Analyzes convergence rates for Gaussian-gated MoE model.
problem Theoretical understanding of Gaussian-gated MoE model is incomplete.
method Maximum likelihood estimation with novel Voronoi loss functions.
result MLE has distinct behaviors under different settings of Gaussian gating function parameters.
This paper tackles model selection for MoE models in high-dimensional data.
problem Model selection for Gaussian-gated localized MoE and block-diagonal covariance localized MoE regression models in high-dimensional data.
method Penalized maximum likelihood estimation framework with non-asymptotic risk bounds.
result Established non-asymptotic risk bounds for model selection in MoE models.
Paper proposes a novel method to accurately determine the number of experts in Gaussian-gated Gaussian MoE models.
problem Challenges in model selection for MoE models, especially with covariates.
method Introduces a novel extension using dendrograms of mixing measures to estimate the true number of mixture components.
result Achieves optimal convergence rates for parameter estimation and accurately approximates the regression function.
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of modeling with high-dimensional predictors with regularized MLE. We examine MoE with …
G-GLN extends GLNs to multiple regression and density modeling.
problem Learning features in deep neural networks.
method G-GLN uses a distributed and local credit assignment mechanism based on optimizing a convex objective.
result G-GLN achieves competitive or state-of-the-art performance on regression benchmarks.
Mobile V-MoEs scale down ViTs for resource-constrained vision tasks.
problem Scaling down Vision Transformers for resource-constrained applications.
method Sparse Mixture-of-Experts (MoEs) applied to entire images, with a stable training procedure.
result Mobile V-MoEs achieve better performance-efficiency trade-offs than dense ViTs.
Sparse Vision MoE matches dense networks in image recognition while using less compute.
problem Scaling vision models efficiently in computer vision.
method Vision MoE (V-MoE) - a sparse version of Vision Transformer.
result V-MoE matches state-of-the-art dense networks in image recognition with half the compute.
MoEs can efficiently model complex tasks with low-dimensionality and sparsity.
problem Understanding the theoretical foundations of MoEs for complex tasks.
method Systematic study of MoEs with two structural priors: low-dimensionality and sparsity.
result MoEs can approximate functions on low-dimensional manifolds and exhibit exponential structured tasks.
Mixture-of-experts (MoE) models are a powerful paradigm for modeling of data arising from complex data generating processes (DGPs). In this article, we demonstrate how different MoE models can be constructed to approximate the underlying DGPs of arbitrary types of data. Due to the probabilistic nature of MoE models, we…
Investigates least squares estimation in deterministic MoE models.
problem Complexity and difficulty in analyzing MoE models.
method Least squares estimation under deterministic MoE models.
result Rates of estimating strongly identifiable experts are faster than polynomial experts.
New method uses temperature to control sparse MoE convergence rates.
problem Sparse MoE convergence rates are slow due to temperature interactions.
method Proposes a novel activation gate to improve convergence rates.
result Improved convergence rates to polynomial rates via novel gate.
The mixture of experts (MoE) model is a popular neural network architecture for nonlinear regression and classification. The class of MoE mean functions is known to be uniformly convergent to any unknown target function, assuming that the target function is from Sobolev space that is sufficiently differentiable and tha…
E3 combines sparse MoEs and ensembles to improve model efficiency and performance.
problem Improving model efficiency and performance in machine learning.
method Combining sparse mixture of experts and ensembles, presenting Efficient Ensemble of Experts (E3). result E3 achieves better accuracy, log-likelihood, few-shot learning, robustness, and uncertainty estimates than baselines. This paper explores how MoE layers improve deep learning performance.
problem Understanding the Mixture-of-Experts (MoE) layer in deep learning.
method Formal study of MoE layer's effectiveness and mechanism.
result MoE layer improves performance by leveraging cluster structure and non-linearity.
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.
Recurrent neural networks can be difficult to train on long sequence data due to the well-known vanishing gradient problem. Some architectures incorporate methods to reduce RNN state updates, therefore allowing the network to preserve memory over long temporal intervals. To address these problems of convergence, this p…
Study compares MoE and RNN models for stock price prediction across volatility profiles.
problem Improving stock price prediction accuracy across different volatility levels.
method Dynamic Mixture of Experts model combining RNN and linear models, adjusting weights through a gating network.
result MoE model outperforms individual models in reducing prediction errors.
