Swarat Chaudhuri

Jennifer J. Sun, Megan Tjandrasuwita, Atharva Sehgal et al. · mit

Neurosymbolic Programming (NP) techniques have the potential to accelerate scientific discovery. These models combine neural and symbolic components to learn complex patterns and representations from data, using high-level concepts or known constraints. NP techniques can interface with symbolic domain knowledge from scientists, such as prior knowledge and experimental context, to produce interpretable outputs. We identify opportunities and challenges between current NP models and scientific workflows, with real-world examples from behavior analysis in science: to enable the use of NP broadly for workflows across the natural and social sciences.

George Tsoukalas, Jasper Lee, John Jennings et al.

We present PutnamBench, a new multi-language benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1692 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the problems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. PutnamBench requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

Zayne Sprague, Xi Ye, Kaj Bostrom et al.

While large language models (LLMs) equipped with techniques like chain-of-thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. However, evaluating LLM reasoning is challenging because system capabilities continue to grow while benchmark datasets for tasks like logical deduction have remained static. We introduce MuSR, a dataset for evaluating language models on multistep soft reasoning tasks specified in a natural language narrative. This dataset has two crucial features. First, it is created through a novel neurosymbolic synthetic-to-natural generation algorithm, enabling the construction of complex reasoning instances that challenge GPT-4 (e.g., murder mysteries roughly 1000 words in length) and which can be scaled further as more capable LLMs are released. Second, our dataset instances are free text narratives corresponding to real-world domains of reasoning; this makes it simultaneously much more challenging than other synthetically-crafted benchmarks while remaining realistic and tractable for human annotators to solve with high accuracy. We evaluate a range of LLMs and prompting techniques on this dataset and characterize the gaps that remain for techniques like chain-of-thought to perform robust reasoning.

Lunyiu Nie, Yilin Xia, Yiren Liu et al.

Classical query optimization searches over algebraically equivalent plans that differ only in cost. This assumption breaks once LLM-backed operators enter the picture: their placement, ordering, and granularity jointly determine both dollar cost and answer quality, and the right choice among the alternatives is often revealed only at runtime. We formalize this setting as agentic query execution, a query execution paradigm in which agent-based planning is interleaved with execution, and agent workflow optimization becomes the analogue of classical query optimization. We then present EnumGRPO, a self-improving optimizer for this setting. During a learning stage, EnumGRPO enumerates query plans over decisions such as execution paradigm, operator type, operator placement, selectivity scope, and projection width, then distills quality-cost feedback into reusable planning heuristics via in-context reinforcement learning. Across four databases in SWAN, EnumGRPO achieves 35.4% execution accuracy at $0.011 per query in LLM-operator cost, a ~317x cost reduction over the hybrid query baseline with an 18% relative improvement in answer accuracy.

Amitayush Thakur, George Tsoukalas, Yeming Wen et al.

We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA, repeatedly asks a high-capacity, general-purpose large language model (GPT-4) to propose tactic applications from within a stateful backtracking search. Proposed tactics are executed in the underlying proof environment. Feedback from the execution is used to build the prompt for the next model query, along with selected information from the search history and lemmas retrieved from an external database. We evaluate our implementation of COPRA on the miniF2F benchmark for Lean and a set of Coq tasks from the CompCert project. On these benchmarks, COPRA significantly outperforms few-shot invocations of GPT-4. It also compares favorably against finetuning-based approaches, outperforming ReProver, a state-of-the-art finetuned approach for Lean, in terms of the pass@1 metric. Our code and data are available at https://github.com/trishullab/copra.

Xu Yang, Lunyiu Nie, Ethan Chandra et al.

Multi-agent Large Language Model (LLM) systems offer a way to decompose complex tasks, such as coding, through parallelization and context isolation. However, adding agents in practice introduces inter-agent communication overhead, which incurs extra cost and can sometimes offset the efficiency gains. We formalize multi-agent orchestration as a graph partitioning problem that captures the communication-to-computation trade-off: task decomposition can shorten critical-path computation, but cross-agent dependencies require costly context transfer. We instantiate this view in repository-level software engineering and present Cohesion-aware Coder (Co-Coder), which builds dependency graphs from static analysis, isolates structural hub files, partitions the graph via community detection, and executes the partition with a dependency-aware scheduler. Across 28 real-world tasks on DevEval and CodeProjectEval, Co-Coder advances the Pareto-frontier over sequential and file-based parallel baselines as well as Claude Code with Agent Teams, lifting pass rate by up to 14.0%, achieving up to a 2.10x wall-clock speedup, and reducing API cost by up to 35%, with the largest gains on the most dependency-dense projects. Co-coder demonstrates how cohesion-aware orchestration can make parallel coding agents both theoretically grounded and practically efficient, suggesting a broader design principle for multi-agent systems.

Arya Grayeli, Atharva Sehgal, Omar Costilla-Reyes et al.

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

Zayne Sprague, Kaj Bostrom, Swarat Chaudhuri et al.

