Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit. Bootstrapping is a classical statistical framework for uncertainty estimation based on resampling, but naively applying it to deep learning is impractical: it requires training many replicas, produces post-hoc estimates that cannot guide learning, and implicitly assumes comparable optima across runs - an assumption that fails in non-convex landscapes. We introduce Twin-Bootstrap Gradient Descent (Twin-Boot), a resampling-based training procedure that integrates uncertainty estimation into optimization. Two identical models are trained in parallel on independent bootstrap samples, and a periodic mean-reset keeps both trajectories in the same basin so that their divergence reflects local (within-basin) uncertainty. During training, we use this estimate to sample weights in an adaptive, data-driven way, providing regularization that favors flatter solutions. In deep neural networks and complex high-dimensional inverse problems, the approach improves calibration and generalization and yields interpretable uncertainty maps.

We propose SPOF (Stabilization of Perturbed Loss Function), a differentially private training mechanism intended for multi-user local differential privacy (LDP). SPOF perturbs a stabilized Taylor expanded polynomial approximation of a model's training loss function, where each user's data is privatized by calibrated noise added to the coefficients of the polynomial. Unlike gradient-based mechanisms such as differentially private stochastic gradient descent (DP-SGD), SPOF does not require injecting noise into the gradients of the loss function, which improves both computational efficiency and stability. This formulation naturally supports simultaneous privacy guarantees across all users. Moreover, SPOF exhibits robustness to environmental noise during training, maintaining stable performance even when user inputs are corrupted. We compare SPOF with a multi-user extension of DP-SGD, evaluating both methods in a wireless body area network (WBAN) scenario involving heterogeneous user data and stochastic channel noise from body sensors. Our results show that SPOF achieves, on average, up to 3.5% higher reconstruction accuracy and reduces mean training time by up to 57.2% compared to DP-SGD, demonstrating superior privacy-utility trade-offs in multi-user environments.

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A substantial number of works in the distributed SGD setting assume a fixed topology for the edge devices. These papers also assume that the contribution of nodes to the global model is uniform. However, experiments have shown that such assumptions are suboptimal and a non uniform aggregation strategy coupled with a dynamically shifting topology and client selection can significantly improve the performance of such models. This paper details a unified framework that covers several Local-Update SGD-based distributed algorithms with dynamic topologies and provides improved or matching theoretical guarantees on convergence compared to existing work.

We propose an efficient hybrid least squares/gradient descent method to accelerate DeepONet training. Since the output of DeepONet can be viewed as linear with respect to the last layer parameters of the branch network, these parameters can be optimized using a least squares (LS) solve, and the remaining hidden layer parameters are updated by means of gradient descent form. However, building the LS system for all possible combinations of branch and trunk inputs yields a prohibitively large linear problem that is infeasible to solve directly. To address this issue, our method decomposes the large LS system into two smaller, more manageable subproblems $\unicode{x2014}$ one for the branch network and one for the trunk network $\unicode{x2014}$ and solves them separately. This method is generalized to a broader type of $L^2$ loss with a regularization term for the last layer parameters, including the case of unsupervised learning with physics-informed loss.

Fine-tuning large language models (LLMs) with low-rank adaptaion (LoRA) is a cost-effective way to incorporate information from a specific dataset. However, it is often unclear how well the fine-tuned LLM will generalize, i.e., how well it will perform on unseen datasets. Methods have been proposed to improve generalization by optimizing with in-context prompts, or by using meta-learning to fine-tune LLMs. However, these methods are expensive in memory and computation, requiring either long-context prompts or saving copies of parameters and using second-order gradient updates. To address these challenges, we propose Amortized Bayesian Meta-Learning for LoRA (ABMLL). This method builds on amortized Bayesian meta-learning for smaller models, adapting this approach to LLMs while maintaining its computational efficiency. We reframe task-specific and global parameters in the context of LoRA and use a set of new hyperparameters to balance reconstruction accuracy and the fidelity of task-specific parameters to the global ones. ABMLL provides effective generalization and scales to large models such as Llama3-8B. Furthermore, as a result of using a Bayesian framework, ABMLL provides improved uncertainty quantification. We test ABMLL on Unified-QA and CrossFit datasets and find that it outperforms existing methods on these benchmarks in terms of both accuracy and expected calibration error.

This paper studies the interplay between learning algorithms and graph structure for graph neural networks (GNNs). Existing theoretical studies on the learning dynamics of GNNs primarily focus on the convergence rates of learning algorithms under the interpolation regime (noise-free) and offer only a crude connection between these dynamics and the actual graph structure (e.g., maximum degree). This paper aims to bridge this gap by investigating the excessive risk (generalization performance) of learning algorithms in GNNs within the generalization regime (with noise). Specifically, we extend the conventional settings from the learning theory literature to the context of GNNs and examine how graph structure influences the performance of learning algorithms such as stochastic gradient descent (SGD) and Ridge regression. Our study makes several key contributions toward understanding the interplay between graph structure and learning in GNNs. First, we derive the excess risk profiles of SGD and Ridge regression in GNNs and connect these profiles to the graph structure through spectral graph theory. With this established framework, we further explore how different graph structures (regular vs. power-law) impact the performance of these algorithms through comparative analysis. Additionally, we extend our analysis to multi-layer linear GNNs, revealing an increasing non-isotropic effect on the excess risk profile, thereby offering new insights into the over-smoothing issue in GNNs from the perspective of learning algorithms. Our empirical results align with our theoretical predictions, \emph{collectively showcasing a coupling relation among graph structure, GNNs and learning algorithms, and providing insights on GNN algorithm design and selection in practice.}

In one-stage multi-object detection tasks, various intersection over union (IoU)-based solutions aim at smooth and stable convergence near the targets during training. However, IoU-based losses fail to correctly update the gradient of small objects due to an extremely flat gradient. During the update of multiple objects, the learning of small objects' gradients suffers more because of insufficient gradient updates. Therefore, we propose an inter-class relational loss to efficiently update the gradient of small objects while not sacrificing the learning efficiency of other objects based on the simple fact that an object has a spatial relationship to another object (e.g., a car plate is attached to a car in a similar position). When the predicted car plate's bounding box is not within its car, a loss punishment is added to guide the learning, which is inversely proportional to the overlapped area of the car's and predicted car plate's bounding box. By leveraging the spatial relationship at the inter-class level, the loss guides small object predictions using larger objects and enhances latent information in deeper feature maps. In this paper, we present twofold contributions using license plate detection as a case study: (1) a new small vehicle multi-license plate dataset (SVMLP), featuring diverse real-world scenarios with high-quality annotations; and (2) a novel inter-class relational loss function designed to promote effective detection performance. We highlight the proposed ICR loss penalty can be easily added to existing IoU-based losses and enhance the performance. These contributions improve the standard mean Average Precision (mAP) metric, achieving gains of 10.3% and 1.6% in mAP$^{\text{test}}_{50}$ for YOLOv12-T and UAV-DETR, respectively, without any additional hyperparameter tuning. Code and dataset will be available soon.

Modern distributed training of machine learning models often suffers from high communication overhead for synchronizing stochastic gradients and model parameters.