Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization | Paper Citation Record

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This paper cites Deep learning with differential privacy.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Deep learning with differential privacy

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This paper cites Federated learning in edge computing: a systematic survey.Sensors, 22(2):450, 2022.(Cited on page 24).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Federated learning in edge computing: a systematic survey.Sensors, 22(2):450, 2022.(Cited on page 24)

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This paper cites Distributed delayed stochastic optimiza- tion.Advances in neural information processing systems, 24, 2011.(Cited on page 350).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Distributed delayed stochastic optimiza- tion.Advances in neural information processing systems, 24, 2011.(Cited on page 350)

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This paper cites Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

Reference 4

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Unresolved cited work

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This paper cites On the Convergence of SGD with Biased Gradients.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On the Convergence of SGD with Biased Gradients

Reference 6

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This paper cites QSGD: Communication-efficient SGD via gradient quantization and encoding.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization QSGD: Communication-efficient SGD via gradient quantization and encoding

Reference 7

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This paper cites Byzantine stochastic gradi- ent descent.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Byzantine stochastic gradi- ent descent

Reference 8

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This paper cites The convergence of sparsified gradient methods.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization The convergence of sparsified gradient methods

Reference 9

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This paper cites Byzantine-resilient non-convex stochastic gradient descent.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Byzantine-resilient non-convex stochastic gradient descent

Reference 10

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Observation 59c7da2c-b3c0-4aee-a554-e677efd1fa34 · outbound

This paper cites Fixing by mixing: A recipe for optimal byzantine ml under heterogeneity.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Fixing by mixing: A recipe for optimal byzantine ml under heterogeneity

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This paper cites Byzantine-Robust Federated Learning: Impact of Client Subsampling and Local Updates.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Byzantine-Robust Federated Learning: Impact of Client Subsampling and Local Updates

Reference 12

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Unresolved cited work

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This paper cites Federated learning for healthcare: Systematic review and architecture proposal.ACM Transactions on Intel- ligent Systems and Technology (TIST), 13(4):1–23, 2022.(Cited on page 104).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Federated learning for healthcare: Systematic review and architecture proposal.ACM Transactions on Intel- ligent Systems and Technology (TIST), 13(4):1–23, 2022.(Cited on page 104)

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This paper cites Communication complexity of distributed convex learning and optimization.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Communication complexity of distributed convex learning and optimization

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This paper cites Lower bounds for non-convex stochastic optimiza- tion.Mathematical Programming, 199(1-2):165–214, 2023.(Cited on pages 123 and 125).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Lower bounds for non-convex stochastic optimiza- tion.Mathematical Programming, 199(1-2):165–214, 2023.(Cited on pages 123 and 125)

Reference 16

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This paper cites Distributed Deep Learning Using Volunteer Computing-Like Paradigm.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Distributed Deep Learning Using Volunteer Computing-Like Paradigm

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Observation 5a5dfccd-b09a-4827-a168-34c457a765a7 · outbound

This paper cites A little is enough: Cir- cumventing defenses for distributed learning.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A little is enough: Cir- cumventing defenses for distributed learning

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This paper cites Qsparse- local-SGD: Distributed SGD with quantization, sparsification and local computations.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Qsparse- local-SGD: Distributed SGD with quantization, sparsification and local computations

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This paper cites Generalized mono- tone operators and their averaged resolvents.Mathematical Programming, 189(1):55–74, 2021.(Cited on page 49).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Generalized mono- tone operators and their averaged resolvents.Mathematical Programming, 189(1):55–74, 2021.(Cited on page 49)

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This paper cites MOS-SIAM Series on Optimization, 2017.(Cited on pages 43 and 63).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization MOS-SIAM Series on Optimization, 2017.(Cited on pages 43 and 63)

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This paper cites Demystifying parallel and distributed deep learning: An in-depth concurrency analysis.ACM Computing Surveys (CSUR), 52(4):1–43, 2019.(Cited on page 23).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Demystifying parallel and distributed deep learning: An in-depth concurrency analysis.ACM Computing Surveys (CSUR), 52(4):1–43, 2019.(Cited on page 23)

