Large Language Models (LLMs) have demonstrated impressive capabilities across various tasks, but fine-tuning them for domain-specific applications often requires substantial domain-specific data that may be distributed across multiple organizations. Federated Learning (FL) offers a privacy-preserving solution, but faces challenges with computational constraints when applied to LLMs. Low-Rank Adaptation (LoRA) has emerged as a parameter-efficient fine-tuning approach, though a single LoRA module often struggles with heterogeneous data across diverse domains. This paper addresses two critical challenges in federated LoRA fine-tuning: 1. determining the optimal number and allocation of LoRA experts across heterogeneous clients, and 2. enabling clients to selectively utilize these experts based on their specific data characteristics. We propose FedLEASE (Federated adaptive LoRA Expert Allocation and SElection), a novel framework that adaptively clusters clients based on representation similarity to allocate and train domain-specific LoRA experts. It also introduces an adaptive top-$M$ Mixture-of-Experts mechanism that allows each client to select the optimal number of utilized experts. Our extensive experiments on diverse benchmark datasets demonstrate that FedLEASE significantly outperforms existing federated fine-tuning approaches in heterogeneous client settings while maintaining communication efficiency.

This paper presents the Task-Parameter Nexus (TPN), a learning-based approach for online determination of the (near-)optimal control parameters of model-based controllers (MBCs) for tracking tasks. In TPN, a deep neural network is introduced to predict the control parameters for any given tracking task at runtime, especially when optimal parameters for new tasks are not immediately available. To train this network, we constructed a trajectory bank with various speeds and curvatures that represent different motion characteristics. Then, for each trajectory in the bank, we auto-tune the optimal control parameters offline and use them as the corresponding ground truth. With this dataset, the TPN is trained by supervised learning. We evaluated the TPN on the quadrotor platform. In simulation experiments, it is shown that the TPN can predict near-optimal control parameters for a spectrum of tracking tasks, demonstrating its robust generalization capabilities to unseen tasks.

On-device LLMs have gained increasing attention for their ability to enhance privacy and provide a personalized user experience. To facilitate learning with private and scarce local data, federated learning has become a standard approach, though it introduces challenges related to system and data heterogeneity among end users. As a solution, we propose a novel Collaborative learning approach with a Mixture of Generalists and Specialists (CoMiGS), being the first to effectively address both. Our approach distinguishes generalists and specialists by aggregating certain experts across end users while keeping others localized to specialize in user-specific datasets. A key innovation of our method is the bi-level optimization formulation of the Mixture-of-Experts learning objective, where the router is updated using a separate validation set that represents the target distribution. CoMiGS effectively balances collaboration and personalization, as demonstrated by its superior performance in scenarios with high data heterogeneity across multiple datasets. By decoupling resource abundance from data quantity, CoMiGS remains robust against overfitting--due to the generalists' regularizing effect--while adapting to local data through specialist expertise. Large Language Models (LLMs) have been showing great success serving as foundation models, evidenced by their capability to understand a wide range of tasks, such as ChatGPT (OpenAI, 2023), Claude (Anthropic, 2023), Gemini (DeepMind, 2023) and etc. However, cloud-based inference introduces significant delays for end users, and it often fails to meet their personalized needs (Ding et al., 2024; Iyengar & Adusumilli, 2024). Recently, there has been growing interest in deploying LLMs on edge devices, which offer benefits like lower latency, data localization, and more personalized user experiences (Xu et al., 2024). For instance, Apple (2024) recently launched on-device foundation models as part of its personal intelligence system. On-device LLMs present challenges such as limited and variable computational resources, scarce and heterogeneous local data, and privacy concerns related to data sharing (Peng et al., 2024; Wagner et al., 2024).

