Abstract--Time series forecasting requires architectures that simultaneously achieve three competing objectives: (1) strict temporal causality for reliable predictions, (2) sub-quadratic complexity for practical scalability, and (3) multi-scale pattern recognition for accurate long-horizon forecasting. We introduce AutoHFormer, a hierarchical autoregressive transformer that addresses these challenges through three key innovations: 1) Hierarchical Temporal Modeling: Our architecture decomposes predictions into segment-level blocks processed in parallel, followed by intra-segment sequential refinement. This dual-scale approach maintains temporal coherence while enabling efficient computation. This design avoids both the anti-causal violations of standard transformers and the sequential bottlenecks of RNN hybrids. It combines fixed oscillating patterns for short-term variations with learnable decay rates for long-term trends. Comprehensive experiments demonstrate that AutoHFormer 10.76 faster training and 6.06 memory reduction compared to PatchTST on PEMS08, while maintaining consistent accuracy across 96-720 step horizons in most of cases. These breakthroughs establish new benchmarks for efficient and precise time series modeling. I. Introduction Time series forecasting [1, 2, 3, 4, 5] stands as a fundamental pillar of modern predictive analytics, enabling data-driven decision making across numerous mission-critical domains. As demonstrated in recent literature [6, 7], this task has become increasingly vital in our data-rich era.

Purpose: Accurate intraoperative X-ray/CT registration is essential for surgical navigation in orthopedic procedures. However, existing methods struggle with consistently achieving sub-millimeter accuracy, robustness under broad initial pose estimates or need manual key-point annotations. This work aims to address these challenges by proposing a novel multi-view X-ray/CT registration method for intraoperative bone registration. Methods: The proposed registration method consists of a multi-view, contour-based iterative closest point (ICP) optimization. Unlike previous methods, which attempt to match bone contours across the entire silhouette in both imaging modalities, we focus on matching specific subcategories of contours corresponding to bone substructures. This leads to reduced ambiguity in the ICP matches, resulting in a more robust and accurate registration solution. This approach requires only two X-ray images and operates fully automatically. Additionally, we contribute a dataset of 5 cadaveric specimens, including real X-ray images, X-ray image poses and the corresponding CT scans. Results: The proposed registration method is evaluated on real X-ray images using mean reprojection error (mRPD). The method consistently achieves sub-millimeter accuracy with a mRPD 0.67mm compared to 5.35mm by a commercial solution requiring manual intervention. Furthermore, the method offers improved practical applicability, being fully automatic. Conclusion: Our method offers a practical, accurate, and efficient solution for multi-view X-ray/CT registration in orthopedic surgeries, which can be easily combined with tracking systems. By improving registration accuracy and minimizing manual intervention, it enhances intraoperative navigation, contributing to more accurate and effective surgical outcomes in computer-assisted surgery (CAS).

We design an efficient algorithm that outputs tests for identifying predominantly homogeneous subcohorts of patients from large in-homogeneous datasets. Our theoretical contribution is a rounding technique, similar to that of Goemans and Wiliamson (1995), that approximates the optimal solution within a factor of $0.82$. As an application, we use our algorithm to trade-off sensitivity for specificity to systematically identify clinically interesting homogeneous subcohorts of patients in the RNA microarray dataset for breast cancer from Curtis et al. (2012). One such clinically interesting subcohort suggests a link between LXR over-expression and BRCA2 and MSH6 methylation levels for patients in that subcohort.

Transformer models exhibit remarkable in-context learning (ICL), adapting to novel tasks from examples within their context, yet the underlying mechanisms remain largely mysterious. Here, we provide an exact analytical characterization of ICL emergence by deriving the closed-form stochastic gradient descent (SGD) dynamics for a simplified linear transformer performing regression tasks. Our analysis reveals key properties: (1) a natural separation of timescales directly governed by the input data's covariance structure, leading to staged learning; (2) an exact description of how ICL develops, including fixed points corresponding to learned algorithms and conservation laws constraining the dynamics; and (3) surprisingly nonlinear learning behavior despite the model's linearity. We hypothesize this phenomenology extends to non-linear models. To test this, we introduce theory-inspired macroscopic measures (spectral rank dynamics, subspace stability) and use them to provide mechanistic explanations for (1) the sudden emergence of ICL in attention-only networks and (2) delayed generalization (grokking) in modular arithmetic models. Our work offers an exact dynamical model for ICL and theoretically grounded tools for analyzing complex transformer training.

Federated learning (FL) enables learning a global machine learning model from local data distributed among a set of participating workers. This makes it possible i) to train more accurate models due to learning from rich joint training data, and ii) to improve privacy by not sharing the workers' local private data with others. However, the distributed nature of FL makes it vulnerable to targeted poisoning attacks that negatively impact the integrity of the learned model while, unfortunately, being difficult to detect. Existing defenses against those attacks are limited by assumptions on the workers' data distribution, may degrade the global model performance on the main task and/or are ill-suited to high-dimensional models. In this paper, we analyze targeted attacks against FL and find that the neurons in the last layer of a deep learning (DL) model that are related to the attacks exhibit a different behavior from the unrelated neurons, making the last-layer gradients valuable features for attack detection. Accordingly, we propose \textit{FL-Defender} as a method to combat FL targeted attacks. It consists of i) engineering more robust discriminative features by calculating the worker-wise angle similarity for the workers' last-layer gradients, ii) compressing the resulting similarity vectors using PCA to reduce redundant information, and iii) re-weighting the workers' updates based on their deviation from the centroid of the compressed similarity vectors. Experiments on three data sets with different DL model sizes and data distributions show the effectiveness of our method at defending against label-flipping and backdoor attacks. Compared to several state-of-the-art defenses, FL-Defender achieves the lowest attack success rates, maintains the performance of the global model on the main task and causes minimal computational overhead on the server.