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Observation de813356-f3cb-4d2a-b44a-f10c77aeaacd · outbound

This paper cites Practical recommendations for gradient-based training of deep architectures.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Practical recommendations for gradient-based training of deep architectures

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This paper cites signSGD with Majority Vote is Communication Efficient And Fault Tolerant.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization signSGD with Majority Vote is Communication Efficient And Fault Tolerant

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This paper cites Incremental proximal methods for large scale convex optimization.Mathematical Programming, 129(2):163–195, 2011.(Cited on page 423).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Incremental proximal methods for large scale convex optimization.Mathematical Programming, 129(2):163–195, 2011.(Cited on page 423)

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This paper cites On biased compression for distributed learning.Journal of Machine Learning Research, 24(276):1–50, 2023.(Cited on pages 114, 121, 269, and 350).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On biased compression for distributed learning.Journal of Machine Learning Research, 24(276):1–50, 2023.(Cited on pages 114, 121, 269, and 350)

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Observation 3062fa6c-744f-4f90-bb04-56cdb9857e29 · outbound

This paper cites LoRA Learns Less and Forgets Less.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization LoRA Learns Less and Forgets Less

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Observation b4ad7a4b-43f2-4639-8271-e0aaaa85dd90 · outbound

This paper cites Machine learning with adversaries: Byzantine tolerant gradient descent.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Machine learning with adversaries: Byzantine tolerant gradient descent

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This paper cites Brendan McMahan, Sarvar Patel, Daniel Ramage, Aaron Segal, and Karn Seth.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Brendan McMahan, Sarvar Patel, Daniel Ramage, Aaron Segal, and Karn Seth

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This paper cites Towards federated learning at scale: System design.Proceedings of machine learning and systems, 1:374–388, 2019.(Cited on page 24).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Towards federated learning at scale: System design.Proceedings of machine learning and systems, 1:374–388, 2019.(Cited on page 24)

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This paper cites Curiously fast convergence of some stochastic gradient descent algorithms.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Curiously fast convergence of some stochastic gradient descent algorithms

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Observation bd92d279-3d4b-4eb3-b21a-97ffd506b1c4 · outbound

This paper cites Democratizing machine learning: Resilient distributed learning with heterogeneous participants.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Democratizing machine learning: Resilient distributed learning with heterogeneous participants

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Observation a60a09f8-7400-43b9-bc1d-66facd631b4b · outbound

This paper cites Minibatch stochastic three points method for unconstrained smooth minimization.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Minibatch stochastic three points method for unconstrained smooth minimization

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Observation 98845fd0-8120-4089-adf0-e318fa4a6c53 · outbound

This paper cites Flpytorch: optimization research simulator for federated learning.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Flpytorch: optimization research simulator for federated learning

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Observation 0600f874-9cad-4c69-92ae-0d1881f37a5a · outbound

This paper cites Tighter lower bounds for shuffling SGD: Random permutations and beyond.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Tighter lower bounds for shuffling SGD: Random permutations and beyond

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This paper cites A first-order primal-dual algorithm for convex problems with applications to imaging.Journal of Mathematical Imaging and Vision, 40(1):120–145, 2011.(Cited on page 78).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A first-order primal-dual algorithm for convex problems with applications to imaging.Journal of Mathematical Imaging and Vision, 40(1):120–145, 2011.(Cited on page 78)

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This paper cites LIBSVM: A library for support 151 vector machines.ACM transactions on intelligent systems and technology (TIST), 2(3):1–27, 2011.(Cited on pages 57, 71, 87, 102, 129, and 269).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization LIBSVM: A library for support 151 vector machines.ACM transactions on intelligent systems and technology (TIST), 2(3):1–27, 2011.(Cited on pages 57, 71, 87, 102, 129, and 269)

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Observation 63122e3e-f66f-4d91-b03e-1042ccb195b2 · outbound

This paper cites On the Outsized Importance of Learning Rates in Local Update Methods.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On the Outsized Importance of Learning Rates in Local Update Methods

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Observation 072b9a17-ffaf-4c27-a479-6a3ba9ea0f6a · outbound

