The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a polynomial rate, such as the widely-used cosine schedule, by demonstrating their increased robustness to initial parameter misspecification due to a coarse grid search. We present an analysis in a stochastic convex optimization setup demonstrating that the convergence rate of stochastic gradient descent with annealed schedules depends sublinearly on the multiplicative misspecification factor $\rho$ (i.e., the grid resolution), achieving a rate of $O(\rho^{1/(2p+1)}/\sqrt{T})$ where $p$ is the degree of polynomial decay and $T$ is the number of steps, in contrast to the $O(\rho/\sqrt{T})$ rate that arises with fixed stepsizes and exhibits a linear dependence on $\rho$. Experiments confirm the increased robustness compared to tuning with a fixed stepsize, that has significant implications for the computational overhead of hyperparameter search in practical training scenarios.

We propose VIBE, a model-agnostic framework that trains classifiers resilient to backdoor attacks. The key concept behind our approach is to treat malicious inputs and corrupted labels from the training dataset as observed random variables, while the actual clean labels are latent. VIBE then recovers the corresponding latent clean label posterior through variational inference. The resulting training procedure follows the expectation-maximization (EM) algorithm. The E-step infers the clean pseudolabels by solving an entropy-regularized optimal transport problem, while the M-step updates the classifier parameters via gradient descent. Being modular, VIBE can seamlessly integrate with recent advancements in self-supervised representation learning, which enhance its ability to resist backdoor attacks. We experimentally validate the method effectiveness against contemporary backdoor attacks on standard datasets, a large-scale setup with 1$k$ classes, and a dataset poisoned with multiple attacks. VIBE consistently outperforms previous defenses across all tested scenarios.

Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be more scalable, they are gradient-based methods and so often require many iterations to converge. Our key insight was that modern massively parallel importance weighting methods (Bowyer et al., 2024) give fast and accurate posterior moment estimates, and we can use these moment estimates to rapidly learn an approximate posterior. Specifically, we propose using expectation maximization to fit the approximate posterior, which we call QEM. The expectation step involves computing the posterior moments using high-quality massively parallel estimates from Bowyer et al. (2024). The maximization step involves fitting the approximate posterior using these moments, which can be done straightforwardly for simple approximate posteriors such as Gaussian, Gamma, Beta, Dirichlet, Binomial, Multinomial, Categorical, etc. (or combinations thereof). We show that QEM is faster than state-of-the-art, massively parallel variants of RWS and VI, and is invariant to reparameterizations of the model that dramatically slow down gradient based methods.

Water quality data can supply a substantial decision support for water resources utilization and pollution prevention. However, there are numerous missing values in water quality data due to inescapable factors like sensor failure, thereby leading to biased result for hydrological analysis and failing to support environmental governance decision accurately. A Latent Factorization of Tensors (LFT) with Stochastic Gradient Descent (SGD) proves to be an efficient imputation method. However, a standard SGD-based LFT model commonly surfers from the slow convergence that impairs its efficiency. To tackle this issue, this paper proposes a Fast Latent Factorization of Tensors (FLFT) model. It constructs an adjusted instance error into SGD via leveraging a nonlinear PID controller to incorporates the past, current and future information of prediction error for improving convergence rate. Comparing with state-of-art models in real world datasets, the results of experiment indicate that the FLFT model achieves a better convergence rate and higher accuracy.

Domain Generalization (DG) research has gained considerable traction as of late, since the ability to generalize to unseen data distributions is a requirement that eludes even state-of-the-art training algorithms. In this paper we observe that the initial iterations of model training play a key role in domain generalization effectiveness, since the loss landscape may be significantly different across the training and test distributions, contrary to the case of i.i.d. data. Conflicts between gradients of the loss components of each domain lead the optimization procedure to undesirable local minima that do not capture the domain-invariant features of the target classes. We propose alleviating domain conflicts in model optimization, by iteratively annealing the parameters of a model in the early stages of training and searching for points where gradients align between domains. By discovering a set of parameter values where gradients are updated towards the same direction for each data distribution present in the training set, the proposed Gradient-Guided Annealing (GGA) algorithm encourages models to seek out minima that exhibit improved robustness against domain shifts. The efficacy of GGA is evaluated on five widely accepted and challenging image classification domain generalization benchmarks, where its use alone is able to establish highly competitive or even state-of-the-art performance. Moreover, when combined with previously proposed domain-generalization algorithms it is able to consistently improve their effectiveness by significant margins.

