13.6LGJun 3, 2022
Adversarial Unlearning: Reducing Confidence Along Adversarial DirectionsAmrith Setlur, Benjamin Eysenbach, Virginia Smith et al. · cmu
Supervised learning methods trained with maximum likelihood objectives often overfit on training data. Most regularizers that prevent overfitting look to increase confidence on additional examples (e.g., data augmentation, adversarial training), or reduce it on training data (e.g., label smoothing). In this work we propose a complementary regularization strategy that reduces confidence on self-generated examples. The method, which we call RCAD (Reducing Confidence along Adversarial Directions), aims to reduce confidence on out-of-distribution examples lying along directions adversarially chosen to increase training loss. In contrast to adversarial training, RCAD does not try to robustify the model to output the original label, but rather regularizes it to have reduced confidence on points generated using much larger perturbations than in conventional adversarial training. RCAD can be easily integrated into training pipelines with a few lines of code. Despite its simplicity, we find on many classification benchmarks that RCAD can be added to existing techniques (e.g., label smoothing, MixUp training) to increase test accuracy by 1-3% in absolute value, with more significant gains in the low data regime. We also provide a theoretical analysis that helps to explain these benefits in simplified settings, showing that RCAD can provably help the model unlearn spurious features in the training data.
Bitrate-Constrained DRO: Beyond Worst Case Robustness To Unknown Group ShiftsAmrith Setlur, Don Dennis, Benjamin Eysenbach et al. · cmu
Training machine learning models robust to distribution shifts is critical for real-world applications. Some robust training algorithms (e.g., Group DRO) specialize to group shifts and require group information on all training points. Other methods (e.g., CVaR DRO) that do not need group annotations can be overly conservative, since they naively upweight high loss points which may form a contrived set that does not correspond to any meaningful group in the real world (e.g., when the high loss points are randomly mislabeled training points). In this work, we address limitations in prior approaches by assuming a more nuanced form of group shift: conditioned on the label, we assume that the true group function (indicator over group) is simple. For example, we may expect that group shifts occur along low bitrate features (e.g., image background, lighting). Thus, we aim to learn a model that maintains high accuracy on simple group functions realized by these low bitrate features, that need not spend valuable model capacity achieving high accuracy on contrived groups of examples. Based on this, we consider the two-player game formulation of DRO where the adversary's capacity is bitrate-constrained. Our resulting practical algorithm, Bitrate-Constrained DRO (BR-DRO), does not require group information on training samples yet matches the performance of Group DRO on datasets that have training group annotations and that of CVaR DRO on long-tailed distributions. Our theoretical analysis reveals that in some settings BR-DRO objective can provably yield statistically efficient and less conservative solutions than unconstrained CVaR DRO.
On Privacy and Personalization in Cross-Silo Federated LearningZiyu Liu, Shengyuan Hu, Zhiwei Steven Wu et al. · stanford
While the application of differential privacy (DP) has been well-studied in cross-device federated learning (FL), there is a lack of work considering DP and its implications for cross-silo FL, a setting characterized by a limited number of clients each containing many data subjects. In cross-silo FL, usual notions of client-level DP are less suitable as real-world privacy regulations typically concern the in-silo data subjects rather than the silos themselves. In this work, we instead consider an alternative notion of silo-specific sample-level DP, where silos set their own privacy targets for their local examples. Under this setting, we reconsider the roles of personalization in federated learning. In particular, we show that mean-regularized multi-task learning (MR-MTL), a simple personalization framework, is a strong baseline for cross-silo FL: under stronger privacy requirements, silos are incentivized to federate more with each other to mitigate DP noise, resulting in consistent improvements relative to standard baseline methods. We provide an empirical study of competing methods as well as a theoretical characterization of MR-MTL for mean estimation, highlighting the interplay between privacy and cross-silo data heterogeneity. Our work serves to establish baselines for private cross-silo FL as well as identify key directions of future work in this area.
Differentially Private Adaptive Optimization with Delayed PreconditionersTian Li, Manzil Zaheer, Ken Ziyu Liu et al. · cmu, stanford
Privacy noise may negate the benefits of using adaptive optimizers in differentially private model training. Prior works typically address this issue by using auxiliary information (e.g., public data) to boost the effectiveness of adaptive optimization. In this work, we explore techniques to estimate and efficiently adapt to gradient geometry in private adaptive optimization without auxiliary data. Motivated by the observation that adaptive methods can tolerate stale preconditioners, we propose differentially private adaptive training with delayed preconditioners (DP^2), a simple method that constructs delayed but less noisy preconditioners to better realize the benefits of adaptivity. Theoretically, we provide convergence guarantees for our method for both convex and non-convex problems, and analyze trade-offs between delay and privacy noise reduction. Empirically, we explore DP^2 across several real-world datasets, demonstrating that it can improve convergence speed by as much as 4x relative to non-adaptive baselines and match the performance of state-of-the-art optimization methods that require auxiliary data.
Variance-Reduced Gradient Estimation via Noise-Reuse in Online Evolution StrategiesOscar Li, James Harrison, Jascha Sohl-Dickstein et al. · anthropic, cmu
Unrolled computation graphs are prevalent throughout machine learning but present challenges to automatic differentiation (AD) gradient estimation methods when their loss functions exhibit extreme local sensitivtiy, discontinuity, or blackbox characteristics. In such scenarios, online evolution strategies methods are a more capable alternative, while being more parallelizable than vanilla evolution strategies (ES) by interleaving partial unrolls and gradient updates. In this work, we propose a general class of unbiased online evolution strategies methods. We analytically and empirically characterize the variance of this class of gradient estimators and identify the one with the least variance, which we term Noise-Reuse Evolution Strategies (NRES). Experimentally, we show NRES results in faster convergence than existing AD and ES methods in terms of wall-clock time and number of unroll steps across a variety of applications, including learning dynamical systems, meta-training learned optimizers, and reinforcement learning.