This paper cites On Large-Cohort Training for Federated Learning.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On Large-Cohort Training for Federated Learning

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Observation 8e6bc20e-b4c4-44db-842a-0bde68b49562 · outbound

This paper cites Draco: Byzantine-resilient distributed training via redundant gradi- ents.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Draco: Byzantine-resilient distributed training via redundant gradi- ents

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Observation 30a75e98-f211-456d-9b9e-64a8eb716522 · outbound

This paper cites A primal–dual fixed point algorithm for convex separable minimization with applications to im- age restoration.Inverse Problems, 29(2):025011, 2013.(Cited on page 186).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A primal–dual fixed point algorithm for convex separable minimization with applications to im- age restoration.Inverse Problems, 29(2):025011, 2013.(Cited on page 186)

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Observation 37c625f0-09de-431d-9476-77e7106427f5 · outbound

This paper cites Optimal client sampling for federated learning.Privacy Preserving Machine Learning (NeurIPS 2020 Workshop), 2020a.(Cited on pages 27, 30, 60, 75, and 90).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Optimal client sampling for federated learning.Privacy Preserving Machine Learning (NeurIPS 2020 Workshop), 2020a.(Cited on pages 27, 30, 60, 75, and 90)

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Observation f9977c3c-9fb0-441d-97d2-3479dc7fcbf1 · outbound

This paper cites Understanding gradient clipping in private SGD: A geometric perspective.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Understanding gradient clipping in private SGD: A geometric perspective

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Unresolved cited work

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This paper cites Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies

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This paper cites On the convergence of federated averaging with cyclic client participation.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On the convergence of federated averaging with cyclic client participation

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This paper cites Emerging trends: A gentle introduction to fine-tuning.Natural Language Engineering, 27(6): 763–778, 2021.(Cited on page 131).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Emerging trends: A gentle introduction to fine-tuning.Natural Language Engineering, 27(6): 763–778, 2021.(Cited on page 131)

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This paper cites Proximal splitting methods in signal processing.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Proximal splitting methods in signal processing

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This paper cites Combettes, Laurent Condat, Jean-Christophe Pesquet, and B˘ ang C.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Combettes, Laurent Condat, Jean-Christophe Pesquet, and B˘ ang C

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This paper cites MURANA: A Generic Framework for Stochastic Variance-Reduced Optimization.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization MURANA: A Generic Framework for Stochastic Variance-Reduced Optimization

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Resolution: verified exact; local_arxiv, observed 2026-08-15T14:39:16.722949Z

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Observation 8e8c59c8-18b3-4542-8759-5828255fd41f · outbound

This paper cites RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization RandProx: Primal-Dual Optimization Algorithms with Randomized Proximal Updates

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This paper cites Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Proximal Splitting Algorithms for Convex Optimization: A Tour of Recent Advances, with New Twists

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Observation ec2b8597-2075-47c3-a425-2b96969b4706 · outbound

This paper cites Distributed proximal splitting algorithms with rates and acceleration.Frontiers in Sig- nal Processing, page 12, 2022.(Cited on page 186).

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Distributed proximal splitting algorithms with rates and acceleration.Frontiers in Sig- nal Processing, page 12, 2022.(Cited on page 186)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Importance sampling for minibatches

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Momentum-based variance re- duction in non-convex SGD

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Asynchronous byzantine machine learning (the case of sgd)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Aggregathor: Byzantine machine learn- ing via robust gradient aggregation.Proceedings of Machine Learning and Systems, 1:81–106, 2019.(Cited on page 118)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Byzantine-resilient high-dimensional SGD with local iterations on heterogeneous data

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A three-operator splitting scheme and its optimization applications.Set-Val

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Large scale distributed deep networks.Advances in neural information processing systems, 25, 2012.(Cited on page 23)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A simple practical accelerated method for finite sums.29th Conference on Neural Information Processing Systems (NeurIPS), 2016

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On the ineffectiveness of variance reduced optimization for deep learning.Advances in Neural Information Processing Systems, 32, 2019.(Cited on page 129)

