Publications
Our teams aspire to make discoveries that impact everyone, and core to our approach is sharing our research and tools to fuel progress in the field.
Our teams aspire to make discoveries that impact everyone, and core to our approach is sharing our research and tools to fuel progress in the field.
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1 - 15 of 1451 publications
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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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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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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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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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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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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Geo experiment is a crucial, privacy-conscious option for measuring media effectiveness. Historically, two primary challenges have hindered the adoption of geo experiments: the high costs required to overcome large variance across geographical regions, and the unreliability of conventional analysis methods under real-world autocorrelation and non-stationary trends. To address these challenges, we introduce Meridian GeoX, Google’s open-source geo experiment framework. As a cornerstone of Google's modern measurement suite, Meridian GeoX is designed to standardize and optimize the end-to-end causal measurement lifecycle. The framework provides a unified suite of methodologies—including data-driven stratified sampling, advanced counterfactual models (Time-Based Regression, Synthetic Control, and Synthetic Difference-in-Differences), and a novel Design-Aware Placebo Inference engine. Extensive empirical benchmarking against industry alternatives demonstrates that Meridian GeoX delivers superior predictive accuracy, lowers Minimum Detectable Effects (MDE), and significantly reduces budget requirements. Furthermore, evaluations demonstrate that the framework's novel placebo inference maintains rigorous control over false positive rates while maximizing sensitivity under challenging conditions. By integrating seamlessly with the Meridian Marketing-Mix Model (MMM), this framework delivers a complete modern measurement solution. Ultimately, Meridian GeoX empowers advertisers with a powerful, cost-efficient, and methodologically robust solution for privacy-safe modern measurement, establishing a new industry standard for causal measurement and media effectiveness.
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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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Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of nonzero entries). A crucial property in applications is \emph{composability} of the sketching map, meaning that the sketch of a union of sets can be computed from individual sketches. Existing designs provide strong statistical guarantees, ensuring that a randomly sampled sketching map is accurate with high probability for a number of queries that is exponential in the sketch size $k$. However, these guarantees degrade to quadratic in $k$ when queries are adaptive, meaning they depend on previous responses.
Prior works on statistical queries (Steinke and Ullman, 2015) and specific MinHash cardinality sketches (Ahmadian and Cohen, 2024) established that this is tight in that they can be compromised using $\tilde{O}(k^2)$ adaptive queries. In this work, we develop a unified attack framework that applies to broad classes of cardinality sketches. We show that any union-composable sketching map can be compromised with $\tilde{O}(k^4)$ adaptive queries. Moreover, this improves to a tight bound of $\tilde{O}(k^2)$ for monotone composable maps (special cases include MinHash, statistical queries, Boolean linear maps), for any linear map over the reals $\mathbb{R}$ and finite fields $\mathbb{F}_p$, and for any linear map over the integers $\mathbb{Z}$ but when the estimator may only use the nonzero structure of the sketch (as in Cormode et al., 2003). Our work is the first to apply to general composable maps and establishes and builds on fundamental properties of these structures. Specifically for linear sketches, we are the first to establish tight quadratic bounds, to any subclass, and our bounds strengthen weaker polynomial bounds recently established by Gribelyuk et al. (2024).
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Regular-polygon geometry is tightly linked to cyclotomic arithmetic: Poonen and Rubinstein’s treatment of three-diagonal concurrence, for example, turns a geometric incidence condition into a short vanishing sum of roots of unity.
We prove an analogous rigidity result for areas. Two congruent crossing diagonals divide a regular n-gon into four regions. For the four regions cut out by the two congruent crossing diagonals V0Vm and VkVn−m+k of a regular n-gon, we completely classify, for all parameters (n, k, m), which sums of the normalized areas a0, . . . , a3 are rational. The classification has a sharp finite–infinite contrast: a0 is rational in only five configurations, whereas the rational cases for a2 and adjacent two-region sums form infinite families. Rationality is delicately sensitive to the parameters: for the configuration (14, 3, 5), no nontrivial subset sum is rational, while the neighboring cut (14, 4, 5) gives a2 = 5/7.
The proof reduces each rationality condition to trigonometric relations at rational multiples of π and combines cyclotomic norm arguments with the classification theorems of Conway–Jones and Poonen–Rubinstein.
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We analyze a balls-and-bins game against an adaptive adversary that sequentially deletes bins. Starting with n balls distributed across n bins, the adversary deletes a bin in each step, forcing the algorithm to redistribute its balls to surviving bins. We prove that after n/2 rounds, uniform random redistribution yields optimal O(n) recourse and $O(\frac{\log n}{\log \log n})$ maximum load. Furthermore, we show that applying the "power of two choices"' reduces the maximum load to $O(\log \log n)$ while maintaining linear recourse.
We also consider a variation of this game where the balls from the deleted bin are partitioned evenly among d<
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We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across $k$ sites while minimizing communication. The communication complexity of this problem is known to be $\Theta(\frac{k}{\eps}\log N)$ for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to $\Theta(\frac{\sqrt{k}}{\eps}\log N)$, but their analysis is restricted to the oblivious setting, where the stream of events is independent of the protocol's outputs.
Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a polylog(k) factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust?
We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of $O(\frac{\sqrt{k}}{\eps} \log N)$. Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.
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We study algorithms in the resettable streaming model, where the value of each key can either be increased or reset to zero. This model is suitable for applications such as active resource monitoring with support for deletions and machine unlearning. We show that all existing sketches for this model are vulnerable to adaptive adversarial attacks that apply even when the sketch size is polynomial in the length of the stream. To overcome these vulnerabilities, we present the first adaptively robust sketches for resettable streams that require only polylogarithmic space complexity in the stream length. Our framework supports (sub) linear statistics including $L_p$ moments for $p\in[0,1]$ (in particular, Cardinality and Sum) and Bernstein statistics. We bypass strong impossibility results known for linear and composable sketches by designing dedicated single-stream sketches robustified via Differential Privacy. Unlike standard robustification techniques, which provide limited benefits in this setting and still require polynomial space in the stream length, we leverage the Binary Tree Mechanism for continual observation to protect the sketch's internal randomness. This enables accurate prefix-max error guarantees with polylogarithmic space.
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This paper proposes RD-LoRA, a rate-distortion (R-D) optimized low-rank adaptation (LoRA) framework for neural post-filtering in the upcoming AV2 coding standard. RD-LoRA adapts a pre-trained base neural model to diverse input content via online updating of LoRA parameters, whose quantity is governed by the matrix ranks. The updated parameters are then quantized, transmitted to the decoder, and merged with the pre-trained weights for post-filtering. While more parameters generally improve coding performance, they also increase transmission bitrate.
To balance distortion reduction against transmission cost, we propose to dynamically allocate rank budget to each layer of the base model in a closed-loop R-D manner. Specifically, it incorporates a cost-aware importance assessment to discourage parameter-heavy updates, together with an RD-rank allocator to guide pruning based on global R-D optimization. To maintain robustness when certain layers are pruned to zero rank, we further introduce a lightweight fallback modulation mechanism. Experimental results show that, when deployed on a lightweight 25 kMACs ResNet model, RD-LoRA achieves a BD-rate reduction of 2.556% over the AV2 anchor, significantly outperforming the base model with only limited decoding overhead.
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