Recent advances have significantly improved our understanding of the generalization performance of gradient descent (GD) methods in deep neural networks. A natural and fundamental question is whether GD can achieve generalization rates comparable to the minimax optimal rates established in the kernel setting. Existing results either yield suboptimal rates of $O(1/\sqrt{n})$, or focus on networks with smooth activation functions, incurring exponential dependence on network depth $L$. In this work, we establish optimal generalization rates for GD with deep ReLU networks by carefully trading off optimization and generalization errors, achieving only polynomial dependence on depth. Specifically, under the assumption that the data are NTK separable from the margin $γ$, we prove an excess risk rate of $\widetilde{O}(L^4 (1 + γL^2) / (n γ^2))$, which aligns with the optimal SVM-type rate $\widetilde{O}(1 / (n γ^2))$ up to depth-dependent factors. A key technical contribution is our novel control of activation patterns near a reference model, enabling a sharper Rademacher complexity bound for deep ReLU networks trained with gradient descent.

Electroencephalogram (EEG)-based P300 speller brain-computer interfaces (BCIs) face three main challenges: low signal-to-noise ratio (SNR), poor generalization, and time-consuming calibration. We propose SpellerSSL, a framework that combines self-supervised learning (SSL) with P300 aggregation to address these issues. First, we introduce an aggregation strategy to enhance SNR. Second, to achieve generalization in training, we employ a customized 1D U-Net backbone and pretrain the model on both cross-domain and in-domain EEG data. The pretrained model is subsequently fine-tuned with a lightweight ERP-Head classifier for P300 detection, which adapts the learned representations to subject-specific data. Our evaluations on calibration time demonstrate that combining the aggregation strategy with SSL significantly reduces the calibration burden per subject and improves robustness across subjects. Experimental results show that SSL learns effective EEG representations in both in-domain and cross-domain, with in-domain achieving a state-of-the-art character recognition rate of 94% with only 7 repetitions and the highest information transfer rate (ITR) of 21.86 bits/min on the public II-B dataset. Moreover, in-domain SSL with P300 aggregation reduces the required calibration size by 60% while maintaining a comparable character recognition rate. To the best of our knowledge, this is the first study to apply SSL to P300 spellers, highlighting its potential to improve both efficiency and generalization in speller BCIs and paving the way toward an EEG foundation model for P300 speller BCIs.

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language models highlights the importance of these laws, their application to deep regression models remains largely unexplored. Here, we empirically investigate neural scaling laws in deep regression using a parameter estimation model for twisted van der Waals magnets. We observe power-law relationships between the loss and both training dataset size and model capacity across a wide range of values, employing various architectures--including fully connected networks, residual networks, and vision transformers. Furthermore, the scaling exponents governing these relationships range from 1 to 2, with specific values depending on the regressed parameters and model details. The consistent scaling behaviors and their large scaling exponents suggest that the performance of deep regression models can improve substantially with increasing data size.

We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a likelihood function is used for representing the measurement and its uncertainty. This likelihood is progressively introduced into the filtering procedure by homotopy continuation over an artificial time. A generalized Cramér distance between particle sets is derived in closed form that is differentiable and invariant to particle order. A Newton flow then continually minimizes this distance over artificial time and thus smoothly moves particles from prior to posterior density. The new filter is surprisingly simple to implement and very efficient. It just requires a prior particle set and a likelihood function, never estimates densities from samples, and can be used as a plugin replacement for classic approaches.

We study cost-aware routing for large language models across diverse and dynamic pools of models. Existing approaches often overlook prompt-specific context, rely on expensive model profiling, assume a fixed set of experts, or use inefficient trial-and-error strategies. We introduce Cost-Spectrum Contrastive Routing (CSCR), a lightweight framework that maps both prompts and models into a shared embedding space to enable fast, cost-sensitive selection. CSCR uses compact, fast-to-compute logit footprints for open-source models and perplexity fingerprints for black-box APIs. A contrastive encoder is trained to favor the cheapest accurate expert within adaptive cost bands. At inference time, routing reduces to a single k-NN lookup via a FAISS index, requiring no retraining when the expert pool changes and enabling microsecond latency. Across multiple benchmarks, CSCR consistently outperforms baselines, improving the accuracy-cost tradeoff by up to 25%, while generalizing robustly to unseen LLMs and out-of-distribution prompts.

Synthetic data generation is a key technique in modern artificial intelligence, addressing data scarcity, privacy constraints, and the need for diverse datasets in training robust models. In this work, we propose a method for generating privacy-preserving high-quality synthetic tabular data using Tensor Networks, specifically Matrix Product States (MPS). We benchmark the MPS-based generative model against state-of-the-art models such as CTGAN, VAE, and PrivBayes, focusing on both fidelity and privacy-preserving capabilities. To ensure differential privacy (DP), we integrate noise injection and gradient clipping during training, enabling privacy guarantees via Rényi Differential Privacy accounting. Across multiple metrics analyzing data fidelity and downstream machine learning task performance, our results show that MPS outperforms classical models, particularly under strict privacy constraints. This work highlights MPS as a promising tool for privacy-aware synthetic data generation. By combining the expressive power of tensor network representations with formal privacy mechanisms, the proposed approach offers an interpretable and scalable alternative for secure data sharing. Its structured design facilitates integration into sensitive domains where both data quality and confidentiality are critical.

