Base Models for Parabolic Partial Differential Equations

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often necessary to compute the solutions or a function of the solutions to a parametric PDE in multiple scenarios corresponding to different parameters of this PDE. This process often requires resolving the PDEs from scratch, which is time-consuming. To better employ existing simulations for the PDEs, we propose a framework for finding solutions to parabolic PDEs across different scenarios by meta-learning an underlying base distribution. We build upon this base distribution to propose a method for computing solutions to parametric PDEs under different parameter settings. Finally, we illustrate the application of the proposed methods through extensive experiments in generative modeling, stochastic control, and finance. The empirical results suggest that the proposed approach improves generalization to solving PDEs under new parameter regimes.

CroMo-Mixup: Augmenting Cross-Model Representations for Continual Self-Supervised Learning

Continual self-supervised learning (CSSL) learns a series of tasks sequentially on the unlabeled data. Two main challenges of continual learning are catastrophic forgetting and task confusion. While CSSL problem has been studied to address the catastrophic forgetting challenge, little work has been done to address the task confusion aspect. In this work, we show through extensive experiments that self-supervised learning (SSL) can make CSSL more susceptible to the task confusion problem, particularly in less diverse settings of class incremental learning because different classes belonging to different tasks are not trained concurrently. Motivated by this challenge, we present a novel cross-model feature Mixup (CroMo-Mixup) framework that addresses this issue through two key components: 1) Cross-Task data Mixup, which mixes samples across tasks to enhance negative sample diversity; and 2) Cross-Model feature Mixup, which learns similarities between embeddings obtained from current and old models of the mixed sample and the original images, facilitating cross-task class contrast learning and old knowledge retrieval. We evaluate the effectiveness of CroMo-Mixup to improve both Task-ID prediction and average linear accuracy across all tasks on three datasets, CIFAR10, CIFAR100, and tinyImageNet under different class-incremental learning settings. We validate the compatibility of CroMo-Mixup on four state-of-the-art SSL objectives. Code is available at \url{https://github.com/ErumMushtaq/CroMo-Mixup}.

Robust Score-Based Quickest Change Detection

Methods in the field of quickest change detection rapidly detect in real-time a change in the data-generating distribution of an online data stream. Existing methods have been able to detect this change point when the densities of the pre- and post-change distributions are known. Recent work has extended these results to the case where the pre- and post-change distributions are known only by their score functions. This work considers the case where the pre- and post-change score functions are known only to correspond to distributions in two disjoint sets. This work employs a pair of "least-favorable" distributions to robustify the existing score-based quickest change detection algorithm, the properties of which are studied. This paper calculates the least-favorable distributions for specific model classes and provides methods of estimating the least-favorable distributions for common constructions. Simulation results are provided demonstrating the performance of our robust change detection algorithm.

Additive-Effect Assisted Learning

It is quite popular nowadays for researchers and data analysts holding different datasets to seek assistance from each other to enhance their modeling performance. We consider a scenario where different learners hold datasets with potentially distinct variables, and their observations can be aligned by a nonprivate identifier. Their collaboration faces the following difficulties: First, learners may need to keep data values or even variable names undisclosed due to, e.g., commercial interest or privacy regulations; second, there are restrictions on the number of transmission rounds between them due to e.g., communication costs. To address these challenges, we develop a two-stage assisted learning architecture for an agent, Alice, to seek assistance from another agent, Bob. In the first stage, we propose a privacy-aware hypothesis testing-based screening method for Alice to decide on the usefulness of the data from Bob, in a way that only requires Bob to transmit sketchy data. Once Alice recognizes Bob's usefulness, Alice and Bob move to the second stage, where they jointly apply a synergistic iterative model training procedure. With limited transmissions of summary statistics, we show that Alice can achieve the oracle performance as if the training were from centralized data, both theoretically and numerically.

ColA: Collaborative Adaptation with Gradient Learning

A primary function of back-propagation is to compute both the gradient of hidden representations and parameters for optimization with gradient descent. Training large models requires high computational costs due to their vast parameter sizes. While Parameter-Efficient Fine-Tuning (PEFT) methods aim to train smaller auxiliary models to save computational space, they still present computational overheads, especially in Fine-Tuning as a Service (FTaaS) for numerous users. We introduce Collaborative Adaptation (ColA) with Gradient Learning (GL), a parameter-free, model-agnostic fine-tuning approach that decouples the computation of the gradient of hidden representations and parameters. In comparison to PEFT methods, ColA facilitates more cost-effective FTaaS by offloading the computation of the gradient to low-cost devices. We also provide a theoretical analysis of ColA and experimentally demonstrate that ColA can perform on par or better than existing PEFT methods on various benchmarks.

