DGMM uses deep layers of Gaussian mixtures for flexible data modeling.
problem Efficiently modeling complex data relationships.
method Deep Gaussian Mixture Models (DGMM) with nested mixtures of linear models and factor models.
result DGMM provides a flexible nonlinear model for data description.
Adaptive RNN using mixture layer for multi-pattern sequences.
problem Inadequate RNN performance on sequences with multiple patterns.
method Introducing a mixture layer to partition and store prototype vectors, enabling adaptive state updates.
result M-RNN outperforms traditional RNN in assimilating sequences with multiple patterns.
Deep neural networks converge to Gaussian mixtures as layer width increases.
problem Understanding the distribution of outputs from deep neural networks.
method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.
result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
New GM layers improve neural network performance.
problem Improving neural network performance.
method Employing Gaussian mixture models and Wasserstein gradient flows.
result GM layers achieve comparable performance to two-layer networks.
Enhances apparel attribute recognition with a two-layer ensemble method.
problem Improving accuracy in apparel attributes classification using deep neural networks.
method Proposes a two-layer mixture framework combining bagging and boosting for ensemble learning.
result The proposed method outperforms individual models and ensemble methods.
TWIST algorithm detects communities in multi-layer networks with tensor decomposition.
problem Community detection in multi-layer networks with multiple node-modality relationships.
method Tensor-based TWIST algorithm for global/local node and layer memberships.
result Accurate community detection with small misclassification error as network size increases.
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.
Study of two-layer NNs under Gaussian mixtures data, proving polynomial models equivalent to neural networks.
problem Training and generalization performance of two-layer NNs under structured Gaussian mixture data.
method Asymptotic analysis of two-layer NNs after one gradient descent step under Gaussian mixture data assumption.
result High-order polynomial models equivalent to nonlinear neural networks under certain conditions.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
An efficient way to learn deep density models that have many layers of latent variables is to learn one layer at a time using a model that has only one layer of latent variables. After learning each layer, samples from the posterior distributions for that layer are used as training data for learning the next layer. Thi…
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.
Study minimax estimation of stratified structure from i.i.d. samples.
problem Estimating stratified structure from i.i.d. samples of stratified mixtures of immersed manifolds.
method Ascending hierarchical co-detection of points belonging to different layers, identifying number of layers and their dimensions, assigning points to layers accurately, estimating tangent spaces optimally.
result Achieves optimal estimation of mixture components at their optimal dimension-specific rates adaptively.
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.
DS-UI improves DNN uncertainty inference by combining a DNN classifier with MoGMM.
problem Improving uncertainty inference in DNN-based image recognition.
method Combines DNN classifier with MoGMM for probabilistic interpretation of features.
result DS-UI outperforms state-of-the-art UI methods in misclassification detection.
Transformers can cluster data from Gaussian mixtures without supervision.
problem Clustering data from Gaussian mixtures without labeled data.
method Theoretical analysis of attention-based layers, focusing on a simplified two-head attention layer and an identity matrix attention layer.
result Attention-based layers can align with true mixture centroids and adapt to input-specific distributions.
ALMA improves clustering of multilayer networks.
problem Clustering multilayer networks with distinct layers and communities.
method Alternating minimization algorithm (ALMA) for simultaneous layer partition and community estimation.
result ALMA achieves higher accuracy than TWIST in clustering multilayer networks.
Deep neural networks can efficiently classify Gaussian mixture models with fewer neurons.
problem Classifying Gaussian mixture models efficiently.
method Used deep neural networks with two hidden layers to classify GMMs optimally.
result Deep neural networks require significantly fewer neurons than shallow ones for optimal classification of GMMs.
SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.
problem Learning new tasks without forgetting old ones in neural networks.
method Sequential function-space variational inference with Gaussian mixture approximation.
result Gaussian mixture SFSVI outperforms other methods in continual learning.
VMoER improves uncertainty quantification in MoE layers for scalable foundation models.
problem Uncertainty quantification in large-scale models like MoE layers.
method Structured Bayesian approach with amortized variational inference over routing logits and temperature parameter inference.
result Improves routing stability, reduces calibration error, and increases AUROC by 12%.
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.
Transformers can learn mixture of linear models efficiently.
problem Existence and generalization of in-context learning for mixture models.
method Theoretical analysis and gradient flow optimization.
result Transformers achieve a prediction error of O ( d / n ) \mathcal{O}(\sqrt{d/n}) O ( d / n ) with high probability. Proposes scale mixture of NNGPs for more flexible stochastic processes.
problem Limited focus on broadening the class of stochastic processes from NNGPs.
method Scale mixture of NNGPs with scale priors on last-layer parameters.
result Turns neural networks into a richer class of stochastic processes.
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.
New dropout method prevents overfitting in hierarchical models.
problem Overfitting in hierarchical mixture of experts.
method Variant of dropout applied hierarchically, not unitwise.
result Prevents overfitting and improves generalization in hierarchical models.
