Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units.

Ensembling has a long history in statistical data analysis, with many impactful applications. However, in many modern machine learning settings, the benefits of ensembling are less ubiquitous and less obvious.

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern, \textit{double-descent}, in which test loss, after peaking near the interpolation threshold, decreases again as model capacity continues to grow. While this behavior has been extensively analyzed in regression and classification, its manifestation in survival analysis remains unexplored. This study investigates overparametrization in four representative survival models: DeepSurv, PC-Hazard, Nnet-Survival, and N-MTLR. We rigorously define \textit{interpolation} and \textit{finite-norm interpolation}, two key characteristics of loss-based models to understand \textit{double-descent}. We then show the existence (or absence) of \textit{(finite-norm) interpolation} of all four models. Our findings clarify how likelihood-based losses and model implementation jointly determine the feasibility of \textit{interpolation} and show that overparametrization should not be regarded as benign for survival models. All theoretical results are supported by numerical experiments that highlight the distinct generalization behaviors of survival models.

S4.1 Decomposition of terms The model's predictions on the training set, ˆ y ( X), take a simple form, ˆ y ( X)= N

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high variance of the predictive function.

Classical learning theory describes a well-characterised U-shaped relationship between model complexity and prediction error, reflecting a transition from underfitting in underparameterised regimes to overfitting as complexity grows. Recent work, however, has introduced the notion of a second descent in test error beyond the interpolation threshold-giving rise to the so-called double descent phenomenon. While double descent has been studied extensively in the context of deep learning, it has also been reported in simpler models, including decision trees and gradient boosting. In this work, we revisit these claims through the lens of classical machine learning applied to a biological classification task: predicting isoniazid resistance in Mycobacterium tuberculosis using whole-genome sequencing data. We systematically vary model complexity along two orthogonal axes-learner capacity (e.g., Pleaf, Pboost) and ensemble size (i.e., Pens)-and show that double descent consistently emerges only when complexity is scaled jointly across these axes. When either axis is held fixed, generalisation behaviour reverts to classical U- or L-shaped patterns. These results are replicated on a synthetic benchmark and support the unfolding hypothesis, which attributes double descent to the projection of distinct generalisation regimes onto a single complexity axis. Our findings underscore the importance of treating model complexity as a multidimensional construct when analysing generalisation behaviour. All code and reproducibility materials are available at: https://github.com/guillermocomesanacimadevila/Demystifying-Double-Descent-in-ML.

Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that discrete diffusion models require larger capacity and more training epochs to escape their underparameterized regime and reach the interpolation threshold. In the strongly overparameterized regime, both models exhibit similar behavior, with neither exhibiting a pronounced second descent in test loss across a large range of model sizes. Overall, our results indicate that autoregressive models are more sample-efficient on small-scale datasets, while discrete diffusion models only become competitive when given sufficient capacity and compute.

Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of high-dimensional, ridge-regularized linear regression under 'data coarse graining.' Inspired by the renormalization group in statistical physics, we analyze coarse-graining schemes that systematically discard features based on their relevance to the learning task. Our results reveal a nonmonotonic dependence of the prediction risk on the degree of coarse graining. A 'high-pass' scheme--which filters out less relevant, lower-signal features--can help models generalize better. By contrast, a 'low-pass' scheme that integrates out more relevant, higher-signal features is purely detrimental. Crucially, using optimal regularization, we demonstrate that this nonmonotonicity is a distinct effect of data coarse graining and not an artifact of double descent. Our framework offers a clear, analytical explanation for why careful data augmentation works: it strips away less relevant degrees of freedom and isolates more predictive signals. Our results highlight a complex, nonmonotonic risk landscape shaped by the structure of the data, and illustrate how ideas from statistical physics provide a principled lens for understanding modern machine learning phenomena.