Demystifying Poisoning Backdoor Attacks from a Statistical Perspective

The growing dependence on machine learning in real-world applications emphasizes the importance of understanding and ensuring its safety. Backdoor attacks pose a significant security risk due to their stealthy nature and potentially serious consequences. Such attacks involve embedding triggers within a learning model with the intention of causing malicious behavior when an active trigger is present while maintaining regular functionality without it. This paper evaluates the effectiveness of any backdoor attack incorporating a constant trigger, by establishing tight lower and upper boundaries for the performance of the compromised model on both clean and backdoor test data. The developed theory answers a series of fundamental but previously underexplored problems, including (1) what are the determining factors for a backdoor attack's success, (2) what is the direction of the most effective backdoor attack, and (3) when will a human-imperceptible trigger succeed. Our derived understanding applies to both discriminative and generative models. We also demonstrate the theory by conducting experiments using benchmark datasets and state-of-the-art backdoor attack scenarios.

Network Robustness Learning via Graph Transformer

Learning and analysis of network robustness, including controllability robustness and connectivity robustness, is critical for various networked systems against attacks. Traditionally, network robustness is determined by attack simulations, which is very time-consuming and even incapable for large-scale networks. Network Robustness Learning, which is dedicated to learning network robustness with high precision and high speed, provides a powerful tool to analyze network robustness by replacing simulations. In this paper, a novel versatile and unified robustness learning approach via graph transformer (NRL-GT) is proposed, which accomplishes the task of controllability robustness learning and connectivity robustness learning from multiple aspects including robustness curve learning, overall robustness learning, and synthetic network classification. Numerous experiments show that: 1) NRL-GT is a unified learning framework for controllability robustness and connectivity robustness, demonstrating a strong generalization ability to ensure high precision when training and test sets are distributed differently; 2) Compared to the cutting-edge methods, NRL-GT can simultaneously perform network robustness learning from multiple aspects and obtains superior results in less time. NRL-GT is also able to deal with complex networks of different size with low learning error and high efficiency; 3) It is worth mentioning that the backbone of NRL-GT can serve as a transferable feature learning module for complex networks of different size and different downstream tasks.

Robust Quickest Change Detection for Unnormalized Models

Detecting an abrupt and persistent change in the underlying distribution of online data streams is an important problem in many applications. This paper proposes a new robust score-based algorithm called RSCUSUM, which can be applied to unnormalized models and addresses the issue of unknown post-change distributions. RSCUSUM replaces the Kullback-Leibler divergence with the Fisher divergence between pre- and post-change distributions for computational efficiency in unnormalized statistical models and introduces a notion of the ``least favorable'' distribution for robust change detection. The algorithm and its theoretical analysis are demonstrated through simulation studies.

A Framework for Incentivized Collaborative Learning

Collaborations among various entities, such as companies, research labs, AI agents, and edge devices, have become increasingly crucial for achieving machine learning tasks that cannot be accomplished by a single entity alone. This is likely due to factors such as security constraints, privacy concerns, and limitations in computation resources. As a result, collaborative learning (CL) research has been gaining momentum. However, a significant challenge in practical applications of CL is how to effectively incentivize multiple entities to collaborate before any collaboration occurs. In this study, we propose ICL, a general framework for incentivized collaborative learning, and provide insights into the critical issue of when and why incentives can improve collaboration performance. Furthermore, we show the broad applicability of ICL to specific cases in federated learning, assisted learning, and multi-armed bandit with both theory and experimental results.

Semi-Supervised Federated Learning for Keyword Spotting

Keyword Spotting (KWS) is a critical aspect of audio-based applications on mobile devices and virtual assistants. Recent developments in Federated Learning (FL) have significantly expanded the ability to train machine learning models by utilizing the computational and private data resources of numerous distributed devices. However, existing FL methods typically require that devices possess accurate ground-truth labels, which can be both expensive and impractical when dealing with local audio data. In this study, we first demonstrate the effectiveness of Semi-Supervised Federated Learning (SSL) and FL for KWS. We then extend our investigation to Semi-Supervised Federated Learning (SSFL) for KWS, where devices possess completely unlabeled data, while the server has access to a small amount of labeled data. We perform numerical analyses using state-of-the-art SSL, FL, and SSFL techniques to demonstrate that the performance of KWS models can be significantly improved by leveraging the abundant unlabeled heterogeneous data available on devices.