Federated learning (FL) enables collaborative model training across distributed clients while preserving data privacy by keeping data local. Traditional FL approaches rely on a centralized, star-shaped topology, where a central server aggregates model updates from clients. However, this architecture introduces several limitations, including a single point of failure, limited personalization, and poor robustness to distribution shifts or vulnerability to malfunctioning clients. Moreover, update selection in centralized FL often relies on low-level parameter differences, which can be unreliable when client data is not independent and identically distributed, and offer clients little control. In this work, we propose a decentralized, peer-to-peer (P2P) FL framework. It leverages the flexibility of the P2P topology to enable each client to identify and aggregate a personalized set of trustworthy and beneficial updates.This framework is the Local Inference Guided Aggregation for Heterogeneous Training Environments to Yield Enhancement Through Agreement and Regularization (LIGHTYEAR). Central to our method is an agreement score, computed on a local validation set, which quantifies the semantic alignment of incoming updates in the function space with respect to the clients reference model. Each client uses this score to select a tailored subset of updates and performs aggregation with a regularization term that further stabilizes the training. Our empirical evaluation across five datasets shows that the proposed approach consistently outperforms both, centralized baselines and existing P2P methods in terms of client-level performance, particularly under adversarial and heterogeneous conditions.

Hydrogen atom transfer (HAT) reactions are essential in many biological processes, such as radical migration in damaged proteins, but their mechanistic pathways remain incompletely understood. Simulating HAT is challenging due to the need for quantum chemical accuracy at biologically relevant scales; thus, neither classical force fields nor DFT-based molecular dynamics are applicable. Machine-learned potentials offer an alternative, able to learn potential energy surfaces (PESs) with near-quantum accuracy. However, training these models to generalize across diverse HAT configurations, especially at radical positions in proteins, requires tailored data generation and careful model selection. Here, we systematically generate HAT configurations in peptides to build large datasets using semiempirical methods and DFT. We benchmark three graph neural network architectures (SchNet, Allegro, and MACE) on their ability to learn HAT PESs and indirectly predict reaction barriers from energy predictions. MACE consistently outperforms the others in energy, force, and barrier prediction, achieving a mean absolute error of 1.13 kcal/mol on out-of-distribution DFT barrier predictions. Using molecular dynamics, we show our MACE potential is stable, reactive, and generalizes beyond training data to model HAT barriers in collagen I. This accuracy enables integration of ML potentials into large-scale collagen simulations to compute reaction rates from predicted barriers, advancing mechanistic understanding of HAT and radical migration in peptides. We analyze scaling laws, model transferability, and cost-performance trade-offs, and outline strategies for improvement by combining ML potentials with transition state search algorithms and active learning. Our approach is generalizable to other biomolecular systems, enabling quantum-accurate simulations of chemical reactivity in complex environments.

Harnessing the power of diffusion models to synthesize auxiliary training data based on latent space features has proven effective in enhancing out-of-distribution (OOD) detection performance. However, extracting effective features outside the in-distribution (ID) boundary in latent space remains challenging due to the difficulty of identifying decision boundaries between classes. This paper proposes a novel framework called Boundary-based Out-Of-Distribution data generation (BOOD), which synthesizes high-quality OOD features and generates human-compatible outlier images using diffusion models. BOOD first learns a text-conditioned latent feature space from the ID dataset, selects ID features closest to the decision boundary, and perturbs them to cross the decision boundary to form OOD features. These synthetic OOD features are then decoded into images in pixel space by a diffusion model. Compared to previous works, BOOD provides a more training efficient strategy for synthesizing informative OOD features, facilitating clearer distinctions between ID and OOD data. Extensive experimental results on common benchmarks demonstrate that BOOD surpasses the state-of-the-art method significantly, achieving a 29.64% decrease in average FPR95 (40.31% vs. 10.67%) and a 7.27% improvement in average AUROC (90.15% vs. 97.42%) on the CIFAR-100 dataset.

Federated learning (FL) collaboratively trains artificial intelligence (AI) models to ensure user data privacy. Sharing only model updates generated from local training on client data with the server enhances user data privacy. However, model performance may suffer due to data and system heterogeneity among clients in FL scenarios. Previous studies have proposed model optimization, fine-tuning, and personalization to achieve improved model performance. Despite these efforts, models resulting from FL scenarios often exhibit catastrophic forgetting, which increases the communication and computational costs of clients for model optimization and raises energy consumption. To address these challenges, we propose a reference model-based fine-tuning method for federated learning that overcomes catastrophic forgetting in each round. Our method is derived from Bayesian parameter-efficient transfer learning and includes an proximal term. It employs a reference model that incorporates previous model parameters and reviews previous global features in the model optimization step to mitigate catastrophic forgetting. As a result, our method achieves higher model performance and lower communication and computational costs for clients than existing methods.