21.9LGJun 18, 2022
Motley: Benchmarking Heterogeneity and Personalization in Federated LearningShanshan Wu, Tian Li, Zachary Charles et al. · cmu, stanford
Personalized federated learning considers learning models unique to each client in a heterogeneous network. The resulting client-specific models have been purported to improve metrics such as accuracy, fairness, and robustness in federated networks. However, despite a plethora of work in this area, it remains unclear: (1) which personalization techniques are most effective in various settings, and (2) how important personalization truly is for realistic federated applications. To better answer these questions, we propose Motley, a benchmark for personalized federated learning. Motley consists of a suite of cross-device and cross-silo federated datasets from varied problem domains, as well as thorough evaluation metrics for better understanding the possible impacts of personalization. We establish baselines on the benchmark by comparing a number of representative personalized federated learning methods. These initial results highlight strengths and weaknesses of existing approaches, and raise several open questions for the community. Motley aims to provide a reproducible means with which to advance developments in personalized and heterogeneity-aware federated learning, as well as the related areas of transfer learning, meta-learning, and multi-task learning.
7.8LGMay 30, 2022
Maximizing Global Model Appeal in Federated LearningYae Jee Cho, Divyansh Jhunjhunwala, Tian Li et al. · cmu
Federated learning typically considers collaboratively training a global model using local data at edge clients. Clients may have their own individual requirements, such as having a minimal training loss threshold, which they expect to be met by the global model. However, due to client heterogeneity, the global model may not meet each client's requirements, and only a small subset may find the global model appealing. In this work, we explore the problem of the global model lacking appeal to the clients due to not being able to satisfy local requirements. We propose MaxFL, which aims to maximize the number of clients that find the global model appealing. We show that having a high global model appeal is important to maintain an adequate pool of clients for training, and can directly improve the test accuracy on both seen and unseen clients. We provide convergence guarantees for MaxFL and show that MaxFL achieves a $22$-$40\%$ and $18$-$50\%$ test accuracy improvement for the training clients and unseen clients respectively, compared to a wide range of FL modeling approaches, including those that tackle data heterogeneity, aim to incentivize clients, and learn personalized or fair models.
13.0LGMar 18, 2022
Fair Federated Learning via Bounded Group LossShengyuan Hu, Zhiwei Steven Wu, Virginia Smith
Fair prediction across protected groups is an important constraint for many federated learning applications. However, prior work studying group fair federated learning lacks formal convergence or fairness guarantees. In this work we propose a general framework for provably fair federated learning. In particular, we explore and extend the notion of Bounded Group Loss as a theoretically-grounded approach for group fairness. Using this setup, we propose a scalable federated optimization method that optimizes the empirical risk under a number of group fairness constraints. We provide convergence guarantees for the method as well as fairness guarantees for the resulting solution. Empirically, we evaluate our method across common benchmarks from fair ML and federated learning, showing that it can provide both fairer and more accurate predictions than baseline approaches.
On Noisy Evaluation in Federated Hyperparameter TuningKevin Kuo, Pratiksha Thaker, Mikhail Khodak et al.
Hyperparameter tuning is critical to the success of federated learning applications. Unfortunately, appropriately selecting hyperparameters is challenging in federated networks. Issues of scale, privacy, and heterogeneity introduce noise in the tuning process and make it difficult to evaluate the performance of various hyperparameters. In this work, we perform the first systematic study on the effect of noisy evaluation in federated hyperparameter tuning. We first identify and rigorously explore key sources of noise, including client subsampling, data and systems heterogeneity, and data privacy. Surprisingly, our results indicate that even small amounts of noise can significantly impact tuning methods-reducing the performance of state-of-the-art approaches to that of naive baselines. To address noisy evaluation in such scenarios, we propose a simple and effective approach that leverages public proxy data to boost the evaluation signal. Our work establishes general challenges, baselines, and best practices for future work in federated hyperparameter tuning.
16.4LGJul 2, 2024
Agreement-Based Cascading for Efficient InferenceSteven Kolawole, Don Dennis, Ameet Talwalkar et al.
Adaptive inference schemes reduce the cost of machine learning inference by assigning smaller models to easier examples, attempting to avoid invocation of larger models when possible. In this work we explore a simple, effective adaptive inference technique we term Agreement-Based Cascading (ABC). ABC builds a cascade of models of increasing size/complexity, and uses agreement between ensembles of models at each level of the cascade as a basis for data-dependent routing. Although ensemble execution introduces additional expense, we show that these costs can be easily offset in practice due to large expected differences in model sizes, parallel inference execution capabilities, and accuracy benefits of ensembling. We examine ABC theoretically and empirically in terms of these parameters, showing that the approach can reliably act as a drop-in replacement for existing models and surpass the best single model it aims to replace in terms of both efficiency and accuracy. Additionally, we explore the performance of ABC relative to existing cascading methods in three common scenarios: (1) edge-to-cloud inference, where ABC reduces communication costs by up to 14x; (2) cloud-based model serving, where it achieves a 3x reduction in rental costs; and (3) inference via model API services, where ABC achieves a 2-25x reduction in average price per token/request relative to state-of-the-art LLM cascades.
6.6LGFeb 16, 2023
Federated Learning as a Network Effects GameShengyuan Hu, Dung Daniel Ngo, Shuran Zheng et al.
Federated Learning (FL) aims to foster collaboration among a population of clients to improve the accuracy of machine learning without directly sharing local data. Although there has been rich literature on designing federated learning algorithms, most prior works implicitly assume that all clients are willing to participate in a FL scheme. In practice, clients may not benefit from joining in FL, especially in light of potential costs related to issues such as privacy and computation. In this work, we study the clients' incentives in federated learning to help the service provider design better solutions and ensure clients make better decisions. We are the first to model clients' behaviors in FL as a network effects game, where each client's benefit depends on other clients who also join the network. Using this setup we analyze the dynamics of clients' participation and characterize the equilibrium, where no client has incentives to alter their decision. Specifically, we show that dynamics in the population naturally converge to equilibrium without needing explicit interventions. Finally, we provide a cost-efficient payment scheme that incentivizes clients to reach a desired equilibrium when the initial network is empty.
Validating Large Language Models with ReLMMichael Kuchnik, Virginia Smith, George Amvrosiadis
Although large language models (LLMs) have been touted for their ability to generate natural-sounding text, there are growing concerns around possible negative effects of LLMs such as data memorization, bias, and inappropriate language. Unfortunately, the complexity and generation capacities of LLMs make validating (and correcting) such concerns difficult. In this work, we introduce ReLM, a system for validating and querying LLMs using standard regular expressions. ReLM formalizes and enables a broad range of language model evaluations, reducing complex evaluation rules to simple regular expression queries. Our results exploring queries surrounding memorization, gender bias, toxicity, and language understanding show that ReLM achieves up to 15x higher system efficiency, 2.5x data efficiency, and increased statistical and prompt-tuning coverage compared to state-of-the-art ad-hoc queries. ReLM offers a competitive and general baseline for the increasingly important problem of LLM validation.