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Observation f3d76e7f-4cca-4c8d-91a4-b90f38acbfce · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization SAGA: A fast incremental gradient method with support for non-strongly convex com- posite objectives

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Optimal dis- tributed online prediction using mini-batches.Journal of Machine Learning Research, 13(1):165–202, January 2012.(Cited on pages 30 and 53)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Mast: Model-agnostic sparsified training.arXiv preprint arXiv:2311.16086, 2023a.(Cited on page 39)

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Observation 701a9742-b520-49ef-bed8-3fb7dbafbe82 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A guide through the Zoo of biased SGD

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Streamlining in the Riemannian Realm: Efficient Riemannian Optimization with Loopless Variance Reduction

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Observation 3a9c108e-17e0-4d89-ae90-aadf73cd8384 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Methods with Local Steps and Random Reshuffling for Generally Smooth Non-Convex Federated Optimization

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Observation e7692ab1-8f9e-4c32-a8b3-95141eb679c7 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Distributed deep learning in open collaborations

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A simple algorithm for a class of nonsmooth convex–concave saddle-point problems.Operations Research Letters, 43(2):209–214, 2015

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization The algorithmic foundations of differential privacy.Foundations and trends®in theoretical computer science, 9(3-4): 211–487, 2014.(Cited on pages 23, 26, and 28)

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Observation ede8a3ce-054f-4b48-8df5-e4070b01e7d0 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Spider: Near- optimal non-convex optimization via stochastic path-integrated differential estimator

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization AFLGuard: Byzantine-robust asynchronous federated learning

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Observation 38bcc988-12ed-4bf9-948a-ccde50506231 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization EF21 with Bells & Whistles: Six Algorithmic Extensions of Modern Error Feedback

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Distributed new- ton can communicate less and resist Byzantine workers

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Sharp bounds for federated averaging (local sgd) and continuous perspective

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Observation e13a42c0-db6a-4167-afac-bcc88db021a9 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Television by pulse code modulation.Bell System Technical Journal, 30(1):33–49, 1951.(Cited on page 121)

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Stochas- tic optimization with heavy-tailed noise via accelerated gradient clipping

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Observation 2a6ff18b-a2a0-4584-87ba-91c5066a0cd2 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization A unified theory of SGD: Variance reduction, sampling, quantization and coordinate descent

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Linearly converging error compensated SGD.Advances in Neural Information Processing Systems, 33:20889–20900, 2020c.(Cited on page 65)

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Observation 45e6f806-b857-4c1c-b2c3-6c28e610468c · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Unresolved cited work

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Observation 1db21339-1087-43f7-ad6a-14e94aa48771 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Local SGD: Unified theory and new efficient methods

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Observation 72a5e46f-f765-41f0-9190-1c0d248f167d · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Secure Distributed Training at Scale

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Observation 34e8dd34-6a15-4277-ad3b-3b8f1ee9fbc0 · outbound

This paper cites an unresolved cited work.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Unresolved cited work

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Observation ba027ad6-bed5-4692-bd64-cdc06fbde200 · outbound

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Observation 2efb3cc9-195a-4544-b9ab-80350fb40e51 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Gower, Peter Richt´ arik, and Francis Bach

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Observation 5ea93c2e-9c6c-47f8-a3b7-50a62de60dcd · outbound

This paper cites SGD: General analysis and improved rates.

Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization SGD: General analysis and improved rates

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Observation b83028b8-c34b-4cc2-aa5a-3b6205863c78 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Can 5th gen- eration local training methods support client sampling? yes! InInterna- tional Conference on Artificial Intelligence and Statistics, pages 1055–1092

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Observation 7a3bcec7-2b3e-4a9e-974a-551b5cd79bf5 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Improving Accelerated Federated Learning with Compression and Importance Sampling

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Observation e9b6cf79-beae-411a-8ff3-45d286249730 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization On the Convergence of Local Descent Methods in Federated Learning

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Observation 7a83a56e-40df-481a-9afb-2a9787a72a16 · outbound

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Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization Federated learning with compression: Unified analysis and sharp guarantees

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