A growing body of work studies how to answer a question or verify a claim by generating a natural language "proof": a chain of deductive inferences yielding the answer based on a set of premises. However, these methods can only make sound deductions when they follow from evidence that is given. We propose a new system that can handle the underspecified setting where not all premises are stated at the outset; that is, additional assumptions need to be materialized to prove a claim. By using a natural language generation model to abductively infer a premise given another premise and a conclusion, we can impute missing pieces of evidence needed for the conclusion to be true. Our system searches over two fringes in a bidirectional fashion, interleaving deductive (forward-chaining) and abductive (backward-chaining) generation steps. We sample multiple possible outputs for each step to achieve coverage of the search space, at the same time ensuring correctness by filtering low-quality generations with a round-trip validation procedure. Results on a modified version of the EntailmentBank dataset and a new dataset called Everyday Norms: Why Not? show that abductive generation with validation can recover premises across in- and out-of-domain settings.

Cameron Voloshin, Hoang M. Le, Swarat Chaudhuri et al.

We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained PO as a systematic framework, decoupling task specification from policy selection, and as an alternative to the standard of cost shaping. With access to a generative model, we develop a model-based approach that enjoys a sample complexity analysis for guaranteeing both task satisfaction and cost optimality (through a reduction to a reachability problem). Empirically, our algorithm can achieve strong performance even in low-sample regimes.

Anja Surina, Arun Suggala, George Tsoukalas et al.

We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient norm, where $p \in (1/2, 1)$, it remained an open problem whether the improved exact $\mathcal{O}(1/t)$ rate is achievable. In this work, we resolve this question in the affirmative. This result was discovered autonomously by an AI system capable of writing formal proofs in Lean. The Lean proof can be accessed at https://github.com/google-deepmind/formal-conjectures/pull/3675/commits/a13226b49fd3b897f4c409194f3bcbeb96a08515

Chenxi Yang, Swarat Chaudhuri

We study the problem of learning worst-case-safe parameters for programs that use neural networks as well as symbolic, human-written code. Such neurosymbolic programs arise in many safety-critical domains. However, because they can use nondifferentiable operations, it is hard to learn their parameters using existing gradient-based approaches to safe learning. Our approach to this problem, Differentiable Symbolic Execution (DSE), samples control flow paths in a program, symbolically constructs worst-case "safety losses" along these paths, and backpropagates the gradients of these losses through program operations using a generalization of the REINFORCE estimator. We evaluate the method on a mix of synthetic tasks and real-world benchmarks. Our experiments show that DSE significantly outperforms the state-of-the-art DiffAI method on these tasks.

Zayne Sprague, Kaj Bostrom, Swarat Chaudhuri et al.

Current natural language systems designed for multi-step claim validation typically operate in two phases: retrieve a set of relevant premise statements using heuristics (planning), then generate novel conclusions from those statements using a large language model (deduction). The planning step often requires expensive Transformer operations and does not scale to arbitrary numbers of premise statements. In this paper, we investigate whether an efficient planning heuristic is possible via embedding spaces compatible with deductive reasoning. Specifically, we evaluate whether embedding spaces exhibit a property we call deductive additivity: the sum of premise statement embeddings should be close to embeddings of conclusions based on those premises. We explore multiple sources of off-the-shelf dense embeddings in addition to fine-tuned embeddings from GPT3 and sparse embeddings from BM25. We study embedding models both intrinsically, evaluating whether the property of deductive additivity holds, and extrinsically, using them to assist planning in natural language proof generation. Lastly, we create a dataset, Single-Step Reasoning Contrast (SSRC), to further probe performance on various reasoning types. Our findings suggest that while standard embedding methods frequently embed conclusions near the sums of their premises, they fall short of being effective heuristics and lack the ability to model certain categories of reasoning.

Atharva Sehgal, Arya Grayeli, Jennifer J. Sun et al.

We introduce Cosmos, a framework for object-centric world modeling that is designed for compositional generalization (CompGen), i.e., high performance on unseen input scenes obtained through the composition of known visual "atoms." The central insight behind Cosmos is the use of a novel form of neurosymbolic grounding. Specifically, the framework introduces two new tools: (i) neurosymbolic scene encodings, which represent each entity in a scene using a real vector computed using a neural encoder, as well as a vector of composable symbols describing attributes of the entity, and (ii) a neurosymbolic attention mechanism that binds these entities to learned rules of interaction. Cosmos is end-to-end differentiable; also, unlike traditional neurosymbolic methods that require representations to be manually mapped to symbols, it computes an entity's symbolic attributes using vision-language foundation models. Through an evaluation that considers two different forms of CompGen on an established blocks-pushing domain, we show that the framework establishes a new state-of-the-art for CompGen in world modeling. Artifacts are available at: https://trishullab.github.io/cosmos-web/

Greg Anderson, Swarat Chaudhuri, Isil Dillig

In reinforcement learning for safety-critical settings, it is often desirable for the agent to obey safety constraints at all points in time, including during training. We present a novel neurosymbolic approach called SPICE to solve this safe exploration problem. SPICE uses an online shielding layer based on symbolic weakest preconditions to achieve a more precise safety analysis than existing tools without unduly impacting the training process. We evaluate the approach on a suite of continuous control benchmarks and show that it can achieve comparable performance to existing safe learning techniques while incurring fewer safety violations. Additionally, we present theoretical results showing that SPICE converges to the optimal safe policy under reasonable assumptions.