6.6LGFeb 20, 2023
Progressive Ensemble Distillation: Building Ensembles for Efficient InferenceDon Kurian Dennis, Abhishek Shetty, Anish Sevekari et al.
We study the problem of progressive ensemble distillation: Given a large, pretrained teacher model $g$, we seek to decompose the model into smaller, low-inference cost student models $f_i$, such that progressively evaluating additional models in this ensemble leads to improved predictions. The resulting ensemble allows for flexibly tuning accuracy vs. inference cost at runtime, which is useful for a number of applications in on-device inference. The method we propose, B-DISTIL , relies on an algorithmic procedure that uses function composition over intermediate activations to construct expressive ensembles with similar performance as $g$ , but with smaller student models. We demonstrate the effectiveness of B-DISTIL by decomposing pretrained models across standard image, speech, and sensor datasets. We also provide theoretical guarantees in terms of convergence and generalization.
Grass: Compute Efficient Low-Memory LLM Training with Structured Sparse GradientsAashiq Muhamed, Oscar Li, David Woodruff et al.
Large language model (LLM) training and finetuning are often bottlenecked by limited GPU memory. While existing projection-based optimization methods address this by projecting gradients into a lower-dimensional subspace to reduce optimizer state memory, they typically rely on dense projection matrices, which can introduce computational and memory overheads. In this work, we propose Grass (GRAdient Stuctured Sparsification), a novel approach that leverages sparse projections to transform gradients into structured sparse updates. This design not only significantly reduces memory usage for optimizer states but also minimizes gradient memory footprint, computation, and communication costs, leading to substantial throughput improvements. Extensive experiments on pretraining and finetuning tasks demonstrate that Grass achieves competitive performance to full-rank training and existing projection-based methods. Notably, Grass enables half-precision pretraining of a 13B parameter LLaMA model on a single 40GB A100 GPU--a feat infeasible for previous methods--and yields up to a $2\times$ throughput improvement on an 8-GPU system. Code can be found at https://github.com/aashiqmuhamed/GRASS .
LEAF: A Benchmark for Federated SettingsSebastian Caldas, Sai Meher Karthik Duddu, Peter Wu et al.
Modern federated networks, such as those comprised of wearable devices, mobile phones, or autonomous vehicles, generate massive amounts of data each day. This wealth of data can help to learn models that can improve the user experience on each device. However, the scale and heterogeneity of federated data presents new challenges in research areas such as federated learning, meta-learning, and multi-task learning. As the machine learning community begins to tackle these challenges, we are at a critical time to ensure that developments made in these areas are grounded with realistic benchmarks. To this end, we propose LEAF, a modular benchmarking framework for learning in federated settings. LEAF includes a suite of open-source federated datasets, a rigorous evaluation framework, and a set of reference implementations, all geared towards capturing the obstacles and intricacies of practical federated environments.
Everybody Prune Now: Structured Pruning of LLMs with only Forward PassesLucio Dery, Steven Kolawole, Jean-François Kagy et al.
Structured pruning is a promising approach to create smaller, faster LLMs. However, existing methods typically rely on backward passes, which can inflate memory requirements and compute costs. In this work we introduce Bonsai, a gradient-free structured pruning method that eliminates the need for backpropagation, significantly reducing memory requirements and compute costs while achieving state-of-the-art pruning performance. Bonsai uses forward-pass-only perturbative pruning to enable efficient compression of large models on a broader range of hardware configurations. Unlike existing structured pruning approaches, Bonsai not only achieves better compression with fewer resources, but also produces models that are twice as fast as those generated by semi-structured pruning. As a concrete demonstration, we use Bonsai to prune an 8B LLaMA-3 model to 50% sparsity on a single A6000 GPU -- a task infeasible with backprop-based methods, which require 2-3x memory. Our results show that removing backprop as a requirement not only enables pruning larger models on constrained hardware but can also lead to state-of-the-art efficiency and performance.
36.6LGJun 10, 2025
e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMsAmrith Setlur, Matthew Y. R. Yang, Charlie Snell et al. · cmu
Test-time scaling offers a promising path to improve LLM reasoning by utilizing more compute at inference time; however, the true promise of this paradigm lies in extrapolation (i.e., improvement in performance on hard problems as LLMs keep "thinking" for longer, beyond the maximum token budget they were trained on). Surprisingly, we find that most existing reasoning models do not extrapolate well. We show that one way to enable extrapolation is by training the LLM to perform in-context exploration: training the LLM to effectively spend its test time budget by chaining operations (such as generation, verification, refinement, etc.), or testing multiple hypotheses before it commits to an answer. To enable in-context exploration, we identify three key ingredients as part of our recipe e3: (1) chaining skills that the base LLM has asymmetric competence in, e.g., chaining verification (easy) with generation (hard), as a way to implement in-context search; (2) leveraging "negative" gradients from incorrect traces to amplify exploration during RL, resulting in longer search traces that chains additional asymmetries; and (3) coupling task difficulty with training token budget during training via a specifically-designed curriculum to structure in-context exploration. Our recipe e3 produces the best known 1.7B model according to AIME'25 and HMMT'25 scores, and extrapolates to 2x the training token budget. Our e3-1.7B model not only attains high pass@1 scores, but also improves pass@k over the base model.
22.0LGApr 11, 2025
SAEs $\textit{Can}$ Improve Unlearning: Dynamic Sparse Autoencoder Guardrails for Precision Unlearning in LLMsAashiq Muhamed, Jacopo Bonato, Mona Diab et al.
