We study the generalization properties of unregularized gradient methods applied to separable linear classification---a setting that has received considerable attention since the pioneering work of Soudry et al. (2018).We establish tight upper and lower (population) risk bounds for gradient descent in this setting, for any smooth loss function, expressed in terms of its tail decay rate.Our bounds take the form \Theta(r_{\ell,T} 2 / \gamma 2 T r_{\ell,T} 2 / \gamma 2 n), where T is the number of gradient steps, n is size of the training set, \gamma is the data margin, and r_{\ell,T} is a complexity term that depends on the tail decay rate of the loss function (and on T).Our upper bound greatly improves the existing risk bounds due to Shamir (2021) and Schliserman and Koren (2022), that either applied to specific loss functions or imposed extraneous technical assumptions, and applies to virtually any convex and smooth loss function.Our risk lower bound is the first in this context and establish the tightness of our general upper bound for any given tail decay rate and in all parameter regimes.The proof technique used to show these results is also markedly simpler compared to previous work, and is straightforward to extend to other gradient methods; we illustrate this by providing analogous results for Stochastic Gradient Descent.

We consider a novel anchorless rigid body localization (RBL) suitable for application in autonomous driving (AD), in so far as the algorithm enables a rigid body to egoistically detect the location (relative translation) and orientation (relative rotation) of another body, without knowledge of the shape of the latter, based only on a set of measurements of the distances between sensors of one vehicle to the other. A key point of the proposed method is that the translation vector between the two-bodies is modeled using the double-centering operator from multidimensional scaling (MDS) theory, enabling the method to be used between rigid bodies regardless of their shapes, in contrast to conventional approaches which require both bodies to have the same shape. Simulation results illustrate the good performance of the proposed technique in terms of root mean square error (RMSE) of the estimates in different setups.

Dynamic graph representation learning plays a crucial role in understanding evolving behaviors. However, existing methods often struggle with flexibility, adaptability, and the preservation of temporal and structural dynamics. To address these issues, we propose Community-aware Temporal Walks (CTWalks), a novel framework for representation learning on continuous-time dynamic graphs. CTWalks integrates three key components: a community-based parameter-free temporal walk sampling mechanism, an anonymization strategy enriched with community labels, and an encoding process that leverages continuous temporal dynamics modeled via ordinary differential equations (ODEs). This design enables precise modeling of both intra- and inter-community interactions, offering a fine-grained representation of evolving temporal patterns in continuous-time dynamic graphs. CTWalks theoretically overcomes locality bias in walks and establishes its connection to matrix factorization. Experiments on benchmark datasets demonstrate that CTWalks outperforms established methods in temporal link prediction tasks, achieving higher accuracy while maintaining robustness.

Automating analog and radio-frequency (RF) circuit design using machine learning (ML) significantly reduces the time and effort required for parameter optimization. This study explores supervised ML-based approaches for designing circuit parameters from performance specifications across various circuit types, including homogeneous and heterogeneous designs. By evaluating diverse ML models, from neural networks like transformers to traditional methods like random forests, we identify the best-performing models for each circuit. Our results show that simpler circuits, such as low-noise amplifiers, achieve exceptional accuracy with mean relative errors as low as 0.3% due to their linear parameter-performance relationships. In contrast, complex circuits, like power amplifiers and voltage-controlled oscillators, present challenges due to their non-linear interactions and larger design spaces. For heterogeneous circuits, our approach achieves an 88% reduction in errors with increased training data, with the receiver achieving a mean relative error as low as 0.23%, showcasing the scalability and accuracy of the proposed methodology. Additionally, we provide insights into model strengths, with transformers excelling in capturing non-linear mappings and k-nearest neighbors performing robustly in moderately linear parameter spaces, especially in heterogeneous circuits with larger datasets. This work establishes a foundation for extending ML-driven design automation, enabling more efficient and scalable circuit design workflows.

Predictive models are often required to produce reliable predictions under statistical conditions that are not matched to the training data. A common type of training-testing mismatch is covariate shift, where the conditional distribution of the target variable given the input features remains fixed, while the marginal distribution of the inputs changes. Weighted conformal risk control (W-CRC) uses data collected during the training phase to convert point predictions into prediction sets with valid risk guarantees at test time despite the presence of a covariate shift. However, while W-CRC provides statistical reliability, its efficiency -- measured by the size of the prediction sets -- can only be assessed at test time. In this work, we relate the generalization properties of the base predictor to the efficiency of W-CRC under covariate shifts. Specifically, we derive a bound on the inefficiency of the W-CRC predictor that depends on algorithmic hyperparameters and task-specific quantities available at training time. This bound offers insights on relationships between the informativeness of the prediction sets, the extent of the covariate shift, and the size of the calibration and training sets. Experiments on fingerprinting-based localization validate the theoretical results.

Cross-hospital collaboration has the potential to address disparities in medical resources across different regions. However, strict privacy regulations prohibit the direct sharing of sensitive patient information between hospitals. Vertical federated learning (VFL) offers a novel privacy-preserving machine learning paradigm that maximizes data utility across multiple hospitals. Traditional VFL methods, however, primarily benefit patients with overlapping data, leaving vulnerable non-overlapping patients without guaranteed improvements in medical prediction services. While some knowledge transfer techniques can enhance the prediction performance for non-overlapping patients, they fall short in addressing scenarios where overlapping and non-overlapping patients belong to different domains, resulting in challenges such as feature heterogeneity and label heterogeneity. To address these issues, we propose a novel unified vertical federated knowledge transfer framework (Unitrans). Our framework consists of three key steps. First, we extract the federated representation of overlapping patients by employing an effective vertical federated representation learning method to model multi-party joint features online. Next, each hospital learns a local knowledge transfer module offline, enabling the transfer of knowledge from the federated representation of overlapping patients to the enriched representation of local non-overlapping patients in a domain-adaptive manner. Finally, hospitals utilize these enriched local representations to enhance performance across various downstream medical prediction tasks. Experiments on real-world medical datasets validate the framework's dual effectiveness in both intra-domain and cross-domain knowledge transfer. The code of \method is available at \url{https://github.com/Chung-ju/Unitrans}.

