Towards Diverse Device Heterogeneous Federated Learning via Task Arithmetic Knowledge Integration

Federated Learning has emerged as a promising paradigm for collaborative machine learning, while preserving user data privacy. Despite its potential, standard FL lacks support for diverse heterogeneous device prototypes, which vary significantly in model and dataset sizes -- from small IoT devices to large workstations. This limitation is only partially addressed by existing knowledge distillation techniques, which often fail to transfer knowledge effectively across a broad spectrum of device prototypes with varied capabilities. This failure primarily stems from two issues: the dilution of informative logits from more capable devices by those from less capable ones, and the use of a single integrated logits as the distillation target across all devices, which neglects their individual learning capacities and and the unique contributions of each. To address these challenges, we introduce TAKFL, a novel KD-based framework that treats the knowledge transfer from each device prototype's ensemble as a separate task, independently distilling each to preserve its unique contributions and avoid dilution. TAKFL also incorporates a KD-based self-regularization technique to mitigate the issues related to the noisy and unsupervised ensemble distillation process. To integrate the separately distilled knowledge, we introduce an adaptive task arithmetic knowledge integration process, allowing each student model to customize the knowledge integration for optimal performance. Additionally, we present theoretical results demonstrating the effectiveness of task arithmetic in transferring knowledge across heterogeneous devices with varying capacities. Comprehensive evaluations of our method across both CV and NLP tasks demonstrate that TAKFL achieves SOTA results in a variety of datasets and settings, significantly outperforming existing KD-based methods. Code is released at https://github.com/MMorafah/TAKFL

Dataset Distillation from First Principles: Integrating Core Information Extraction and Purposeful Learning

Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter. While DD has a wide range of applications, the theory supporting it is less well evolved. New methods of DD are compared on a common set of benchmarks, rather than oriented towards any particular learning task. In this work, we present a formal model of DD, arguing that a precise characterization of the underlying optimization problem must specify the inference task associated with the application of interest. Without this task-specific focus, the DD problem is under-specified, and the selection of a DD algorithm for a particular task is merely heuristic. Our formalization reveals novel applications of DD across different modeling environments. We analyze existing DD methods through this broader lens, highlighting their strengths and limitations in terms of accuracy and faithfulness to optimal DD operation. Finally, we present numerical results for two case studies important in contemporary settings. Firstly, we address a critical challenge in medical data analysis: merging the knowledge from different datasets composed of intersecting, but not identical, sets of features, in order to construct a larger dataset in what is usually a small sample setting. Secondly, we consider out-of-distribution error across boundary conditions for physics-informed neural networks (PINNs), showing the potential for DD to provide more physically faithful data. By establishing this general formulation of DD, we aim to establish a new research paradigm by which DD can be understood and from which new DD techniques can arise.

Probabilistic Iterative Hard Thresholding for Sparse Learning

For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called "l0 norm" which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing sparsity when incorporated into an optimization problem. However, in big data settings wherein noisy estimates of the gradient must be evaluated out of computational necessity, the literature is scant on methods that reliably converge. In this paper we present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying stochastic process, and demonstrate the performance on two Machine Learning problems.

Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisons

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

Empirical Bayes for Dynamic Bayesian Networks Using Generalized Variational Inference

In this work, we demonstrate the Empirical Bayes approach to learning a Dynamic Bayesian Network. By starting with several point estimates of structure and weights, we can use a data-driven prior to subsequently obtain a model to quantify uncertainty. This approach uses a recent development of Generalized Variational Inference, and indicates the potential of sampling the uncertainty of a mixture of DAG structures as well as a parameter posterior.

