The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both discrete and continuous spectra, complicating direct computations. In this paper, we introduce a kernel-based method to construct the principal eigenfunctions of the Koopman operator without explicitly computing the operator itself. These principal eigenfunctions are associated with the equilibrium dynamics, and their eigenvalues match those of the linearization of the nonlinear system at the equilibrium point. We exploit the structure of the principal eigenfunctions by decomposing them into linear and nonlinear components. The linear part corresponds to the left eigenvector of the system's linearization at the equilibrium, while the nonlinear part is obtained by solving a partial differential equation (PDE) using kernel methods. Our approach avoids common issues such as spectral pollution and spurious eigenvalues, which can arise in previous methods. We demonstrate the effectiveness of our algorithm through numerical examples.

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often necessary for downstream tasks. Finding an accurate approximation to this posterior is challenging, due to the large number of possible causal graphs, as well as the difficulty in the subproblem of finding posteriors over the functional relationships of the causal edges. Recent works have used meta-learning to view the problem of estimating the maximum a-posteriori causal graph as supervised learning. Yet, these methods are limited when estimating the full posterior as they fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. Further, these methods also cannot reliably sample from the posterior over causal structures. To address these limitations, we propose a Bayesian meta learning model that allows for sampling causal structures from the posterior and encodes these key properties. We compare our meta-Bayesian causal discovery against existing Bayesian causal discovery methods, demonstrating the advantages of directly learning a posterior over causal structure.

Music Genre Classification is one of the most popular topics in the fields of Music Information Retrieval (MIR) and digital signal processing. Deep Learning has emerged as the top performer for classifying music genres among various methods. The letter introduces a novel approach by combining ensemble learning with attention to sub-components, aiming to enhance the accuracy of identifying music genres. The core innovation of our work is the proposal to classify the subcomponents of the music pieces separately, allowing our model to capture distinct characteristics from those sub components. By applying ensemble learning techniques to these individual classifications, we make the final classification decision on the genre of the music. The proposed method has superior advantages in terms of accuracy compared to the other state-of-the-art techniques trained and tested on the GTZAN dataset.

In recent years, as data and problem sizes have increased, distributed learning has become an essential tool for training high-performance models. However, the communication bottleneck, especially for high-dimensional data, is a challenge. Several techniques have been developed to overcome this problem. These include communication compression and implementation of local steps, which work particularly well when there is similarity of local data samples. In this paper, we study the synergy of these approaches for efficient distributed optimization. We propose the first theoretically grounded accelerated algorithms utilizing unbiased and biased compression under data similarity, leveraging variance reduction and error feedback frameworks. Our results are of record and confirmed by experiments on different average losses and datasets.

As machine learning (ML) systems are increasingly adopted across industries, addressing fairness and bias has become essential. While many solutions focus on ethical challenges in ML, recent studies highlight that data itself is a major source of bias. Pre-processing techniques, which mitigate bias before training, are effective but may impact model performance and pose integration difficulties. In contrast, fairness-aware Data Preparation practices are both familiar to practitioners and easier to implement, providing a more accessible approach to reducing bias. Objective. This registered report proposes an empirical evaluation of how optimally selected fairness-aware practices, applied in early ML lifecycle stages, can enhance both fairness and performance, potentially outperforming standard pre-processing bias mitigation methods. Method. To this end, we will introduce FATE, an optimization technique for selecting 'Data Preparation' pipelines that optimize fairness and performance. Using FATE, we will analyze the fairness-performance trade-off, comparing pipelines selected by FATE with results by pre-processing bias mitigation techniques.

NOAA's Deep-ocean Assessment and Reporting of Tsunamis (DART) data are critical for NASA-JPL's tsunami detection, real-time operations, and oceanographic research. However, these time-series data often contain spikes, steps, and drifts that degrade data quality and obscure essential oceanographic features. To address these anomalies, the work introduces an Iterative Encoding-Decoding Variational Autoencoders (Iterative Encoding-Decoding VAEs) model to improve the quality of DART time series. Unlike traditional filtering and thresholding methods that risk distorting inherent signal characteristics, Iterative Encoding-Decoding VAEs progressively remove anomalies while preserving the data's latent structure. A hybrid thresholding approach further retains genuine oceanographic features near boundaries. Applied to complex DART datasets, this approach yields reconstructions that better maintain key oceanic properties compared to classical statistical techniques, offering improved robustness against spike removal and subtle step changes. The resulting high-quality data supports critical verification and validation efforts for the GRACE-FO mission at NASA-JPL, where accurate surface measurements are essential to modeling Earth's gravitational field and global water dynamics. Ultimately, this data processing method enhances tsunami detection and underpins future climate modeling with improved interpretability and reliability.