George Tsoukalas, Rahul Saha, Amitayush Thakur et al.

We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through $\emph{FERMAT}$: automatically scoring the $\emph{interestingness}$ of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines. We open-source the $\emph{FERMAT}$ environment at this URL(https://github.com/trishullab/Fermat).

Lazar Valkov, Akash Srivastava, Swarat Chaudhuri et al.

Modular approaches that use a different composition of modules for each problem are a promising direction in continual learning (CL). However, searching through the large, discrete space of module compositions is challenging, especially because evaluating a composition's performance requires a round of neural network training. We address this challenge through a modular CL framework, PICLE, that uses a probabilistic model to cheaply compute the fitness of each composition, allowing PICLE to achieve both perceptual, few-shot and latent transfer. The model combines prior knowledge about good module compositions with dataset-specific information. We evaluate PICLE using two benchmark suites designed to assess different desiderata of CL techniques. Comparing to a wide range of approaches, we show that PICLE is the first modular CL algorithm to achieve perceptual, few-shot and latent transfer while scaling well to large search spaces, outperforming previous state-of-the-art modular CL approaches on long problem sequences.

Chenxi Yang, Greg Anderson, Swarat Chaudhuri

We present a reinforcement learning (RL) framework in which the learned policy comes with a machine-checkable certificate of provable adversarial robustness. Our approach, called CAROL, learns a model of the environment. In each learning iteration, it uses the current version of this model and an external abstract interpreter to construct a differentiable signal for provable robustness. This signal is used to guide learning, and the abstract interpretation used to construct it directly leads to the robustness certificate returned at convergence. We give a theoretical analysis that bounds the worst-case accumulative reward of CAROL. We also experimentally evaluate CAROL on four MuJoCo environments with continuous state and action spaces. On these tasks, CAROL learns policies that, when contrasted with policies from the state-of-the-art robust RL algorithms, exhibit: (i) markedly enhanced certified performance lower bounds; and (ii) comparable performance under empirical adversarial attacks.

Eric Hsiung, Joydeep Biswas, Swarat Chaudhuri

Active automata learning from membership and equivalence queries is a foundational problem with numerous applications. We propose a novel variant of the active automata learning problem: actively learn finite automata using preference queries -- i.e., queries about the relative position of two sequences in a total order -- instead of membership queries. Our solution is REMAP, a novel algorithm which leverages a symbolic observation table along with unification and constraint solving to navigate a space of symbolic hypotheses (each representing a set of automata), and uses satisfiability-solving to construct a concrete automaton from a symbolic hypothesis. REMAP is guaranteed to correctly infer the minimal automaton with polynomial query complexity under exact equivalence queries, and achieves PAC-identification ($\varepsilon$-approximate, with high probability) of the minimal automaton using sampling-based equivalence queries. Our empirical evaluations of REMAP on the task of learning reward machines for two reinforcement learning domains indicate REMAP scales to large automata and is effective at learning correct automata from consistent teachers, under both exact and sampling-based equivalence queries.

George Tsoukalas, Anton Kovsharov, Sergey Shirobokov et al.

Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the first large-scale evaluation of this method's ability to solve open problems. Our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars, proved 44/492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. A basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes but proved costlier on the hardest problems. These findings demonstrate the power of AI-aided formal proof search and shed light on the agent designs that enable it.

Amitayush Thakur, Jasper Lee, George Tsoukalas et al.

We introduce ${\rm C{\small LEVER}}$, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, ${\rm C{\small LEVER}}$ avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use ${\rm C{\small LEVER}}$ to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

Meghana Aparna Sistla, Swarat Chaudhuri, Thomas W. Reps

Binary Decision Diagrams (BDDs) are a widely used data structure for efficient Boolean function representation. Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs) are a recently introduced hierarchical data structure that can, in the best case, exhibit exponential compression over BDDs and double-exponential compression over decision trees. Roughly speaking, a CFLOBDD is a finite, acyclic, non-recursive hierarchical finite-state machine (HFSM) (with some additional restrictions). In this paper, we investigate the role of \emph{linear structure} in CFLOBDDs -- a property that connects them to Nested-Word Automata (NWAs) and Visibly Pushdown Automata (VPAs) -- and examine whether CFLOBDDs actively exploit this structure beyond their well-studied hierarchical properties. We demonstrate that linear structure, in conjunction with hierarchical structure, plays a crucial role in enabling CFLOBDDs to achieve efficient function compression. Furthermore, we show that removing linearity from CFLOBDDs leads to a significant blowup in representation size, resulting in degraded performance in the domain of quantum-circuit simulation.

Atharva Sehgal, James Hou, Akanksha Sarkar et al.

