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Swarat Chaudhuri

Publications and source records attributed to Swarat Chaudhuri.

At least 19 recordsLinked to original sources
arXiv2026

Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration

AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations. Specifically, while the precise value of $K_G$ is not known, we recently tightened the best known bounds to \[ \frac{6π}{11} \;\le\; K_G \;\le\; \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Crucially, these improvements were achieved using an AI research system that could arrive at insights deemed novel by domain experts. We give a detailed discussion of our experience using AI for mathematics research, particularly touching upon its strengths and weaknesses, as well as our experience with creating ideal conditions for AI to arrive at breakthrough insights.

cs.AI↗
arXiv2026

New Lower and Upper Bounds for the Grothendieck Constant

We establish new bounds on the Grothendieck constant $K_G$: \[ \frac{6π}{11} \le K_G \le \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our lower bound approach differs from previous works by establishing limitations on the asymptotically optimal Krivine schemes, rather than giving explicit constructions of gap instances. Our upper bound is obtained by proposing and analyzing the first asymptotic construction of rounding schemes, whereas previous works only consider low-dimensional schemes. Together, these bounds determine the previously unknown tenths digit of $K_G$ to be $7$. The bounds were discovered by a long-running collaborative effort of humans and a long-horizon AI research system that we engineered.

cs.CC↗
arXiv2026

FormulaCode: Evaluating Agentic Optimization on Large Codebases

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

cs.SE↗
arXiv2026

Advancing Mathematics Research with AI-Driven Formal Proof Search

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.

cs.AI↗
arXiv2026

Cost-Aware Optimization for Agentic Query Execution

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.

cs.DB↗
arXiv2026

When Parallelism Pays Off: Cohesion-Aware Task Partitioning for Multi-Agent Coding

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.

cs.LG↗
arXiv2026

ProofWala: A Framework for Multilingual Proof Data Synthesis and Theorem-Proving

Neural approaches to theorem proving require robust infrastructure for interfacing with interactive theorem provers (ITPs), extracting structured proof data, and executing proof search at scale. However, existing tooling is often assistant-specific and oriented toward file-level execution, making repository-scale analysis and parallel experimentation challenging. We present ProofWala, a multilingual proof engineering framework built around \texttt{itp-interface}, a reusable library for programmatic interaction with ITPs. For Lean 4, we implement a meta-programmed interaction layer executing inside the elaborator, enabling semantically faithful tactic-level tracing alongside declaration- and dependency-level extraction across entire repositories. This design extends beyond traditional REPL-style interaction by supporting project-wide analysis, environment cloning, and pooled execution of proof states. The same interface abstraction supports multiple versions of Rocq, yielding a unified cross-assistant pipeline. Built on this infrastructure, ProofWala provides standardized multilingual proof datasets, model training utilities, and parallel proof search algorithms. Using the framework, we demonstrate that multilingual training across Lean and Rocq enables cross-lingual and cross-domain transfer. We observe statistically significant improvements on Lean Mathlib and in domain adaptation (CategoryTheory), while other settings exhibit consistent upward trends. We open-source the full framework, parallel proof search module, datasets, and models across two repositories: ProofWala (https://github.com/trishullab/proof-wala) and the itp-interface library (https://github.com/trishullab/itp-interface).

cs.AI↗
arXiv2026

Do CFLOBDDs Actually Make Use of Linear Structure?

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.

cs.FL↗
arXiv2026

An Improved Last-Iterate Convergence Rate for Anchored Gradient Descent Ascent

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

math.OC↗
arXiv2026

Efficient Tree-Structured Deep Research with Adaptive Resource Allocation

Deep research agents, which synthesize information across diverse sources, are significantly constrained by the sequential nature of reasoning. This bottleneck results in high latency, poor runtime adaptability, and inefficient resource allocation, making today's deep research systems impractical for interactive applications. To overcome this, we introduce ParallelResearch, 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 based on query complexity; (2) a runtime orchestration layer that prunes redundant paths to reallocate resources and enables speculative execution; and (3) a fully-asynchronous execution infrastructure that enables concurrency across both research breadth and depth. Experiments on two benchmarks show up to 5x speedups with comparable final report quality, and consistent quality improvements with the same time budgets.

cs.DC↗
arXiv2026

Lean Finder: Semantic Search for Mathlib That Understands User Intents

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

cs.LG↗
arXiv2026

CSLib: The Lean Computer Science Library

We introduce CSLib, an open-source framework for proving computer-science-related theorems and writing formally verified code in the Lean proof assistant. CSLib aims to be for computer science what Lean's Mathlib is for mathematics. Mathlib has been tremendously impactful: it is a key reason for Lean's popularity within the mathematics research community, and it has also played a critical role in the training of AI systems for mathematical reasoning. However, the base of computer science knowledge in Lean is currently quite limited. CSLib will vastly enhance this knowledge base and provide infrastructure for using this knowledge in real-world verification projects. By doing so, CSLib will (1) enable the broad use of Lean in computer science education and research, and (2) facilitate the manual and AI-aided engineering of large-scale formally verified systems.

cs.LO↗
arXiv2026

Canopy: Property-Driven Learning for Congestion Control

Learning-based congestion controllers offer better adaptability compared to traditional heuristics. However, the 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 Canopy, a new property-driven framework that integrates learning with formal reasoning in the learning loop. Canopy uses novel quantitative certification with an abstract interpreter to guide the training process, rewarding models, and evaluating robust and safe model performance on worst-case inputs. Our evaluation demonstrates that unlike state-of-the-art learned controllers, Canopy-trained controllers provide both adaptability and worst-case reliability across a range of network conditions.

cs.LG↗
arXiv2025

Learning Interestingness in Automated Mathematical Theory Formation

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).

cs.AI↗
arXiv2025

CLEVER: A Curated Benchmark for Formally Verified Code Generation

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).

cs.LG↗
arXiv2025

Man-Made Heuristics Are Dead. Long Live Code Generators!

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.

cs.OS↗
arXiv2025

Resource-efficient Inference with Foundation Model Programs

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.

cs.LG↗