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Blaise Agüera y Arcas

Blaise Agüera y Arcas contributes to research discovery and scholarly infrastructure.

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Published work

4 published item(s)

preprint2026arXiv

Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematics

As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of currently 2615 mathematical problem statements formalized in Lean 4. Sourced from areas of active mathematical research, the dataset features 1029 open research conjectures providing a zero-contamination benchmark for mathematical proof discovery, and 836 solved problems for proof autoformalization. Notably, the repository provides a structured interface connecting mathematicians who formalize and clarify problems with the AI systems and humans attempting to solve them. Demonstrating its immediate utility, the benchmark has already been leveraged to make new mathematical discoveries, including the resolution of open research conjectures. We describe our approach to ensuring the correctness of these formalizations in a collaborative open-source project where contributions stem from an active community. In this framework, AI-generated proofs and disproofs serve as a valuable auditing mechanism to iteratively improve the fidelity of the benchmark. Finally, we provide a standardized evaluation setup and report baseline results on frozen evaluation subsets, demonstrating a climbable signal that measures the current frontier of automated reasoning on research-level mathematics.

preprint2026arXiv

Reasoning Models Generate Societies of Thought

Large language models have achieved remarkable capabilities across domains, yet mechanisms underlying sophisticated reasoning remain elusive. Recent reasoning models outperform comparable instruction-tuned models on complex cognitive tasks, attributed to extended computation through longer chains of thought. Here we show that enhanced reasoning emerges not from extended computation alone, but from simulating multi-agent-like interactions -- a society of thought -- which enables diversification and debate among internal cognitive perspectives characterized by distinct personality traits and domain expertise. Through quantitative analysis and mechanistic interpretability methods applied to reasoning traces, we find that reasoning models like DeepSeek-R1 and QwQ-32B exhibit much greater perspective diversity than instruction-tuned models, activating broader conflict between heterogeneous personality- and expertise-related features during reasoning. This multi-agent structure manifests in conversational behaviors, including question-answering, perspective shifts, and the reconciliation of conflicting views, and in socio-emotional roles that characterize sharp back-and-forth conversations, together accounting for the accuracy advantage in reasoning tasks. Controlled reinforcement learning experiments reveal that base models increase conversational behaviors when rewarded solely for reasoning accuracy, and fine-tuning models with conversational scaffolding accelerates reasoning improvement over base models. These findings indicate that the social organization of thought enables effective exploration of solution spaces. We suggest that reasoning models establish a computational parallel to collective intelligence in human groups, where diversity enables superior problem-solving when systematically structured, which suggests new opportunities for agent organization to harness the wisdom of crowds.

preprint2022arXiv

Federated Select: A Primitive for Communication- and Memory-Efficient Federated Learning

Federated learning (FL) is a framework for machine learning across heterogeneous client devices in a privacy-preserving fashion. To date, most FL algorithms learn a "global" server model across multiple rounds. At each round, the same server model is broadcast to all participating clients, updated locally, and then aggregated across clients. In this work, we propose a more general procedure in which clients "select" what values are sent to them. Notably, this allows clients to operate on smaller, data-dependent slices. In order to make this practical, we outline a primitive, federated select, which enables client-specific selection in realistic FL systems. We discuss how to use federated select for model training and show that it can lead to drastic reductions in communication and client memory usage, potentially enabling the training of models too large to fit on-device. We also discuss the implications of federated select on privacy and trust, which in turn affect possible system constraints and design. Finally, we discuss open questions concerning model architectures, privacy-preserving technologies, and practical FL systems.

preprint2021arXiv

ActionBert: Leveraging User Actions for Semantic Understanding of User Interfaces

As mobile devices are becoming ubiquitous, regularly interacting with a variety of user interfaces (UIs) is a common aspect of daily life for many people. To improve the accessibility of these devices and to enable their usage in a variety of settings, building models that can assist users and accomplish tasks through the UI is vitally important. However, there are several challenges to achieve this. First, UI components of similar appearance can have different functionalities, making understanding their function more important than just analyzing their appearance. Second, domain-specific features like Document Object Model (DOM) in web pages and View Hierarchy (VH) in mobile applications provide important signals about the semantics of UI elements, but these features are not in a natural language format. Third, owing to a large diversity in UIs and absence of standard DOM or VH representations, building a UI understanding model with high coverage requires large amounts of training data. Inspired by the success of pre-training based approaches in NLP for tackling a variety of problems in a data-efficient way, we introduce a new pre-trained UI representation model called ActionBert. Our methodology is designed to leverage visual, linguistic and domain-specific features in user interaction traces to pre-train generic feature representations of UIs and their components. Our key intuition is that user actions, e.g., a sequence of clicks on different UI components, reveals important information about their functionality. We evaluate the proposed model on a wide variety of downstream tasks, ranging from icon classification to UI component retrieval based on its natural language description. Experiments show that the proposed ActionBert model outperforms multi-modal baselines across all downstream tasks by up to 15.5%.