Monte Carlo Dropout

Context: We developed a probabilistic machine learning method with the aim of performing the O(10)-way classification of low- and high-resolution spectra of stellar and extragalactic targets for the upcoming 4MOST survey. In fulfilment of the survey requirements, this method should be able to express uncertainty in the input data as well as uncertainty introduced in its prediction. Aims: Four different methods are explored: (1) convolutional neural networks (CNNs), (2) the Dirichlet distribution, (3) Monte Carlo dropout (MCD), (4) Bayesian neural Networks (BNNs) + variational inference (VI). Training and validation was performed using labelled spectra from the SDSS database and a custom 4MOST mock dataset. All the methods were compared in terms of the same metrics: accuracy, area under the curve (AUC), expected calibration error (ECE), Shannon entropy, negative log-likelihood (NLL), Brier score, training time, and inference time. Methods: A CNN with simple architecture and about 20,000 parameters was trained to achieve classification accuracies of 91.5% on SDSS data and 92.8% on 4MOST mock data. The direct Dirichlet prediction and VI models tested provide uncertainties on class membership probabilities, but they confuse classes more often. The MCD on a CNN is found to be the most suitable; it boosts the point-estimate accuracies to 92.6% and 93.9%, while still providing fast training and sufficiently fast inference. Compared to a standard CNN, the method additionally provides well-calibrated uncertainties at marginal extra cost.

Reliability estimation of large language models is in many cases as crucial as their accuracy, as reliable models are more trustworthy, robust, and suitable for practical applications. Recent advancements in natural language processing (NLP), particularly those based on transformer architectures, have significantly accelerated progress across various NLP tasks. This study focuses on the reliability of transformer-based question answering (QA) models, specifically BERT models and its variants (RoBERTa, ALBERT, DistilBERT). These encoder-only pretrained transformers have demonstrated remarkable accuracy in QA tasks that can be treated as classification tasks. However, their reliability remains underexplored. This study evaluates the reliability of four BERT-based models by assessing response stability under two conditions: (1) internal model variations induced via Monte Carlo Dropout (MCD) and (2) input perturbations through paraphrasing. Using the SQuAD and QuAC datasets, we investigate how dropout rates affect prediction consistency and whether lexical changes impact answer stability. Our findings reveal that RoBERTa maintains higher reliability, whereas AlBERT and DistilBERT exhibit significant inconsistencies. Statistical analyses confirm that enabling MCD during prediction does not disrupt inference dynamics, validating its effectiveness as a reliability metric. These findings underscore the importance of evaluating both accuracy and stability in QA models to ensure stability in real-world applications.

The deployment of deep neural networks in safety-critical domains demands reliable estimates of predictive confidence, yet conventional architectures lack principled uncertainty quantification. This survey provides a structured, critical review of methods for Uncertainty Quantification (UQ) in deep learning, scoped to ensemble-based and approximate Bayesian approaches and the measures used to summarize their outputs. Relative to existing UQ surveys, our contribution is depth on efficient ensemble approximations and single-pass methods, and a unified treatment that separates the method producing a predictive distribution from the measure that summarizes its uncertainty. We organize methods into five families: Bayesian neural networks, Monte Carlo Dropout, deep ensembles, efficient ensemble approximations, and last-layer or single-pass approaches. We situate adjacent work on evidential and prior networks, conformal prediction, and post-hoc calibration, together with the decision-time tasks of out-of-distribution detection and selective prediction. For each, we examine theoretical motivation, implementation, empirical performance, and limitations. We then review ensemble diversity theory and uncertainty measures and their decompositions, contrasting the entropy decomposition with pairwise divergence measures, and consolidate evaluation methodology so that our qualitative comparisons share a common basis. We close with a brief treatment of uncertainty in large language models and open research directions, including efficient epistemic measures for classification, last-layer diversity, diversity and calibration under shift, and hybrid architectures.

Machine learning models for medical image analysis typically lack a reliable measure of confidence, limiting their use in ambiguous or atypical cases. Here we show that Monte Carlo dropout, applied to a multi-task chest-radiograph classifier (eight thoracic findings, 137,593 training images), provides an epistemic uncertainty signal that tracks generalisation across training-set scales and flags confident yet error-prone predictions. Adding this signal to the point prediction raised error-detection AUROC from 0.74 to 0.77 ($Δ$AUROC +0.023, 95% CI [+0.014, +0.033]). In a controlled 2x2 factorial experiment, a clinical-decision-support agent exploited this uncertainty only when it was delivered as a binary error-risk flag rather than as raw scores, cutting confident misdiagnoses on unreliable findings from 8.5% to 2.7%. Epistemic uncertainty estimation thus carries decision-relevant information beyond point predictions, but its value for downstream agents depends on how it is communicated.

