Rajeev Alur’s research while affiliated with University of Pennsylvania and other places

Recent advances in deep learning have enabled the development of autonomous systems that use deep neural networks for perception. Formal verification of these systems is challenging due to the size and complexity of the perception DNNs as well as hard-to-quantify, changing environment conditions. To address these challenges, we propose a probabilistic verification framework for autonomous systems based on the following key concepts: (1) Scenario-based Modeling: We decompose the task (e.g., car navigation) into a composition of scenarios, each representing a different environment condition. (2) Probabilistic Abstractions: For each scenario, we build a compact abstraction of perception based on the DNN's performance on an offline dataset that represents the scenario's environment condition. (3) Symbolic Reasoning and Acceleration: The abstractions enable efficient compositional verification of the autonomous system via symbolic reasoning and a novel acceleration proof rule that bounds the error probability of the system under arbitrary variations of environment conditions. We illustrate our approach on two case studies: an experimental autonomous system that guides airplanes on taxiways using high-dimensional perception DNNs and a simulation model of an F1Tenth autonomous car using LiDAR observations.

Many computational tasks benefit from being formulated as the composition of neural networks followed by a discrete symbolic program. The goal of neurosymbolic learning is to train the neural networks using only end-to-end input-output labels of the composite. We introduce CTSketch, a novel, scalable neurosymbolic learning algorithm. CTSketch uses two techniques to improve the scalability of neurosymbolic inference: decompose the symbolic program into sub-programs and summarize each sub-program with a sketched tensor. This strategy allows us to approximate the output distribution of the program with simple tensor operations over the input distributions and summaries. We provide theoretical insight into the maximum error of the approximation. Furthermore, we evaluate CTSketch on many benchmarks from the neurosymbolic literature, including some designed for evaluating scalability. Our results show that CTSketch pushes neurosymbolic learning to new scales that have previously been unattainable by obtaining high accuracy on tasks involving over one thousand inputs.

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.

We study how to subvert language models from following the rules. We model rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if P and Q, then R" for some propositions P, Q, and R. We prove that although transformers can faithfully abide by such rules, maliciously crafted prompts can nevertheless mislead even theoretically constructed models. Empirically, we find that attacks on our theoretical models mirror popular attacks on large language models. Our work suggests that studying smaller theoretical models can help understand the behavior of large language models in rule-based settings like logical reasoning and jailbreak attacks.

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 neurosymolic 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.

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.

We study the problem of synthesizing a core fragment of relational queries called select-project-join (SPJ) queries from input-output examples. Search-based synthesis techniques are suited to synthesizing projections and joins by navigating the network of relational tables but require additional supervision for synthesizing comparison predicates. On the other hand, decision tree learning techniques are suited to synthesizing comparison predicates when the input database can be summarized as a single labelled relational table. In this paper, we adapt and interleave methods from the domains of relational query synthesis and decision tree learning, and present an end-to-end framework for synthesizing relational queries with categorical and numerical comparison predicates. Our technique guarantees the completeness of the synthesis procedure and strongly encourages minimality of the synthesized program. We present Libra, an implementation of this technique and evaluate it on a benchmark suite of 1,475 instances of queries over 159 databases with multiple tables. Libra solves 1,361 of these instances in an average of 59 seconds per instance. It outperforms state-of-the-art program synthesis tools Scythe and PatSQL in terms of both the running time and the quality of the synthesized programs.

Synthesizing relational queries from data is challenging in the presence of recursion and invented predicates. We propose a fully automated approach to synthesize such queries. Our approach comprises of two steps: it first synthesizes a non-recursive query consistent with the given data, and then identifies recursion schemes in it and thereby generalizes to arbitrary data. This generalization is achieved by an iterative predicate unification procedure which exploits the notion of data provenance to accelerate convergence. In each iteration of the procedure, a constraint solver proposes a candidate query, and a query evaluator checks if the proposed program is consistent with the given data. The data provenance for a failed query allows us to construct additional constraints for the constraint solver and refine the search. We have implemented our approach in a tool named Mobius. On a suite of 21 challenging recursive query synthesis tasks, Mobius outperforms three state-of-the-art baselines Gensynth, ILASP, and Popper, both in terms of runtime and accuracy. We also demonstrate that the synthesized queries generalize well to unseen data.