available at https: //github. com/DebugML/sqrl.

AAAI Conference 2023 Conference Paper

Learning to Select Pivotal Samples for Meta Re-weighting

  • Yinjun Wu
  • Adam Stein
  • Jacob Gardner
  • Mayur Naik

Sample re-weighting strategies provide a promising mechanism to deal with imperfect training data in machine learning, such as noisily labeled or class-imbalanced data. One such strategy involves formulating a bi-level optimization problem called the meta re-weighting problem, whose goal is to optimize performance on a small set of perfect pivotal samples, called meta samples. Many approaches have been proposed to efficiently solve this problem. However, all of them assume that a perfect meta sample set is already provided while we observe that the selections of meta sample set is performance-critical. In this paper, we study how to learn to identify such a meta sample set from a large, imperfect training set, that is subsequently cleaned and used to optimize performance in the meta re-weighting setting. We propose a learning framework which reduces the meta samples selection problem to a weighted K-means clustering problem through rigorously theoretical analysis. We propose two clustering methods within our learning framework, Representation-based clustering method (RBC) and Gradient-based clustering method (GBC), for balancing performance and computational efficiency. Empirical studies demonstrate the performance advantage of our methods over various baseline methods

ICLR Conference 2022 Conference Paper

CodeTrek: Flexible Modeling of Code using an Extensible Relational Representation

  • Pardis Pashakhanloo
  • Aaditya Naik
  • Yuepeng Wang 0001
  • Hanjun Dai
  • Petros Maniatis
  • Mayur Naik

Designing a suitable representation for code-reasoning tasks is challenging in aspects such as the kinds of program information to model, how to combine them, and how much context to consider. We propose CodeTrek, a deep learning approach that addresses these challenges by representing codebases as databases that conform to rich relational schemas. The relational representation not only allows CodeTrek to uniformly represent diverse kinds of program information, but also to leverage program-analysis queries to derive new semantic relations, which can be readily incorporated without further architectural engineering. CodeTrek embeds this relational representation using a set of walks that can traverse different relations in an unconstrained fashion, and incorporates all relevant attributes along the way. We evaluate CodeTrek on four diverse and challenging Python tasks: variable misuse, exception prediction, unused definition, and variable shadowing. CodeTrek achieves an accuracy of 91%, 63%, 98%, and 94% on these tasks respectively, and outperforms state-of-the-art neural models by 2-19% points.

AAAI Conference 2021 Conference Paper

GENSYNTH: Synthesizing Datalog Programs without Language Bias

  • Jonathan Mendelson
  • Aaditya Naik
  • Mukund Raghothaman
  • Mayur Naik

Techniques for learning logic programs from data typically rely on language bias mechanisms to restrict the hypothesis space. These methods are therefore limited by the user’s ability to tune them such that the hypothesis space is simultaneously large enough to include the target program but small enough to admit a tractable search. We propose a technique to learn Datalog programs from input-output examples without requiring the user to specify any language bias. It employs an evolutionary search strategy that mutates candidate programs and evaluates their fitness on the examples using an off-the-shelf Datalog interpreter. We have implemented our approach in a tool called GENSYNTH and evaluate it on diverse tasks from knowledge discovery, program analysis, and relational queries. Our experiments show that GENSYNTH can learn correct programs from few examples, including for tasks that require recursion and invented predicates, and is robust to noise.

NeurIPS Conference 2021 Conference Paper

Scallop: From Probabilistic Deductive Databases to Scalable Differentiable Reasoning

  • Jiani Huang
  • Ziyang Li
  • Binghong Chen
  • Karan Samel
  • Mayur Naik
  • Le Song
  • Xujie Si

Deep learning and symbolic reasoning are complementary techniques for an intelligent system. However, principled combinations of these techniques have limited scalability, rendering them ill-suited for real-world applications. We propose Scallop, a system that builds upon probabilistic deductive databases, to bridge this gap. The key insight underlying Scallop is a provenance framework that introduces a tunable parameter to specify the level of reasoning granularity. Scallop thereby i) generalizes exact probabilistic reasoning, ii) asymptotically reduces computational cost, and iii) provides relative accuracy guarantees. On a suite of tasks that involve mathematical and logical reasoning, Scallop scales significantly better without sacrificing accuracy compared to DeepProbLog, a principled neural logic programming approach. We also create and evaluate on a real-world Visual Question Answering (VQA) benchmark that requires multi-hop reasoning. Scallop outperforms two VQA-tailored models, a Neural Module Networks based and a transformer based model, by 12. 42% and 21. 66% respectively.

