Federated learning enables multiple actors to collaboratively train models without sharing private data. This unlocks the potential for scaling machine learning to diverse applications. Existing algorithms for this task are well-justified when clients and the intended target domain share the same distribution of features and labels, but this assumption is often violated in real-world scenarios. One common violation is label shift, where the label distributions differ across clients or between clients and the target domain, which can significantly degrade model performance. To address this problem, we propose FedPALS, a novel model aggregation scheme that adapts to label shifts by leveraging knowledge of the target label distribution at the central server. Our approach ensures unbiased updates under stochastic gradient descent, ensuring robust generalization across clients with diverse, label-shifted data. Extensive experiments on image classification demonstrate that FedPALS consistently outperforms standard baselines by aligning model aggregation with the target domain. Our findings reveal that conventional federated learning methods suffer severely in cases of extreme client sparsity, highlighting the critical need for target-aware aggregation. FedPALS offers a principled and practical solution to mitigate label distribution mismatch, ensuring models trained in federated settings can generalize effectively to label-shifted target domains.

Implicit bias describes the phenomenon where optimization-based training algorithms, without explicit regularization, show a preference for simple estimators even when more complex estimators have equal objective values. Multiple works have developed the theory of implicit bias for binary classification under the assumption that the loss satisfies an exponential tail property. However, there is a noticeable gap in analysis for multiclass classification, with only a handful of results which themselves are restricted to the cross-entropy loss. In this work, we employ the framework of Permutation Equivariant and Relative Margin-based (PERM) losses [Wang and Scott, 2024] to introduce a multiclass extension of the exponential tail property. This class of losses includes not only cross-entropy but also other losses. Using this framework, we extend the implicit bias result of Soudry et al. [2018] to multiclass classification. Furthermore, our proof techniques closely mirror those of the binary case, thus illustrating the power of the PERM framework for bridging the binary-multiclass gap.

Although nearly 20 years have passed since its conception, the feasibility pump algorithm remains a widely used heuristic to find feasible primal solutions to mixed-integer linear problems. Many extensions of the initial algorithm have been proposed. Yet, its core algorithm remains centered around two key steps: solving the linear relaxation of the original problem to obtain a solution that respects the constraints, and rounding it to obtain an integer solution. This paper shows that the traditional feasibility pump and many of its follow-ups can be seen as gradient-descent algorithms with specific parameters. A central aspect of this reinterpretation is observing that the traditional algorithm differentiates the solution of the linear relaxation with respect to its cost. This reinterpretation opens many opportunities for improving the performance of the original algorithm. We study how to modify the gradient-update step as well as extending its loss function. We perform extensive experiments on MIPLIB instances and show that these modifications can substantially reduce the number of iterations needed to find a solution.

In the domain of deep learning, the challenge of protecting sensitive data while maintaining model utility is significant. Traditional Differential Privacy (DP) techniques such as Differentially Private Stochastic Gradient Descent (DP-SGD) typically employ strategies like direct or per-sample adaptive gradient clipping. These methods, however, compromise model accuracy due to their critical influence on gradient handling, particularly neglecting the significant contribution of small gradients during later training stages. In this paper, we introduce an enhanced version of DP-SGD, named Differentially Private Per-sample Adaptive Scaling Clipping (DP-PSASC). This approach replaces traditional clipping with non-monotonous adaptive gradient scaling, which alleviates the need for intensive threshold setting and rectifies the disproportionate weighting of smaller gradients. Our contribution is twofold. First, we develop a novel gradient scaling technique that effectively assigns proper weights to gradients, particularly small ones, thus improving learning under differential privacy. Second, we integrate a momentum-based method into DP-PSASC to reduce bias from stochastic sampling, enhancing convergence rates. Our theoretical and empirical analyses confirm that DP-PSASC preserves privacy and delivers superior performance across diverse datasets, setting new standards for privacy-sensitive applications.

We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based methods asymptotically. In contrast with previous literature, where convergence is established based on worst-case analysis, our framework provides a strong convergence guarantee with respect to the optimal scaling matrix for the iteration trajectory. For smooth strongly convex optimization, our results provide an $O(\kappa^\star \log(1/\varepsilon)$) complexity result, where $\kappa^\star$ is the condition number achievable by the optimal preconditioner, improving on the previous $O(\sqrt{n}\kappa^\star \log(1/\varepsilon))$ result. In particular, a variant of our method achieves superlinear convergence on convex quadratics. For smooth convex optimization, we show for the first time that the widely-used hypergradient descent heuristic improves on the convergence of gradient descent.

