The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam -- when treated as a function that maps initial conditions to optimized results -- is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

The long-awaited V4 is more efficient and a win for Chinese chipmakers. On Friday, Chinese AI firm DeepSeek released a preview of V4, its long-awaited new flagship model. Notably, the model can process much longer prompts than its last generation, thanks to a new design that helps it handle large amounts of text more efficiently. Like DeepSeek's previous models, V4 is open source, meaning it is available for anyone to download, use, and modify. V4 marks DeepSeek's most significant release since R1, the reasoning model it launched in January 2025. R1, which was trained on limited computing resources, stunned the global AI industry with its strong performance and efficiency, turning DeepSeek from a little-known research team into China's best-known AI company almost overnight.

Machine learning models can frequently produce systematic errors on critical subsets (or slices) of data that share common attributes. Discovering and explaining such model bugs is crucial for reliable model deployment. However, existing bug discovery and interpretation methods usually involve heavy human intervention and annotation, which can be cumbersome and have low bug coverage. In this paper, we propose HiBug, an automated framework for interpretable model debugging. Our approach utilizes large pre-trained models, such as chatGPT, to suggest human-understandable attributes that are related to the targeted computer vision tasks. By leveraging pre-trained vision-language models, we can efficiently identify common visual attributes of underperforming data slices using humanunderstandable terms. This enables us to uncover rare cases in the training data, identify spurious correlations in the model, and use the interpretable debug results to select or generate new training data for model improvement. Experimental results demonstrate the efficacy of the HiBug framework. Code is available at: https://github.com/cure-lab/HiBug.

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d.

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches which lack generalizability. For an unseen architecture, one cannot use the subset chosen for a different model. To tackle this problem, we propose SUBSELNET, a trainable subset selection framework, that generalizes across architectures. Here, we first introduce an attention-based neural gadget that leverages the graph structure of architectures and acts as a surrogate to trained deep neural networks for quick model prediction. Then, we use these predictions to build subset samplers.

Here we note our problem definition of pre-training is fundamentally different from domain adaptation [S1, S2, S3, S4, S5, S6]1 in order to prevent any confusion between this work and domain adaptation methods. DA applies a model trained on a pre-training dataset (i.e., source dataset) to a different target dataset [21, 42]. In contrast, self-supervised pre-training has four key differences with domain adaptation. In contrast, domain adaptation methods usually restrict pre-training and target datasets to have the same feature space (but possible different distributions), e.g., [S22, S18, S19, S20, S13]. In summary, to support transfer learning across different time series datasets, a pre-training approach needs a capability to capture a generalizable property of time series, one that is shared across different time series datasets regardless of the specific semantic meaning of a time series signal (e.g., ECG, EMG, acceleration, vibration), conditions of data acquisition (e.g., variation across subjects and devices), sampling frequencies, etc. This work develops a self-supervised contrastive pre-training strategy that fulfills these requirements by injecting an appropriate inductive bias (called Time-Frequency Consistency, TF-C, into the model (Sec. Further, we clarify that the term'self-supervised' has different meanings in DA and in pretraining [S23, S24, S25, S26]. The'self-supervised domain adaptation' [S27, S16, S21, S15] or'unsupervised domain adaptation' [S1, S22, S28, S11, S14] means that there are no labels in the target dataset, however that still requires labels in the pre-training dataset. In contrast, 'self-supervised pretraining' [S29, S30, S31] (i.e., the problem studied here, in line with a breadth of existing literature on pre-training) indicates the setting where no labels are available in pre-training. Up to the submission of this manuscript, there is no existing contrastive augmentations in time series' frequency domain. There are two models, CoST [49] and BTSF [50], that involved frequency domain in contrastive learning, however, the proposed TF-C is fundamentally different with them in the following aspects. We take BTSF as an example while the differences also apply to CoST. Problem definitions for both papers are different. Our method is designed to produce generalizable representations that can transfer to a different time series dataset (going from pre-training to a fine-tuning dataset) for the purpose of transfer learning.

Pre-training on time series poses a unique challenge due to the potential mismatch between pre-training and target domains, such as shifts in temporal dynamics, fast-evolving trends, and long-range and short-cyclic effects, which can lead to poor downstream performance. While domain adaptation methods can mitigate these shifts, most methods need examples directly from the target domain, making them suboptimal for pre-training. To address this challenge, methods need to accommodate target domains with different temporal dynamics and be capable of doing so without seeing any target examples during pre-training. Relative to other modalities, in time series, we expect that time-based and frequencybased representations of the same example are located close together in the timefrequency space. To this end, we posit that time-frequency consistency (TF-C) -- embedding a time-based neighborhood of an example close to its frequency-based neighborhood -- is desirable for pre-training. Motivated by TF-C, we define a decomposable pre-training model, where the self-supervised signal is provided by the distance between time and frequency components, each individually trained by contrastive estimation. We evaluate the new method on eight datasets, including electrodiagnostic testing, human activity recognition, mechanical fault detection, and physical status monitoring. Experiments against eight state-of-the-art methods show that TF-C outperforms baselines by 15.4% (F1 score) on average in one-toone settings (e.g., fine-tuning an EEG-pretrained model on EMG data) and by 8.4% (precision) in challenging one-to-many settings (e.g., fine-tuning an EEG-pretrained model for either hand-gesture recognition or mechanical fault prediction), reflecting the breadth of scenarios that arise in real-world applications.