arXiv subjects

Aaditya Naik

Publications and source records attributed to Aaditya Naik.

10 recordsLinked to original sources

arXiv2026

Do We Need Frontier Models to Verify Mathematical Proofs?

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

cs.LG↗

arXiv2026

On Improving Neurosymbolic Learning by Exploiting the Representation Space

We study the problem of learning neural classifiers in a neurosymbolic setting where the hidden gold labels of input instances must satisfy a logical formula. Learning in this setting proceeds by first computing (a subset of) the possible combinations of labels that satisfy the formula and then computing a loss using those combinations and the classifiers' scores. One challenge is that the space of label combinations can grow exponentially, making learning difficult. We propose a technique that prunes this space by exploiting the intuition that instances with similar latent representations are likely to share the same label. While this intuition has been widely used in weakly supervised learning, its application in our setting is challenging due to label dependencies imposed by logical constraints. We formulate the pruning process as an integer linear program that discards inconsistent label combinations while respecting logical structure. Our approach, CLIPPER, is orthogonal to existing training algorithms and can be seamlessly integrated with them. Across 16 benchmarks over complex neurosymbolic tasks, we demonstrate that CLIPPER boosts the performance of state-of-the-art neurosymbolic engines like Scallop, Dolphin, and ISED by up to 48%, 53%, and 8%, leading to state-of-the-art accuracies.

cs.LG↗

arXiv2025

The Road to Generalizable Neuro-Symbolic Learning Should be Paved with Foundation Models

Neuro-symbolic learning was proposed to address challenges with training neural networks for complex reasoning tasks with the added benefits of interpretability, reliability, and efficiency. Neuro-symbolic learning methods traditionally train neural models in conjunction with symbolic programs, but they face significant challenges that limit them to simplistic problems. On the other hand, purely-neural foundation models now reach state-of-the-art performance through prompting rather than training, but they are often unreliable and lack interpretability. Supplementing foundation models with symbolic programs, which we call neuro-symbolic prompting, provides a way to use these models for complex reasoning tasks. Doing so raises the question: What role does specialized model training as part of neuro-symbolic learning have in the age of foundation models? To explore this question, we highlight three pitfalls of traditional neuro-symbolic learning with respect to the compute, data, and programs leading to generalization problems. This position paper argues that foundation models enable generalizable neuro-symbolic solutions, offering a path towards achieving the original goals of neuro-symbolic learning without the downsides of training from scratch.

cs.LG↗

arXiv2025

Where's the Bug? Attention Probing for Scalable Fault Localization

Ensuring code correctness remains a challenging problem even as large language models (LLMs) become increasingly capable at code-related tasks. While LLM-based program repair systems can propose bug fixes using only a user's bug report, their effectiveness is fundamentally limited by their ability to perform fault localization (FL), a challenging problem for both humans and LLMs. Existing FL approaches rely on executable test cases, require training on costly and often noisy line-level annotations, or demand resource-intensive LLMs. In this paper, we present Bug Attention Probe (BAP), a method which learns state-of-the-art fault localization without any direct localization labels, outperforming traditional FL baselines and prompting of large-scale LLMs. We evaluate our approach across a variety of code settings, including real-world Java bugs from the standard Defects4J dataset as well as seven other datasets which span a diverse set of bug types and languages. Averaged across all eight datasets, BAP improves by 34.6% top-1 accuracy compared to the strongest baseline and 93.4% over zero-shot prompting GPT-4o. BAP is also significantly more efficient than prompting, outperforming large open-weight models at a small fraction of the computational cost.

cs.SE↗

arXiv2024

TorchQL: A Programming Framework for Integrity Constraints in Machine Learning

Finding errors in machine learning applications requires a thorough exploration of their behavior over data. Existing approaches used by practitioners are often ad-hoc and lack the abstractions needed to scale this process. We present TorchQL, a programming framework to evaluate and improve the correctness of machine learning applications. TorchQL allows users to write queries to specify and check integrity constraints over machine learning models and datasets. It seamlessly integrates relational algebra with functional programming to allow for highly expressive queries using only eight intuitive operators. We evaluate TorchQL on diverse use-cases including finding critical temporal inconsistencies in objects detected across video frames in autonomous driving, finding data imputation errors in time-series medical records, finding data labeling errors in real-world images, and evaluating biases and constraining outputs of language models. Our experiments show that TorchQL enables up to 13x faster query executions than baselines like Pandas and MongoDB, and up to 40% shorter queries than native Python. We also conduct a user study and find that TorchQL is natural enough for developers familiar with Python to specify complex integrity constraints.

cs.DB↗

arXiv2024

Dolphin: A Programmable Framework for Scalable Neurosymbolic Learning

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 black-box 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.

cs.LG↗

arXiv2024

LLM-Based Test-Driven Interactive Code Generation: User Study and Empirical Evaluation

Large language models (LLMs) have shown great potential in automating significant aspects of coding by producing natural code from informal natural language (NL) intent. However, given NL is informal, it does not lend easily to checking that the generated code correctly satisfies the user intent. In this paper, we propose a novel interactive workflow TiCoder for guided intent clarification (i.e., partial formalization) through tests to support the generation of more accurate code suggestions. Through a mixed methods user study with 15 programmers, we present an empirical evaluation of the effectiveness of the workflow to improve code generation accuracy. We find that participants using the proposed workflow are significantly more likely to correctly evaluate AI generated code, and report significantly less task-induced cognitive load. Furthermore, we test the potential of the workflow at scale with four different state-of-the-art LLMs on two python datasets, using an idealized proxy for a user feedback. We observe an average absolute improvement of 45.97% in the pass@1 code generation accuracy for both datasets and across all LLMs within 5 user interactions, in addition to the automatic generation of accompanying unit tests.

cs.SE↗

arXiv2024

Towards Compositionality in Concept Learning

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. Code and data are available at https://github.com/adaminsky/compositional_concepts .

cs.CL↗

arXiv2023

Interactive Code Generation via Test-Driven User-Intent Formalization

Large language models (LLMs) have shown great potential in automating significant aspects of coding by producing natural code from informal natural language (NL) intent. However, when interacting with LLMs, users have no guarantees that the code suggestions produced correctly satisfy the intent they provided. In fact, it is hard to define a notion of correctness since natural language can be ambiguous and lacks a formal semantics. In this paper, we propose the workflow of {\it interactive test-driven code generation}, which leverages lightweight user feedback to (a) formalize the user intent using generated tests that can be useful for debugging, and (b) produce an improved set of code suggestions by pruning and ranking candidate code suggestions. We describe a language-agnostic abstract algorithm and a concrete implementation TiCoder. We perform an automated evaluation of TiCoder on the \emph{MBPP} and \emph{HumanEval} code generation benchmarks. Our results are promising with using the OpenAI Codex LLM: our best algorithm improves the \passk{1} code generation accuracy (in absolute percentages) between $22.49\%$ to $37.71\%$ for MBPP and between $24.79\%$ to $53.98\%$ for HumanEval using between 1 to 5 simulated user queries.

cs.SE↗

arXiv2023

Do Machine Learning Models Learn Statistical Rules Inferred from Data?

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.

cs.LG↗