Federated learning is a distributed learning framework that takes full advantage of private data samples kept on edge devices. In real-world federated learning systems, these data samples are often decentralized and Non-Independently Identically Distributed (Non-IID), causing divergence and performance degradation in the federated learning process. As a new solution, clustered federated learning groups federated clients with similar data distributions to impair the Non-IID effects and train a better model for every cluster. This paper proposes StoCFL, a novel clustered federated learning approach for generic Non-IID issues. In detail, StoCFL implements a flexible CFL framework that supports an arbitrary proportion of client participation and newly joined clients for a varying FL system, while maintaining a great improvement in model performance. The intensive experiments are conducted by using four basic Non-IID settings and a real-world dataset. The results show that StoCFL could obtain promising cluster results even when the number of clusters is unknown. Based on the client clustering results, models trained with StoCFL outperform baseline approaches in a variety of contexts.

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying," was proposed by Meehan et. al. (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.

Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions--smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the minimizers of MIE converge to the target measure. Optimizing this energy with proper discretization yields a practical firstorder particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems, our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives. Sampling from an unnormalized probability density is a ubiquitous task in statistics, mathematical physics, and machine learning. While Markov chain Monte Carlo (MCMC) methods (Brooks et al., 2011) provide a way to obtain unbiased samples at the price of potentially long mixing times, variational inference (VI) methods (Blei et al., 2017) approximate the target measure with simpler (e.g., parametric) distributions at a lower computational cost. In this work, we focus on a particular class of VI methods that approximate the target measure using a collection of interacting particles.

Classical wisdom suggests that estimators should avoid fitting noise to achieve good generalization. In contrast, modern overparameterized models can yield small test error despite interpolating noise -- a phenomenon often called "benign overfitting" or "harmless interpolation". This paper argues that the degree to which interpolation is harmless hinges upon the strength of an estimator's inductive bias, i.e., how heavily the estimator favors solutions with a certain structure: while strong inductive biases prevent harmless interpolation, weak inductive biases can even require fitting noise to generalize well. Our main theoretical result establishes tight non-asymptotic bounds for high-dimensional kernel regression that reflect this phenomenon for convolutional kernels, where the filter size regulates the strength of the inductive bias. We further provide empirical evidence of the same behavior for deep neural networks with varying filter sizes and rotational invariance.

For tabular data sets, we explore data and model distillation, as well as data denoising. These techniques improve both gradient-boosting models and a specialized DNN architecture. While gradient boosting is known to outperform DNNs on tabular data, we close the gap for datasets with 100K+ rows and give DNNs an advantage on small data sets. We extend these results with input-data distillation and optimized ensembling to help DNN performance match or exceed that of gradient boosting. As a theoretical justification of our practical method, we prove its equivalence to classical cross-entropy knowledge distillation. We also qualitatively explain the superiority of DNN ensembles over XGBoost on small data sets. For an industry end-to-end real-time ML platform with 4M production inferences per second, we develop a model-training workflow based on data sampling that distills ensembles of models into a single gradient-boosting model favored for high-performance real-time inference, without performance loss. Empirical evaluation shows that the proposed combination of methods consistently improves model accuracy over prior best models across several production applications deployed worldwide.

The transfer learning paradigm of model pre-training and subsequent fine-tuning produces high-accuracy models. While most studies recommend scaling the pre-training size to benefit most from transfer learning, a question remains: what data and method should be used for pre-training? We investigate the impact of pre-training data distribution on the few-shot and full fine-tuning performance using 3 pre-training methods (supervised, contrastive language-image and image-image), 7 pre-training datasets, and 9 downstream datasets. Through extensive controlled experiments, we find that the choice of the pre-training data source is essential for the few-shot transfer, but its role decreases as more data is made available for fine-tuning. Additionally, we explore the role of data curation and examine the trade-offs between label noise and the size of the pre-training dataset. We find that using 2000X more pre-training data from LAION can match the performance of supervised ImageNet pre-training. Furthermore, we investigate the effect of pre-training methods, comparing language-image contrastive vs. image-image contrastive, and find that the latter leads to better downstream accuracy

Evaluating the performance of machine learning models under distribution shift is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on the cross entropy loss results in better performance. By focusing on two-layer ReLU networks, which can be fully characterized by measures over their feature space, we explore how the implicit bias induced by gradient-based optimization could partly explain the above phenomenon. We provide theoretical evidence that the regression formulation yields a measure whose support can differ greatly from that for classification, in the case of one-dimensional data. Our proposed optimal supports correspond directly to the features learned by the input layer of the network. The different nature of these supports sheds light on possible optimization difficulties the square loss could encounter during training, and we present empirical results illustrating this phenomenon.

Privacy and security concerns in real-world applications have led to the development of adversarially robust federated models. However, the straightforward combination between adversarial training and federated learning in one framework can lead to the undesired robustness deterioration. We discover that the attribution behind this phenomenon is that the generated adversarial data could exacerbate the data heterogeneity among local clients, making the wrapped federated learning perform poorly. To deal with this problem, we propose a novel framework called Slack Federated Adversarial Training (SFAT), assigning the client-wise slack during aggregation to combat the intensified heterogeneity. Theoretically, we analyze the convergence of the proposed method to properly relax the objective when combining federated learning and adversarial training. Experimentally, we verify the rationality and effectiveness of SFAT on various benchmarked and real-world datasets with different adversarial training and federated optimization methods. The code is publicly available at https://github.com/ZFancy/SFAT.

We consider the problem of clustering in the learning-augmented setting, where we are given a data set in $d$-dimensional Euclidean space, and a label for each data point given by an oracle indicating what subsets of points should be clustered together. This setting captures situations where we have access to some auxiliary information about the data set relevant for our clustering objective, for instance the labels output by a neural network. Following prior work, we assume that there are at most an $\alpha \in (0,c)$ for some $c<1$ fraction of false positives and false negatives in each predicted cluster, in the absence of which the labels would attain the optimal clustering cost $\mathrm{OPT}$. For a dataset of size $m$, we propose a deterministic $k$-means algorithm that produces centers with improved bound on clustering cost compared to the previous randomized algorithm while preserving the $O( d m \log m)$ runtime. Furthermore, our algorithm works even when the predictions are not very accurate, i.e. our bound holds for $\alpha$ up to $1/2$, an improvement over $\alpha$ being at most $1/7$ in the previous work. For the $k$-medians problem we improve upon prior work by achieving a biquadratic improvement in the dependence of the approximation factor on the accuracy parameter $\alpha$ to get a cost of $(1+O(\alpha))\mathrm{OPT}$, while requiring essentially just $O(md \log^3 m/\alpha)$ runtime.