Graph neural networks (GNNs) have achieved impressive performance in graph domain adaptation. However, extensive source graphs could be unavailable in real-world scenarios due to privacy and storage concerns. To this end, we investigate an underexplored yet practical problem of source-free graph domain adaptation, which transfers knowledge from source models instead of source graphs to a target domain. To solve this problem, we introduce a novel GNN-based approach called Rank and Align (RNA), which ranks graph similarities with spectral seriation for robust semantics learning, and aligns inharmonic graphs with harmonic graphs which close to the source domain for subgraph extraction. In particular, to overcome label scarcity, we employ the spectral seriation algorithm to infer the robust pairwise rankings, which can guide semantic learning using a similarity learning objective. To depict distribution shifts, we utilize spectral clustering and the silhouette coefficient to detect harmonic graphs, which the source model can easily classify. To reduce potential domain discrepancy, we extract domain-invariant subgraphs from inharmonic graphs by an adversarial edge sampling process, which guides the invariant learning of GNNs. Extensive experiments on several benchmark datasets demonstrate the effectiveness of our proposed RNA.

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. We sharpen prior work, proving that accurate recovery in the Wasserstein distance is possible with more noise than previously known. As a main application, our result yields a simple "linear query" algorithm for constructing a differentially private synthetic data distribution with Wasserstein-1 error $\tilde{O}(1/n)$ based on a dataset of $n$ points in $[-1,1]$. This bound is optimal up to log factors and matches a recent breakthrough of Boedihardjo, Strohmer, and Vershynin [Probab. Theory. Rel., 2024], which uses a more complex "superregular random walk" method to beat an $O(1/\sqrt{n})$ accuracy barrier inherent to earlier approaches. We illustrate a second application of our new moment-based recovery bound in numerical linear algebra: by improving an approach of Braverman, Krishnan, and Musco [STOC 2022], our result yields a faster algorithm for estimating the spectral density of a symmetric matrix up to small error in the Wasserstein distance.

We present results of numerical experiments for neural networks with stochastic gradient-based optimization with adaptive momentum. This widely applied optimization has proved convergence and practical efficiency, but for long-run training becomes numerically unstable. We show that numerical artifacts are observable not only for large-scale models and finally lead to divergence also for case of shallow narrow networks. We argue this theory by experiments with more than 1600 neural networks trained for 50000 epochs. Local observations show presence of the same behavior of network parameters in both stable and unstable training segments. Geometrical behavior of parameters forms double twisted spirals in the parameter space and is caused by alternating of numerical perturbations with next relaxation oscillations in values for 1st and 2nd momentum.

Evolving networks are complex data structures that emerge in a wide range of systems in science and engineering. Learning expressive representations for such networks that encode their structural connectivity and temporal evolution is essential for downstream data analytics and machine learning applications. In this study, we introduce a self-supervised method for learning representations of temporal networks and employ these representations in the dynamic link prediction task. While temporal networks are typically characterized as a sequence of interactions over the continuous time domain, our study focuses on their discrete-time versions. This enables us to balance the trade-off between computational complexity and precise modeling of the interactions. We propose a recurrent message-passing neural network architecture for modeling the information flow over time-respecting paths of temporal networks. The key feature of our method is the contrastive training objective of the model, which is a combination of three loss functions: link prediction, graph reconstruction, and contrastive predictive coding losses. The contrastive predictive coding objective is implemented using infoNCE losses at both local and global scales of the input graphs. We empirically show that the additional self-supervised losses enhance the training and improve the model's performance in the dynamic link prediction task. The proposed method is tested on Enron, COLAB, and Facebook datasets and exhibits superior results compared to existing models.

In particular, for the current ω 2.371 [Alman, Duan, Williams, Xu, Xu, Zhou 2024], our running times boil down to O(d This running time is due to the analysis of the lazy update behavior in iterative maintenance problems, such as [Deng, Song, Weinstein 2022, Brand, Song, Zhou ICML 2024]. Large Language Models (LLMs) have been widely applied in many AI applications.

