#01Nov 10, 2026
stat.ML
A Theory of Cross-Validation Variance
Nathaniel S. O'Connell, Jaime L. Speiser
Cross-validation estimates predictive performance by repeatedly splitting the data into training and validation sets, fitting the model on the first and evaluating it on the second. Every observation influences the estimate in two roles, through its own evaluation when it is held out and through the models it helps fit when it trains. The random splits determine its weight in each role. From this representation, we prove an exact finite-sample identity for the variance of the cross-validated estimate. For a given splitting scheme with a common training set size, the variance is a function of these weights, with constants of the model, the metric, and the population. It covers metrics averaged over observations, such as mean squared error, and over case--control pairs, such as the AUC. The identity shows which schemes to use. The variance decomposes into sampling variance, which depends only on the training size, and variance due to the random fold splitting, which arises when the weights change from one draw of the splits to the next. K-fold cross-validation, whose weights are equal across observations by design, is therefore variance optimal at first order; Monte Carlo and bootstrap cross-validation are not. The first-order variance of K-fold does not depend on K, and under reasonable conditions on the model leave-one-out has the smallest variance of any K-fold scheme. For the AUC the same holds for leave-pair-out, which evaluates every case--control pair. Finally, we show the cross-validated estimate is asymptotically normal with the identity's full variance. Together, these results provide a general theoretical foundation for inference on cross-validated performance and establish principles for selecting variance-optimal cross-validation designs.
#02Nov 10, 2026
cs.LG
TimeSeek: Multi-Task and Multi-Domain Pretraining for Generalized Time Series Analytics
Peng Chen, Yihang Wang, Zhongwen Rao and 6 more
Time series analytics has been widely applied across various domains. While existing time series foundation models (TSFMs) have demonstrated promising results, they still face two major challenges: 1) Most TSFMs mainly rely on stacking Transformer layers to increase parameter size, lacking the ability to adaptively model complex time series patterns from multi-domain data. 2) Current TSFMs are primarily pre-trained for specific tasks, e.g., forecasting or anomaly detection, and a few models support multiple tasks, but they fail to fully leverage task specificity and commonality, resulting in suboptimal performance. To address these challenges, we propose TimeSeek, a novel generalized time series analytics model that adaptively models time series patterns from multi-domain data and unifies multiple tasks in pre-training. Conceptually, TimeSeek is guided by selective information sharing under domain and task heterogeneity. From the perspective of multi-domain data, we propose a Multi-Domain Feature Extractor that adaptively captures temporal dependencies and channel correlations based on domain-specific characteristics, including progressive multi-scale modeling and adaptive slot channel modeling. From the perspective of the diversity of tasks, we propose multi-task collaborative training, which leverages task specificity and task commonality through task customization and cross-task training, effectively unifying multiple tasks in pre-training and better adapting to diverse downstream scenarios. After pre-training on large-scale time series data, TimeSeek achieves state-of-the-art performance in forecasting, anomaly detection, and classification tasks across both few-shot learning and zero-shot situations, together with favorable inference efficiency.
#03Nov 10, 2026
cs.LG
When Does the Real Wiring Win? Testing connectome structure-function claims against unmeasured physiology
Yeyuan Liu
Connectome-constrained models are often used to argue that a measured wiring diagram outperforms shuffled or rewired wiring, and hence that structure shapes function. Such comparisons can confound wiring with how the models are tuned: a connectome fixes who connects to whom, not the excitability, gains or plasticity rates the model also needs, and modellers often tune these until the real-wiring model works. We separate three estimands: physiology tuned on the real wiring and transferred to nulls (P1), each wiring tuned on its own (P2), and P2 restricted to physiology consistent with independent data (P3). The biases involved are known in machine learning (under-tuned baselines, inherited weights, winner's curse); we measure what they do to biological conclusions, using synthetic ground truth, placebo nulls and three Drosophila circuit models. Some claims survive every protocol we test: segregated reward and punishment dopamine improves learning, and head-direction topography is required for a persistent bump. Others do not. In the mushroom body, the real Kenyon-cell output wiring beats a cross-subtype identity shuffle by 0.09 under P1 and P2 but loses to it by 0.09 under P3 (95% CIs exclude zero; held-out runs confirm). The verdict is set by the share of alpha'beta' cells among active Kenyon cells, which P1 selects low; at the share implied by imaging (about 44%) the real-wiring model fails to learn, exposing a model inadequacy rather than a deficit of the fly's wiring. In flyvis, P1 penalises a mirrored connectome, which has a constructed solution within 0.07 (median) of the real error, more than a spatially shuffled one in 50 of 50 members; the ranking survives ten-fold longer retraining but depends on the checkpoint at fifty-fold. A credible structural claim needs matched optimisation, data-constrained physiology and a model that still works there.
#04Nov 10, 2026
cs.LG
DnNP: Denoising Input Uncertainty in Neural Processes
Fatemeh Tohidian, Chengzhi Shi, Soomi Lee and 4 more
Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM2.5 spatial interpolation from real-world air quality sensors, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes-optimal predictor under noisy inputs belongs to the DnNP model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNP provably avoids.
#05Nov 10, 2026
cs.LG
TorchCurves: Differentiable Parametric Curves
Alex Shtoff
We present TorchCurves, a PyTorch library that treats vector-valued parametric curves as learnable primitives. Its central operation maps batches of scalar inputs to points on curves represented in B-spline or Legendre polynomial bases, with differentiation through both inputs and coefficients. Curve coefficients can be optimized jointly with the surrounding model or produced by another network. The library provides trainable modules, reusable basis modules, and a functional interface, supporting applications ranging from continuous feature embeddings to Kolmogorov-Arnold networks and functional regression. Its implementation combines classical evaluation algorithms with vectorized PyTorch operations, emphasizing readability and maintainability without custom hardware kernels. Timing experiments compare curve evaluation against NumPy and SciPy and KAN training against EfficientKAN across a range of problem sizes. The results illustrate where this generality remains computationally practical and where overhead is substantial. Library is available on GitHub at https://github.com/alexshtf/torchcurves.