Machine unlearning is a promising approach to improve LLM safety by removing unwanted knowledge from the model. However, prevailing gradient-based unlearning methods suffer from issues such as high computational costs, hyperparameter instability, poor sequential unlearning capability, vulnerability to relearning attacks, low data efficiency, and lack of interpretability. While Sparse Autoencoders are well-suited to improve these aspects by enabling targeted activation-based unlearning, prior approaches underperform gradient-based methods. This work demonstrates that, contrary to these earlier findings, SAEs can significantly improve unlearning when employed dynamically. We introduce $\textbf{Dynamic DAE Guardrails}$ (DSG), a novel method for precision unlearning that leverages principled feature selection and a dynamic classifier. Our experiments show DSG substantially outperforms leading unlearning methods, achieving superior forget-utility trade-offs. DSG addresses key drawbacks of gradient-based approaches for unlearning -- offering enhanced computational efficiency and stability, robust performance in sequential unlearning, stronger resistance to relearning attacks, better data efficiency including zero-shot settings, and more interpretable unlearning.
22.6LGApr 6, 2025
Exact Unlearning of Finetuning Data via Model Merging at ScaleKevin Kuo, Amrith Setlur, Kartik Srinivas et al. · cmu
Approximate unlearning has gained popularity as an approach to efficiently update an LLM so that it behaves (roughly) as if it was not trained on a subset of data to begin with. However, existing methods are brittle in practice and can easily be attacked to reveal supposedly unlearned information. To alleviate issues with approximate unlearning, we instead propose SIFT-Masks (SIgn-Fixed Tuning-Masks), an exact unlearning method based on model merging. SIFT-Masks addresses two key limitations of standard model merging: (1) merging a large number of tasks can severely harm utility; and (2) methods that boost utility by sharing extra information across tasks make exact unlearning prohibitively expensive. SIFT-Masks solves these issues by (1) applying local masks to recover task-specific performance; and (2) constraining finetuning to align with a global sign vector as a lightweight approach to determine masks independently before merging. Across four settings where we merge up to 500 models, SIFT-Masks improves accuracy by 5-80% over naive merging and uses up to 250x less compute for exact unlearning compared to other merging baselines.
8.8LGDec 6, 2023
Complementary Benefits of Contrastive Learning and Self-Training Under Distribution ShiftSaurabh Garg, Amrith Setlur, Zachary Chase Lipton et al. · cmu
Self-training and contrastive learning have emerged as leading techniques for incorporating unlabeled data, both under distribution shift (unsupervised domain adaptation) and when it is absent (semi-supervised learning). However, despite the popularity and compatibility of these techniques, their efficacy in combination remains unexplored. In this paper, we undertake a systematic empirical investigation of this combination, finding that (i) in domain adaptation settings, self-training and contrastive learning offer significant complementary gains; and (ii) in semi-supervised learning settings, surprisingly, the benefits are not synergistic. Across eight distribution shift datasets (e.g., BREEDs, WILDS), we demonstrate that the combined method obtains 3--8% higher accuracy than either approach independently. We then theoretically analyze these techniques in a simplified model of distribution shift, demonstrating scenarios under which the features produced by contrastive learning can yield a good initialization for self-training to further amplify gains and achieve optimal performance, even when either method alone would fail.
23.1LGNov 1, 2024
Decoding Dark Matter: Specialized Sparse Autoencoders for Interpreting Rare Concepts in Foundation ModelsAashiq Muhamed, Mona Diab, Virginia Smith
Understanding and mitigating the potential risks associated with foundation models (FMs) hinges on developing effective interpretability methods. Sparse Autoencoders (SAEs) have emerged as a promising tool for disentangling FM representations, but they struggle to capture rare, yet crucial concepts in the data. We introduce Specialized Sparse Autoencoders (SSAEs), designed to illuminate these elusive dark matter features by focusing on specific subdomains. We present a practical recipe for training SSAEs, demonstrating the efficacy of dense retrieval for data selection and the benefits of Tilted Empirical Risk Minimization as a training objective to improve concept recall. Our evaluation of SSAEs on standard metrics, such as downstream perplexity and $L_0$ sparsity, show that they effectively capture subdomain tail concepts, exceeding the capabilities of general-purpose SAEs. We showcase the practical utility of SSAEs in a case study on the Bias in Bios dataset, where SSAEs achieve a 12.5\% increase in worst-group classification accuracy when applied to remove spurious gender information. SSAEs provide a powerful new lens for peering into the inner workings of FMs in subdomains.
8.8LGDec 24, 2023
On the Benefits of Public Representations for Private Transfer Learning under Distribution ShiftPratiksha Thaker, Amrith Setlur, Zhiwei Steven Wu et al. · cmu
Public pretraining is a promising approach to improve differentially private model training. However, recent work has noted that many positive research results studying this paradigm only consider in-distribution tasks, and may not apply to settings where there is distribution shift between the pretraining and finetuning data -- a scenario that is likely when finetuning private tasks due to the sensitive nature of the data. In this work, we show empirically across three tasks that even in settings with large distribution shift, where both zero-shot performance from public data and training from scratch with private data give unusably weak results, public features can in fact improve private training accuracy by up to 67\% over private training from scratch. We provide a theoretical explanation for this phenomenon, showing that if the public and private data share a low-dimensional representation, public representations can improve the sample complexity of private training even if it is impossible to learn the private task from the public data alone. Altogether, our results provide evidence that public data can indeed make private training practical in realistic settings of extreme distribution shift.
10.4LGMar 6, 2024
Many-Objective Multi-Solution TransportZiyue Li, Tian Li, Virginia Smith et al.
Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on a few number of objectives and cannot scale to many objectives that outnumber the solutions, leading to either subpar performance or ignored objectives. We introduce Many-objective multi-solution Transport (MosT), a framework that finds multiple diverse solutions in the Pareto front of many objectives. Our insight is to seek multiple solutions, each performing as a domain expert and focusing on a specific subset of objectives while collectively covering all of them. MosT formulates the problem as a bi-level optimization of weighted objectives for each solution, where the weights are defined by an optimal transport between the objectives and solutions. Our algorithm ensures convergence to Pareto stationary solutions for complementary subsets of objectives. On a range of applications in federated learning, multi-task learning, and mixture-of-prompt learning for LLMs, MosT distinctly outperforms strong baselines, delivering high-quality, diverse solutions that profile the entire Pareto frontier, thus ensuring balanced trade-offs across many objectives.
6.4LGNov 6, 2024
NeurIPS 2023 Competition: Privacy Preserving Federated Learning Document VQAMarlon Tobaben, Mohamed Ali Souibgui, Rubèn Tito et al.
