Deep End-to-End Survival Analysis with Temporal Consistency

Flexible continuous-time survival modeling is critical for capturing complex time-varying hazard dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary hazard dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.

Survival analysis on tabular data is a well-studied problem. However, existing deep learning methods are often highly task-specific, which can limit the transfer of new approaches from other domains and introduce constraints that may affect performance. We propose TabSurv, an approach that adapts modern tabular architectures to survival analysis using either the Weibull distribution or non-parametric survival prediction. TabSurv optimizes SurvHL, a novel histogram loss function supporting censored data. In addition to a baseline feed-forward network, we implement deep ensembles of MLPs for survival analysis within TabSurv. In contrast to prior work, the ensemble components are trained in parallel, optimizing survival distribution parameters before averaging, which promotes diversity across ensemble component predictions. We perform a comprehensive empirical evaluation of different proposed architectures on 10 diverse real-world survival datasets. Our results show that TabSurv consistently outperforms on average established classical and deep learning baselines, such as RSF, DeepSurv, DeepHit, SurvTRACE. Notably, deep ensembles with Weibull parametrization instead of non-parametric models achieve the highest average rank by C-index. Overall, our study clarifies how modern tabular neural networks can be adapted and trained to tackle survival analysis problems, offering a strong and reliable approach. The TabSurv implementation is publicly available.

Long-term time series forecasting requires temporal dependency modeling that remains stable and generalizable under temporal distribution shifts. However, real-world time series are often noisy and non-stationary, making deep learning models prone to fitting incidental temporal interactions in the training data. A key question is whether there exist temporal relationship structures that recur across different temporal positions and variables. We analyze temporal relationship matrices on commonly used time series datasets and find that samples from different temporal positions and different variables exhibit shared dominant temporal relationship structures. This indicates that temporal relationship structures contain patterns that recur stably across samples and variables. To learn such shared structures, we propose Temporal Structure Network (TStruct), a simple yet effective network for directly learning shared and generalizable temporal dependencies. Specifically, TStruct directly parameterizes a set of shared temporal dependency matrices and generates normalized combination weights using dynamic sample information and static variable priors. These weights represent a soft allocation of each sample-variable pair over shared temporal dependency structures, enabling the model to generate adaptive temporal dependency matrices under shared structural constraints, rather than fitting incidental interactions in a fully unconstrained manner. Notably, this simple structure-aware design consistently outperforms several strong baselines across all datasets, achieving superior accuracy while maintaining high computational efficiency.