Group Distributionally Robust Dataset Distillation with Risk Minimization

Dataset distillation (DD) has emerged as a widely adopted technique for crafting a synthetic dataset that captures the essential information of a training dataset, facilitating the training of accurate neural models. Its applications span various domains, including transfer learning, federated learning, and neural architecture search. The most popular methods for constructing the synthetic data rely on matching the convergence properties of training the model with the synthetic dataset and the training dataset. However, targeting the training dataset must be thought of as auxiliary in the same sense that the training set is an approximate substitute for the population distribution, and the latter is the data of interest. Yet despite its popularity, an aspect that remains unexplored is the relationship of DD to its generalization, particularly across uncommon subgroups. That is, how can we ensure that a model trained on the synthetic dataset performs well when faced with samples from regions with low population density? Here, the representativeness and coverage of the dataset become salient over the guaranteed training error at inference. Drawing inspiration from distributionally robust optimization, we introduce an algorithm that combines clustering with the minimization of a risk measure on the loss to conduct DD. We provide a theoretical rationale for our approach and demonstrate its effective generalization and robustness across subgroups through numerical experiments.

Unlocking the Potential of Federated Learning: The Symphony of Dataset Distillation via Deep Generative Latents

Data heterogeneity presents significant challenges for federated learning (FL). Recently, dataset distillation techniques have been introduced, and performed at the client level, to attempt to mitigate some of these challenges. In this paper, we propose a highly efficient FL dataset distillation framework on the server side, significantly reducing both the computational and communication demands on local devices while enhancing the clients' privacy. Unlike previous strategies that perform dataset distillation on local devices and upload synthetic data to the server, our technique enables the server to leverage prior knowledge from pre-trained deep generative models to synthesize essential data representations from a heterogeneous model architecture. This process allows local devices to train smaller surrogate models while enabling the training of a larger global model on the server, effectively minimizing resource utilization. We substantiate our claim with a theoretical analysis, demonstrating the asymptotic resemblance of the process to the hypothetical ideal of completely centralized training on a heterogeneous dataset. Empirical evidence from our comprehensive experiments indicates our method's superiority, delivering an accuracy enhancement of up to 40% over non-dataset-distillation techniques in highly heterogeneous FL contexts, and surpassing existing dataset-distillation methods by 18%. In addition to the high accuracy, our framework converges faster than the baselines because rather than the server trains on several sets of heterogeneous data distributions, it trains on a multi-modal distribution. Our code is available at https://github.com/FedDG23/FedDG-main.git

Efficient Dataset Distillation via Minimax Diffusion

Dataset distillation reduces the storage and computational consumption of training a network by generating a small surrogate dataset that encapsulates rich information of the original large-scale one. However, previous distillation methods heavily rely on the sample-wise iterative optimization scheme. As the images-per-class (IPC) setting or image resolution grows larger, the necessary computation will demand overwhelming time and resources. In this work, we intend to incorporate generative diffusion techniques for computing the surrogate dataset. Observing that key factors for constructing an effective surrogate dataset are representativeness and diversity, we design additional minimax criteria in the generative training to enhance these facets for the generated images of diffusion models. We present a theoretical model of the process as hierarchical diffusion control demonstrating the flexibility of the diffusion process to target these criteria without jeopardizing the faithfulness of the sample to the desired distribution. The proposed method achieves state-of-the-art validation performance while demanding much less computational resources. Under the 100-IPC setting on ImageWoof, our method requires less than one-twentieth the distillation time of previous methods, yet yields even better performance. Source code available in https://github.com/vimar-gu/MinimaxDiffusion.

Quantum Solutions to the Privacy vs. Utility Tradeoff

In this work, we propose a novel architecture (and several variants thereof) based on quantum cryptographic primitives with provable privacy and security guarantees regarding membership inference attacks on generative models. Our architecture can be used on top of any existing classical or quantum generative models. We argue that the use of quantum gates associated with unitary operators provides inherent advantages compared to standard Differential Privacy based techniques for establishing guaranteed security from all polynomial-time adversaries.

A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth (nonconvex) optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique in its use of inner neighborhoods of the feasible region -- defined by a positive and vanishing neighborhood-parameter sequence -- in which the iterates are forced to remain. It is shown that with a careful balance between the barrier, step-size, and neighborhood sequences, the proposed algorithm satisfies convergence guarantees in both deterministic and stochastic settings. The results of numerical experiments show that in both settings the algorithm can outperform a projected-(stochastic)-gradient method.