@article{14815,
  abstract     = {In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show superior performance in practice when compared to the much more studied and understood unbiased compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. We prove that distributed compressed SGD method, employed with error feedback mechanism, enjoys the ergodic rate O(δLexp[−μKδL]+(C+δD)Kμ), where δ≥1 is a compression parameter which grows when more compression is applied, L and μ are the smoothness and strong convexity constants, C captures stochastic gradient noise (C=0 if full gradients are computed on each node) and D captures the variance of the gradients at the optimum (D=0 for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose several new biased compressors with promising theoretical guarantees and practical performance.},
  author       = {Beznosikov, Aleksandr and Horvath, Samuel and Richtarik, Peter and Safaryan, Mher},
  issn         = {1533-7928},
  journal      = {Journal of Machine Learning Research},
  pages        = {1--50},
  publisher    = {Journal of Machine Learning Research},
  title        = {{On biased compression for distributed learning}},
  volume       = {24},
  year         = {2023},
}

@article{10802,
  abstract     = {Addressing fairness concerns about machine learning models is a crucial step towards their long-term adoption in real-world automated systems. While many approaches have been developed for training fair models from data, little is known about the robustness of these methods to data corruption. In this work we consider fairness-aware learning under worst-case data manipulations. We show that an adversary can in some situations force any learner to return an overly biased classifier, regardless of the sample size and with or without degrading
accuracy, and that the strength of the excess bias increases for learning problems with underrepresented protected groups in the data. We also prove that our hardness results are tight up to constant factors. To this end, we study two natural learning algorithms that optimize for both accuracy and fairness and show that these algorithms enjoy guarantees that are order-optimal in terms of the corruption ratio and the protected groups frequencies in the large data
limit.},
  author       = {Konstantinov, Nikola H and Lampert, Christoph},
  issn         = {1533-7928},
  journal      = {Journal of Machine Learning Research},
  keywords     = {Fairness, robustness, data poisoning, trustworthy machine learning, PAC learning},
  pages        = {1--60},
  publisher    = {ML Research Press},
  title        = {{Fairness-aware PAC learning from corrupted data}},
  volume       = {23},
  year         = {2022},
}

@article{11420,
  abstract     = {Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via noisy-SGD for a univariate regularized regression problem. Our main result is that SGD with vanishingly small noise injected in the gradients is biased towards a simple solution: at convergence, the ReLU network implements a piecewise linear map of the inputs, and the number of “knot” points -- i.e., points where the tangent of the ReLU network estimator changes -- between two consecutive training inputs is at most three. In particular, as the number of neurons of the network grows, the SGD dynamics is captured by the solution of a gradient flow and, at convergence, the distribution of the weights approaches the unique minimizer of a related free energy, which has a Gibbs form. Our key technical contribution consists in the analysis of the estimator resulting from this minimizer: we show that its second derivative vanishes everywhere, except at some specific locations which represent the “knot” points. We also provide empirical evidence that knots at locations distinct from the data points might occur, as predicted by our theory.},
  author       = {Shevchenko, Aleksandr and Kungurtsev, Vyacheslav and Mondelli, Marco},
  issn         = {1533-7928},
  journal      = {Journal of Machine Learning Research},
  number       = {130},
  pages        = {1--55},
  publisher    = {Journal of Machine Learning Research},
  title        = {{Mean-field analysis of piecewise linear solutions for wide ReLU networks}},
  volume       = {23},
  year         = {2022},
}

@article{10180,
  abstract     = {The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, sometimes even better than, the original dense networks. Sparsity promises to reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.},
  author       = {Hoefler, Torsten and Alistarh, Dan-Adrian and Ben-Nun, Tal and Dryden, Nikoli and Peste, Elena-Alexandra},
  issn         = {1533-7928},
  journal      = {Journal of Machine Learning Research},
  number       = {241},
  pages        = {1--124},
  publisher    = {Journal of Machine Learning Research},
  title        = {{Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks}},
  volume       = {22},
  year         = {2021},
}