In distributed learning, sign-based compression algorithms such as signSGD with majority vote provide a lightweight alternative to SGD with an additional advantage: fault tolerance (almost) for free. However, for signSGD with majority vote, this fault tolerance has been shown to cover only the case of weaker adversaries, i.e., ones that are not omniscient or cannot collude to base their attack on common knowledge and strategy. In this work, we close this gap and provide new insights into how signSGD with majority vote can be resilient against omniscient and colluding adversaries, which craft an attack after communicating with other adversaries, thus having better information to perform the most damaging attack based on a common optimal strategy. Our core contribution is in providing a proof that begins by defining the omniscience framework and the strongest possible damage against signSGD with majority vote without imposing any restrictions on the attacker. Thanks to the filtering effect of the sign-based method, we upper-bound the space of attacks to the optimal strategy for maximizing damage by an attacker. Hence, we derive an explicit probabilistic bound in terms of incorrect aggregation without resorting to unknown constants, providing a convergence bound on signSGD with majority vote in the presence of Byzantine attackers, along with a precise convergence rate. Our findings are supported by experiments on the MNIST dataset in a distributed learning environment with adversaries of varying strength.

This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client drift--is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms

Training an energy-based model (EBM) with maximum likelihood is challenging due to the intractable normalisation constant. Traditional methods rely on expensive Markov chain Monte Carlo (MCMC) sampling to estimate the gradient of logartihm of the normalisation constant. We propose a novel objective called self-normalised log-likelihood (SNL) that introduces a single additional learnable parameter representing the normalisation constant compared to the regular log-likelihood. SNL is a lower bound of the log-likelihood, and its optimum corresponds to both the maximum likelihood estimate of the model parameters and the normalisation constant. We show that the SNL objective is concave in the model parameters for exponential family distributions. Unlike the regular log-likelihood, the SNL can be directly optimised using stochastic gradient techniques by sampling from a crude proposal distribution. We validate the effectiveness of our proposed method on various density estimation tasks as well as EBMs for regression. Our results show that the proposed method, while simpler to implement and tune, outperforms existing techniques.

Federated Averaging remains the most widely used aggregation strategy in federated learning due to its simplicity and scalability. However, its performance degrades significantly in non-IID data settings, where client distributions are highly imbalanced or skewed. Additionally, it relies on clients transmitting metadata, specifically the number of training samples, which introduces privacy risks and may conflict with regulatory frameworks like the European GDPR. In this paper, we propose a novel aggregation strategy that addresses these challenges by introducing class-aware gradient masking. Unlike traditional approaches, our method relies solely on gradient updates, eliminating the need for any additional client metadata, thereby enhancing privacy protection. Furthermore, our approach validates and dynamically weights client contributions based on class-specific importance, ensuring robustness against non-IID distributions, convergence prevention, and backdoor attacks. Extensive experiments on benchmark datasets demonstrate that our method not only outperforms FedAvg and other widely accepted aggregation strategies in non-IID settings but also preserves model integrity in adversarial scenarios. Our results establish the effectiveness of gradient masking as a practical and secure solution for federated learning.

Dataset Distillation (DD) is a powerful technique for reducing large datasets into compact, representative synthetic datasets, accelerating Machine Learning training. However, traditional DD methods operate in a centralized manner, which poses significant privacy threats and reduces its applicability. To mitigate these risks, we propose a Secure Federated Data Distillation (SFDD) framework to decentralize the distillation process while preserving privacy. Unlike existing Federated Distillation techniques that focus on training global models with distilled knowledge, our approach aims to produce a distilled dataset without exposing local contributions. We leverage the gradient-matching-based distillation method, adapting it for a distributed setting where clients contribute to the distillation process without sharing raw data. The central aggregator iteratively refines a synthetic dataset by integrating client-side updates while ensuring data confidentiality. To make our approach resilient to inference attacks perpetrated by the server that could exploit gradient updates to reconstruct private data, we create an optimized Local Differential Privacy approach, called LDPO-RLD. Furthermore, we assess the framework's resilience against malicious clients executing backdoor attacks (such as Doorping) and demonstrate robustness under the assumption of a sufficient number of participating clients. Our experimental results demonstrate the effectiveness of SFDD and that the proposed defense concretely mitigates the identified vulnerabilities, with minimal impact on the performance of the distilled dataset. By addressing the interplay between privacy and federation in dataset distillation, this work advances the field of privacy-preserving Machine Learning making our SFDD framework a viable solution for sensitive data-sharing applications.