Large language model (LLM) coding agents increasingly operate at the repository level, motivating benchmarks that evaluate their ability to optimize entire codebases under realistic constraints. Existing code benchmarks largely rely on synthetic tasks, binary correctness signals, or single-objective evaluation, limiting their ability to assess holistic optimization behavior. We introduce FormulaCode, a benchmark for evaluating agentic optimization on large, real-world codebases with fine-grained, multi-objective performance metrics. FormulaCode comprises 957 performance bottlenecks mined from scientific Python repositories on GitHub, each paired with expert-authored patches and, on average, 264.6 community-maintained performance workloads per task, enabling the holistic ability of LLM agents to optimize codebases under realistic correctness and performance constraints. Our evaluations reveal that repository-scale, multi-objective optimization remains a major challenge for frontier LLM agents. Project website at: https://formula-code.github.io

Amitayush Thakur, George Tsoukalas, Greg Durrett et al.

Neural networks have shown substantial promise at automatic theorem-proving in interactive proof assistants (ITPs) like Lean and Coq. However, most neural theorem-proving models are restricted to specific ITPs, leaving out opportunities for cross-lingual $\textit{transfer}$ between ITPs. We address this weakness with a multilingual proof framework, ${\rm P{\small ROOF}W{\small ALA}}$, that allows a standardized form of interaction between neural theorem-provers and two established ITPs (Coq and Lean). It enables the collection of multilingual proof step data -- data recording the result of proof actions on ITP states -- for training neural provers. ${\rm P{\small ROOF}W{\small ALA}}$ allows the systematic evaluation of a model's performance across different ITPs and problem domains via efficient parallel proof search algorithms. We show that multilingual training enabled by ${\rm P{\small ROOF}W{\small ALA}}$ can lead to successful transfer across ITPs. Specifically, a model trained on a mix of ${\rm P{\small ROOF}W{\small ALA}}$-generated Coq and Lean data outperforms Lean-only and Coq-only models on the standard prove-at-$k$ metric. We open source all code including code for the ${\rm P{\small ROOF}W{\small ALA}}$ Framework (https://github.com/trishullab/proof-wala), and the Multilingual ITP interaction framework (https://github.com/trishullab/itp-interface).

Rohit Dwivedula, Divyanshu Saxena, Aditya Akella et al.

Policy design for various systems controllers has conventionally been a manual process, with domain experts carefully tailoring heuristics for the specific instance in which the policy will be deployed. In this paper, we re-imagine policy design via a novel automated search technique fueled by recent advances in generative models, specifically Large Language Model (LLM)-driven code generation. We outline the design and implementation of PolicySmith, a framework that applies LLMs to synthesize instance-optimal heuristics. We apply PolicySmith to two long-standing systems policies - web caching and congestion control, highlighting the opportunities unraveled by this LLM-driven heuristic search. For caching, PolicySmith discovers heuristics that outperform established baselines on standard open-source traces. For congestion control, we show that PolicySmith can generate safe policies that integrate directly into the Linux kernel.

Alexander Novikov, Ngân Vũ, Marvin Eisenberger et al. · deepmind

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific problems or optimizing critical pieces of computational infrastructure. AlphaEvolve orchestrates an autonomous pipeline of LLMs, whose task is to improve an algorithm by making direct changes to the code. Using an evolutionary approach, continuously receiving feedback from one or more evaluators, AlphaEvolve iteratively improves the algorithm, potentially leading to new scientific and practical discoveries. We demonstrate the broad applicability of this approach by applying it to a number of important computational problems. When applied to optimizing critical components of large-scale computational stacks at Google, AlphaEvolve developed a more efficient scheduling algorithm for data centers, found a functionally equivalent simplification in the circuit design of hardware accelerators, and accelerated the training of the LLM underpinning AlphaEvolve itself. Furthermore, AlphaEvolve discovered novel, provably correct algorithms that surpass state-of-the-art solutions on a spectrum of problems in mathematics and computer science, significantly expanding the scope of prior automated discovery methods (Romera-Paredes et al., 2023). Notably, AlphaEvolve developed a search algorithm that found a procedure to multiply two $4 \times 4$ complex-valued matrices using $48$ scalar multiplications; offering the first improvement, after 56 years, over Strassen's algorithm in this setting. We believe AlphaEvolve and coding agents like it can have a significant impact in improving solutions of problems across many areas of science and computation.

Kaiyu Yang, Gabriel Poesia, Jingxuan He et al.

AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large language models on carefully curated math datasets in text form. As a complementary yet less explored avenue, formal mathematical reasoning is grounded in formal systems such as proof assistants, which can verify the correctness of reasoning and provide automatic feedback. In this position paper, we advocate for formal mathematical reasoning and argue that it is indispensable for advancing AI4Math to the next level. In recent years, we have seen steady progress in using AI to perform formal reasoning, including core tasks such as theorem proving and autoformalization, as well as emerging applications such as verifiable generation of code and hardware designs. However, significant challenges remain to be solved for AI to truly master mathematics and achieve broader impact. We summarize existing progress, discuss open challenges, and envision critical milestones to measure future success. At this inflection point for formal mathematical reasoning, we call on the research community to come together to drive transformative advancements in this field.

