Loss functions play a central role in supervised classification. Cross-entropy (CE) is widely used, whereas the mean absolute error (MAE) loss can offer robustness but is difficult to optimize. Interpolating between the CE and MAE losses, generalized cross-entropy (GCE) has recently been introduced to provide a trade-off between optimization difficulty and robustness. Existing formulations of GCE result in a non-convex optimization over classification margins that is prone to underfitting, leading to poor performances with complex datasets. In this paper, we propose a minimax formulation of generalized cross-entropy (MGCE) that results in a convex optimization over classification margins. Moreover, we show that MGCEs can provide an upper bound on the classification error. The proposed bilevel convex optimization can be efficiently implemented using stochastic gradient computed via implicit differentiation. Using benchmark datasets, we show that MGCE achieves strong accuracy, faster convergence, and better calibration, especially in the presence of label noise.

We derive posterior contraction rates (PCRs) and finite-sample Bernstein von Mises (BvM) results for non-parametric Bayesian models by extending the diffusion-based framework of Mou et al. (2024) to the infinite-dimensional setting. The posterior is represented as the invariant measure of a Langevin stochastic partial differential equation (SPDE) on a separable Hilbert space, which allows us to control posterior moments and obtain non-asymptotic concentration rates in Hilbert norms under various likelihood curvature and regularity conditions. We also establish a quantitative Laplace approximation for the posterior. The theory is illustrated in a nonparametric linear Gaussian inverse problem.

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

Prior work on partial labels learning (PLL) has shown that learning is possible even when each instance is associated with a bag of labels, rather than a single accurate but costly label. However, the necessary conditions for learning with partial labels remain unclear, and existing PLL methods are effective only in specific scenarios. In this work, we mathematically characterize the settings in which PLL is feasible. In addition, we present PL A-$k$NN, an adaptive nearest-neighbors algorithm for PLL that is effective in general scenarios and enjoys strong performance guarantees. Experimental results corroborate that PL A-$k$NN can outperform state-of-the-art methods in general PLL scenarios.

AML Trends in 2022: What Y ou Need to Know .

The UN estimates 2-5% of global GDP or $0.8 - $2.0 trillion dollars are laundered

However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols.

Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution and OOD data.