New framework finds more efficient linear layers over structured matrices.
problem Efficient alternatives for dense linear layers in neural networks.
method Unified framework searching over all linear operators, developing a taxonomy based on computational and algebraic properties.
result BTT-MoE provides substantial compute-efficiency gains over dense layers and standard MoE.
Paper connects MoE and self-attention, proposing active-attention.
problem Improving efficiency and performance of self-attention mechanisms.
method Established connection between MoE and self-attention, analyzed quadratic gating functions, proposed active-attention mechanism.
result Active-attention outperforms standard self-attention in various tasks.
Optimal transport aggregation combines distributed MoE models efficiently.
problem Combining local MoE models trained on distributed datasets.
method Optimal transport for minimizing divergence between local and global estimators, with MM algorithm for optimization.
result Aggregated estimator achieves performance comparable to centralized training but with reduced computation time.
N-BEATS-MOE improves time series forecasting by adapting to series characteristics.
problem Forecasting heterogeneous time series with varying characteristics.
method Mixture-of-Experts layer with dynamic block weighting.
result Consistent improvements across 12 benchmark datasets, especially for heterogeneous series.
Moirai-MoE improves time series forecasting by automatically specializing tokens without human-defined frequency.
problem Unified training on time series data remains challenging due to heterogeneity and non-stationarity.
method Uses sparse mixture of experts (MoE) within Transformers to automatically specialize tokens for diverse time series patterns.
result Moirai-MoE outperforms existing foundation models in both in-distribution and zero-shot scenarios.
The paper establishes convergence rates for MoE models in classification problems.
problem Understanding the behavior of MoE models in classification settings.
method Established convergence rates for density and parameter estimation in softmax gating multinomial logistic MoE models.
result Parameter estimation rates are significantly improved with a novel modified softmax gating function.
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification and clustering. For continuous data which we consider here in the context of regression and cluster analysis, MoE usually use normal experts, that is, expert components following the Gaussian distribution. …
Paper hypothesizes MLP layers in LLMs can be approximated by sparse Mixture of Experts.
problem Understanding dense MLP layers in LLMs.
method Theoretical connection between MoE models and SAE structure in activation space.
result MLP layers in LLMs can be well approximated by sparse Mixture of Experts.
MoE-F combines LLMs online for better time-series prediction.
problem Combining multiple LLMs for online time-series prediction.
method Time-adaptive stochastic filtering techniques to combine experts.
result MoE-F achieves 17% absolute and 48.5% relative F1 measure improvement.
This study analyzes communication constraints in MoE architectures using information theory.
problem Communication constraints in Mixture-of-Experts (MoE) architectures.
method Developed a rate-distortion characterization of finite-rate gating in MoE architectures using information theory.
result Yielded capacity-aware limits for communication-constrained MoE systems.
Theory of MoE Transformers' generalization and scaling.
problem Understanding the generalization and scaling of Mixture-of-Experts (MoE) Transformers.
method Developed a theory that separates active capacity from routing combinatorics, derived a sup-norm covering-number bound, and proved a constructive approximation theorem.
result Generalization and scaling laws for MoE Transformers, showing how active capacity and routing structure affect performance.
A framework uses a mixture of predictors for semi-supervised inference.
problem Limited labeled data, abundant unlabeled data.
method Mixture of Experts (MOE) for semi-supervised inference.
result MOE-powered inference framework achieves smallest possible variance.
Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification, and clustering. For regression and cluster analyses of continuous data, MoE usually use normal experts following the Gaussian distribution. However, for a set of data containing a group or groups of observ…
MoE outperforms vanilla networks in detecting latent cluster structures in regression tasks.
problem Detecting latent cluster structures in regression tasks with gradient-based learning.
method Theoretical analysis of Mixture of Experts (MoE) using stochastic gradient descent (SGD).
result MoE can successfully divide the problem into subproblems, allowing each expert to recover simpler functions corresponding to individual clusters.
DSelect-k improves MoE models for multi-task learning with better performance and smoother training.
problem Smoothness and convergence issues in sparse gate selection for MoE models.
method Developed DSelect-k, a differentiable and sparse gate for MoE models.
result DSelect-k achieves statistically significant improvements in prediction and expert selection over Top-k.
