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By allowing users to erase their data's impact on federated learning models, federated unlearning protects users' right to be forgotten and data privacy. Despite a burgeoning body of research on federated unlearning's technical feasibility, there is a paucity of literature investigating the considerations behind users' requests for data revocation. This paper proposes a non-cooperative game framework to study users' data revocation strategies in federated unlearning. We prove the existence of a Nash equilibrium. However, users' best response strategies are coupled via model performance and unlearning costs, which makes the equilibrium computation challenging. We obtain the Nash equilibrium by establishing its equivalence with a much simpler auxiliary optimization problem. We also summarize users' multi-dimensional attributes into a single-dimensional metric and derive the closed-form characterization of an equilibrium, when users' unlearning costs are negligible. Moreover, we compare the cases of allowing and forbidding partial data revocation in federated unlearning. Interestingly, the results reveal that allowing partial revocation does not necessarily increase users' data contributions or payoffs due to the game structure. Additionally, we demonstrate that positive externalities may exist between users' data revocation decisions when users incur unlearning costs, while this is not the case when their unlearning costs are negligible.

This paper delves into the problem of safe reinforcement learning (RL) in a partially observable environment with the aim of achieving safe-reachability objectives. In traditional partially observable Markov decision processes (POMDP), ensuring safety typically involves estimating the belief in latent states. However, accurately estimating an optimal Bayesian filter in POMDP to infer latent states from observations in a continuous state space poses a significant challenge, largely due to the intractable likelihood. To tackle this issue, we propose a stochastic model-based approach that guarantees RL safety almost surely in the face of unknown system dynamics and partial observation environments. We leveraged the Predictive State Representation (PSR) and Reproducing Kernel Hilbert Space (RKHS) to represent future multi-step observations analytically, and the results in this context are provable. Furthermore, we derived essential operators from the kernel Bayes' rule, enabling the recursive estimation of future observations using various operators. Under the assumption of \textit{undercompleness}, a polynomial sample complexity is established for the RL algorithm for the infinite size of observation and action spaces, ensuring an $\epsilon-$suboptimal safe policy guarantee.

Activation functions are the linchpins of deep learning, profoundly influencing both the representational capacity and training dynamics of neural networks. They shape not only the nature of representations but also optimize convergence rates and enhance generalization potential. Appreciating this critical role, we present the Linear Oscillation (LoC) activation function, defined as $f(x) = x \times \sin(\alpha x + \beta)$. Distinct from conventional activation functions which primarily introduce non-linearity, LoC seamlessly blends linear trajectories with oscillatory deviations. The nomenclature "Linear Oscillation" is a nod to its unique attribute of infusing linear activations with harmonious oscillations, capturing the essence of the "Importance of Confusion". This concept of "controlled confusion" within network activations is posited to foster more robust learning, particularly in contexts that necessitate discerning subtle patterns. Our empirical studies reveal that, when integrated into diverse neural architectures, the LoC activation function consistently outperforms established counterparts like ReLU and Sigmoid. The stellar performance exhibited by the avant-garde Vision Transformer model using LoC further validates its efficacy. This study illuminates the remarkable benefits of the LoC over other prominent activation functions. It champions the notion that intermittently introducing deliberate complexity or "confusion" during training can spur more profound and nuanced learning. This accentuates the pivotal role of judiciously selected activation functions in shaping the future of neural network training.

Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs. Sparse Gaussian processes (GP) have shown promise as a leading candidate for the experts in such models, and in this article, we propose to design the gating network for selecting the experts from such mixtures of sparse GPs using a deep neural network (DNN). Furthermore, a fast one pass algorithm called Cluster-Classify-Regress (CCR) is leveraged to approximate the maximum a posteriori (MAP) estimator extremely quickly. This powerful combination of model and algorithm together delivers a novel method which is flexible, robust, and extremely efficient. In particular, the method is able to outperform competing methods in terms of accuracy and uncertainty quantification. The cost is competitive on low-dimensional and small data sets, but is significantly lower for higher-dimensional and big data sets. Iteratively maximizing the distribution of experts given allocations and allocations given experts does not provide significant improvement, which indicates that the algorithm achieves a good approximation to the local MAP estimator very fast. This insight can be useful also in the context of other mixture of experts models.

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and outputs its solution. However, the architectural design space, especially given structural knowledge of the PDE family of interest, is still poorly understood. We seek to remedy this gap by studying the benefits of weight-tied neural network architectures for steady-state PDEs. To achieve this, we first demonstrate that the solution of most steady-state PDEs can be expressed as a fixed point of a non-linear operator. Motivated by this observation, we propose FNO-DEQ, a deep equilibrium variant of the FNO architecture that directly solves for the solution of a steady-state PDE as the infinite-depth fixed point of an implicit operator layer using a black-box root solver and differentiates analytically through this fixed point resulting in $\mathcal{O}(1)$ training memory. Our experiments indicate that FNO-DEQ-based architectures outperform FNO-based baselines with $4\times$ the number of parameters in predicting the solution to steady-state PDEs such as Darcy Flow and steady-state incompressible Navier-Stokes. Finally, we show FNO-DEQ is more robust when trained with datasets with more noisy observations than the FNO-based baselines, demonstrating the benefits of using appropriate inductive biases in architectural design for different neural network based PDE solvers. Further, we show a universal approximation result that demonstrates that FNO-DEQ can approximate the solution to any steady-state PDE that can be written as a fixed point equation.

Counterfactual explanations (CFE) are methods that explain a machine learning model by giving an alternate class prediction of a data point with some minimal changes in its features. It helps the users to identify their data attributes that caused an undesirable prediction like a loan or credit card rejection. We describe an efficient and an actionable counterfactual (CF) generation method based on particle swarm optimization (PSO). We propose a simple objective function for the optimization of the instance-centric CF generation problem. The PSO brings in a lot of flexibility in terms of carrying out multi-objective optimization in large dimensions, capability for multiple CF generation, and setting box constraints or immutability of data attributes. An algorithm is proposed that incorporates these features and it enables greater control over the proximity and sparsity properties over the generated CFs. The proposed algorithm is evaluated with a set of action-ability metrics in real-world datasets, and the results were superior compared to that of the state-of-the-arts.

Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and under-represented in others. This paper defines a novel $\ell_1$-regularized pseudo-likelihood approach for fair graphical model selection. In particular, we assume there is some community or clustering structure in the true underlying graph, and we seek to learn a sparse undirected graph and its communities from the data such that demographic groups are fairly represented within the communities. In the case when the graph is known a priori, we provide a convex semidefinite programming approach for fair community detection. We establish the statistical consistency of the proposed method for both a Gaussian graphical model and an Ising model for, respectively, continuous and binary data, proving that our method can recover the graphs and their fair communities with high probability.

Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.

Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.