Glioma segmentation in multiparametric MRI is a critical component of treatment planning. A segmentation model that fails silently on treatment-critical sub-regions represents a patient safety risk that overlap-based metrics such as Dice scores cannot expose. We ask whether voxel-level uncertainty estimation via Monte Carlo (MC) Dropout can reliably identify segmentation errors in clinically critical sub-regions, and whether calibration failure modes are detectable from standard reporting metrics alone. In an empirical two-model case study on 126 BraTS21 patients, we evaluate a high-performance pretrained SegResNet and a locally trained UNet with residual units (UNet-Res). MC dropout preserved segmentation accuracy ($|Δ\text{Dice}|$ $<0.01$) while achieving strong uncertainty-error alignment (AUROC for entropy (H) $\approx$0.97), indicating uncertainty correctly ranks erroneous voxels above correct ones. Entropy-based patient stratification identified a high-uncertainty subgroup with substantially lower segmentation performance (median whole-tumour Dice $0.835$ vs. $0.925$), supporting uncertainty as a practical triage signal. However, global alignment can mask important region-specific differences. Despite similar AUROC, UNet-Res exhibited near-zero enhancing tumour entropy ($0.054$) and Expected Calibration Error (ECE) of $0.915$, with a Dice of only $0.714$, indicating severely miscalibrated confidence on the most clinically critical sub-region, a failure mode invisible to standard Dice and AUROC reporting. These findings demonstrate that strong uncertainty-error alignment is necessary but insufficient for clinical safety: sub-region-specific calibration assessment must accompany AUROC evaluation when selecting models for clinical deployment.

Scaling data-driven energy forecasting to district level requires models that can be re-used across buildings with minimal target-domain data and honest uncertainty estimates. We present an uncertainty-aware transfer learning (TL) framework for cross-building energy forecasting based on the Temporal Fusion Transformer (TFT), evaluated on a newly released high-resolution real sub-meter dataset: an educational building at Aalborg University, Denmark (source) and the multi-typology NEST building at EMPA, Switzerland (target). We introduce the Transfer Robustness Index (TRI), an architecture-agnostic metric for quantifying generalization quality across domain gaps. A four-strategy layer-freezing ablation shows that Probe-Only fine-tuning, updating only 455 output-layer parameters out of 806K, achieves the best transfer quality (TRI = 3,097), outperforming full fine-tuning and suggesting that TFT encoders learn transferable temporal representations. Monte Carlo Dropout yields a prediction interval coverage probability of 93.2%, close to the nominal 95% target. A data-scarcity analysis further shows monotonic improvement with increasing target-domain data, providing practical guidance for district energy deployment.

Traditional neural networks provide deterministic predictions without inherent uncertainty estimates. While Bayesian Neural Networks (BNNs) offer a principled approach to uncertainty quantification, their computational complexity limits scalability. Monte Carlo (MC) Dropout, initially introduced as a regularization technique, has been shown to approximate Bayesian inference by enabling probabilistic modeling through multiple stochastic forward passes. In this work, we enhance uncertainty estimation in deep learning by integrating a Dirichlet-based framework within MC Dropout. Specifically, we leverage the formulation proposed by Sensoy et al. (2018), where class probabilities are modeled using a Dirichlet distribution, allowing for a more informative uncertainty representation. The proposed approach maintains the computational efficiency of MC Dropout while improving the quality of uncertainty estimates. We discuss the theoretical foundations of our method and compare it with existing uncertainty quantification techniques. The results highlight the effectiveness of the proposed method in producing well-calibrated uncertainty estimates, offering a practical solution for uncertainty-aware deep learning models.

Accurate methane sorption prediction across heterogeneous coal ranks requires models that combine thermodynamic consistency, efficient knowledge transfer across data-scarce geological systems, and calibrated uncertainty estimates, capabilities that are rarely addressed together in existing frameworks. We present a physics-informed transfer learning framework that adapts a hydrogen sorption PINN to methane sorption prediction via Elastic Weight Consolidation, coal-specific feature engineering, and a three-phase curriculum that progressively balances transfer preservation with thermodynamic fine-tuning. Trained on 993 equilibrium measurements from 114 independent coal experiments spanning lignite to anthracite, the framework achieves R2 = 0.932 on held-out coal samples, a 227% improvement over pressure-only classical isotherms, while hydrogen pre-training delivers 18.9% lower RMSE and 19.4% faster convergence than random initialization. Five Bayesian uncertainty quantification approaches reveal a systematic divergence in performance across physics-constrained architectures. Monte Carlo Dropout achieves well-calibrated uncertainty at minimal overhead, while deep ensembles, regardless of architectural diversity or initialization strategy, exhibit performance degradation because shared physics constraints narrow the admissible solution manifold. SHAP and ALE analyses confirm that learned representations remain physically interpretable and aligned with established coal sorption mechanisms: moisture-volatile interactions are most influential, pressure-temperature coupling captures thermodynamic co-dependence, and features exhibit non-monotonic effects. These results identify Monte Carlo Dropout as the best-performing UQ method in this physics-constrained transfer learning framework, and demonstrate cross-gas transfer learning as a data-efficient strategy for geological material modeling.

