Recent studies have shown that combining parameter-efficient fine-tuning (PEFT) with mixture-of-experts (MoE) is an effective strategy for adapting large language models (LLMs) to the downstream tasks. However, most existing approaches rely on conventional TopK routing, which requires careful hyperparameter tuning and assigns a fixed number of experts to each token. In this work, we propose LD-MoLE, a Learnable Dynamic routing mechanism for Mixture of LoRA Experts that enables adaptive, token-dependent, and layer-wise expert allocation. Our method replaces the non-differentiable TopK selection with a differentiable routing function and a closed-form solution. Moreover, our design allows the model to adaptively determine the number of experts to activate for each token at different layers. In addition, we introduce an analytical sparsity control objective to regularize the number of activated experts. Our method not only achieves superior performance, but also demonstrates the ability to learn token-dependent and layer-wise expert allocation. Large language models (LLMs) have demonstrated impressive capabilities across a wide range of natural language processing (NLP) tasks. However, their growing size requires significant computational resources for full-parameter fine-tuning. To address this, Parameter-Efficient Fine-tuning (PEFT) methods, such as Adapter-tuning (Houlsby et al., 2019) and LoRA (Hu et al., 2021), have emerged as crucial techniques for reducing training costs. Recently, the Mixture-of-Experts (MoE) design (Jacobs et al., 1991; Shazeer et al., 2017) has been successfully integrated into transformer feed-forward networks during LLMs pretraining (Dai et al., 2024; Y ang et al., 2025), demonstrating that MoE can reduce computational cost while maintaining strong performance.

Parameter-efficient fine-tuning (PEFT) methods, particularly Low-Rank Adaptation (LoRA), offer an efficient way to adapt large language models with reduced computational costs. However, their performance is limited by the small number of trainable parameters. Recent work combines LoRA with the Mixture-of-Experts (MoE), i.e., LoRA-MoE, to enhance capacity, but two limitations remain in hindering the full exploitation of its potential: 1) the influence of downstream tasks when assigning expert numbers, and 2) the uniform rank assignment across all LoRA experts, which restricts representational diversity. To mitigate these gaps, we propose GuiLoMo, a fine-grained layer-wise expert numbers and ranks allocation strategy with GuidedSelection Vectors (GSVs). GSVs are learned via a prior bilevel optimization process to capture both model- and task-specific needs, and are then used to allocate optimal expert numbers and ranks. Experiments on three backbone models across diverse benchmarks show that GuiLoMo consistently achieves superior or comparable performance to all baselines. Further analysis offers key insights into how expert numbers and ranks vary across layers and tasks, highlighting the benefits of adaptive expert configuration. Our code is available at https://github.com/Liar406/Gui-LoMo.git.

Multi-task forecasting has become the standard approach for time-series forecasting (TSF). However, we show that it suffers from an Expressiveness Bottleneck, where predictions at different time steps share the same representation, leading to unavoidable errors even with optimal representations. To address this issue, we propose a two-stage framework: first, pre-train a foundation model for one-step-ahead prediction; then, adapt it using step-specific LoRA modules.This design enables the foundation model to handle any number of forecast steps while avoiding the expressiveness bottleneck. We further introduce the Mixture-of-LoRA (MoLA) model, which employs adaptively weighted LoRA experts to achieve partial parameter sharing across steps. This approach enhances both efficiency and forecasting performance by exploiting interdependencies between forecast steps. Experiments show that MoLA significantly improves model expressiveness and outperforms state-of-the-art time-series forecasting methods. Code is available at https://anonymous.4open.science/r/MoLA-BC92.

Large language models (LLMs) have demonstrated remarkable success across various tasks, accompanied by a continuous increase in their parameter size. Parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), address the challenges of fine-tuning LLMs by significantly reducing the number of trainable parameters. Recent studies have integrated LoRA with Mixture of Experts (MoE) architectures, leveraging multiple adapter experts and gating mechanisms to further improve fine-tuning performance. However, existing approaches primarily focus on adjusting the allocations of adapter experts per layer to optimize the introduced trainable parameter size, while neglecting a critical factor of adapters' rank. To this end, we propose a hierarchical scheme for expert allocation and rank configuration, HILO, which dynamically adjusts the number and rank of adapter experts across layers, matching the varying representational complexity of model layers in adapter-granularity. Extensive experiments on multiple benchmark tasks demonstrate that HILO outperforms existing methods in accuracy while introducing fewer trainable parameters, providing an efficient and practical solution for fine-tuning LLMs.

