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Federated Learning (FL) allows several clients to construct a common global machine-learning model without having to share their data. FL, however, faces the challenge of statistical heterogeneity between the client's data, which degrades performance and slows down the convergence toward the global model. In this paper, we provide theoretical proof that minimizing heterogeneity between clients facilitates the convergence of a global model for every single client. This becomes particularly important under empirical concept shifts among clients, rather than merely considering imbalanced classes, which have been studied until now. Therefore, we propose a method for knowledge transfer between clients where the server trains client-specific generators. Each generator generates samples for the corresponding client to remove the conflict with other clients' models. Experiments conducted on synthetic and real data, along with a theoretical study, support the effectiveness of our method in constructing a well-generalizable global model by reducing the conflict between local models.

This paper presents a transient forward harmonic adjoint sensitivity analysis (TFHA), which is a combination of a transient forward circuit analysis with a harmonic balance based adjoint sensitivity analysis. TFHA provides sensitivities of quantities of interest from time-periodic problems w.r.t. many design parameters, as used in the design process of power-electronics devices. The TFHA shows advantages in applications where the harmonic balance based adjoint sensitivity analysis or finite difference approaches for sensitivity analysis perform poorly. In contrast to existing methods, the TFHA can be used in combination with arbitrary forward solvers, i.e. general transient solvers.

Federated Learning (FL), a distributed learning paradigm that scales on-device learning collaboratively, has emerged as a promising approach for decentralized AI applications. Local optimization methods such as Federated Averaging (FedAvg) are the most prominent methods for FL applications. Despite their simplicity and popularity, the theoretical understanding of local optimization methods is far from clear. This dissertation aims to advance the theoretical foundation of local methods in the following three directions. First, we establish sharp bounds for FedAvg, the most popular algorithm in Federated Learning. We demonstrate how FedAvg may suffer from a notion we call iterate bias, and how an additional third-order smoothness assumption may mitigate this effect and lead to better convergence rates. We explain this phenomenon from a Stochastic Differential Equation (SDE) perspective. Second, we propose Federated Accelerated Stochastic Gradient Descent (FedAc), the first principled acceleration of FedAvg, which provably improves the convergence rate and communication efficiency. Our technique uses on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability. Third, we study the Federated Composite Optimization problem, which extends the classic smooth setting by incorporating a shared non-smooth regularizer. We show that direct extensions of FedAvg may suffer from the "curse of primal averaging," resulting in slow convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging, which overcomes the curse of primal averaging by employing a novel inter-client dual averaging procedure.

Recent advancements in federated learning (FL) have greatly facilitated the development of decentralized collaborative applications, particularly in the domain of Artificial Intelligence of Things (AIoT). However, a critical aspect missing from the current research landscape is the ability to enable data-driven client models with symbolic reasoning capabilities. Specifically, the inherent heterogeneity of participating client devices poses a significant challenge, as each client exhibits unique logic reasoning properties. Failing to consider these device-specific specifications can result in critical properties being missed in the client predictions, leading to suboptimal performance. In this work, we propose a new training paradigm that leverages temporal logic reasoning to address this issue. Our approach involves enhancing the training process by incorporating mechanically generated logic expressions for each FL client. Additionally, we introduce the concept of aggregation clusters and develop a partitioning algorithm to effectively group clients based on the alignment of their temporal reasoning properties. We evaluate the proposed method on two tasks: a real-world traffic volume prediction task consisting of sensory data from fifteen states and a smart city multi-task prediction utilizing synthetic data. The evaluation results exhibit clear improvements, with performance accuracy improved by up to 54% across all sequential prediction models.

Improving the alignment of language models with human preferences remains an active research challenge. Previous approaches have primarily utilized Reinforcement Learning from Human Feedback (RLHF) via online RL methods such as Proximal Policy Optimization (PPO). Recently, offline methods such as Sequence Likelihood Calibration (SLiC) and Direct Preference Optimization (DPO) have emerged as attractive alternatives, offering improvements in stability and scalability while maintaining competitive performance. SLiC refines its loss function using sequence pairs sampled from a supervised fine-tuned (SFT) policy, while DPO directly optimizes language models based on preference data, foregoing the need for a separate reward model. However, the maximum likelihood estimator (MLE) of the target optimal policy requires labeled preference pairs sampled from that policy. DPO's lack of a reward model constrains its ability to sample preference pairs from the optimal policy, and SLiC is restricted to sampling preference pairs only from the SFT policy. To address these limitations, we introduce a novel approach called Statistical Rejection Sampling Optimization (RSO) that aims to source preference data from the target optimal policy using rejection sampling, enabling a more accurate estimation of the optimal policy. We also propose a unified framework that enhances the loss functions used in both SLiC and DPO from a preference modeling standpoint. Through extensive experiments across three diverse tasks, we demonstrate that RSO consistently outperforms both SLiC and DPO on evaluations from both Large Language Model (LLM) and human raters.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.

We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.

Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.