VLAC clusters data hierarchically, outperforming GMM.
problem Clustering with multiple attributes or hierarchies.
method Disentangled latent representations for hierarchical clustering.
result VLAC outperforms Gaussian Mixture Models in clustering accuracy.
GCNs improve multi-layer network classification by expanding the distance between means.
problem Improving multi-layer network classification with graphical information.
method Theoretical and empirical study of graph convolutions in multi-layer networks.
result Graph convolutions expand the classification regime by a factor of 1 / E m d e g 4 1/\sqrt[4]{\mathbb{E}{
m deg}} 1/ 4 E m d e g . Improves training speed of CNNs by separating batch statistics into sub-populations.
problem Training deep CNNs is slow and requires careful normalization.
method Proposes Mixture Normalization (MN) to improve BN by separating mini-batch statistics into sub-populations.
result MN accelerates training of CNNs and produces higher quality models.
Study of deep neural networks with dependent weights leading to new model limits and properties.
problem Characterizing deep neural networks with dependent weights in the infinite-width limit.
method Modeling weights as a mixture of Gaussian distributions and analyzing the infinite-width limit.
result Characterization of neural network layers by scalar parameters and Lévy measures, leading to new model limits.
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.
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.
A new 1-iteration GMM learning algorithm improves robustness and accuracy.
problem Improving robustness and accuracy in Gaussian Mixture Model learning.
method GMM expansion idea, 1-iteration learning algorithm, theoretical proof of convergence.
result Guaranteed convergence of the new algorithm regardless initial parameters.
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.
New method prevents forgetting in learning new tasks.
problem Poor ability of models to solve new problems without forgetting.
method Task-agnostic hierarchical information-theoretic optimality principle with Mixture-of-Variational-Experts layer.
result Demonstrated competitive performance in continual supervised and reinforcement learning.
Stochastic gradient descent converges to universal limits in high dimensions.
problem Statistical tasks in high dimensions with specific data projections.
method Stochastic gradient descent applied to mixture distributions, proving universality of limits.
result The ODE limits are universal for mixtures of arbitrary product distributions.
A new model improves the performance of knowledge distillation in GNNs.
problem Inconsistent performance of existing knowledge distillation techniques in GNNs.
method Proposes a new model, Routing-by-Memory (RbM), a form of Mixture-of-Experts (MoE), to address performance concerns.
result Demonstrates experimentally that RbM achieves considerably more consistent performance across multiple datasets.
Designs an MLP from LDA for multi-Gaussian class classification.
problem Classifying inputs with multiple Gaussian distributions.
method Interprets MLP as generalized LDA, using LDAs for half-space partitioning, neurons for subspace isolation, and merging for class-wise representation.
result Automatic feedforward design for MLP architecture and weights.
Model infers diffusion networks from heterogeneous cascade data.
problem Understanding and predicting diffusion processes in interconnected populations.
method Double mixture directed graph model with layer-specific constraints.
result Convex formulation allows for statistical and computational guarantees.
Transformers converge linearly to optimal models for Gaussian mixtures classification.
problem Theoretical understanding of transformers' in-context classification.
method Gradient descent training of a single-layer transformer for Gaussian mixtures classification.
result Transformers converge linearly to globally optimal models for Gaussian mixtures classification.
This research explores using kernels in the softmax layer for better contextual word classification.
problem Improving contextual word classification accuracy.
method Replacing the inner product in the softmax layer with various kernel functions and comparing their performance.
result Different kernel settings yield varying performance in contextual word classification tasks.
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of kernel functions centered at a subset of training points. The weights are deter…
Paper finds conditions for benign overfitting in neural networks.
problem Benign overfitting in leaky ReLU two-layer neural networks.
method Established directional convergence and classification error bounds.
result Benign overfitting occurs with high probability on mixture data.
The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice…
New layers estimate complex time-frequency masks without phase wrapping issues.
problem Lack of phase estimation in deep learning-based speech enhancement and source separation.
method Proposes magbook, phasebook, and combook layers for complex mask estimation.
result Match state-of-the-art performance on speaker separation datasets.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
Develops rMultiNet R package for multilayer network analysis.
problem Analyzing multilayer network data.
method Two frameworks: MMSBM and MMLSM for generating multilayer networks; methods for node and layer embedding; clustering.
result Provides tools for multilayer network analysis.
Gradient-free method improves predictive accuracy for probabilistic models.
problem Balancing computational efficiency and robust predictive performance in deep learning.
method CAVI-CMN, a gradient-free variational method for conditional mixture networks.
result CAVI-CMN achieves competitive and often superior predictive accuracy compared to MLE with backpropagation.
Deep Mixtures of Unigrams improve clustering of high-dimensional sparse text data.
problem Challenging unsupervised classification of very short documents with many terms.
method Developed a deep version of mixtures of Unigrams in a Bayesian framework.
result Deep Mixtures of Unigrams outperform traditional methods in classification accuracy.