This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient tracking to mitigate the influence of data heterogeneity, without exploring other well-known heterogeneity-correction techniques such as EXTRA or Exact Diffusion. Additionally, these studies often employ identical decentralized strategies for both upper- and lower-level problems, neglecting to leverage distinct mechanisms across different levels. To address these limitations, this paper proposes SPARKLE, a unified Single-loop Primal-dual AlgoRithm frameworK for decentraLized bilEvel optimization. SPARKLE offers the flexibility to incorporate various heterogeneitycorrection strategies into the algorithm. Moreover, SPARKLE allows for different strategies to solve upper- and lower-level problems. We present a unified convergence analysis for SPARKLE, applicable to all its variants, with state-of-the-art convergence rates compared to existing decentralized bilevel algorithms. Our results further reveal that EXTRA and Exact Diffusion are more suitable for decentralized bilevel optimization, and using mixed strategies in bilevel algorithms brings more benefits than relying solely on gradient tracking.

In this paper, we propose a bilevel joint unsupervised and supervised training (BL-JUST) framework for automatic speech recognition. Compared to the conventional pre-training and fine-tuning strategy which is a disconnected two-stage process, BL-JUST tries to optimize an acoustic model such that it simultaneously minimizes both the unsupervised and supervised loss functions. Because BL-JUST seeks matched local optima of both loss functions, acoustic representations learned by the acoustic model strike a good balance between being generic and task-specific. We solve the BL-JUST problem using penalty-based bilevel gradient descent and evaluate the trained deep neural network acoustic models on various datasets with a variety of architectures and loss functions. We show that BL-JUST can outperform the widely-used pre-training and fine-tuning strategy and some other popular semi-supervised techniques.

Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the theoretical understanding of how to train a Transformer to achieve the CoT ability remains less explored. This is primarily due to the technical challenges involved in analyzing the nonconvex optimization on nonlinear attention models. To the best of our knowledge, this work provides the first theoretical study of training Transformers with nonlinear attention to obtain the CoT generalization capability so that the resulting model can inference on unseen tasks when the input is augmented by examples of the new task. We first quantify the required training samples and iterations to train a Transformer model towards CoT ability. We then prove the success of its CoT generalization on unseen tasks with distribution-shifted testing data. Moreover, we theoretically characterize the conditions for an accurate reasoning output by CoT even when the provided reasoning examples contain noises and are not always accurate. In contrast, in-context learning (ICL), which can be viewed as one-step CoT without intermediate steps, may fail to provide an accurate output when CoT does. These theoretical findings are justified through experiments.

Federated learning (FL) enables multiple clients to collaboratively train machine learning models without revealing their private training data. In conventional FL, the system follows the server-assisted architecture (server-assisted FL), where the training process is coordinated by a central server. However, the server-assisted FL framework suffers from poor scalability due to a communication bottleneck at the server, and trust dependency issues. To address challenges, decentralized federated learning (DFL) architecture has been proposed to allow clients to train models collaboratively in a serverless and peer-to-peer manner. However, due to its fully decentralized nature, DFL is highly vulnerable to poisoning attacks, where malicious clients could manipulate the system by sending carefully-crafted local models to their neighboring clients. To date, only a limited number of Byzantine-robust DFL methods have been proposed, most of which are either communication-inefficient or remain vulnerable to advanced poisoning attacks. In this paper, we propose a new algorithm called BALANCE (Byzantine-robust averaging through local similarity in decentralization) to defend against poisoning attacks in DFL. In BALANCE, each client leverages its own local model as a similarity reference to determine if the received model is malicious or benign. We establish the theoretical convergence guarantee for BALANCE under poisoning attacks in both strongly convex and non-convex settings. Furthermore, the convergence rate of BALANCE under poisoning attacks matches those of the state-of-the-art counterparts in Byzantine-free settings. Extensive experiments also demonstrate that BALANCE outperforms existing DFL methods and effectively defends against poisoning attacks.

Transformer-based large language models have displayed impressive in-context learning capabilities, where a pre-trained model can handle new tasks without fine-tuning by simply augmenting the query with some input-output examples from that task. Despite the empirical success, the mechanics of how to train a Transformer to achieve ICL and the corresponding ICL capacity is mostly elusive due to the technical challenges of analyzing the nonconvex training problems resulting from the nonlinear self-attention and nonlinear activation in Transformers. To the best of our knowledge, this paper provides the first theoretical analysis of the training dynamics of Transformers with nonlinear self-attention and nonlinear MLP, together with the ICL generalization capability of the resulting model. Focusing on a group of binary classification tasks, we train Transformers using data from a subset of these tasks and quantify the impact of various factors on the ICL generalization performance on the remaining unseen tasks with and without data distribution shifts. We also analyze how different components in the learned Transformers contribute to the ICL performance. Furthermore, we provide the first theoretical analysis of how model pruning affects ICL performance and prove that proper magnitude-based pruning can have a minimal impact on ICL while reducing inference costs. These theoretical findings are justified through numerical experiments.

Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL learning involves directly acquiring data from downstream tasks, which is not feasible for federated learning (FL). To address this limitation, we shift the focus from such a one-to-one interactive neuro-symbolic paradigm to one-to-many Federated Neuro-Symbolic Learning framework (FedNSL) with latent variables as the FL communication medium. Built on the basis of our novel reformulation of the NSL theory, FedNSL is capable of identifying and addressing rule distribution heterogeneity through a simple and effective Kullback-Leibler (KL) divergence constraint on rule distribution applicable under the FL setting. It further theoretically adjusts variational expectation maximization (V-EM) to reduce the rule search space across domains. This is the first incorporation of distribution-coupled bilevel optimization into FL. Extensive experiments based on both synthetic and real-world data demonstrate significant advantages of FedNSL compared to five state-of-the-art methods. It outperforms the best baseline by 17% and 29% in terms of unbalanced average training accuracy and unseen average testing accuracy, respectively.

This paper studies the transfer reinforcement learning (RL) problem where multiple RL problems have different reward functions but share the same underlying transition dynamics. In this setting, the Q-function of each RL problem (task) can be decomposed into a successor feature (SF) and a reward mapping: the former characterizes the transition dynamics, and the latter characterizes the task-specific reward function. This Q-function decomposition, coupled with a policy improvement operator known as generalized policy improvement (GPI), reduces the sample complexity of finding the optimal Q-function, and thus the SF \& GPI framework exhibits promising empirical performance compared to traditional RL methods like Q-learning. However, its theoretical foundations remain largely unestablished, especially when learning the successor features using deep neural networks (SF-DQN). This paper studies the provable knowledge transfer using SFs-DQN in transfer RL problems. We establish the first convergence analysis with provable generalization guarantees for SF-DQN with GPI. The theory reveals that SF-DQN with GPI outperforms conventional RL approaches, such as deep Q-network, in terms of both faster convergence rate and better generalization. Numerical experiments on real and synthetic RL tasks support the superior performance of SF-DQN \& GPI, aligning with our theoretical findings.

Stochastic bilevel optimization (SBO) is becoming increasingly essential in machine learning due to its versatility in handling nested structures. To address large-scale SBO, decentralized approaches have emerged as effective paradigms in which nodes communicate with immediate neighbors without a central server, thereby improving communication efficiency and enhancing algorithmic robustness. However, current decentralized SBO algorithms face challenges, including expensive inner-loop updates and unclear understanding of the influence of network topology, data heterogeneity, and the nested bilevel algorithmic structures. In this paper, we introduce a single-loop decentralized SBO (D-SOBA) algorithm and establish its transient iteration complexity, which, for the first time, clarifies the joint influence of network topology and data heterogeneity on decentralized bilevel algorithms. D-SOBA achieves the state-of-the-art asymptotic rate, asymptotic gradient/Hessian complexity, and transient iteration complexity under more relaxed assumptions compared to existing methods. Numerical experiments validate our theoretical findings.

BL-JUST employs a lower and upper level optimization In general, bilevel optimization problems are optimization problems with an unsupervised loss and a supervised loss respectively, where the feasible set is determined (in part) using the solution leveraging recent advances in penalty-based bilevel optimization to set of a second optimization problem [10]. Determining the feasible solve this challenging ASR problem with affordable complexity and set is generally called the lower-level problem and the second parametric rigorous convergence guarantees. To evaluate BL-JUST, extensive optimization problem is called the upper-level problem [31, 29].

Ontology revision aims to seamlessly incorporate a new ontology into an existing ontology and plays a crucial role in tasks such as ontology evolution, ontology maintenance, and ontology alignment. Similar to repair single ontologies, resolving logical incoherence in the task of ontology revision is also important and meaningful, because incoherence is a main potential factor to cause inconsistency and reasoning with an inconsistent ontology will obtain meaningless answers.To deal with this problem, various ontology revision approaches have been proposed to define revision operators and design ranking strategies for axioms in an ontology. However, they rarely consider axiom semantics which provides important information to differentiate axioms. In addition, pre-trained models can be utilized to encode axiom semantics, and have been widely applied in many natural language processing tasks and ontology-related ones in recent years.Therefore, in this paper, we study how to apply pre-trained models to revise ontologies. We first define four scoring functions to rank axioms based on a pre-trained model by considering various information from an ontology. Based on the functions, an ontology revision algorithm is then proposed to deal with unsatisfiable concepts at once. To improve efficiency, an adapted revision algorithm is designed to deal with unsatisfiable concepts group by group. We conduct experiments over 19 ontology pairs and compare our algorithms and scoring functions with existing ones. According to the experiments, our algorithms could achieve promising performance.