Improved logistic MoE with sigmoid gate shows better sample efficiency.
problem Improving sample efficiency in logistic MoE models.
method Comprehensive analysis of multinomial logistic MoE with modified sigmoid gate, incorporating temperature parameter and using Euclidean score.
result The sigmoid gate leads to lower sample complexity than softmax gate for both parameter and expert estimation.
The paper analyzes convergence rates of softmax gating in MoE models.
problem The effectiveness and scalability of machine learning models using MoE.
method Convergence analysis of parameter and expert estimation under MoE with softmax gating and its variants.
result Theoretical results show polynomially many data points are needed for strong identifiability conditions, while exponential points are required for linear experts.
Study examines Lasso performance in high-dimensional MoE models.
problem Estimating MoE models in high-dimensional settings with Lasso.
method Investigates SGMoE models with Lasso regularization under mild assumptions.
result Provides non-asymptotic bounds for Lasso regularization parameter.
Improved MoE performance through perturbing cosine router.
problem Representation collapse and parameter redundancy in MoE models.
method Least square estimation of cosine router in MoE, followed by noise addition to improve convergence rates.
result Perturbed cosine router leads to polynomial convergence rates for MoE models.
Proposes a new deep learning model for uncertainty quantification and propagation.
problem High-dimensional uncertainty quantification and propagation problems.
method Integrates U-net with Gaussian Gated Linear Network (GGLN) to create GLU-net.
result Less complex architecture with 44% fewer parameters than existing models.
Clustering high-dimensional data, such as images or biological measurements, is a long-standingproblem and has been studied extensively. Recently, Deep Clustering has gained popularity due toits flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variat…
Paper analyzes approximation and learning of MoEs with (P)ReLU activation.
problem Scaling up deep learning models with MoEs and (P)ReLU activation.
method Approximation and learning-theoretic analysis of MoMLPs with (P)ReLU.
result MoMLPs can uniformly approximate Lipschitz functions with ε accuracy using O(ε−1) parameters. Bayesian MoE framework improves LLMs' uncertainty detection.
problem Brittleness and overconfidence in deterministic routing of LLMs.
method Structured Bayesian routing in weight-space, logit-space, and selection-space.
result Significant improvements in routing stability, calibration, and OoD detection.
The paper studies estimation rates for MoE models with a new prompt.
problem Estimating parameters in a softmax-contaminated MoE model.
method Analytic notion of distinguishability, minimax optimal estimation rates.
result Estimation rates are minimax optimal under distinguishability, but slower otherwise.
The paper analyzes EM for Mixtures of Experts and shows its equivalence to projected Mirror Descent.
problem Training Mixtures of Experts (MoE) models.
method Rigorously analyzes Expectation Maximization (EM) for MoE models using a Mirror Descent perspective.
result Derives new convergence results and identifies conditions for local linear convergence.
New scaling framework for MoE architectures ensures stability and optimal performance at scale.
problem Lack of principled understanding of how hyperparameters should scale in MoE architectures.
method Developed a novel Dynamical Mean Field Theory (DMFT) for three scaling regimes of MoE architectures.
result Derived Maximally Scale-Stable Parameterization (MSSP) for SGD and Adam, providing robust learning rate transfer and monotonic improvement with scale.
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known EM algorithm, their application to high-dimensional problems is still therefore c…
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
Bidirectional attention is shown to be equivalent to a continuous bag of words model with mixture-of-experts.
problem Understanding the statistical underpinnings of bidirectional attention.
method Exploring bidirectional attention as a mixture-of-experts model and reparameterizing it.
result Bidirectional attention can be viewed as a continuous bag of words model with mixture-of-experts weights.
NAMEx merges experts using Nash bargaining for improved performance.
problem Sparse Mixture of Experts merging strategies lack a principled weighting mechanism.
method Reinterpreting expert merging through game theory, introducing Nash Merging and complex momentum.
result NAMEx consistently outperforms competing methods across various tasks and system sizes.
Higher granularity in MoE models boosts expressivity exponentially.
problem Expressivity of Mixture-of-Experts models with varying granularity.
method Comparing models with different numbers of active experts (granularity).
result Exponential separation in network expressivity based on granularity.