The Privacy Preserving Federated Learning Document VQA (PFL-DocVQA) competition challenged the community to develop provably private and communication-efficient solutions in a federated setting for a real-life use case: invoice processing. The competition introduced a dataset of real invoice documents, along with associated questions and answers requiring information extraction and reasoning over the document images. Thereby, it brings together researchers and expertise from the document analysis, privacy, and federated learning communities. Participants fine-tuned a pre-trained, state-of-the-art Document Visual Question Answering model provided by the organizers for this new domain, mimicking a typical federated invoice processing setup. The base model is a multi-modal generative language model, and sensitive information could be exposed through either the visual or textual input modality. Participants proposed elegant solutions to reduce communication costs while maintaining a minimum utility threshold in track 1 and to protect all information from each document provider using differential privacy in track 2. The competition served as a new testbed for developing and testing private federated learning methods, simultaneously raising awareness about privacy within the document image analysis and recognition community. Ultimately, the competition analysis provides best practices and recommendations for successfully running privacy-focused federated learning challenges in the future.
4.2CRMar 7, 2024
Privacy Amplification for the Gaussian Mechanism via Bounded SupportShengyuan Hu, Saeed Mahloujifar, Virginia Smith et al.
Data-dependent privacy accounting frameworks such as per-instance differential privacy (pDP) and Fisher information loss (FIL) confer fine-grained privacy guarantees for individuals in a fixed training dataset. These guarantees can be desirable compared to vanilla DP in real world settings as they tightly upper-bound the privacy leakage for a $\textit{specific}$ individual in an $\textit{actual}$ dataset, rather than considering worst-case datasets. While these frameworks are beginning to gain popularity, to date, there is a lack of private mechanisms that can fully leverage advantages of data-dependent accounting. To bridge this gap, we propose simple modifications of the Gaussian mechanism with bounded support, showing that they amplify privacy guarantees under data-dependent accounting. Experiments on model training with DP-SGD show that using bounded support Gaussian mechanisms can provide a reduction of the pDP bound $ε$ by as much as 30% without negative effects on model utility.
RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-FoldAmrith Setlur, Saurabh Garg, Xinyang Geng et al.
Training on model-generated synthetic data is a promising approach for finetuning LLMs, but it remains unclear when it helps or hurts. In this paper, we investigate this question for math reasoning via an empirical study, followed by building a conceptual understanding of our observations. First, we find that while the typical approach of finetuning a model on synthetic correct or positive problem-solution pairs generated by capable models offers modest performance gains, sampling more correct solutions from the finetuned learner itself followed by subsequent fine-tuning on this self-generated data $\textbf{doubles}$ the efficiency of the same synthetic problems. At the same time, training on model-generated positives can amplify various spurious correlations, resulting in flat or even inverse scaling trends as the amount of data increases. Surprisingly, we find that several of these issues can be addressed if we also utilize negative responses, i.e., model-generated responses that are deemed incorrect by a final answer verifier. Crucially, these negatives must be constructed such that the training can appropriately recover the utility or advantage of each intermediate step in the negative response. With this per-step scheme, we are able to attain consistent gains over only positive data, attaining performance similar to amplifying the amount of synthetic data by $\mathbf{8 \times}$. We show that training on per-step negatives can help to unlearn spurious correlations in the positive data, and is equivalent to advantage-weighted reinforcement learning (RL), implying that it inherits robustness benefits of RL over imitating positive data alone.
Private Adaptive Optimization with Side InformationTian Li, Manzil Zaheer, Sashank J. Reddi et al.
Adaptive optimization methods have become the default solvers for many machine learning tasks. Unfortunately, the benefits of adaptivity may degrade when training with differential privacy, as the noise added to ensure privacy reduces the effectiveness of the adaptive preconditioner. To this end, we propose AdaDPS, a general framework that uses non-sensitive side information to precondition the gradients, allowing the effective use of adaptive methods in private settings. We formally show AdaDPS reduces the amount of noise needed to achieve similar privacy guarantees, thereby improving optimization performance. Empirically, we leverage simple and readily available side information to explore the performance of AdaDPS in practice, comparing to strong baselines in both centralized and federated settings. Our results show that AdaDPS improves accuracy by 7.7% (absolute) on average -- yielding state-of-the-art privacy-utility trade-offs on large-scale text and image benchmarks.
Plumber: Diagnosing and Removing Performance Bottlenecks in Machine Learning Data PipelinesMichael Kuchnik, Ana Klimovic, Jiri Simsa et al.
Input pipelines, which ingest and transform input data, are an essential part of training Machine Learning (ML) models. However, it is challenging to implement efficient input pipelines, as it requires reasoning about parallelism, asynchrony, and variability in fine-grained profiling information. Our analysis of over two million ML jobs in Google datacenters reveals that a significant fraction of model training jobs could benefit from faster input data pipelines. At the same time, our analysis indicates that most jobs do not saturate host hardware, pointing in the direction of software-based bottlenecks. Motivated by these findings, we propose Plumber, a tool for finding bottlenecks in ML input pipelines. Plumber uses an extensible and interpretable operational analysis analytical model to automatically tune parallelism, prefetching, and caching under host resource constraints. Across five representative ML pipelines, Plumber obtains speedups of up to 47x for misconfigured pipelines. By automating caching, Plumber obtains end-to-end speedups of over 50% compared to state-of-the-art tuners.
On Tilted Losses in Machine Learning: Theory and ApplicationsTian Li, Ahmad Beirami, Maziar Sanjabi et al.
Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen widespread use in machine learning. In this work, we aim to bridge this gap by exploring the use of tilting in risk minimization. We study a simple extension to ERM -- tilted empirical risk minimization (TERM) -- which uses exponential tilting to flexibly tune the impact of individual losses. The resulting framework has several useful properties: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to the tail probability of losses. Our work makes rigorous connections between TERM and related objectives, such as Value-at-Risk, Conditional Value-at-Risk, and distributionally robust optimization (DRO). We develop batch and stochastic first-order optimization methods for solving TERM, provide convergence guarantees for the solvers, and show that the framework can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications in machine learning, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. Despite the straightforward modification TERM makes to traditional ERM objectives, we find that the framework can consistently outperform ERM and deliver competitive performance with state-of-the-art, problem-specific approaches.