Recently, LoRA has emerged as a crucial technique for fine-tuning large pre-trained models, yet its performance in multi-task learning scenarios often falls short. In contrast, the MoE architecture presents a natural solution to this issue. However, it introduces challenges such as mutual interference of data across multiple domains and knowledge forgetting of various tasks. Additionally, MoE significantly increases the number of parameters, posing a computational cost challenge. Therefore, in this paper, we propose MoSLD, a mixture-of-shared-LoRAs model with a dropout strategy. MoSLD addresses these challenges by sharing the upper projection matrix in LoRA among different experts, encouraging the model to learn general knowledge across tasks, while still allowing the lower projection matrix to focus on the unique features of each task. The application of dropout alleviates the imbalanced update of parameter matrix and mitigates parameter overfitting in LoRA. Extensive experiments demonstrate that our model exhibits excellent performance in both single-task and multi-task scenarios, with robust out-of-domain generalization capabilities.

In this work, we introduce MOLA: a Multi-block Orthogonal Long short-term memory Autoencoder paradigm, to conduct accurate, reliable fault detection of industrial processes. To achieve this, MOLA effectively extracts dynamic orthogonal features by introducing an orthogonality-based loss function to constrain the latent space output. This helps eliminate the redundancy in the features identified, thereby improving the overall monitoring performance. On top of this, a multi-block monitoring structure is proposed, which categorizes the process variables into multiple blocks by leveraging expert process knowledge about their associations with the overall process. Each block is associated with its specific Orthogonal Long short-term memory Autoencoder model, whose extracted dynamic orthogonal features are monitored by distance-based Hotelling's $T^2$ statistics and quantile-based cumulative sum (CUSUM) designed for multivariate data streams that are nonparametric, heterogeneous in nature. Compared to having a single model accounting for all process variables, such a multi-block structure improves the overall process monitoring performance significantly, especially for large-scale industrial processes. Finally, we propose an adaptive weight-based Bayesian fusion (W-BF) framework to aggregate all block-wise monitoring statistics into a global statistic that we monitor for faults, with the goal of improving fault detection speed by assigning weights to blocks based on the sequential order where alarms are raised. We demonstrate the efficiency and effectiveness of our MOLA framework by applying it to the Tennessee Eastman Process and comparing the performance with various benchmark methods.

Parameter-efficient tuning (PEFT) techniques like low-rank adaptation (LoRA) offer training efficiency on Large Language Models, but their impact on model performance remains limited. Recent efforts integrate LoRA and Mixture-of-Experts (MoE) to improve the performance of PEFT methods. Despite promising results, research on improving the efficiency of LoRA with MoE is still in its early stages. Recent studies have shown that experts in the MoE architecture have different strengths and also exhibit some redundancy. Does this statement also apply to parameter-efficient MoE? In this paper, we introduce a novel parameter-efficient MoE method, \textit{\textbf{M}oE-L\textbf{o}RA with \textbf{L}ayer-wise Expert \textbf{A}llocation (MoLA)} for Transformer-based models, where each model layer has the flexibility to employ a varying number of LoRA experts. We investigate several architectures with varying layer-wise expert configurations. Experiments on six well-known NLP and commonsense QA benchmarks demonstrate that MoLA achieves equal or superior performance compared to all baselines. We find that allocating more LoRA experts to higher layers further enhances the effectiveness of models with a certain number of experts in total. With much fewer parameters, this allocation strategy outperforms the setting with the same number of experts in every layer. This work can be widely used as a plug-and-play parameter-efficient tuning approach for various applications. The code is available at https://github.com/GCYZSL/MoLA.

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two approaches by proposing to predict with a Gaussian mixture model posterior that consists of a weighted sum of Laplace approximations of independently trained deep neural networks. The method can be used post hoc with any set of pre-trained networks and only requires a small computational and memory overhead compared to regular ensembles. We theoretically validate that our approach mitigates overconfidence "far away" from the training data and empirically compare against state-of-the-art baselines on standard uncertainty quantification benchmarks.