In machine learning, it is often valuable for models to be parsimonious orsparsefor a variety of reasons, from memory savings and computational speedups tomodel interpretability and generalizability.

We would like to thank the reviewers for their valuable comments and encouraging feedback. Q. Could the authors elaborate a little on r We appreciate the reviewer's positive comments about our submission. Q. Omega notation throughout the paper is erroneous? We agree that our choice of this notation might cause confusion. We will correct the Ω notation to Θ throughout the paper.

This paper improves contrastive learning for sentence embeddings from two perspectives: handling dropout noise and addressing feature corruption. Specifically, for the first perspective, we identify that the dropout noise from negative pairs affects the model's performance. Therefore, we propose a simple yet effective method to deal with such type of noise. Secondly, we pinpoint the rank bottleneck of current solutions to feature corruption and propose a dimension-wise contrastive learning objective to address this issue. Both proposed methods are generic and can be applied to any contrastive learning based models for sentence embeddings. Experimental results on standard benchmarks demonstrate that combining both proposed methods leads to a gain of 1.8 points compared to the strong baseline SimCSE configured with BERT base. Furthermore, applying the proposed method to DiffCSE, another strong contrastive learning based baseline, results in a gain of 1.4 points.

This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric errors-in-variables model. In this game---known as a Distributionally Robust Optimization problem---nature's least favorable distribution is dropout noise, where nature independently deletes entries of the covariate vector with some fixed probability $\delta$. Our decision-theoretic analysis shows that dropout training---the statistician's minimax strategy in the game---indeed provides out-of-sample expected loss guarantees for distributions that arise from multiplicative perturbations of in-sample data. This paper also provides a novel, parallelizable, Unbiased Multi-Level Monte Carlo algorithm to speed-up the implementation of dropout training. Our algorithm has a much smaller computational cost compared to the naive implementation of dropout, provided the number of data points is much smaller than the dimension of the covariate vector.

Due to its robust and precise distance measurements, LiDAR plays an important role in scene understanding for autonomous driving. Training deep neural networks (DNNs) on LiDAR data requires large-scale point-wise annotations, which are time-consuming and expensive to obtain. Instead, simulation-to-real domain adaptation (SRDA) trains a DNN using unlimited synthetic data with automatically generated labels and transfers the learned model to real scenarios. Existing SRDA methods for LiDAR point cloud segmentation mainly employ a multi-stage pipeline and focus on feature-level alignment. They require prior knowledge of real-world statistics and ignore the pixel-level dropout noise gap and the spatial feature gap between different domains. In this paper, we propose a novel end-to-end framework, named ePointDA, to address the above issues. Specifically, ePointDA consists of three components: self-supervised dropout noise rendering, statistics-invariant and spatially-adaptive feature alignment, and transferable segmentation learning. The joint optimization enables ePointDA to bridge the domain shift at the pixel-level by explicitly rendering dropout noise for synthetic LiDAR and at the feature-level by spatially aligning the features between different domains, without requiring the real-world statistics. Extensive experiments adapting from synthetic GTA-LiDAR to real KITTI and SemanticKITTI demonstrate the superiority of ePointDA for LiDAR point cloud segmentation.

Recently, compression and acceleration of deep neural networks are in critic need. Bayesian generalization of structured pruning represents an important research direction to solve the above problem. However, the existing Bayesian methods ignore the dependency among neurons and filters for computational simplicity. In this study, we explore, under Bayesian framework, a structured pruning method with layer-wise sequential dependency assumed, a more general learning setting. Based on the property of Dirac distribution, we further derive a new dropout noise, which makes it possible to approximate the posterior of dropout noise knowing that of the previous layer. With the Dirac-like dropout noise, we further propose a recursive strategy, named \emph{Recursive Bayesian Pruning} (RBP), to train and prune networks in a layer-by-layer fashion. The unimportant neurons and filters are directly targeted and removed, taking the influence from the previous layer. Experiments on typical neural networks LeNet-300-100, LeNet-5 and VGG-16 have demonstrated the proposed method are competitive with or even outperform the state-of-the-art methods in several compression and acceleration metrics.

Single-cell RNA sequencing (scRNA-seq) is a fast growing approach to measure the genome-wide transcriptome of many individual cells in parallel, but results in noisy data with many dropout events. Existing methods to learn molecular signatures from bulk transcriptomic data may therefore not be adapted to scRNA-seq data, in order to automatically classify individual cells into predefined classes. We propose a new method called DropLasso to learn a molecular signature from scRNA-seq data. DropLasso extends the dropout regularisation technique, popular in neural network training, to esti- mate sparse linear models. It is well adapted to data corrupted by dropout noise, such as scRNA-seq data, and we clarify how it relates to elastic net regularisation. We provide promising results on simulated and real scRNA-seq data, suggesting that DropLasso may be better adapted than standard regularisa- tions to infer molecular signatures from scRNA-seq data.

Feature noising is an effective mechanism on reducing the risk of overfitting. To avoid an explosive searching space, existing work typically assumes that all features share a single noise level, which is often cross-validated. In this paper, we present a Bayesian feature noising model that flexibly allows for dimension-specific or group-specific noise levels, and we derive a learning algorithm that adaptively updates these noise levels. Our adaptive rule is simple and interpretable, by drawing a direct connection to the fitness of each individual feature or feature group. Empirical results on various datasets demonstrate the effectiveness on avoiding extensive tuning and sometimes improving the performance due to its flexibility.