Private Multi-Task Learning: Formulation and Applications to Federated LearningShengyuan Hu, Zhiwei Steven Wu, Virginia Smith
Many problems in machine learning rely on multi-task learning (MTL), in which the goal is to solve multiple related machine learning tasks simultaneously. MTL is particularly relevant for privacy-sensitive applications in areas such as healthcare, finance, and IoT computing, where sensitive data from multiple, varied sources are shared for the purpose of learning. In this work, we formalize notions of client-level privacy for MTL via joint differential privacy (JDP), a relaxation of differential privacy for mechanism design and distributed optimization. We then propose an algorithm for mean-regularized MTL, an objective commonly used for applications in personalized federated learning, subject to JDP. We analyze our objective and solver, providing certifiable guarantees on both privacy and utility. Empirically, we find that our method provides improved privacy/utility trade-offs relative to global baselines across common federated learning benchmarks.
A Field Guide to Federated OptimizationJianyu Wang, Zachary Charles, Zheng Xu et al.
Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compatibility with privacy and system requirements, and other constraints that are not primary considerations in other problem settings. This paper provides recommendations and guidelines on formulating, designing, evaluating and analyzing federated optimization algorithms through concrete examples and practical implementation, with a focus on conducting effective simulations to infer real-world performance. The goal of this work is not to survey the current literature, but to inspire researchers and practitioners to design federated learning algorithms that can be used in various practical applications.
25.0LGJun 15, 2021
On Large-Cohort Training for Federated LearningZachary Charles, Zachary Garrett, Zhouyuan Huo et al.
Federated learning methods typically learn a model by iteratively sampling updates from a population of clients. In this work, we explore how the number of clients sampled at each round (the cohort size) impacts the quality of the learned model and the training dynamics of federated learning algorithms. Our work poses three fundamental questions. First, what challenges arise when trying to scale federated learning to larger cohorts? Second, what parallels exist between cohort sizes in federated learning and batch sizes in centralized learning? Last, how can we design federated learning methods that effectively utilize larger cohort sizes? We give partial answers to these questions based on extensive empirical evaluation. Our work highlights a number of challenges stemming from the use of larger cohorts. While some of these (such as generalization issues and diminishing returns) are analogs of large-batch training challenges, others (including training failures and fairness concerns) are unique to federated learning.
23.0LGJun 8, 2021
Federated Hyperparameter Tuning: Challenges, Baselines, and Connections to Weight-SharingMikhail Khodak, Renbo Tu, Tian Li et al.
Tuning hyperparameters is a crucial but arduous part of the machine learning pipeline. Hyperparameter optimization is even more challenging in federated learning, where models are learned over a distributed network of heterogeneous devices; here, the need to keep data on device and perform local training makes it difficult to efficiently train and evaluate configurations. In this work, we investigate the problem of federated hyperparameter tuning. We first identify key challenges and show how standard approaches may be adapted to form baselines for the federated setting. Then, by making a novel connection to the neural architecture search technique of weight-sharing, we introduce a new method, FedEx, to accelerate federated hyperparameter tuning that is applicable to widely-used federated optimization methods such as FedAvg and recent variants. Theoretically, we show that a FedEx variant correctly tunes the on-device learning rate in the setting of online convex optimization across devices. Empirically, we show that FedEx can outperform natural baselines for federated hyperparameter tuning by several percentage points on the Shakespeare, FEMNIST, and CIFAR-10 benchmarks, obtaining higher accuracy using the same training budget.
25.9LGMar 1, 2021
Heterogeneity for the Win: One-Shot Federated ClusteringDon Kurian Dennis, Tian Li, Virginia Smith
In this work, we explore the unique challenges -- and opportunities -- of unsupervised federated learning (FL). We develop and analyze a one-shot federated clustering scheme, $k$-FED, based on the widely-used Lloyd's method for $k$-means clustering. In contrast to many supervised problems, we show that the issue of statistical heterogeneity in federated networks can in fact benefit our analysis. We analyse $k$-FED under a center separation assumption and compare it to the best known requirements of its centralized counterpart. Our analysis shows that in heterogeneous regimes where the number of clusters per device $(k')$ is smaller than the total number of clusters over the network $k$, $(k'\le \sqrt{k})$, we can use heterogeneity to our advantage -- significantly weakening the cluster separation requirements for $k$-FED. From a practical viewpoint, $k$-FED also has many desirable properties: it requires only round of communication, can run asynchronously, and can handle partial participation or node/network failures. We motivate our analysis with experiments on common FL benchmarks, and highlight the practical utility of one-shot clustering through use-cases in personalized FL and device sampling.
Two Sides of Meta-Learning Evaluation: In vs. Out of DistributionAmrith Setlur, Oscar Li, Virginia Smith
We categorize meta-learning evaluation into two settings: $\textit{in-distribution}$ [ID], in which the train and test tasks are sampled $\textit{iid}$ from the same underlying task distribution, and $\textit{out-of-distribution}$ [OOD], in which they are not. While most meta-learning theory and some FSL applications follow the ID setting, we identify that most existing few-shot classification benchmarks instead reflect OOD evaluation, as they use disjoint sets of train (base) and test (novel) classes for task generation. This discrepancy is problematic because -- as we show on numerous benchmarks -- meta-learning methods that perform better on existing OOD datasets may perform significantly worse in the ID setting. In addition, in the OOD setting, even though current FSL benchmarks seem befitting, our study highlights concerns in 1) reliably performing model selection for a given meta-learning method, and 2) consistently comparing the performance of different methods. To address these concerns, we provide suggestions on how to construct FSL benchmarks to allow for ID evaluation as well as more reliable OOD evaluation. Our work aims to inform the meta-learning community about the importance and distinction of ID vs. OOD evaluation, as well as the subtleties of OOD evaluation with current benchmarks.
Label Leakage and Protection in Two-party Split LearningOscar Li, Jiankai Sun, Xin Yang et al.