ICML Conference 2020 Conference Paper

Generating Programmatic Referring Expressions via Program Synthesis

  • Jiani Huang
  • Calvin Smith
  • Osbert Bastani
  • Rishabh Singh
  • Aws Albarghouthi
  • Mayur Naik

Incorporating symbolic reasoning into machine learning algorithms is a promising approach to improve performance on learning tasks that require logical reasoning. We study the problem of generating a programmatic variant of referring expressions that we call referring relational programs. In particular, given a symbolic representation of an image and a target object in that image, the goal is to generate a relational program that uniquely identifies the target object in terms of its attributes and its relations to other objects in the image. We propose a neurosymbolic program synthesis algorithm that combines a policy neural network with enumerative search to generate such relational programs. The policy neural network employs a program interpreter that provides immediate feedback on the consequences of the decisions made by the policy, and also takes into account the uncertainty in the symbolic representation of the image. We evaluate our algorithm on challenging benchmarks based on the CLEVR dataset, and demonstrate that our approach significantly outperforms several baselines.

ICLR Conference 2020 Conference Paper

Hoppity: Learning Graph Transformations to Detect and Fix Bugs in Programs

  • Elizabeth Dinella
  • Hanjun Dai
  • Ziyang Li 0002
  • Mayur Naik
  • Le Song
  • Ke Wang 0022

We present a learning-based approach to detect and fix a broad range of bugs in Javascript programs. We frame the problem in terms of learning a sequence of graph transformations: given a buggy program modeled by a graph structure, our model makes a sequence of predictions including the position of bug nodes and corresponding graph edits to produce a fix. Unlike previous works that use deep neural networks, our approach targets bugs that are more complex and semantic in nature (i.e.~bugs that require adding or deleting statements to fix). We have realized our approach in a tool called HOPPITY. By training on 290,715 Javascript code change commits on Github, HOPPITY correctly detects and fixes bugs in 9,490 out of 36,361 programs in an end-to-end fashion. Given the bug location and type of the fix, HOPPITY also outperforms the baseline approach by a wide margin.

ICML Conference 2019 Conference Paper

Learning Neurosymbolic Generative Models via Program Synthesis

  • Halley Young
  • Osbert Bastani
  • Mayur Naik

Generative models have become significantly more powerful in recent years. However, these models continue to have difficulty capturing global structure in data. For example, images of buildings typically contain spatial patterns such as windows repeating at regular intervals, but state-of-the-art models have difficulty generating these patterns. We propose to address this problem by incorporating programs representing global structure into generative models{—}e. g. , a 2D for-loop may represent a repeating pattern of windows{—}along with a framework for learning these models by leveraging program synthesis to obtain training data. On both synthetic and real-world data, we demonstrate that our approach substantially outperforms state-of-the-art at both generating and completing images with global structure.

IJCAI Conference 2019 Conference Paper

Synthesizing Datalog Programs using Numerical Relaxation

  • Xujie Si
  • Mukund Raghothaman
  • Kihong Heo
  • Mayur Naik

The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems, or performing parameter estimation in complex statistical models. In this paper, we present Difflog, a technique to extend the logic programming language Datalog to the continuous setting. By attaching real-valued weights to individual rules of a Datalog program, we naturally associate numerical values with individual conclusions of the program. Analogous to the strategy of numerical relaxation in optimization problems, we can now first determine the rule weights which cause the best agreement between the training labels and the induced values of output tuples, and subsequently recover the classical discrete-valued target program from the continuous optimum. We evaluate Difflog on a suite of 34~benchmark problems from recent literature in knowledge discovery, formal verification, and database query-by-example, and demonstrate significant improvements in learning complex programs with recursive rules, invented predicates, and relations of arbitrary arity.

