MoLEx: Mixture of Layer Experts for Finetuning with Sparse Upcycling

Large-scale pre-training of deep models, followed by fine-tuning them, has become the cornerstone of natural language processing (NLP). The prevalence of data coupled with computational resources has led to large models with a considerable number of parameters. While the massive size of these models has led to remarkable success in many NLP tasks, a detriment is the expense required to retrain all the base model's parameters for the adaptation to each task or domain. Parameter Efficient Fine-Tuning (PEFT) provides an effective solution for this challenge by minimizing the number of parameters required to be fine-tuned while maintaining the quality of the model. While existing methods have achieved impressive results, they mainly focus on adapting a subset of parameters, weight reparameterization, and prompt engineering. In this paper, we study layers as extractors of different types of linguistic information that are valuable when used in conjunction. We then propose the Mixture of Layer Experts (MoLEx), a novel sparse mixture of experts (SMoE) whose experts are layers in the pre-trained model. It performs a conditional computation of a mixture of layers during fine-tuning to provide the model with more structural knowledge about the data. By providing an avenue for information exchange between layers, MoLEx enables the model to make a more well-informed prediction for the downstream task, leading to better fine-tuning results with the same number of effective parameters. As experts can be processed in parallel, MoLEx introduces minimal additional computational overhead. We empirically corroborate the advantages of MoLEx when combined with popular PEFT baseline methods on a variety of downstream fine-tuning tasks, including the popular GLUE benchmark as well as the End-to-End Challenge (E2E). The code is publicly available at https://github.com/rachtsy/molex.

CAMEx: Curvature-aware Merging of Experts

Existing methods for merging experts during model training and fine-tuning predominantly rely on Euclidean geometry, which assumes a flat parameter space. This assumption can limit the model's generalization ability, especially during the pre-training phase, where the parameter manifold might exhibit more complex curvature. Curvature-aware merging methods typically require additional information and computational resources to approximate the Fisher Information Matrix, adding memory overhead. In this paper, we introduce CAMEx (\textbf{C}urvature-\textbf{A}ware \textbf{M}erging of \textbf{Ex}perts), a novel expert merging protocol that incorporates natural gradients to account for the non-Euclidean curvature of the parameter manifold. By leveraging natural gradients, CAMEx adapts more effectively to the structure of the parameter space, improving alignment between model updates and the manifold's geometry. This approach enhances both pre-training and fine-tuning, resulting in better optimization trajectories and improved generalization without the substantial memory overhead typically associated with curvature-aware methods. Our contributions are threefold: (1) CAMEx significantly outperforms traditional Euclidean-based expert merging techniques across various natural language processing tasks, leading to enhanced performance during pre-training and fine-tuning; (2) we introduce a dynamic merging architecture that optimizes resource utilization, achieving high performance while reducing computational costs, facilitating efficient scaling of large language models; and (3) we provide both theoretical and empirical evidence to demonstrate the efficiency of our proposed method.

Tight Clusters Make Specialized Experts

Sparse Mixture-of-Experts (MoE) architectures have emerged as a promising approach to decoupling model capacity from computational cost. At the core of the MoE model is the router, which learns the underlying clustering structure of the input distribution in order to send input tokens to appropriate experts. However, latent clusters may be unidentifiable in high dimension, which causes slow convergence, susceptibility to data contamination, and overall degraded representations as the router is unable to perform appropriate token-expert matching. We examine the router through the lens of clustering optimization and derive optimal feature weights that maximally identify the latent clusters. We use these weights to compute the token-expert routing assignments in an adaptively transformed space that promotes well-separated clusters, which helps identify the best-matched expert for each token. In particular, for each expert cluster, we compute a set of weights that scales features according to whether that expert clusters tightly along that feature. We term this novel router the Adaptive Clustering (AC) router. Our AC router enables the MoE model to obtain three connected benefits: 1) faster convergence, 2) better robustness to data corruption, and 3) overall performance improvement, as experts are specialized in semantically distinct regions of the input space. We empirically demonstrate the advantages of our AC router over baseline routing methods when applied on a variety of MoE backbones for language modeling and image recognition tasks in both clean and corrupted settings.

MomentumSMoE: Integrating Momentum into Sparse Mixture of Experts

Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a small subset of these parameters for a given sample. However, it has been observed that SMoE suffers from unstable training and has difficulty adapting to new distributions, leading to the model's lack of robustness to data contamination. To overcome these limitations, we first establish a connection between the dynamics of the expert representations in SMoEs and gradient descent on a multi-objective optimization problem. Leveraging our framework, we then integrate momentum into SMoE and propose a new family of SMoEs named MomentumSMoE. We theoretically prove and numerically demonstrate that MomentumSMoE is more stable and robust than SMoE. In particular, we verify the advantages of MomentumSMoE over SMoE on a variety of practical tasks including ImageNet-1K object recognition and WikiText-103 language modeling. We demonstrate the applicability of MomentumSMoE to many types of SMoE models, including those in the Sparse MoE model for vision (V-MoE) and the Generalist Language Model (GLaM). We also show that other advanced momentum-based optimization methods, such as Adam, can be easily incorporated into the MomentumSMoE framework for designing new SMoE models with even better performance, almost negligible additional computation cost, and simple implementations.

Unveiling the Hidden Structure of Self-Attention via Kernel Principal Component Analysis

The remarkable success of transformers in sequence modeling tasks, spanning various applications in natural language processing and computer vision, is attributed to the critical role of self-attention. Similar to the development of most deep learning models, the construction of these attention mechanisms rely on heuristics and experience. In our work, we derive self-attention from kernel principal component analysis (kernel PCA) and show that self-attention projects its query vectors onto the principal component axes of its key matrix in a feature space. We then formulate the exact formula for the value matrix in self-attention, theoretically and empirically demonstrating that this value matrix captures the eigenvectors of the Gram matrix of the key vectors in self-attention. Leveraging our kernel PCA framework, we propose Attention with Robust Principal Components (RPC-Attention), a novel class of robust attention that is resilient to data contamination. We empirically demonstrate the advantages of RPC-Attention over softmax attention on the ImageNet-1K object classification, WikiText-103 language modeling, and ADE20K image segmentation task.