Two-party split learning is a popular technique for learning a model across feature-partitioned data. In this work, we explore whether it is possible for one party to steal the private label information from the other party during split training, and whether there are methods that can protect against such attacks. Specifically, we first formulate a realistic threat model and propose a privacy loss metric to quantify label leakage in split learning. We then show that there exist two simple yet effective methods within the threat model that can allow one party to accurately recover private ground-truth labels owned by the other party. To combat these attacks, we propose several random perturbation techniques, including $\texttt{Marvell}$, an approach that strategically finds the structure of the noise perturbation by minimizing the amount of label leakage (measured through our quantification metric) of a worst-case adversary. We empirically demonstrate the effectiveness of our protection techniques against the identified attacks, and show that $\texttt{Marvell}$ in particular has improved privacy-utility tradeoffs relative to baseline approaches.
Ditto: Fair and Robust Federated Learning Through PersonalizationTian Li, Shengyuan Hu, Ahmad Beirami et al.
Fairness and robustness are two important concerns for federated learning systems. In this work, we identify that robustness to data and model poisoning attacks and fairness, measured as the uniformity of performance across devices, are competing constraints in statistically heterogeneous networks. To address these constraints, we propose employing a simple, general framework for personalized federated learning, Ditto, that can inherently provide fairness and robustness benefits, and develop a scalable solver for it. Theoretically, we analyze the ability of Ditto to achieve fairness and robustness simultaneously on a class of linear problems. Empirically, across a suite of federated datasets, we show that Ditto not only achieves competitive performance relative to recent personalization methods, but also enables more accurate, robust, and fair models relative to state-of-the-art fair or robust baselines.
10.6LGNov 28, 2020
Is Support Set Diversity Necessary for Meta-Learning?Amrith Setlur, Oscar Li, Virginia Smith
Meta-learning is a popular framework for learning with limited data in which an algorithm is produced by training over multiple few-shot learning tasks. For classification problems, these tasks are typically constructed by sampling a small number of support and query examples from a subset of the classes. While conventional wisdom is that task diversity should improve the performance of meta-learning, in this work we find evidence to the contrary: we propose a modification to traditional meta-learning approaches in which we keep the support sets fixed across tasks, thus reducing task diversity. Surprisingly, we find that not only does this modification not result in adverse effects, it almost always improves the performance for a variety of datasets and meta-learning methods. We also provide several initial analyses to understand this phenomenon. Our work serves to: (i) more closely investigate the effect of support set construction for the problem of meta-learning, and (ii) suggest a simple, general, and competitive baseline for few-shot learning.
Tilted Empirical Risk MinimizationTian Li, Ahmad Beirami, Maziar Sanjabi et al.
Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address these problems individually, in this work, we explore them through a unified framework -- tilted empirical risk minimization (TERM). In particular, we show that it is possible to flexibly tune the impact of individual losses through a straightforward extension to ERM using a hyperparameter called the tilt. We provide several interpretations of the resulting framework: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to a superquantile method. We develop batch and stochastic first-order optimization methods for solving TERM, and show that the problem can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. TERM is not only competitive with existing solutions tailored to these individual problems, but can also enable entirely new applications, such as simultaneously addressing outliers and promoting fairness.
FedDANE: A Federated Newton-Type MethodTian Li, Anit Kumar Sahu, Manzil Zaheer et al.
Federated learning aims to jointly learn statistical models over massively distributed remote devices. In this work, we propose FedDANE, an optimization method that we adapt from DANE, a method for classical distributed optimization, to handle the practical constraints of federated learning. We provide convergence guarantees for this method when learning over both convex and non-convex functions. Despite encouraging theoretical results, we find that the method has underwhelming performance empirically. In particular, through empirical simulations on both synthetic and real-world datasets, FedDANE consistently underperforms baselines of FedAvg and FedProx in realistic federated settings. We identify low device participation and statistical device heterogeneity as two underlying causes of this underwhelming performance, and conclude by suggesting several directions of future work.
8.6LGNov 5, 2019
Enhancing the Privacy of Federated Learning with SketchingZaoxing Liu, Tian Li, Virginia Smith et al.
In response to growing concerns about user privacy, federated learning has emerged as a promising tool to train statistical models over networks of devices while keeping data localized. Federated learning methods run training tasks directly on user devices and do not share the raw user data with third parties. However, current methods still share model updates, which may contain private information (e.g., one's weight and height), during the training process. Existing efforts that aim to improve the privacy of federated learning make compromises in one or more of the following key areas: performance (particularly communication cost), accuracy, or privacy. To better optimize these trade-offs, we propose that \textit{sketching algorithms} have a unique advantage in that they can provide both privacy and performance benefits while maintaining accuracy. We evaluate the feasibility of sketching-based federated learning with a prototype on three representative learning models. Our initial findings show that it is possible to provide strong privacy guarantees for federated learning without sacrificing performance or accuracy. Our work highlights that there exists a fundamental connection between privacy and communication in distributed settings, and suggests important open problems surrounding the theoretical understanding, methodology, and system design of practical, private federated learning.
15.1LGNov 3, 2019
Privacy for Free: Communication-Efficient Learning with Differential Privacy Using SketchesTian Li, Zaoxing Liu, Vyas Sekar et al.
Communication and privacy are two critical concerns in distributed learning. Many existing works treat these concerns separately. In this work, we argue that a natural connection exists between methods for communication reduction and privacy preservation in the context of distributed machine learning. In particular, we prove that Count Sketch, a simple method for data stream summarization, has inherent differential privacy properties. Using these derived privacy guarantees, we propose a novel sketch-based framework (DiffSketch) for distributed learning, where we compress the transmitted messages via sketches to simultaneously achieve communication efficiency and provable privacy benefits. Our evaluation demonstrates that DiffSketch can provide strong differential privacy guarantees (e.g., $\varepsilon$= 1) and reduce communication by 20-50x with only marginal decreases in accuracy. Compared to baselines that treat privacy and communication separately, DiffSketch improves absolute test accuracy by 5%-50% while offering the same privacy guarantees and communication compression.