Mixture-of-Experts (MoE) large language models (LLM) have memory requirements that often exceed the GPU memory capacity, requiring costly parameter movement from secondary memories to the GPU for expert computation. In this work, we present Mixture of Near-Data Experts (MoNDE), a near-data computing solution that efficiently enables MoE LLM inference. MoNDE reduces the volume of MoE parameter movement by transferring only the $\textit{hot}$ experts to the GPU, while computing the remaining $\textit{cold}$ experts inside the host memory device. By replacing the transfers of massive expert parameters with the ones of small activations, MoNDE enables far more communication-efficient MoE inference, thereby resulting in substantial speedups over the existing parameter offloading frameworks for both encoder and decoder operations.

Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several applications owing to their scalability, the mathematical and statistical properties of MoE models are complex and difficult to analyze. As a result, previous theoretical works have primarily focused on probabilistic MoE models by imposing the impractical assumption that the data are generated from a Gaussian MoE model. In this work, we investigate the performance of the least squares estimators (LSE) under a deterministic MoE model where the data are sampled according to a regression model, a setting that has remained largely unexplored. We establish a condition called strong identifiability to characterize the convergence behavior of various types of expert functions. We demonstrate that the rates for estimating strongly identifiable experts, namely the widely used feed forward networks with activation functions $\mathrm{sigmoid}(\cdot)$ and $\tanh(\cdot)$, are substantially faster than those of polynomial experts, which we show to exhibit a surprising slow estimation rate. Our findings have important practical implications for expert selection.

In the era of large language models, Mixture-of-Experts (MoE) is a promising architecture for managing computational costs when scaling up model parameters. However, conventional MoE architectures like GShard, which activate the top-$K$ out of $N$ experts, face challenges in ensuring expert specialization, i.e. each expert acquires non-overlapping and focused knowledge. In response, we propose the DeepSeekMoE architecture towards ultimate expert specialization. It involves two principal strategies: (1) finely segmenting the experts into $mN$ ones and activating $mK$ from them, allowing for a more flexible combination of activated experts; (2) isolating $K_s$ experts as shared ones, aiming at capturing common knowledge and mitigating redundancy in routed experts. Starting from a modest scale with 2B parameters, we demonstrate that DeepSeekMoE 2B achieves comparable performance with GShard 2.9B, which has 1.5 times the expert parameters and computation. In addition, DeepSeekMoE 2B nearly approaches the performance of its dense counterpart with the same number of total parameters, which set the upper bound of MoE models. Subsequently, we scale up DeepSeekMoE to 16B parameters and show that it achieves comparable performance with LLaMA2 7B, with only about 40% of computations. Further, our preliminary efforts to scale up DeepSeekMoE to 145B parameters consistently validate its substantial advantages over the GShard architecture, and show its performance comparable with DeepSeek 67B, using only 28.5% (maybe even 18.2%) of computations.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

Large language models (LLMs) based on transformers have made significant strides in recent years, the success of which is driven by scaling up their model size. Despite their high algorithmic performance, the computational and memory requirements of LLMs present unprecedented challenges. To tackle the high compute requirements of LLMs, the Mixture-of-Experts (MoE) architecture was introduced which is able to scale its model size without proportionally scaling up its computational requirements. Unfortunately, MoE's high memory demands and dynamic activation of sparse experts restrict its applicability to real-world problems. Previous solutions that offload MoE's memory-hungry expert parameters to CPU memory fall short because the latency to migrate activated experts from CPU to GPU incurs high performance overhead. Our proposed Pre-gated MoE system effectively tackles the compute and memory challenges of conventional MoE architectures using our algorithm-system co-design. Pre-gated MoE employs our novel pre-gating function which alleviates the dynamic nature of sparse expert activation, allowing our proposed system to address the large memory footprint of MoEs while also achieving high performance. We demonstrate that Pre-gated MoE is able to improve performance, reduce GPU memory consumption, while also maintaining the same level of model quality. These features allow our Pre-gated MoE system to cost-effectively deploy large-scale LLMs using just a single GPU with high performance.