CompeteSMoE -- Effective Training of Sparse Mixture of Experts via Competition

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, effective training of SMoE has proven to be challenging due to the representation collapse issue, which causes parameter redundancy and limited representation potentials. In this work, we propose a competition mechanism to address this fundamental challenge of representation collapse. By routing inputs only to experts with the highest neural response, we show that, under mild assumptions, competition enjoys the same convergence rate as the optimal estimator. We further propose CompeteSMoE, an effective and efficient algorithm to train large language models by deploying a simple router that predicts the competition outcomes. Consequently, CompeteSMoE enjoys strong performance gains from the competition routing policy while having low computation overheads. Our extensive empirical evaluations on two transformer architectures and a wide range of tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies.

Semidefinite Relaxations of the Gromov-Wasserstein Distance

The Gromov-Wasserstein (GW) distance is a variant of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is specified as the solution of a non-convex quadratic program and is not known to be tractable to solve. In particular, existing solvers for the GW distance are only able to find locally optimal solutions. In this work, we propose a semi-definite programming (SDP) relaxation of the GW distance. The relaxation can be viewed as the dual of the GW distance augmented with constraints that relate the linear and quadratic terms of transportation maps. Our relaxation provides a principled manner to compute the approximation ratio of any transport map to the global optimal solution. Finally, our numerical experiments suggest that the proposed relaxation is strong in that it frequently computes the global optimal solution, together with a proof of global optimality.

On the Out of Distribution Robustness of Foundation Models in Medical Image Segmentation

Constructing a robust model that can effectively generalize to test samples under distribution shifts remains a significant challenge in the field of medical imaging. The foundational models for vision and language, pre-trained on extensive sets of natural image and text data, have emerged as a promising approach. It showcases impressive learning abilities across different tasks with the need for only a limited amount of annotated samples. While numerous techniques have focused on developing better fine-tuning strategies to adapt these models for specific domains, we instead examine their robustness to domain shifts in the medical image segmentation task. To this end, we compare the generalization performance to unseen domains of various pre-trained models after being fine-tuned on the same in-distribution dataset and show that foundation-based models enjoy better robustness than other architectures. From here, we further developed a new Bayesian uncertainty estimation for frozen models and used them as an indicator to characterize the model's performance on out-of-distribution (OOD) data, proving particularly beneficial for real-world applications. Our experiments not only reveal the limitations of current indicators like accuracy on the line or agreement on the line commonly used in natural image applications but also emphasize the promise of the introduced Bayesian uncertainty. Specifically, lower uncertainty predictions usually tend to higher out-of-distribution (OOD) performance.

A Generalization Bound of Deep Neural Networks for Dependent Data

Existing generalization bounds for deep neural networks require data to be independent and identically distributed (iid). This assumption may not hold in real-life applications such as evolutionary biology, infectious disease epidemiology, and stock price prediction. This work establishes a generalization bound of feed-forward neural networks for non-stationary $\phi$-mixing data.

LVM-Med: Learning Large-Scale Self-Supervised Vision Models for Medical Imaging via Second-order Graph Matching

Obtaining large pre-trained models that can be fine-tuned to new tasks with limited annotated samples has remained an open challenge for medical imaging data. While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images. To bridge this gap, we introduce LVM-Med, the first family of deep networks trained on large-scale medical datasets. We have collected approximately 1.3 million medical images from 55 publicly available datasets, covering a large number of organs and modalities such as CT, MRI, X-ray, and Ultrasound. We benchmark several state-of-the-art self-supervised algorithms on this dataset and propose a novel self-supervised contrastive learning algorithm using a graph-matching formulation. The proposed approach makes three contributions: (i) it integrates prior pair-wise image similarity metrics based on local and global information; (ii) it captures the structural constraints of feature embeddings through a loss function constructed via a combinatorial graph-matching objective; and (iii) it can be trained efficiently end-to-end using modern gradient-estimation techniques for black-box solvers. We thoroughly evaluate the proposed LVM-Med on 15 downstream medical tasks ranging from segmentation and classification to object detection, and both for the in and out-of-distribution settings. LVM-Med empirically outperforms a number of state-of-the-art supervised, self-supervised, and foundation models. For challenging tasks such as Brain Tumor Classification or Diabetic Retinopathy Grading, LVM-Med improves previous vision-language models trained on 1 billion masks by 6-7% while using only a ResNet-50.

Correlation visualization under missing values: a comparison between imputation and direct parameter estimation methods

Correlation matrix visualization is essential for understanding the relationships between variables in a dataset, but missing data can pose a significant challenge in estimating correlation coefficients. In this paper, we compare the effects of various missing data methods on the correlation plot, focusing on two common missing patterns: random and monotone. We aim to provide practical strategies and recommendations for researchers and practitioners in creating and analyzing the correlation plot. Our experimental results suggest that while imputation is commonly used for missing data, using imputed data for plotting the correlation matrix may lead to a significantly misleading inference of the relation between the features. We recommend using DPER, a direct parameter estimation approach, for plotting the correlation matrix based on its performance in the experiments.

Blockwise Principal Component Analysis for monotone missing data imputation and dimensionality reduction

Monotone missing data is a common problem in data analysis. However, imputation combined with dimensionality reduction can be computationally expensive, especially with the increasing size of datasets. To address this issue, we propose a Blockwise principal component analysis Imputation (BPI) framework for dimensionality reduction and imputation of monotone missing data. The framework conducts Principal Component Analysis (PCA) on the observed part of each monotone block of the data and then imputes on merging the obtained principal components using a chosen imputation technique. BPI can work with various imputation techniques and can significantly reduce imputation time compared to conducting dimensionality reduction after imputation. This makes it a practical and efficient approach for large datasets with monotone missing data. Our experiments validate the improvement in speed. In addition, our experiments also show that while applying MICE imputation directly on missing data may not yield convergence, applying BPI with MICE for the data may lead to convergence.

Adaptive-saturated RNN: Remember more with less instability

Orthogonal parameterization is a compelling solution to the vanishing gradient problem (VGP) in recurrent neural networks (RNNs). With orthogonal parameters and non-saturated activation functions, gradients in such models are constrained to unit norms. On the other hand, although the traditional vanilla RNNs are seen to have higher memory capacity, they suffer from the VGP and perform badly in many applications. This work proposes Adaptive-Saturated RNNs (asRNN), a variant that dynamically adjusts its saturation level between the two mentioned approaches. Consequently, asRNN enjoys both the capacity of a vanilla RNN and the training stability of orthogonal RNNs. Our experiments show encouraging results of asRNN on challenging sequence learning benchmarks compared to several strong competitors. The research code is accessible at https://github.com/ndminhkhoi46/asRNN/.