Progressive Compressed Records: Taking a Byte out of Deep Learning DataMichael Kuchnik, George Amvrosiadis, Virginia Smith
Deep learning accelerators efficiently train over vast and growing amounts of data, placing a newfound burden on commodity networks and storage devices. A common approach to conserve bandwidth involves resizing or compressing data prior to training. We introduce Progressive Compressed Records (PCRs), a data format that uses compression to reduce the overhead of fetching and transporting data, effectively reducing the training time required to achieve a target accuracy. PCRs deviate from previous storage formats by combining progressive compression with an efficient storage layout to view a single dataset at multiple fidelities---all without adding to the total dataset size. We implement PCRs and evaluate them on a range of datasets, training tasks, and hardware architectures. Our work shows that: (i) the amount of compression a dataset can tolerate exceeds 50% of the original encoding for many DL training tasks; (ii) it is possible to automatically and efficiently select appropriate compression levels for a given task; and (iii) PCRs enable tasks to readily access compressed data at runtime---utilizing as little as half the training bandwidth and thus potentially doubling training speed.
Fair Resource Allocation in Federated LearningTian Li, Maziar Sanjabi, Ahmad Beirami et al.
Federated learning involves training statistical models in massive, heterogeneous networks. Naively minimizing an aggregate loss function in such a network may disproportionately advantage or disadvantage some of the devices. In this work, we propose q-Fair Federated Learning (q-FFL), a novel optimization objective inspired by fair resource allocation in wireless networks that encourages a more fair (specifically, a more uniform) accuracy distribution across devices in federated networks. To solve q-FFL, we devise a communication-efficient method, q-FedAvg, that is suited to federated networks. We validate both the effectiveness of q-FFL and the efficiency of q-FedAvg on a suite of federated datasets with both convex and non-convex models, and show that q-FFL (along with q-FedAvg) outperforms existing baselines in terms of the resulting fairness, flexibility, and efficiency.
12.8LGMar 29, 2019
MLSys: The New Frontier of Machine Learning SystemsAlexander Ratner, Dan Alistarh, Gustavo Alonso et al.
Machine learning (ML) techniques are enjoying rapidly increasing adoption. However, designing and implementing the systems that support ML models in real-world deployments remains a significant obstacle, in large part due to the radically different development and deployment profile of modern ML methods, and the range of practical concerns that come with broader adoption. We propose to foster a new systems machine learning research community at the intersection of the traditional systems and ML communities, focused on topics such as hardware systems for ML, software systems for ML, and ML optimized for metrics beyond predictive accuracy. To do this, we describe a new conference, MLSys, that explicitly targets research at the intersection of systems and machine learning with a program committee split evenly between experts in systems and ML, and an explicit focus on topics at the intersection of the two.
29.4LGFeb 28, 2019
One-Shot Federated LearningNeel Guha, Ameet Talwalkar, Virginia Smith
We present one-shot federated learning, where a central server learns a global model over a network of federated devices in a single round of communication. Our approach - drawing on ensemble learning and knowledge aggregation - achieves an average relative gain of 51.5% in AUC over local baselines and comes within 90.1% of the (unattainable) global ideal. We discuss these methods and identify several promising directions of future work.
Federated Optimization in Heterogeneous NetworksTian Li, Anit Kumar Sahu, Manzil Zaheer et al.
Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the network (statistical heterogeneity). In this work, we introduce a framework, FedProx, to tackle heterogeneity in federated networks. FedProx can be viewed as a generalization and re-parametrization of FedAvg, the current state-of-the-art method for federated learning. While this re-parameterization makes only minor modifications to the method itself, these modifications have important ramifications both in theory and in practice. Theoretically, we provide convergence guarantees for our framework when learning over data from non-identical distributions (statistical heterogeneity), and while adhering to device-level systems constraints by allowing each participating device to perform a variable amount of work (systems heterogeneity). Practically, we demonstrate that FedProx allows for more robust convergence than FedAvg across a suite of realistic federated datasets. In particular, in highly heterogeneous settings, FedProx demonstrates significantly more stable and accurate convergence behavior relative to FedAvg---improving absolute test accuracy by 22% on average.
9.1LGOct 11, 2018
Efficient Augmentation via Data SubsamplingMichael Kuchnik, Virginia Smith
Data augmentation is commonly used to encode invariances in learning methods. However, this process is often performed in an inefficient manner, as artificial examples are created by applying a number of transformations to all points in the training set. The resulting explosion of the dataset size can be an issue in terms of storage and training costs, as well as in selecting and tuning the optimal set of transformations to apply. In this work, we demonstrate that it is possible to significantly reduce the number of data points included in data augmentation while realizing the same accuracy and invariance benefits of augmenting the entire dataset. We propose a novel set of subsampling policies, based on model influence and loss, that can achieve a 90% reduction in augmentation set size while maintaining the accuracy gains of standard data augmentation.
4.1LGMay 20, 2018
Model Aggregation via Good-Enough Model SpacesNeel Guha, Virginia Smith
In many applications, the training data for a machine learning task is partitioned across multiple nodes, and aggregating this data may be infeasible due to communication, privacy, or storage constraints. Existing distributed optimization methods for learning global models in these settings typically aggregate local updates from each node in an iterative fashion. However, these approaches require many rounds of communication between nodes, and assume that updates can be synchronously shared across a connected network. In this work, we present Good-Enough Model Spaces (GEMS), a novel framework for learning a global model by carefully intersecting the sets of "good-enough" models across each node. Our approach utilizes minimal communication and does not require sharing of data between nodes. We present methods for learning both convex models and neural networks within this framework and discuss how small samples of held-out data can be used for post-learning fine-tuning. In experiments on image and medical datasets, our approach on average improves upon other baseline aggregation techniques such as ensembling or model averaging by as much as 15 points (accuracy).
A Kernel Theory of Modern Data AugmentationTri Dao, Albert Gu, Alexander J. Ratner et al.
Data augmentation, a technique in which a training set is expanded with class-preserving transformations, is ubiquitous in modern machine learning pipelines. In this paper, we seek to establish a theoretical framework for understanding data augmentation. We approach this from two directions: First, we provide a general model of augmentation as a Markov process, and show that kernels appear naturally with respect to this model, even when we do not employ kernel classification. Next, we analyze more directly the effect of augmentation on kernel classifiers, showing that data augmentation can be approximated by first-order feature averaging and second-order variance regularization components. These frameworks both serve to illustrate the ways in which data augmentation affects the downstream learning model, and the resulting analyses provide novel connections between prior work in invariant kernels, tangent propagation, and robust optimization. Finally, we provide several proof-of-concept applications showing that our theory can be useful for accelerating machine learning workflows, such as reducing the amount of computation needed to train using augmented data, and predicting the utility of a transformation prior to training.