Yeming Wen, Swarat Chaudhuri

Low-Rank Adaptation (LoRA) has recently gained attention for fine-tuning foundation models by incorporating trainable low-rank matrices, thereby reducing the number of trainable parameters. While LoRA offers numerous advantages, its applicability for real-time serving to a diverse and global user base is constrained by its incapability to handle multiple task-specific adapters efficiently. This imposes a performance bottleneck in scenarios requiring personalized, task-specific adaptations for each incoming request. To mitigate this constraint, we introduce Fast LoRA (FLoRA), a framework in which each input example in a minibatch can be associated with its unique low-rank adaptation weights, allowing for efficient batching of heterogeneous requests. We empirically demonstrate that FLoRA retains the performance merits of LoRA, showcasing competitive results on the MultiPL-E code generation benchmark spanning over 8 languages and a multilingual speech recognition task across 6 languages.

Yeming Wen, Pengcheng Yin, Kensen Shi et al.

Large language models (LLMs) have recently demonstrated a remarkable ability to generate code from natural language (NL) prompts. However, in the real world, NL is often too ambiguous to capture the true intent behind programming problems, requiring additional input-output (I/O) specifications. Unfortunately, LLMs can have difficulty aligning their outputs with both the NL prompt and the I/O specification. In this paper, we give a way to mitigate this issue in the context of data science programming, where tasks require explicit I/O specifications for clarity. Specifically, we propose GIFT4Code, a novel approach for the instruction fine-tuning of LLMs with respect to I/O specifications. Our method leverages synthetic data produced by the LLM itself and utilizes execution-derived feedback as a key learning signal. This feedback, in the form of program I/O specifications, is provided to the LLM to facilitate instruction fine-tuning. We evaluated our approach on two challenging data science benchmarks, Arcade and DS-1000. The results demonstrate a significant improvement in the LLM's ability to generate code that is not only executable but also accurately aligned with user specifications, substantially improving the quality of code generation for complex data science tasks.

Lunyiu Nie, Zhimin Ding, Erdong Hu et al.

Large Language Models (LLMs) have a natural role in answering complex queries about data streams, but the high computational cost of LLM inference makes them infeasible in many such tasks. We propose online cascade learning, the first approach to address this challenge. The objective here is to learn a "cascade" of models, starting with lower-capacity models (such as logistic regression) and ending with a powerful LLM, along with a deferral policy that determines the model to be used on a given input. We formulate the task of learning cascades online as an imitation-learning problem, where smaller models are updated over time imitating the collected LLM demonstrations, and give a no-regret algorithm for the problem. Experimental results across four benchmarks show that our method parallels LLMs in accuracy while cutting down inference costs by as much as 90% with strong robustness against input distribution shifts, underscoring its efficacy and adaptability in stream processing.

Abhinav Jain, Swarat Chaudhuri, Thomas Reps et al.

Parameter-Efficient Fine-Tuning (PEFT) has become the standard for customising Foundation Models (FMs) to user-specific downstream tasks. However, typical PEFT methods require storing multiple task-specific adapters, creating scalability issues as these adapters must be housed and run at the FM server. Traditional prompt tuning offers a potential solution by customising them through task-specific input prefixes, but it under-performs compared to other PEFT methods like LoRA. To address this gap, we propose Low-Rank Prompt Adaptation (LoPA), a prompt-tuning-based approach that performs on par with state-of-the-art PEFT methods and full fine-tuning while being more parameter-efficient and not requiring a server-based adapter. LoPA generates soft prompts by balancing between sharing task-specific information across instances and customization for each instance. It uses a low-rank decomposition of the soft-prompt component encoded for each instance to achieve parameter efficiency. We provide a comprehensive evaluation on multiple natural language understanding and code generation and understanding tasks across a wide range of foundation models with varying sizes.

Ameesh Shah, Cameron Voloshin, Chenxi Yang et al.

Linear Temporal Logic (LTL) offers a precise means for constraining the behavior of reinforcement learning agents. However, in many settings where both satisfaction and optimality conditions are present, LTL is insufficient to capture both. Instead, LTL-constrained policy optimization, where the goal is to optimize a scalar reward under LTL constraints, is needed. This constrained optimization problem proves difficult in deep Reinforcement Learning (DRL) settings, where learned policies often ignore the LTL constraint due to the sparse nature of LTL satisfaction. To alleviate the sparsity issue, we introduce Cycle Experience Replay (CyclER), a novel reward shaping technique that exploits the underlying structure of the LTL constraint to guide a policy towards satisfaction by encouraging partial behaviors compliant with the constraint. We provide a theoretical guarantee that optimizing CyclER will achieve policies that satisfy the LTL constraint with near-optimal probability. We evaluate CyclER in three continuous control domains. Our experimental results show that optimizing CyclER in tandem with the existing scalar reward outperforms existing reward-shaping methods at finding performant LTL-satisfying policies.

Divyanshu Saxena, Nihal Sharma, Donghyun Kim et al.

