We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse--fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing sampling variance at fixed evaluation budget. We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels. Numerical experiments on forward and inverse PINNs--Uzawa benchmarks confirm the predicted variance rates and demonstrate efficiency gains over single-level MC-dropout at matched cost.

Each picture represents a news article clicked by the user. Dash borders indicate behaviors replaced by the augmentation method. The data augmentation proportion is set as 0.6. We also find that the behavior sequence augmented by masking well preserves the user's The pseudo-codes of the pre-training procedure with our AdaptSSR are shown in Algorithm 1. Randomly select two augmentation operators f and g from A. With independently sampled dropout masks. With independently sampled dropout masks.

In this work, we identify dropout induced sparsity for LSTMs as a suitable mode of computation reduction. Dropout is a widely used regularization mechanism, which randomly drops computed neuron values during each iteration of training.

The gradient inversion attack has been demonstrated as a significant privacy threat to federated learning (FL), particularly in continuous domains such as vision models. In contrast, it is often considered less effective or highly dependent on impractical training settings when applied to language models, due to the challenges posed by the discrete nature of tokens in text data. As a result, its potential privacy threats remain largely underestimated, despite FL being an emerging training method for language models. In this work, we propose a domain-specific gradient inversion attack named Grab (gradient inversion with hybrid optimization). Grab features two alternating optimization processes to address the challenges caused by practical training settings, including a simultaneous optimization on dropout masks between layers for improved token recovery and a discrete optimization for effective token sequencing. Grab can recover a significant portion (up to 92.9% recovery rate) of the private training data, outperforming the attack strategy of utilizing discrete optimization with an auxiliary model by notable improvements of up to 28.9% recovery rate in benchmark settings and 48.5% recovery rate in practical settings. Grab provides a valuable step forward in understanding this privacy threat in the emerging FL training mode of language models.

Accurate individual treatment-effect estimation in high-stakes applications demands both reliable point predictions and interpretable uncertainty quantification. We propose a factorized Monte Carlo Dropout framework for deep twin-network models that splits total predictive variance into representation uncertainty (sigma_rep) in the shared encoder and prediction uncertainty (sigma_pred) in the outcome heads. Across three synthetic covariate-shift regimes, our intervals are well-calibrated (ECE < 0.03) and satisfy sigma_rep^2 + sigma_pred^2 ~ sigma_tot^2. Additionally, we observe a crossover: head uncertainty leads on in-distribution data, but representation uncertainty dominates under shift. Finally, on a real-world twins cohort with induced multivariate shifts, only sigma_rep spikes on out-of-distribution samples (delta sigma ~ 0.0002) and becomes the primary error predictor (rho_rep <= 0.89), while sigma_pred remains flat. This module-level decomposition offers a practical diagnostic for detecting and interpreting uncertainty sources in deep causal-effect models.

We propose a combinatorial and graph-theoretic theory of dropout by modeling training as a random walk over a high-dimensional graph of binary subnetworks. Each node represents a masked version of the network, and dropout induces stochastic traversal across this space. We define a subnetwork contribution score that quantifies generalization and show that it varies smoothly over the graph. Using tools from spectral graph theory, PAC-Bayes analysis, and combinatorics, we prove that generalizing subnetworks form large, connected, low-resistance clusters, and that their number grows exponentially with network width. This reveals dropout as a mechanism for sampling from a robust, structured ensemble of well-generalizing subnetworks with built-in redundancy. Extensive experiments validate every theoretical claim across diverse architectures. Together, our results offer a unified foundation for understanding dropout and suggest new directions for mask-guided regularization and subnetwork optimization.

The deployment of Deep Neural Networks in energy-constrained environments, such as Energy Harvesting Wireless Sensor Networks, presents unique challenges, primarily due to the intermittent nature of power availability. To address these challenges, this study introduces and evaluates a novel training methodology tailored for DNNs operating within such contexts. In particular, we propose a dynamic dropout technique that adapts to both the architecture of the device and the variability in energy availability inherent in energy harvesting scenarios. Our proposed approach leverages a device model that incorporates specific parameters of the network architecture and the energy harvesting profile to optimize dropout rates dynamically during the training phase. By modulating the network's training process based on predicted energy availability, our method not only conserves energy but also ensures sustained learning and inference capabilities under power constraints. Our preliminary results demonstrate that this strategy provides 6 to 22 percent accuracy improvements compared to the state of the art with less than 5 percent additional compute. This paper details the development of the device model, describes the integration of energy profiles with intermittency aware dropout and quantization algorithms, and presents a comprehensive evaluation of the proposed approach using real-world energy harvesting data.

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is challenging and requires restrictive approximations. Monte Carlo Dropout has been widely used as a relatively cheap way for approximate Inference and to estimate uncertainty with deep neural networks. Traditionally, the dropout mask is sampled independently from a fixed distribution. Recent works show that the dropout mask can be viewed as a latent variable, which can be inferred with variational inference. These methods face two important challenges: (a) the posterior distribution over masks can be highly multi-modal which can be difficult to approximate with standard variational inference and (b) it is not trivial to fully utilize sample-dependent information and correlation among dropout masks to improve posterior estimation. In this work, we propose GFlowOut to address these issues. GFlowOut leverages the recently proposed probabilistic framework of Generative Flow Networks (GFlowNets) to learn the posterior distribution over dropout masks. We empirically demonstrate that GFlowOut results in predictive distributions that generalize better to out-of-distribution data, and provide uncertainty estimates which lead to better performance in downstream tasks.

Recently, machine learning systems have gained prominence in real-time, critical decision-making domains, such as autonomous driving and industrial automation. Their implementations should avoid overconfident predictions through uncertainty estimation. Bayesian Neural Networks (BayNNs) are principled methods for estimating predictive uncertainty. However, their computational costs and power consumption hinder their widespread deployment in edge AI. Utilizing Dropout as an approximation of the posterior distribution, binarizing the parameters of BayNNs, and further to that implementing them in spintronics-based computation-in-memory (CiM) hardware arrays provide can be a viable solution. However, designing hardware Dropout modules for convolutional neural network (CNN) topologies is challenging and expensive, as they may require numerous Dropout modules and need to use spatial information to drop certain elements. In this paper, we introduce MC-SpatialDropout, a spatial dropout-based approximate BayNNs with spintronics emerging devices. Our method utilizes the inherent stochasticity of spintronic devices for efficient implementation of the spatial dropout module compared to existing implementations. Furthermore, the number of dropout modules per network layer is reduced by a factor of $9\times$ and energy consumption by a factor of $94.11\times$, while still achieving comparable predictive performance and uncertainty estimates compared to related works.