In the downstream information retrieval process of DNA storage technology, specific hybridization techniques, such as Polymerase Chain Reaction (PCR) or magnetic bead separation, are commonly used to access data [1]. However, this technology faces several challenges, including high base error rates (insertions, deletions, substitutions, etc.) and the loss of storage sequences, which pose significant threats to the reliability of stored data [2]. To address these issues, clustering and alignment of sequencing data can be employed. A commonly used feature extraction method is based on k-mer frequency matrices, where the dimensionality of the extracted features increases exponentially with the value of k [3] [4] [5]. Therefore, selecting an appropriate dimensionality reduction technique becomes a critical challenge that needs to be addressed. This study aims to develop an adaptive classification model to identify the optimal dimensionality reduction method, thereby mitigating the curse of dimensionality caused by k-mer feature extraction and enhancing the effectiveness of K-means clustering in restoring the original sequence information. Specifically, among the numerous available algorithms, Principal Component Analysis (PCA) [6], t-distributed Stochastic Neighbor Embedding (t-SNE) [7], and Uniform Manifold Approximation and Projection (UMAP) [8] are particularly prominent in the fields of cell biology, bioinformatics, and data visualization [9]. This study addresses the challenge of selecting the appropriate dimensionality reduction method to mitigate the curse of dimensionality in K-means clustering.

Recent technological advancements have enhanced our ability to collect and analyze rich multimodal data (e.g., speech, video, and eye gaze) to better inform learning and training experiences. While previous reviews have focused on parts of the multimodal pipeline (e.g., conceptual models and data fusion), a comprehensive literature review on the methods informing multimodal learning and training environments has not been conducted. This literature review provides an in-depth analysis of research methods in these environments, proposing a taxonomy and framework that encapsulates recent methodological advances in this field and characterizes the multimodal domain in terms of five modality groups: Natural Language, Video, Sensors, Human-Centered, and Environment Logs. We introduce a novel data fusion category -- mid fusion -- and a graph-based technique for refining literature reviews, termed citation graph pruning. Our analysis reveals that leveraging multiple modalities offers a more holistic understanding of the behaviors and outcomes of learners and trainees. Even when multimodality does not enhance predictive accuracy, it often uncovers patterns that contextualize and elucidate unimodal data, revealing subtleties that a single modality may miss. However, there remains a need for further research to bridge the divide between multimodal learning and training studies and foundational AI research.

In contemporary data-driven environments, the generation and processing of multivariate time series data is an omnipresent challenge, often complicated by time delays between different time series. These delays, originating from a multitude of sources like varying data transmission dynamics, sensor interferences, and environmental changes, introduce significant complexities. Traditional Time Delay Estimation methods, which typically assume a fixed constant time delay, may not fully capture these variabilities, compromising the precision of predictive models in diverse settings. To address this issue, we introduce the Time Series Model Bootstrap (TSMB), a versatile framework designed to handle potentially varying or even nondeterministic time delays in time series modeling. Contrary to traditional approaches that hinge on the assumption of a single, consistent time delay, TSMB adopts a nonparametric stance, acknowledging and incorporating time delay uncertainties. TSMB significantly bolsters the performance of models that are trained and make predictions using this framework, making it highly suitable for a wide range of dynamic and interconnected data environments.

In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we study the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps. Furthermore, we establish information-theoretic lower bounds for meta-learners w.r.t. both the number of tasks and in-context examples. These findings shed light on the roles of task diversity and representation learning for ICL.

Embedding models play a crucial role in Natural Language Processing (NLP) by creating text embeddings used in various tasks such as information retrieval and assessing semantic text similarity. This paper focuses on research related to embedding models in the Russian language. It introduces a new Russian-focused embedding model called ru-en-RoSBERTa and the ruMTEB benchmark, the Russian version extending the Massive Text Embedding Benchmark (MTEB). Our benchmark includes seven categories of tasks, such as semantic textual similarity, text classification, reranking, and retrieval. The research also assesses a representative set of Russian and multilingual models on the proposed benchmark. The findings indicate that the new model achieves results that are on par with state-of-the-art models in Russian. We release the model ru-en-RoSBERTa, and the ruMTEB framework comes with open-source code, integration into the original framework and a public leaderboard.