This paper lays down the research agenda for a domain-specific foundation model for operating systems (OSes). Our case for a foundation model revolves around the observations that several OS components such as CPU, memory, and network subsystems are interrelated and that OS traces offer the ideal dataset for a foundation model to grasp the intricacies of diverse OS components and their behavior in varying environments and workloads. We discuss a wide range of possibilities that then arise, from employing foundation models as policy agents to utilizing them as generators and predictors to assist traditional OS control algorithms. Our hope is that this paper spurs further research into OS foundation models and creating the next generation of operating systems for the evolving computing landscape.

Jialin Lu, Kye Emond, Kaiyu Yang et al.

We present Lean Finder, a semantic search engine for Lean and mathlib that understands and aligns with the intents of mathematicians. Progress in formal theorem proving is often hindered by the difficulty of locating relevant theorems and the steep learning curve of the Lean 4 language, making advancement slow and labor-intensive. Existing Lean search engines, though helpful, rely primarily on informalizations (natural language translation of the formal statements), while largely overlooking the mismatch with real-world user queries. In contrast, we propose a user-centered semantic search tailored to the needs of mathematicians. Our approach begins by analyzing and clustering the semantics of public Lean discussions, then fine-tuning text embeddings on synthesized queries that emulate user intents. We further align Lean Finder with mathematicians' preferences using diverse feedback signals, encoding it with a rich awareness of their goals from multiple perspectives. Evaluations on real-world queries, informalized statements, and proof states demonstrate that our Lean Finder achieves over $30\%$ relative improvement compared to previous search engines and GPT-4o. In addition, Lean Finder is compatible with LLM-based theorem provers, bridging retrieval with formal reasoning. Lean Finder is available at: https://leanfinder.github.io

Atharva Sehgal, Patrick Yuan, Ziniu Hu et al.

We study the problem of building a visual concept library for visual recognition. Building effective visual concept libraries is challenging, as manual definition is labor-intensive, while relying solely on LLMs for concept generation can result in concepts that lack discriminative power or fail to account for the complex interactions between them. Our approach, ESCHER, takes a library learning perspective to iteratively discover and improve visual concepts. ESCHER uses a vision-language model (VLM) as a critic to iteratively refine the concept library, including accounting for interactions between concepts and how they affect downstream classifiers. By leveraging the in-context learning abilities of LLMs and the history of performance using various concepts, ESCHER dynamically improves its concept generation strategy based on the VLM critic's feedback. Finally, ESCHER does not require any human annotations, and is thus an automated plug-and-play framework. We empirically demonstrate the ability of ESCHER to learn a concept library for zero-shot, few-shot, and fine-tuning visual classification tasks. This work represents, to our knowledge, the first application of concept library learning to real-world visual tasks.

Lunyiu Nie, Zhimin Ding, Kevin Yu et al.

The inference-time resource costs of large language and vision models present a growing challenge in production deployments. We propose the use of foundation model programs, i.e., programs that can invoke foundation models with varying resource costs and performance, as an approach to this problem. Specifically, we present a method that translates a task into a program, then learns a policy for resource allocation that, on each input, selects foundation model "backends" for each program module. The policy uses smaller, cheaper backends to handle simpler subtasks, while allowing more complex subtasks to leverage larger, more capable models. We evaluate the method on two new "streaming" visual question-answering tasks in which a system answers a question on a sequence of inputs, receiving ground-truth feedback after each answer. Compared to monolithic multi-modal models, our implementation achieves up to 98% resource savings with minimal accuracy loss, demonstrating its potential for scalable and resource-efficient multi-modal inference.

Chenxi Yang, Divyanshu Saxena, Rohit Dwivedula et al.

Learning-based congestion controllers offer better adaptability compared to traditional heuristic algorithms. However, the inherent unreliability of learning techniques can cause learning-based controllers to behave poorly, creating a need for formal guarantees. While methods for formally verifying learned congestion controllers exist, these methods offer binary feedback that cannot optimize the controller toward better behavior. We improve this state-of-the-art via C3, a new learning framework for congestion control that integrates the concept of formal certification in the learning loop. C3 uses an abstract interpreter that can produce robustness and performance certificates to guide the training process, rewarding models that are robust and performant even on worst-case inputs. Our evaluation demonstrates that unlike state-of-the-art learned controllers, C3-trained controllers provide both adaptability and worst-case reliability across a range of network conditions.

Lunyiu Nie, Nedim Lipka, Ryan A. Rossi et al.

Deep research agents, which synthesize information across diverse sources, are significantly constrained by their sequential reasoning processes. This architectural bottleneck results in high latency, poor runtime adaptability, and inefficient resource allocation, making them impractical for interactive applications. To overcome this, we introduce FlashResearch, a novel framework for efficient deep research that transforms sequential processing into parallel, runtime orchestration by dynamically decomposing complex queries into tree-structured sub-tasks. Our core contributions are threefold: (1) an adaptive planner that dynamically allocates computational resources by determining research breadth and depth based on query complexity; (2) a real-time orchestration layer that monitors research progress and prunes redundant paths to reallocate resources and optimize efficiency; and (3) a multi-dimensional parallelization framework that enables concurrency across both research breadth and depth. Experiments show that FlashResearch consistently improves final report quality within fixed time budgets, and can deliver up to a 5x speedup while maintaining comparable quality.

