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
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Modern transformers have been scaled up in size, data, training-time compute, and more recently test-time compute based on Chain-of-Thought (CoT), but the consequences of trading off these parameters are unknown. We construct explicit tradeoffs between two of these aspects: the number of layers in a transformer and the number of CoT tokens. Our first result is general: with mild assumptions and a single-token prompt, for any integer k, a transformer using soft attention and SwiGLU MLP layers with L layers and n CoT tokens can be converted to a transformer with at most ckL layers and ⌈n/k⌉ CoT tokens, and vice versa, although with an increase to the size of other parameters. We then a multi-token prompt path following task, finding that additional preprocessing from the multi-token prompt changes the depth-CoT relationship in this case. We construct an attention-only network with L layers and 2^(L−2) heads that can traverse 2^(L−1) − 1 edges along a path with a single CoT token, demonstrating at least an exponential relationship between increases in depth and reductions in the number of CoT tokens needed to traverse the entire path. This relationship for the path following task holds empirically as well, as demonstrated by training networks with up to 5 layers, with the tradeoff between depth and the maximum number of edge traversals in a single CoT token exactly matching our theoretical constructions.
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Surviving the perfect storm: how hardware PMs can beat the AI tax and trade tariffs
Mind The Product (2026)
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This piece analyzes how hardware product managers can navigate the financial pressure of AI-related costs and trade tariffs. It presents a practical framework for deploying the Joint Development Model (JDM) as a product development strategy to balance innovation with cost efficiency, enabling sustainable growth for next-generation AI-native consumer devices.
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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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Cardio Load in exercise and everyday life: A modified TRIMP metric for continuously-sensing consumer wearables
Justin Phillips
YongSuk Cho
Robert Harle
Medicine & Science in Sports & Exercise (2026)
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PURPOSE: To introduce Cardio Load (CL), a metric quantifying cardiovascular work from all activities across the day, and to investigate its distribution by age, gender, and workout profiles. CL adapts the Training Impulse (TRIMP) model by leveraging continuous heart rate and movement data from wearables, enabling minute-level intensity estimation. We also discuss the derivation of weekly target loads, intended to guide fitness maintenance.
METHODS: A retrospective analysis was conducted on 31.2 million hours of wrist-worn wearable data collected over a six-week period. The dataset comprised a 40,000-subject subset (37.9% female) of consenting Google Pixel Watch® users in the United States, aged 18 to 80 years (18-39: 41.8%, 40-59: 43.5%, 60+: 14.6%). Measured data included minute-interval heart rate averages, resting and maximum heart rates, minute-interval averaged accelerometer log energy, and manually-logged or auto-detected activity types. Cardio Load scores and target loads were calculated daily for each subject and compared across age and gender. We also compared the proportions of CL gained during workouts and incidental daily activities for these groups.
RESULTS: Overall, the study population's mean ± SD weekly CL scores were 221 ± 156 (female) and 259 ± 169 (male). Median weekly Cardio Load (CL) values exhibited consistency for individuals between 30 and 75 years of age. When analyzed in five-year age groups, the coefficient of variation (CV%) of median weekly CL values within this age range was less than 4.5%, with younger and older subjects demonstrating higher and lower median CL, respectively. The median proportion of CL accumulated during structured workouts versus incidental daily activity was 41.0% (female) and 49.0% (male) for all subjects, though this varied considerably with average weekly workout duration. CV% of weekly target load and daily target load over 6 weeks was 23.6% and 35.2% respectively.
CONCLUSION: Cardio Load provides a continuous quantification of activity load from wearables, acknowledging both structured workouts and everydayincidental activity. CL is equitably rewarded for age ranges spanning 30-75 years. Weekly target loads were found to have little measurement variability and be more consistent and, consequently, more practical for planning training and physical activity than daily targets.
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A simple and efficient implementation of strong call by need by an abstract machine
Małgorzata Biernacka
Witold Charatonik
Journal of Functional Programming, Volume 36 (2026)
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We present an abstract machine for a strong call-by-need strategy in the lambda calculus. The machine has been derived automatically from a higher-order evaluator that uses the technique of memothunks to implement laziness. The derivation has been done with the use of an off-the-shelf transformation tool implementing the "functional correspondence" between higher-order interpreters and abstract machines, and it yields a simple and concise description of the machine. We prove that the resulting machine conservatively extends the lazy version of Krivine machine for the weak call-by-need strategy, and that it simulates the normal-order strategy in bilinear number of steps.
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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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