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.

Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches. However, we identify a critical issue in these methods, which we term ''wandering in contours''. This behavior refers to sampling new different solutions that share very similar objective values for a long time, leading to computational inefficiency and suboptimal exploration of potential solutions. In this paper, we introduce a novel reheating mechanism inspired by the concept of critical temperature and specific heat in physics, aimed at overcoming this limitation. Empirically, our method demonstrates superiority over existing sampling-based and data-driven algorithms across a diverse array of CO problems.

Recent advances in deep learning optimization have unveiled two intriguing phenomena under large learning rates: Edge of Stability (EoS) and Progressive Sharpening (PS), challenging classical Gradient Descent (GD) analyses. Current research approaches, using either generalist frameworks or minimalist examples, face significant limitations in explaining these phenomena. This paper advances the minimalist approach by introducing a two-layer network with a two-dimensional input, where one dimension is relevant to the response and the other is irrelevant. Through this model, we rigorously prove the existence of progressive sharpening and self-stabilization under large learning rates, and establish non-asymptotic analysis of the training dynamics and sharpness along the entire GD trajectory. Besides, we connect our minimalist example to existing works by reconciling the existence of a well-behaved ``stable set" between minimalist and generalist analyses, and extending the analysis of Gradient Flow Solution sharpness to our two-dimensional input scenario. These findings provide new insights into the EoS phenomenon from both parameter and input data distribution perspectives, potentially informing more effective optimization strategies in deep learning practice.

The Unlearning Sensitive Content from Large Language Models task aims to remove targeted datapoints from trained models while minimally affecting their general knowledge. In our work, we leverage parameter-efficient, gradient-based unlearning using low-rank (LoRA) adaptation and layer-focused fine-tuning. To further enhance unlearning effectiveness, we employ data chunking, splitting forget data into disjoint partitions and merging them with cyclically sampled retain samples at a pre-defined ratio. Our task-agnostic method achieves an outstanding forget-retain balance, ranking first on leaderboards and significantly outperforming baselines and competing systems.

Machine unlearning aims to remove the influence of problematic training data after a model has been trained. The primary challenge in machine unlearning is ensuring that the process effectively removes specified data without compromising the model's overall performance on the remaining dataset. Many existing machine unlearning methods address this challenge by carefully balancing gradient ascent on the unlearn data with the gradient descent on a retain set representing the training data. Here, we propose OrthoGrad, a novel approach that mitigates interference between the unlearn set and the retain set rather than competing ascent and descent processes. Our method projects the gradient of the unlearn set onto the subspace orthogonal to all gradients in the retain batch, effectively avoiding any gradient interference. We demonstrate the effectiveness of OrthoGrad on multiple machine unlearning benchmarks, including automatic speech recognition, outperforming competing methods.

This study reviews popular stochastic gradient-based schemes based on large least-square problems. These schemes, often called optimizers in machine learning, play a crucial role in finding better model parameters. Hence, this study focuses on viewing such optimizers with different hyper-parameters and analyzing them based on least square problems. Codes that produced results in this work are available on https://github.com/q-viper/gradients-based-methods-on-large-least-square.

We consider nonconvex optimization problem over simplex, and more generally, a product of simplices. We provide an algorithm, Langevin Multiplicative Weights Update (LMWU) for solving global optimization problems by adding a noise scaling with the non-Euclidean geometry in the simplex. Non-convex optimization has been extensively studied by machine learning community due to its application in various scenarios such as neural network approximation and finding Nash equilibrium. Despite recent progresses on provable guarantee of escaping and avoiding saddle point (convergence to local minima) and global convergence of Langevin gradient based method without constraints, the global optimization with constraints is less studied. We show that LMWU algorithm is provably convergent to interior global minima with a non-asymptotic convergence analysis. We verify the efficiency of the proposed algorithm in real data set from polynomial portfolio management, where optimization of a highly non-linear objective function plays a crucial role.