Eric Hsiung, Swarat Chaudhuri, Joydeep Biswas

Quantitative automata are useful representations for numerous applications, including modeling probability distributions over sequences to Markov chains and reward machines. Actively learning such automata typically occurs using explicitly gathered input-output examples under adaptations of the L-star algorithm. However, obtaining explicit input-output pairs can be expensive, and there exist scenarios, including preference-based learning or learning from rankings, where providing constraints is a less exerting and a more natural way to concisely describe desired properties. Consequently, we propose the problem of learning deterministic quantitative automata from sets of constraints over the valuations of input sequences. We present QUINTIC, an active learning algorithm, wherein the learner infers a valid automaton through deductive reasoning, by applying a theory to a set of currently available constraints and an assumed preference model and quantitative automaton class. QUINTIC performs a complete search over the space of automata, and is guaranteed to be minimal and correctly terminate. Our evaluations utilize theory of rationals in order to learn summation, discounted summation, product, and classification quantitative automata, and indicate QUINTIC is effective at learning these types of automata.

Yeming Wen, Swarat Chaudhuri

Presenting users with diverse responses from foundation models is crucial for enhancing user experience and accommodating varying preferences. However, generating multiple high-quality and diverse responses without sacrificing accuracy remains a challenge, especially when using greedy sampling. In this work, we propose a novel framework, Synthesize-Partition-Adapt (SPA), that leverages the abundant synthetic data available in many domains to elicit diverse responses from foundation models. By leveraging signal provided by data attribution methods such as influence functions, SPA partitions data into subsets, each targeting unique aspects of the data, and trains multiple model adaptations optimized for these subsets. Experimental results demonstrate the effectiveness of our approach in diversifying foundation model responses while maintaining high quality, showcased through the HumanEval and MBPP tasks in the code generation domain and several tasks in the natural language understanding domain, highlighting its potential to enrich user experience across various applications.

Abhinav Jain, Chima Adiole, Swarat Chaudhuri et al.

Large Language Models (LLMs) pre-trained on code have recently emerged as the dominant approach to program synthesis. However, these models are trained using next-token prediction, which ignores the syntax and semantics of code. We propose RLCF, that further trains a pre-trained LLM via reinforcement learning, using feedback from a grounding function that scores the quality of the code. The grounding function uses (i) compiler-derived feedback on whether the code it generates passes a set of correctness checks; and (ii) feedback from a different LLM that compares the generated code to a reference code. RLCF is model- and language-agnostic. We empirically evaluate it on the MBJP and MathQA tasks for Java. Our experiments show that RLCF raises the odds that an LLM-generated program compiles, is executable, and produces the right output on tests, often allowing LLMs to match the performance of 2x-8x larger LLMs.

Kaj Bostrom, Zayne Sprague, Swarat Chaudhuri et al.

In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but less work has treated the generative version in which a model searches over the space of statements entailed by the premises to constructively derive the hypothesis. We propose a system for doing this kind of deductive reasoning in natural language by decomposing the task into separate steps coordinated by a search procedure, producing a tree of intermediate conclusions that faithfully reflects the system's reasoning process. Our experiments on the EntailmentBank dataset (Dalvi et al., 2021) demonstrate that the proposed system can successfully prove true statements while rejecting false ones. Moreover, it produces natural language explanations with a 17% absolute higher step validity than those produced by an end-to-end T5 model.

Rohan Mukherjee, Yeming Wen, Dipak Chaudhari et al.

State-of-the-art neural models of source code tend to be evaluated on the generation of individual expressions and lines of code, and commonly fail on long-horizon tasks such as the generation of entire method bodies. We propose to address this deficiency using weak supervision from a static program analyzer. Our neurosymbolic method allows a deep generative model to symbolically compute, using calls to a static-analysis tool, long-distance semantic relationships in the code that it has already generated. During training, the model observes these relationships and learns to generate programs conditioned on them. We apply our approach to the problem of generating entire Java methods given the remainder of the class that contains the method. Our experiments show that the approach substantially outperforms state-of-the-art transformers and a model that explicitly tries to learn program semantics on this task, both in terms of producing programs free of basic semantic errors and in terms of syntactically matching the ground truth.

Eric Zhan, Jennifer J. Sun, Ann Kennedy et al.

We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic expert knowledge into the learning process, which leads to more interpretable and factorized latent representations compared to fully neural encoders. We integrate modern program synthesis techniques with the variational autoencoding (VAE) framework, in order to learn a neurosymbolic encoder in conjunction with a standard decoder. The programmatic descriptions from our encoders can benefit many analysis workflows, such as in behavior modeling where interpreting agent actions and movements is important. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation of meaningful categories than standard VAEs and leads to practical gains on downstream analysis tasks, such as for behavior classification.

Megan Tjandrasuwita, Jennifer J. Sun, Ann Kennedy et al.

