Algorithms and theory
Google’s mission presents many exciting algorithmic and optimization challenges across different product areas including Search, Ads, Social, and Google Infrastructure. These include optimizing internal systems such as scheduling the machines that power the numerous computations done each day, as well as optimizations that affect core products and users, from online allocation of ads to page-views to automatic management of ad campaigns, and from clustering large-scale graphs to finding best paths in transportation networks. Other than employing new algorithmic ideas to impact millions of users, Google researchers contribute to the state-of-the-art research in these areas by publishing in top conferences and journals.
Recent Publications
Mind the Gap: Structure-Aware Consistency in Preference Learning
Proceedings of the 43rd International Conference on Machine Learning (ICML 2026)
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Aligning Large Language Models (LLMs) with human intent, whether through explicit reward modeling or direct methods such as DPO, fundamentally relies on minimizing a surrogate loss as a proxy for the true pairwise ranking objective. We prove that this reliance is flawed for the standard surrogate losses used: for the equicontinuous hypothesis sets characteristic of neural networks, no standard surrogate provides a meaningful consistency guarantee. Minimizing the surrogate loss to zero can leave the true ranking error arbitrarily high. To resolve this, we formulate LLM alignment within a margin-shifted ranking framework and derive $H$-consistency bounds showing that enforcing a confidence margin $\gamma$ is not merely beneficial but necessary for consistency. We further introduce Structure-Aware $H$-consistency and a corresponding objective (SA-DPO) that adapts the margin to the semantic distance between responses, preventing instability on near-synonymous pairs. Finally, we analyze the trade-off between the margin required for consistency and the model's finite capacity to satisfy it, revealing a strict hierarchy of surrogate losses: heavy-tailed surrogates (e.g., the Polynomial Hinge family) offer strictly superior consistency guarantees for capacity-bounded models compared to the logistic loss used in DPO. Experiments on UltraFeedback and Argilla DPO-Mix-7k confirm that SA-DPO consistently outperforms DPO and SimPO, with a 58.5% head-to-head win-rate in downstream generation quality.
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Beyond Tsybakov: Model Margin Noise and H-Consistency Bounds
The Nineteenth International Symposium on Artificial Intelligence and Mathematics (ISAIM 2026)
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We introduce a new low-noise condition for classification, the *Model Margin Noise (MM noise)* assumption, and derive enhanced $H$-consistency bounds under this condition. MM noise is *weaker* than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because it depends on the discrepancy between a given hypothesis and the Bayes-classifier rather than on the intrinsic distributional minimal margin (see Figure 1 for an illustration of an explicit example). This hypothesis-dependent assumption yields enhanced $H$-consistency bounds for both binary and multi-class classification. Our results extend the enhanced $H$-consistency bounds of Mao, Mohri, and Zhong (2025a) with the same favorable exponents but under a weaker assumption than the Tsybakov noise condition; they interpolate smoothly between linear and square-root regimes for intermediate noise levels. We also instantiate these bounds for common surrogate loss families and provide illustrative tables.
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Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates
Shengjie Zhu
Xiaoming Liu
Vincent Chu
International Conference on 3D Vision (2026)
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Structure-from-Motion (SfM) is a classical 3D vision task for recovering camera parameters and scene geometry from multi-view images. Recent advances in deep learning enable accurate monocular depth estimation (MDE) that infers structure from a single image without depending on camera motion. But integrating MDE into SfM remains challenging. Unlike classical triangulated sparse pointclouds, MDE produces dense depthmaps with significantly higher error variance. Inspired by modern RANSAC estimators, we propose a Marginalized Bundle Adjustment (MBA) to accommodate MDE error variance with its density. With MBA, we show that MDE depthmaps are sufficiently accurate to support SoTA or competitive results in Structure-from-Motion and camera relocalization. Our benchmark demonstrates consistent remarkable results from two-view, few-frames small multiview, to thousands-frames large multiview system. Our method highlights the significant potential of MDE on multi-view 3D vision tasks.
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In large-scale distributed enterprises, traditional Knowledge Management (KM) systems face a critical failure mode: static documentation cannot keep pace with evolving operational realities and regional nuances. This "knowledge latency" forces employees out of self-service workflows and into costly support ticketing queues. This paper introduces SENTINEL, a geo-contextual AI framework designed to shift enterprise support from reactive retrieval to proactive interception. The architecture employs a novel dual-engine system integrated into an omni-present interface. The first engine utilizes Large Language Models (LLMs) to conduct pre-emptive, historical case-grounded audits of documentation, generating a "Contextual Density" score that identifies friction zones. The second engine is an autonomous Retrieval-Augmented Generation (RAG) agent that surfaces in-situ via a location-intelligent assistant window, resolving queries in real-time. By functioning as a strategic "defensive barrier" at the point of origin, SENTINEL demonstrates how a proactive AI assistant can drive high-fidelity, in-situ case deflection.
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A Theoretical Framework for Modular Learning of Robust Generative Models
Proceedings of the 43rd International Conference on Machine Learning (ICML 2026)
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Training large-scale generative models is resource-intensive and relies heavily on heuristic dataset weighting. We address two fundamental questions: Can we train Large Language Models (LLMs) modularly, combining small, domain-specific experts to match monolithic performance, and can we do so robustly for any data mixture, eliminating heuristic tuning? We present a theoretical framework for modular generative modeling where a set of pre-trained experts are combined via a gating mechanism. We define the space of normalized gating functions $\mathcal{G}_{1}$ and formulate the problem as a minimax game to find a single robust gate that minimizes divergence to the worst-case data mixture. We prove the existence of such a robust gate using Kakutani's fixed-point theorem and show that modularity acts as a strong regularizer, with generalization bounds scaling with the lightweight gate's complexity. Furthermore, we prove that this modular approach can theoretically outperform models retrained on aggregate data, with the gap characterized by the Jensen-Shannon Divergence. Finally, we introduce a scalable Stochastic Primal-Dual algorithm and a Structural Distillation method for efficient inference. Empirical results on synthetic and real-world datasets confirm that our modular architecture effectively mitigates gradient conflict and can robustly outperform monolithic baselines.
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Julia's strength in mathematical computation and high performance makes it a popular choice across scientific fields, mostly due to its focus on mathematics in a broad sense and execution performance. It is a language of choice to implement new numerical algorithms, but it really shines in modelling for optimisation thanks to JuMP.jl and MathOptInterface.jl.
These libraries are, first and foremost, made for mathematical optimisation (linear, mixed-integer, conic, etc.), yet they are now generic enough to support more paradigms, such as constraint programming. This talk will introduce the basic principles behind the current implementation of JuMP.jl and explain why and how they are very good matches for modelling using constraint programming… and solving using any kind of mixed-integer-programming solver.
Constraint-programming solvers can also be implemented using linear programming, in a great collaboration between discrete and continuous optimisation. This talk will briefly explain the connection and its implementation in Google’s CP-SAT, a leading, award-winning constraint solver that uses linear programs in its solving process — a solver that will soon be available in Julia too.
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