Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

This paper proposes a theoretical framework to evaluate and compare the performance of gradient-descent algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have noticed that convergence toward flat local minima tend to enhance the generalization ability of learning algorithms. This work discovers two interesting results. First, it shows that decentralized learning strategies are able to escape faster away from local minimizers and favor convergence toward flatter minima relative to the centralized solution in the large-batch training regime. Second, and importantly, the ultimate classification accuracy is not solely dependent on the flatness of the local minimizer but also on how well a learning algorithm can approach that minimum. In other words, the classification accuracy is a function of both flatness and optimization performance. The paper examines the interplay between the two measures of flatness and optimization error closely. One important conclusion is that decentralized strategies of the diffusion type deliver enhanced classification accuracy because it strikes a more favorable balance between flatness and optimization performance.

The rapid evolution of deep learning and large language models has led to an exponential growth in the demand for training data, prompting the development of Dataset Distillation methods to address the challenges of managing large datasets. Among these, Matching Training Trajectories (MTT) has been a prominent approach, which replicates the training trajectory of an expert network on real data with a synthetic dataset. However, our investigation found that this method suffers from three significant limitations: 1. Instability of expert trajectory generated by Stochastic Gradient Descent (SGD); 2. Low convergence speed of the distillation process; 3. High storage consumption of the expert trajectory. To address these issues, we offer a new perspective on understanding the essence of Dataset Distillation and MTT through a simple transformation of the objective function, and introduce a novel method called Matching Convexified Trajectory (MCT), which aims to provide better guidance for the student trajectory. MCT leverages insights from the linearized dynamics of Neural Tangent Kernel methods to create a convex combination of expert trajectories, guiding the student network to converge rapidly and stably. This trajectory is not only easier to store, but also enables a continuous sampling strategy during distillation, ensuring thorough learning and fitting of the entire expert trajectory.

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of dynamical systems formulates this problem as a linear equation system. Here, we explore several simulation-based optimization approaches, which allow much greater freedom in the objective formulation and weaker conditions on the available data. We show that even for relatively small stochastic population models, simultaneous estimation of parameters and structure poses major challenges for optimization procedures. Particularly, we investigate the application of the local stochastic gradient descent method, commonly used for training machine learning models. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty. We give an outlook on how this challenge can be overcome.

Stochastic Gradient Descent is used for large datasets to train models to reduce the training time. On top of that data parallelism is widely used as a method to efficiently train neural networks using multiple worker nodes in parallel. Synchronous and asynchronous approach to data parallelism is used by most systems to train the model in parallel. However, both of them have their drawbacks. We propose a third approach to data parallelism which is a hybrid between synchronous and asynchronous approaches, using both approaches to train the neural network. When the threshold function is selected appropriately to gradually shift all parameter aggregation from asynchronous to synchronous, we show that in a given time period our hybrid approach outperforms both asynchronous and synchronous approaches.

Imagine training a machine learning model with Differentially Private Stochastic Gradient Descent (DP-SGD), only to discover post-training that the noise level was either too high, crippling your model's utility, or too low, compromising privacy. The dreaded realization hits: you must start the lengthy training process from scratch. But what if you could avoid this retraining nightmare? In this study, we introduce a groundbreaking approach (to our knowledge) that applies differential privacy noise to the model's weights after training. We offer a comprehensive mathematical proof for this novel approach's privacy bounds, use formal methods to validate its privacy guarantees, and empirically evaluate its effectiveness using membership inference attacks and performance evaluations. This method allows for a single training run, followed by post-hoc noise adjustments to achieve optimal privacy-utility trade-offs. We compare this novel fine-tuned model (DP-Weights model) to a traditional DP-SGD model, demonstrating that our approach yields statistically similar performance and privacy guarantees. Our results validate the efficacy of post-training noise application, promising significant time savings and flexibility in fine-tuning differential privacy parameters, making it a practical alternative for deploying differentially private models in real-world scenarios.