Hand-annotated data can vary due to factors such as subjective differences, intra-rater variability, and differing annotator expertise. We study annotations from different experts who labelled the same behavior classes on a set of animal behavior videos, and observe a variation in annotation styles. We propose a new method using program synthesis to help interpret annotation differences for behavior analysis. Our model selects relevant trajectory features and learns a temporal filter as part of a program, which corresponds to estimated importance an annotator places on that feature at each timestamp. Our experiments on a dataset from behavioral neuroscience demonstrate that compared to baseline approaches, our method is more accurate at capturing annotator labels and learns interpretable temporal filters. We believe that our method can lead to greater reproducibility of behavior annotations used in scientific studies. We plan to release our code.

Kaj Bostrom, Xinyu Zhao, Swarat Chaudhuri et al.

An interpretable system for open-domain reasoning needs to express its reasoning process in a transparent form. Natural language is an attractive representation for this purpose -- it is both highly expressive and easy for humans to understand. However, manipulating natural language statements in logically consistent ways is hard: models must cope with variation in how meaning is expressed while remaining precise. In this paper, we describe ParaPattern, a method for building models to generate deductive inferences from diverse natural language inputs without direct human supervision. We train BART-based models (Lewis et al., 2020) to generate the result of applying a particular logical operation to one or more premise statements. Crucially, we develop a largely automated pipeline for constructing suitable training examples from Wikipedia. We evaluate our models using out-of-domain sentence compositions from the QASC (Khot et al., 2020) and EntailmentBank (Dalvi et al., 2021) datasets as well as targeted perturbation sets. Our results show that our models are substantially more accurate and flexible than baseline systems. ParaPattern achieves 85% validity on examples of the 'substitution' operation from EntailmentBank without the use of any in-domain training data, matching the performance of a model fine-tuned for EntailmentBank. The full source code for our method is publicly available.

Jiayi Wei, Tongrui Li, Swarat Chaudhuri et al.

We propose a new algorithm to simplify the controller development for distributed robotic systems subject to external observations, disturbances, and communication delays. Unlike prior approaches that propose specialized solutions to handling communication latency for specific robotic applications, our algorithm uses an arbitrary centralized controller as the specification and automatically generates distributed controllers with communication management and delay compensation. We formulate our goal as nonlinear optimal control -- using a regret minimizing objective that measures how much the distributed agents behave differently from the delay-free centralized response -- and solve for optimal actions w.r.t. local estimations of this objective using gradient-based optimization. We analyze our proposed algorithm's behavior under a linear time-invariant special case and prove that the closed-loop dynamics satisfy a form of input-to-state stability w.r.t. unexpected disturbances and observations. Our experimental results on both simulated and real-world robotic tasks demonstrate the practical usefulness of our approach and show significant improvement over several baseline approaches.

Arkabandhu Chowdhury, Mingchao Jiang, Swarat Chaudhuri et al.

Recent papers have suggested that transfer learning can outperform sophisticated meta-learning methods for few-shot image classification. We take this hypothesis to its logical conclusion, and suggest the use of an ensemble of high-quality, pre-trained feature extractors for few-shot image classification. We show experimentally that a library of pre-trained feature extractors combined with a simple feed-forward network learned with an L2-regularizer can be an excellent option for solving cross-domain few-shot image classification. Our experimental results suggest that this simpler sample-efficient approach far outperforms several well-established meta-learning algorithms on a variety of few-shot tasks.

Greg Anderson, Abhinav Verma, Isil Dillig et al.

We present Revel, a partially neural reinforcement learning (RL) framework for provably safe exploration in continuous state and action spaces. A key challenge for provably safe deep RL is that repeatedly verifying neural networks within a learning loop is computationally infeasible. We address this challenge using two policy classes: a general, neurosymbolic class with approximate gradients and a more restricted class of symbolic policies that allows efficient verification. Our learning algorithm is a mirror descent over policies: in each iteration, it safely lifts a symbolic policy into the neurosymbolic space, performs safe gradient updates to the resulting policy, and projects the updated policy into the safe symbolic subset, all without requiring explicit verification of neural networks. Our empirical results show that Revel enforces safe exploration in many scenarios in which Constrained Policy Optimization does not, and that it can discover policies that outperform those learned through prior approaches to verified exploration.

Ameesh Shah, Eric Zhan, Jennifer J. Sun et al.

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.

Arkabandhu Chowdhury, Dipak Chaudhari, Swarat Chaudhuri et al.

We present a new approach, called meta-meta classification, to learning in small-data settings. In this approach, one uses a large set of learning problems to design an ensemble of learners, where each learner has high bias and low variance and is skilled at solving a specific type of learning problem. The meta-meta classifier learns how to examine a given learning problem and combine the various learners to solve the problem. The meta-meta learning approach is especially suited to solving few-shot learning tasks, as it is easier to learn to classify a new learning problem with little data than it is to apply a learning algorithm to a small data set. We evaluate the approach on a one-shot, one-class-versus-all classification task and show that it is able to outperform traditional meta-learning as well as ensembling approaches.