Deep learning models have recently shown great success in classifying epileptic patients using EEG recordings. Unfortunately, classification-based methods lack a sound mechanism to detect the onset of seizure events. In this work, we propose a two-stage framework, \method, that explicitly models seizure onset through a novel task formulation of subsequence clustering. Given an EEG sequence, the framework first learns a set of second-level embeddings with label supervision. It then employs model-based clustering to explicitly capture long-term temporal dependencies in EEG sequences and identify meaningful subsequences. Epochs within a subsequence share a common cluster assignment (normal or seizure), with cluster or state transitions representing successful onset detections. Extensive experiments on three datasets demonstrate that our method can correct misclassifications, achieving 5%-11% classification improvements over other baselines and accurately detecting seizure onsets.

In federated learning, federated unlearning is a technique that provides clients with a rollback mechanism that allows them to withdraw their data contribution without training from scratch. However, existing research has not considered scenarios with skewed label distributions. Unfortunately, the unlearning of a client with skewed data usually results in biased models and makes it difficult to deliver high-quality service, complicating the recovery process. This paper proposes a recovery method of federated unlearning with skewed label distributions. Specifically, we first adopt a strategy that incorporates oversampling with deep learning to supplement the skewed class data for clients to perform recovery training, therefore enhancing the completeness of their local datasets. Afterward, a density-based denoising method is applied to remove noise from the generated data, further improving the quality of the remaining clients' datasets. Finally, all the remaining clients leverage the enhanced local datasets and engage in iterative training to effectively restore the performance of the unlearning model. Extensive evaluations on commonly used federated learning datasets with varying degrees of skewness show that our method outperforms baseline methods in restoring the performance of the unlearning model, particularly regarding accuracy on the skewed class.

The debate between scientific realism and anti-realism remains at a stalemate, making reconciliation seem hopeless. Yet, important work remains: exploring a common ground, even if only to uncover deeper points of disagreement and, ideally, to benefit both sides of the debate. I propose such a common ground. Specifically, many anti-realists, such as instrumentalists, have yet to seriously engage with Sober's call to justify their preferred version of Ockham's razor through a positive account. Meanwhile, realists face a similar challenge: providing a non-circular explanation of how their version of Ockham's razor connects to truth. The common ground I propose addresses these challenges for both sides; the key is to leverage the idea that everyone values some truths and to draw on insights from scientific fields that study scientific inference -- namely, statistics and machine learning. This common ground also isolates a distinctively epistemic root of the irreconcilability in the realism debate.

Training data attribution (TDA) methods aim to attribute model outputs back to specific training examples, and the application of these methods to large language model (LLM) outputs could significantly advance model transparency and data curation. However, it has been challenging to date to apply these methods to the full scale of LLM pretraining. In this paper, we refine existing gradient-based methods to work effectively at scale, allowing us to retrieve influential examples for an 8B-parameter language model from a pretraining corpus of over 160B tokens with no need for subsampling or pre-filtering. Our method combines several techniques, including optimizer state correction, a task-specific Hessian approximation, and normalized encodings, which we find to be critical for performance at scale. In quantitative evaluations on a fact tracing task, our method performs best at identifying examples that influence model predictions, but classical, model-agnostic retrieval methods such as BM25 still perform better at finding passages which explicitly contain relevant facts. These results demonstrate a misalignment between factual *attribution* and causal *influence*. With increasing model size and training tokens, we find that influence more closely aligns with factual attribution. Finally, we examine different types of examples identified as influential by our method, finding that while many directly entail a particular fact, others support the same output by reinforcing priors on relation types, common entities, and names. We release our prompt set and model outputs, along with a web-based visualization tool to explore influential examples for factual predictions, commonsense reasoning, arithmetic, and open-ended generation for an 8B-parameter LLM.