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and hence can mix better than standard reversible MCMC samplers. Furthermore, they can incorporate exact sub-sampling schemes which only require access to a single (randomly selected) data point at each iteration, yet without introducing bias to the algorithm's stationary distribution. However, the range of models for which PDMPs can be used, particularly with sub-sampling, is limited. We propose approximate simulation of PDMPs with sub-sampling for scalable sampling from posterior distributions. The approximation takes the form of an Euler approximation to the true PDMP dynamics, and involves using an estimate of the gradient of the log-posterior based on a data sub-sample. We thus call this class of algorithms stochastic-gradient PDMPs. Importantly, the trajectories of stochastic-gradient PDMPs are continuous and can leverage recent ideas for sampling from measures with continuous and atomic components. We show these methods are easy to implement, present results on their approximation error and demonstrate numerically that this class of algorithms has similar efficiency to, but is more robust than, stochastic gradient Langevin dynamics.

Federated learning enables the training of machine learning models on distributed data without compromising user privacy, as data remains on personal devices and only model updates, such as gradients, are shared with a central coordinator. However, recent research has shown that the central entity can perfectly reconstruct private data from shared model updates by maliciously initializing the model's parameters. In this paper, we propose QBI, a novel bias initialization method that significantly enhances reconstruction capabilities. This is accomplished by directly solving for bias values yielding sparse activation patterns. Further, we propose PAIRS, an algorithm that builds on QBI. PAIRS can be deployed when a separate dataset from the target domain is available to further increase the percentage of data that can be fully recovered. Measured by the percentage of samples that can be perfectly reconstructed from batches of various sizes, our approach achieves significant improvements over previous methods with gains of up to 50% on ImageNet and up to 60% on the IMDB sentiment analysis text dataset. Furthermore, we establish theoretical limits for attacks leveraging stochastic gradient sparsity, providing a foundation for understanding the fundamental constraints of these attacks. We empirically assess these limits using synthetic datasets. Finally, we propose and evaluate AGGP, a defensive framework designed to prevent gradient sparsity attacks, contributing to the development of more secure and private federated learning systems.

Federated learning (FL), a novel branch of distributed machine learning (ML), develops global models through a private procedure without direct access to local datasets. However, it is still possible to access the model updates (gradient updates of deep neural networks) transferred between clients and servers, potentially revealing sensitive local information to adversaries using model inversion attacks. Differential privacy (DP) offers a promising approach to addressing this issue by adding noise to the parameters. On the other hand, heterogeneities in data structure, storage, communication, and computational capabilities of devices can cause convergence problems and delays in developing the global model. A personalized weighted averaging of local parameters based on the resources of each device can yield a better aggregated model in each round. In this paper, to efficiently preserve privacy, we propose a personalized DP framework that injects noise based on clients' relative impact factors and aggregates parameters while considering heterogeneities and adjusting properties. To fulfill the DP requirements, we first analyze the convergence boundary of the FL algorithm when impact factors are personalized and fixed throughout the learning process. We then further study the convergence property considering time-varying (adaptive) impact factors.

Large language models (LLMs) have shown the emergent capability of in-context learning (ICL). One line of research has explained ICL as functionally performing gradient descent. In this paper, we introduce a new way of diagnosing whether ICL is functionally equivalent to gradient-based learning. Our approach is based on the inverse frequency effect (IFE) -- a phenomenon in which an error-driven learner is expected to show larger updates when trained on infrequent examples than frequent ones. The IFE has previously been studied in psycholinguistics because humans show this effect in the context of structural priming (the tendency for people to produce sentence structures they have encountered recently); the IFE has been used as evidence that human structural priming must involve error-driven learning mechanisms. In our experiments, we simulated structural priming within ICL and found that LLMs display the IFE, with the effect being stronger in larger models. We conclude that ICL is indeed a type of gradient-based learning, supporting the hypothesis that a gradient component is implicitly computed in the forward pass during ICL. Our results suggest that both humans and LLMs make use of gradient-based, error-driven processing mechanisms.