Graph Neural Networks (GNNs) demonstrate significant potential in various applications but remain highly vulnerable to adversarial attacks, which can greatly degrade their performance. Existing graph purification methods attempt to address this issue by filtering attacked graphs; however, they struggle to effectively defend against multiple types of adversarial attacks simultaneously due to their limited flexibility, and they lack comprehensive modeling of graph data due to their heavy reliance on heuristic prior knowledge. To overcome these challenges, we propose a more versatile approach for defending against adversarial attacks on graphs. In this work, we introduce the Graph Defense Diffusion Model (GDDM), a flexible purification method that leverages the denoising and modeling capabilities of diffusion models. The iterative nature of diffusion models aligns well with the stepwise process of adversarial attacks, making them particularly suitable for defense. By iteratively adding and removing noise, GDDM effectively purifies attacked graphs, restoring their original structure and features. Our GDDM consists of two key components: (1) Graph Structure-Driven Refiner, which preserves the basic fidelity of the graph during the denoising process, and ensures that the generated graph remains consistent with the original scope; and (2) Node Feature-Constrained Regularizer, which removes residual impurities from the denoised graph, further enhances the purification effect. Additionally, we design tailored denoising strategies to handle different types of adversarial attacks, improving the model's adaptability to various attack scenarios. Extensive experiments conducted on three real-world datasets demonstrate that GDDM outperforms state-of-the-art methods in defending against a wide range of adversarial attacks, showcasing its robustness and effectiveness.

Transformers, a cornerstone of deep-learning architectures for sequential data, have achieved state-of-the-art results in tasks like Natural Language Processing (NLP). Models such as BERT and GPT-3 exemplify their success and have driven the rise of large language models (LLMs). However, a critical challenge persists: safeguarding the privacy of data used in LLM training. Privacy-preserving techniques like Federated Learning (FL) offer potential solutions, but practical limitations hinder their effectiveness for Transformer training. Two primary issues are (I) the risk of sensitive information leakage due to aggregation methods like FedAvg or FedSGD, and (II) the high communication overhead caused by the large size of Transformer models. This paper introduces a novel FL method that reduces communication overhead while maintaining competitive utility. Our approach avoids sharing full model weights by simulating a global model locally. We apply k-means clustering to each Transformer layer, compute centroids locally, and transmit only these centroids to the server instead of full weights or gradients. To enhance security, we leverage Intel SGX for secure transmission of centroids. Evaluated on a translation task, our method achieves utility comparable to state-of-the-art baselines while significantly reducing communication costs. This provides a more efficient and privacy-preserving FL solution for Transformer models.

The state-of-the-art recommendation systems have shifted the attention to efficient recommendation, e.g., on-device recommendation, under memory constraints. To this end, the existing methods either focused on the lightweight embeddings for both users and items, or involved on-device systems enjoying the compact embeddings to enhance reusability and reduces space complexity. However, they focus solely on the coarse granularity of embedding, while overlook the fine-grained semantic nuances, to adversarially downgrade the efficacy of meta-embeddings in capturing the intricate relationship over both user and item, consequently resulting into the suboptimal recommendations. In this paper, we aim to study how the meta-embedding can efficiently learn varied grained semantics, together with how the fine-grained meta-embedding can strengthen the representation of coarse-grained meta-embedding. To answer these questions, we develop a novel graph neural networks (GNNs) based recommender where each user and item serves as the node, linked directly to coarse-grained virtual nodes and indirectly to fine-grained virtual nodes, ensuring different grained semantic learning, while disclosing: 1) In contrast to coarse-grained semantics, fine-grained semantics are well captured through sparse meta-embeddings, which adaptively 2) balance the embedding uniqueness and memory constraint. Additionally, the initialization method come up upon SparsePCA, along with a soft thresholding activation function to render the sparseness of the meta-embeddings. We propose a weight bridging update strategy that focuses on matching each coarse-grained meta-embedding with several fine-grained meta-embeddings based on the users/items' semantics. Extensive experiments substantiate our method's superiority over existing baselines. Our code is available at https://github.com/htyjers/C2F-MetaEmbed.

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing operational conditions, unknown interactions, excitations, and parametric drift. While data-based models can capture the current state of complex systems, they face significant challenges, including excessive data dependence, limited generalizability to changing conditions, and inability to predict parametric dependence. This has led to combining physics and data in modeling, termed physics-infused machine learning, often using numerical simulations from physics-based models. This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. The goal is to create a hybrid adaptive modeling framework that integrates data-based modeling with newly measured data and analytical nonlinear dynamical models for enhanced accuracy, parametric dependence, and improved generalizability. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations. In particular, perturbation methods are utilized to derive asymptotic solutions which are parameterized to generate frequency responses. Frequency responses provide comprehensive insights into dynamics and nonlinearity which are quantified and extracted as high-quality features. A machine-learning model, trained by these features, tracks parameter variations and updates the mismatched model. The results demonstrate that this adaptive modeling method outperforms numerical gray box models in prediction accuracy and computational efficiency.