The information plane (Tishby et al. arXiv:physics/0004057, Shwartz-Ziv et al. arXiv:1703.00810) has been proposed as an analytical tool for studying the learning dynamics of neural networks. It provides quantitative insight on how the model approaches the learned state by approximating a minimal sufficient statistics. In this paper we extend this tool to the domain of quantum learning models. In a second step, we study how the insight on how much the model compresses the input data (provided by the information plane) can be used to improve a learning algorithm. Specifically, we consider two ways to do so: via a multiplicative regularization of the loss function, or with a compression-gnostic scheduler of the learning rate (for algorithms based on gradient descent). Both ways turn out to be equivalent in our implementation. Finally, we benchmark the proposed learning algorithms on several classification and regression tasks using variational quantum circuits. The results demonstrate an improvement in test accuracy and convergence speed for both synthetic and real-world datasets. Additionally, with one example we analyzed the impact of the proposed modifications on the performances of neural networks in a classification task.

Deep neural network ensembles are powerful tools for uncertainty quantification, which have recently been re-interpreted from a Bayesian perspective. However, current methods inadequately leverage second-order information of the loss landscape, despite the recent availability of efficient Hessian approximations. We propose a novel approximate Bayesian inference method that modifies deep ensembles to incorporate Stein Variational Newton updates. Our approach uniquely integrates scalable modern Hessian approximations, achieving faster convergence and more accurate posterior distribution approximations. We validate the effectiveness of our method on diverse regression and classification tasks, demonstrating superior performance with a significantly reduced number of training epochs compared to existing ensemble-based methods, while enhancing uncertainty quantification and robustness against overfitting.

Point processes are widely used statistical models for uncovering the temporal patterns in dependent event data. In many applications, the event time cannot be observed exactly, calling for the incorporation of time uncertainty into the modeling of point process data. In this work, we introduce a framework to model time-uncertain point processes possibly on a network. We start by deriving the formulation in the continuous-time setting under a few assumptions motivated by application scenarios. After imposing a time grid, we obtain a discrete-time model that facilitates inference and can be computed by first-order optimization methods such as Gradient Descent or Variation inequality (VI) using batch-based Stochastic Gradient Descent (SGD). The parameter recovery guarantee is proved for VI inference at an $O(1/k)$ convergence rate using $k$ SGD steps. Our framework handles non-stationary processes by modeling the inference kernel as a matrix (or tensor on a network) and it covers the stationary process, such as the classical Hawkes process, as a special case. We experimentally show that the proposed approach outperforms previous General Linear model (GLM) baselines on simulated and real data and reveals meaningful causal relations on a Sepsis-associated Derangements dataset.

Transformers can efficiently learn in-context from example demonstrations. Most existing theoretical analyses studied the in-context learning (ICL) ability of transformers for linear function classes, where it is typically shown that the minimizer of the pretraining loss implements one gradient descent step on the least squares objective. However, this simplified linear setting arguably does not demonstrate the statistical efficiency of ICL, since the pretrained transformer does not outperform directly solving linear regression on the test prompt. In this paper, we study ICL of a nonlinear function class via transformer with nonlinear MLP layer: given a class of \textit{single-index} target functions $f_*(\boldsymbol{x}) = \sigma_*(\langle\boldsymbol{x},\boldsymbol{\beta}\rangle)$, where the index features $\boldsymbol{\beta}\in\mathbb{R}^d$ are drawn from a $r$-dimensional subspace, we show that a nonlinear transformer optimized by gradient descent (with a pretraining sample complexity that depends on the \textit{information exponent} of the link functions $\sigma_*$) learns $f_*$ in-context with a prompt length that only depends on the dimension of the distribution of target functions $r$; in contrast, any algorithm that directly learns $f_*$ on test prompt yields a statistical complexity that scales with the ambient dimension $d$. Our result highlights the adaptivity of the pretrained transformer to low-dimensional structures of the function class, which enables sample-efficient ICL that outperforms estimators that only have access to the in-context data.

Federated learning is an efficient machine learning tool for dealing with heterogeneous big data and privacy protection. Federated learning methods with regularization can control the level of communications between the central and local machines. Stochastic gradient descent is often used for implementing such methods on heterogeneous big data, to reduce the communication costs. In this paper, we consider such an algorithm called Loopless Local Gradient Descent which has advantages in reducing the expected communications by controlling a probability level. We improve the method by allowing flexible step sizes and carry out novel analysis for the convergence of the algorithm in a non-convex setting in addition to the standard strongly convex setting. In the non-convex setting, we derive rates of convergence when the smooth objective function satisfies a Polyak-{\L}ojasiewicz condition. When the objective function is strongly convex, a sufficient and necessary condition for the convergence in expectation is presented.