Flow-matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets. Independent sampling often yields high-variance estimates, especially when rare but with high-impact outcomes dominate the expectation. W e propose an importance-weighted non-IID sampling framework that jointly draws multiple samples to cover diverse, salient regions of a flow's distribution while maintaining unbiased estimation via estimated importance weights. T o balance diversity and quality, we introduce a score-based regularization for the diversity mechanism, which uses the score function, i.e., the gradient of the log probability, to ensure samples are pushed apart within high-density regions of the data manifold, mitigating off-manifold drift. W e further develop the first approach for importance weighting of non-IID flow samples by learning a residual velocity field that reproduces the marginal distribution of the non-IID samples. Empirically, our method produces diverse, high-quality samples and accurate estimates of both importance weights and expectations, advancing the reliable characterization of flow-matching model outputs. Our code will be publicly available on GitHub.

Procedural activities, ranging from routine cooking to complex surgical operations, are highly structured as a set of actions conducted in a specific temporal order. Despite their success on static images and short clips, current self-supervised learning methods often overlook the procedural nature that underpins such activities. We expose the lack of procedural awareness in current SSL methods with a motivating experiment: models pretrained on forward and time-reversed sequences produce highly similar features, confirming that their representations are blind to the underlying procedural order. To address this shortcoming, we propose PL-Stitch, a self-supervised framework that harnesses the inherent temporal order of video frames as a powerful supervisory signal. Our approach integrates two novel probabilistic objectives based on the Plackett-Luce (PL) model. The primary PL objective trains the model to sort sampled frames chronologically, compelling it to learn the global workflow progression. The secondary objective, a spatio-temporal jigsaw loss, complements the learning by capturing fine-grained, cross-frame object correlations. Our approach consistently achieves superior performance across five surgical and cooking benchmarks. Specifically, PL-Stitch yields significant gains in surgical phase recognition (e.g., +11.4 pp k-NN accuracy on Cholec80) and cooking action segmentation (e.g., +5.7 pp linear probing accuracy on Breakfast), demonstrating its effectiveness for procedural video representation learning.

Deterministic Lateral Displacement (DLD) devices are widely used in microfluidics for label-free, size-based separation of particles and cells, with particular promise in isolating circulating tumor cells (CTCs) for early cancer diagnostics. This study focuses on the optimization of DLD design parameters, such as row shift fraction, post size, and gap distance, to enhance the selective isolation of lung cancer cells based on their physical properties. To overcome the challenges of rare CTC detection and reduce reliance on computationally intensive simulations, machine learning models including gradient boosting, k-nearest neighbors, random forest, and multilayer perceptron (MLP) regressors are employed. Trained on a large, numerically validated dataset, these models predict particle trajectories and identify optimal device configurations, enabling high-throughput and cost-effective DLD design. Beyond trajectory prediction, the models aid in isolating critical design variables, offering a systematic, data-driven framework for automated DLD optimization. This integrative approach advances the development of scalable and precise microfluidic systems for cancer diagnostics, contributing to the broader goals of early detection and personalized medicine.

Efficiently and meaningfully estimating prediction uncertainty is important for exploration in active learning campaigns in materials discovery, where samples with high uncertainty are interpreted as containing information missing from the model. In this work, the effect of different uncertainty estimation and calibration methods are evaluated for active learning when using ensembles of ALIGNN, eXtreme Gradient Boost, Random Forest, and Neural Network model architectures. We compare uncertainty estimates from ALIGNN deep ensembles to loss landscape uncertainty estimates obtained for solubility, bandgap, and formation energy prediction tasks. We then evaluate how the quality of the uncertainty estimate impacts an active learning campaign that seeks model generalization to out-of-distribution data. Uncertainty calibration methods were found to variably generalize from in-domain data to out-of-domain data. Furthermore, calibrated uncertainties were generally unsuccessful in reducing the amount of data required by a model to improve during an active learning campaign on out-of-distribution data when compared to random sampling and uncalibrated uncertainties. The impact of poor-quality uncertainty persists for random forest and eXtreme Gradient Boosting models trained on the same data for the same tasks, indicating that this is at least partially intrinsic to the data and not due to model capacity alone. Analysis of the target, in-distribution uncertainty, out-of-distribution uncertainty, and training residual distributions suggest that future work focus on understanding empirical uncertainties in the feature input space for cases where ensemble prediction variances do not accurately capture the missing information required for the model to generalize.

Pediatric pancreatitis is a progressive and debilitating inflammatory condition, including acute pancreatitis and chronic pancreatitis, that presents significant clinical diagnostic challenges. Machine learning-based methods also face diagnostic challenges due to limited sample availability and multimodal imaging complexity. To address these challenges, this paper introduces Upstream Probabilistic Meta-Imputation (UPMI), a light-weight augmentation strategy that operates upstream of a meta-learner in a low-dimensional meta-feature space rather than in image space. Modality-specific logistic regressions (T1W and T2W MRI radiomics) produce probability outputs that are transformed into a 7-dimensional meta-feature vector. Class-conditional Gaussian mixture models (GMMs) are then fit within each cross-validation fold to sample synthetic meta-features that, combined with real meta-features, train a Random Forest (RF) meta-classifier. On 67 pediatric subjects with paired T1W/T2W MRIs, UPMI achieves a mean AUC of 0.908 $\pm$ 0.072, a $\sim$5% relative gain over a real-only baseline (AUC 0.864 $\pm$ 0.061).