AI-based weather forecasting now rivals traditional physics-based ensembles, but state-of-the-art (SOTA) models rely on specialized architectures and massive computational budgets, creating a high barrier to entry. We demonstrate that such complexity is unnecessary for frontier performance. We introduce \ours, a probabilistic forecaster built on a standard U-Net backbone trained with a simple recipe: deterministic pre-training on Mean Absolute Error followed by short probabilistic fine-tuning on the Continuous Ranked Probability Score (CRPS) using Monte Carlo Dropout for stochasticity. As a result, our model matches or exceeds the probabilistic skill of GenCast and IFS ENS at $1.5^\circ$ resolution while reducing training compute by over $10\times$ compared to leading CRPS-based models and inference latency by over $10\times$ compared to diffusion-based models. U-Cast trains in under 12 H200 GPU-days and generates a 15-day ensemble forecast in 3 seconds. These results suggest that scalable, general-purpose architectures paired with efficient training curricula can match complex domain-specific designs at a fraction of the cost, opening the training of frontier probabilistic weather models to the broader community.

Breast cancer is a highly heterogeneous disease with diverse molecular profiles. The PAM50 gene signature is widely recognized as a standard for classifying breast cancer into intrinsic subtypes, enabling more personalized treatment strategies. In this study, we introduce a novel optimization-driven deep learning framework that aims to reduce reliance on costly molecular assays by directly predicting PAM50 subtypes from H&E-stained whole-slide images (WSIs). Our method jointly optimizes patch informativeness, spatial diversity, uncertainty, and patch count by combining the non-dominated sorting genetic algorithm II (NSGA-II) with Monte Carlo dropout-based uncertainty estimation. The proposed method can identify a small but highly informative patch subset for classification. We used a ResNet18 backbone for feature extraction and a custom CNN head for classification. For evaluation, we used the internal TCGA-BRCA dataset as the training cohort and the external CPTAC-BRCA dataset as the test cohort. On the internal dataset, an F1-score of 0.8812 and an AUC of 0.9841 using 627 WSIs from the TCGA-BRCA cohort were achieved. The performance of the proposed approach on the external validation dataset showed an F1-score of 0.7952 and an AUC of 0.9512. These findings indicate that the proposed optimization-guided, uncertainty-aware patch selection can achieve high performance and improve the computational efficiency of histopathology-based PAM50 classification compared to existing methods, suggesting a scalable imaging-based replacement that has the potential to support clinical decision-making.

Transformer-based language models are widely deployed for reasoning, yet their behavior under inference-time stochasticity remains underexplored. While dropout is common during training, its inference-time effects via Monte Carlo sampling lack systematic evaluation across architectures, limiting understanding of model reliability in uncertainty-aware applications. This work analyzes dropout-induced variability across 19 transformer models using MC Dropout with 100 stochastic forward passes per sample. Dropout robustness is defined as maintaining high accuracy and stable predictions under stochastic inference, measured by standard deviation of per-run accuracies. A cognitive decomposition framework disentangles performance into memory and reasoning components. Experiments span five dropout configurations yielding 95 unique evaluations on 1,000 samples. Results reveal substantial architectural variation. Smaller models demonstrate perfect prediction stability while medium-sized models exhibit notable volatility. Mid-sized models achieve the best overall performance; larger models excel at memory tasks. Critically, 53% of models suffer severe accuracy degradation under baseline MC Dropout, with task-specialized models losing up to 24 percentage points, indicating unsuitability for uncertainty quantification in these architectures. Asymmetric effects emerge: high dropout reduces memory accuracy by 27 percentage points while reasoning degrades only 1 point, suggesting memory tasks rely on stable representations that dropout disrupts. 84% of models demonstrate memory-biased performance. This provides the first comprehensive MC Dropout benchmark for transformers, revealing dropout robustness is architecture-dependent and uncorrelated with scale. The cognitive profiling framework offers actionable guidance for model selection in uncertainty-aware applications.