NeurIPS Conference 2018 Conference Paper

Learning Loop Invariants for Program Verification

  • Xujie Si
  • Hanjun Dai
  • Mukund Raghothaman
  • Mayur Naik
  • Le Song

A fundamental problem in program verification concerns inferring loop invariants. The problem is undecidable and even practical instances are challenging. Inspired by how human experts construct loop invariants, we propose a reasoning framework Code2Inv that constructs the solution by multi-step decision making and querying an external program graph memory block. By training with reinforcement learning, Code2Inv captures rich program features and avoids the need for ground truth solutions as supervision. Compared to previous learning tasks in domains with graph-structured data, it addresses unique challenges, such as a binary objective function and an extremely sparse reward that is given by an automated theorem prover only after the complete loop invariant is proposed. We evaluate Code2Inv on a suite of 133 benchmark problems and compare it to three state-of-the-art systems. It solves 106 problems compared to 73 by a stochastic search-based system, 77 by a heuristic search-based system, and 100 by a decision tree learning-based system. Moreover, the strategy learned can be generalized to new programs: compared to solving new instances from scratch, the pre-trained agent is more sample efficient in finding solutions.

AAAI Conference 2016 Conference Paper

Scaling Relational Inference Using Proofs and Refutations

  • Ravi Mangal
  • Xin Zhang
  • Aditya Kamath
  • Aditya Nori
  • Mayur Naik

Many inference problems are naturally formulated using hard and soft constraints over relational domains: the desired solution must satisfy the hard constraints, while optimizing the objectives expressed by the soft constraints. Existing techniques for solving such constraints rely on efficiently grounding a sufficient subset of constraints that is tractable to solve. We present an eager-lazy grounding algorithm that eagerly exploits proofs and lazily refutes counterexamples. We show that our algorithm achieves significant speedup over existing approaches without sacrificing soundness for real-world applications from information retrieval and program analysis.

SAT Conference 2015 Conference Paper

Volt: A Lazy Grounding Framework for Solving Very Large MaxSAT Instances

  • Ravi Mangal
  • Xin Zhang 0035
  • Aditya V. Nori
  • Mayur Naik

Abstract Very large MaxSAT instances, comprising \(10^{20}\) clauses and beyond, commonly arise in a variety of domains. We present VOLT, a framework for solving such instances, using an iterative, lazy grounding approach. In each iteration, VOLT grounds a subset of clauses in the MaxSAT problem, and solves it using an off-the-shelf MaxSAT solver. VOLT provides a common ground to compare and contrast different lazy grounding approaches for solving large MaxSAT instances. We cast four diverse approaches from the literature on information retrieval and program analysis as instances of VOLT. We have implemented VOLT and evaluate its performance under different state-of-the-art MaxSAT solvers.

NeurIPS Conference 2010 Conference Paper

Predicting Execution Time of Computer Programs Using Sparse Polynomial Regression

  • Ling Huang
  • Jinzhu Jia
  • Bin Yu
  • Byung-Gon Chun
  • Petros Maniatis
  • Mayur Naik

Predicting the execution time of computer programs is an important but challenging problem in the community of computer systems. Existing methods require experts to perform detailed analysis of program code in order to construct predictors or select important features. We recently developed a new system to automatically extract a large number of features from program execution on sample inputs, on which prediction models can be constructed without expert knowledge. In this paper we study the construction of predictive models for this problem. We propose the SPORE (Sparse POlynomial REgression) methodology to build accurate prediction models of program performance using feature data collected from program execution on sample inputs. Our two SPORE algorithms are able to build relationships between responses (e. g. , the execution time of a computer program) and features, and select a few from hundreds of the retrieved features to construct an explicitly sparse and non-linear model to predict the response variable. The compact and explicitly polynomial form of the estimated model could reveal important insights into the computer program (e. g. , features and their non-linear combinations that dominate the execution time), enabling a better understanding of the program’s behavior. Our evaluation on three widely used computer programs shows that SPORE methods can give accurate prediction with relative error less than 7% by using a moderate number of training data samples. In addition, we compare SPORE algorithms to state-of-the-art sparse regression algorithms, and show that SPORE methods, motivated by real applications, outperform the other methods in terms of both interpretability and prediction accuracy.

ICML Conference 2006 Conference Paper

Statistical debugging: simultaneous identification of multiple bugs

  • Alice X. Zheng
  • Michael I. Jordan
  • Ben Liblit
  • Mayur Naik
  • Alexander Aiken

We describe a statistical approach to software debugging in the presence of multiple bugs. Due to sparse sampling issues and complex interaction between program predicates, many generic off-the-shelf algorithms fail to select useful bug predictors. Taking inspiration from bi-clustering algorithms, we propose an iterative collective voting scheme for the program runs and predicates. We demonstrate successful debugging results on several real world programs and a large debugging benchmark suite.

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