Federated efficient fine-tuning has emerged as an approach that leverages distributed data and computational resources across nodes to address the challenges of large-scale fine-tuning and privacy preservation. The Low-Rank Adaptation (LoRA) enables efficient fine-tuning of large-scale pre-trained models by introducing trainable low-rank matrices into weight updates.However, in heterogeneous data scenarios, client drift weakens the generalization of the global model, and local models often fail to meet the personalized needs of individual clients.Moreover, existing federated LoRA efficient fine-tuning techniques overlook fine-grained analysis of the tuning matrices. To address this, we conducted preliminary experiments and found that different LoRA matrices exhibit different sensitivity to changes in the direction and magnitude of their vectors.We thus propose a fine-grained federated LoRA tuning method. By fine-tuning the more sensitive directional vectors in the A matrix, which encode shared knowledge, our method learns shared features more effectively across clients and enhances global generalization. Simultaneously, by fine-tuning the more sensitive magnitude vectors in the B matrix, which encode personalized knowledge, our method better captures personalized knowledge, enabling detailed adaptation to local data. The method uses a pipeline combining global and local optimizers. Global optimization further improves local models, achieving collaborative optimization between global and local levels. This improves both the generalization ability of the global model and the personalized adaptation of local models under heterogeneous data scenarios. Experiments on Databricks-Dolly-15k and Natural Instructions with LLaMA2-7B and Deepseek-7B confirm that our method improves global performance by 0.39% and local performance by 0.59%.

Optimizing black-box functions in high-dimensional search spaces has been known to be challenging for traditional Bayesian Optimization (BO). In this paper, we introduce HiBO, a novel hierarchical algorithm integrating global-level search space partitioning information into the acquisition strategy of a local BO-based optimizer. HiBO employs a search-tree-based global-level navigator to adaptively split the search space into partitions with different sampling potential. The local optimizer then utilizes this global-level information to guide its acquisition strategy towards most promising regions within the search space. A comprehensive set of evaluations demonstrates that HiBO outperforms state-of-the-art methods in high-dimensional synthetic benchmarks and presents significant practical effectiveness in the real-world task of tuning configurations of database management systems (DBMSs).

In this paper, we start by training End-to-End Automatic Speech Recognition (ASR) models using Federated Learning (FL) and examining the fundamental considerations that can be pivotal in minimizing the performance gap in terms of word error rate between models trained using FL versus their centralized counterpart. Specifically, we study the effect of (i) adaptive optimizers, (ii) loss characteristics via altering Connectionist Temporal Classification (CTC) weight, (iii) model initialization through seed start, (iv) carrying over modeling setup from experiences in centralized training to FL, e.g., pre-layer or post-layer normalization, and (v) FL-specific hyperparameters, such as number of local epochs, client sampling size, and learning rate scheduler, specifically for ASR under heterogeneous data distribution. We shed light on how some optimizers work better than others via inducing smoothness. We also summarize the applicability of algorithms, trends, and propose best practices from prior works in FL (in general) toward End-to-End ASR models.

Clustering is one of the most important unsupervised learning techniques for understanding the underlying data structures. The goal is to partition a data set into many subsets, called clusters, such that the observations within the subsets are the most homogeneous and the observations between the subsets are the most heterogeneous. Clustering is usually carried out by specifying a similarity or dissimilarity measure between observations. Examples include the k-means [17, 19, 29, 37], the k-medians [3], the k-modes [5], and the generalized k-means [2, 31, 45], as well as many of their modifications [21, 24, 42]. Among those, the k-means has been considered as one of the most straightforward and popular methods since it was proposed sixty years ago [23, 36]. Although it is well known, the investigation of the theoretical properties is still far behind, leading to difficulties in developing more precise k-means methods in practice. The goal of the present research is to propose a new concept called clustering consistency for the asymptotics of the k-means with a resulting clustering method better than the existing k-means methods adopted by many software packages, including those adopted by R and Python.

This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote column sparsity of factors and lower rank solutions. For this nonconvex nonsmooth and non-Lipschitz problem, we develop an alternating majorization-minimization (AMM) method with extrapolation, and a hybrid AMM in which a majorized alternating proximal method is first proposed to seek an initial factor pair with less nonzero columns and then the AMM with extrapolation is applied to the minimization of smooth nonconvex loss. We provide the global convergence analysis for the proposed AMM methods and apply them to the matrix completion problem with non-uniform sampling schemes. Numerical experiments are conducted with synthetic and real data examples, and comparison results with the nuclear-norm regularized factorization model and the max-norm regularized convex model demonstrate that the column $\ell_{2,0}$-regularized factorization model has an advantage in offering solutions of lower error and rank within less time.

Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and corresponding function value, repeating these two procedures: (i) learning a surrogate model for the objective function using the data observed so far; (ii) the maximization of an acquisition function to determine where next to query the objective function. Convergence guarantees are only valid when the global optimizer of the acquisition function is found and selected as the next query point. In practice, however, local optimizers of acquisition functions are also used, since searching the exact optimizer of the acquisition function is often a non-trivial or time-consuming task. In this paper we present an analysis on the behavior of local optimizers of acquisition functions, in terms of instantaneous regrets over global optimizers. We also present the performance analysis when multi-started local optimizers are used to find the maximum of the acquisition function. Numerical experiments confirm the validity of our theoretical analysis.

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper, we take a novel approach to this problem by asking whether one can constrain neural network weights to make its optimization landscape have good theoretical properties while at the same time, be a good approximation for the unconstrained one. For two-layer neural networks, we provide affirmative answers to these questions by introducing Porcupine Neural Networks (PNNs) whose weight vectors are constrained to lie over a finite set of lines. We show that most local optima of PNN optimizations are global while we have a characterization of regions where bad local optimizers may exist. Moreover, our theoretical and empirical results suggest that an unconstrained neural network can be approximated using a polynomially-large PNN.