#01Jul 22, 2026
stat.ML
Adaptive Bayesian Online Learning via Expert Aggregation
Jungbin Jun, Ilsang Ohn
Bayesian online learning promises uncertainty-aware prediction on data streams, but its performance hinges on inferential choices, including learning rates, prior distributions and variational families, which are usually fixed before seeing the stream. We address this by treating Bayesian update rules as experts and aggregating the Bayesian experts according to sequential predictive losses. We prove that the resulting aggregate competes with the best expert in hindsight at an aggregation cost determined by how each expert's per-round performance is evaluated. We instantiate the framework in online conformal inference and Gaussian process regression. The conformal inference application yields a smoothed Bayesian counterpart of adaptive conformal inference with long-run randomized coverage, while the Gaussian process application gives an oracle inequality in cumulative predictive Kullback-Leibler risk and adaptation to unknown Hölder smoothness up to logarithmic factors. Experiments show that the aggregate tracks strong experts without oracle expert selection.
#02Jul 22, 2026
cs.LG
ELSAA: Efficient Low-Rank and Sparse Attention Approximation for Training Transformers
Mahdi Heidari, Mohammad Mahdi Rahimi, Jaekyun Moon
The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths. Existing efficient attention methods usually reduce this bottleneck by either imposing sparsity, so that each query attends to only a small subset of keys, or by using low-rank/kernel sketches, so that global interactions are compressed into a lower-dimensional representation. We propose \emph{ELSAA}, an efficient low-rank and sparse approximation of attention. Importantly, ELSAA does \emph{not} decompose the learned projection or output matrices of the Transformer into sparse and low-rank factors. Instead, after dense projections produce $Q,K,V$, ELSAA approximates the induced attention score operator itself: a sparse branch captures selected high-similarity interactions, while a low-rank branch summarizes diffuse global interactions. Since the two branches can be normalized over supports with very different denominator mass, ELSAA introduces a denominator-aware fusion term that scales the sparse branch according to its estimated attention mass relative to the low-rank branch. This gives a practical framework for constructing low-rank and sparse attention outputs without materializing the full quadratic score matrix, aiming to enable longer-context training while preserving both sharp token-level interactions and broad contextual mixing.
#03Jul 22, 2026
physics.flu-dyn
Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fields
Tianyu Li, Zhiwei Cao, Qingang Zhang and 3 more
Neural surrogates are widely used in scientific machine learning for fast prediction of three-dimensional (3D) thermo-fluid fields. However, generating training data using conventional numerical solvers often incurs substantial computational and storage costs. We propose to train an attention graph neural network by minimizing the finite-volume method (FVM) residuals of the governing equations. These residuals are evaluated directly on the mesh, requiring no labeled data. We evaluate the trained surrogates against computational fluid dynamics (CFD) references and a data-supervised baseline across four scenarios. On the two steady-state benchmarks, the FVM-loss model achieves an all-field normalized root-mean-square error (nRMSE) of 2.3-2.8%. It demonstrates close agreement with the CFD references, including the buoyancy-energy coupling. On the two parametric transient cases, the FVM-loss model outperforms the supervised baseline in terms of accuracy, while avoiding the data-generation cost entirely. These results indicate that the FVM loss can provide a practical training signal for neural surrogates and reduce the model development cost.
#04Jul 22, 2026
cs.LG
Instance Hardness-Based Relevance for Imbalanced Regression
Vitor M. Leitao, Juscimara G. Avelino, George D. C. Cavalcanti and 1 more
Imbalanced regression problems arise when the target variable has an asymmetric distribution, resulting in underrepresented value ranges in the dataset. Traditional approaches for identifying rare instances rely on a relevance function that assigns higher importance to specific regions of the target distribution. However, the effectiveness of imbalance-aware learning methods depends strongly on how relevance is defined. In more complex scenarios, such as bimodal distributions, traditional relevance functions struggle to capture rarity, as they assign fixed relevance values based solely on target values, thereby compromising the distinction between truly rare and normal instances. To address these limitations, this study proposes an Instance Hardness-based relevance function (InHaR) for identifying rare instances in regression problems. Unlike traditional relevance functions, the proposed approach incorporates learning difficulty, allowing rarity to be inferred not only from the target distribution but also from the difficulty of instances for the learning algorithm. This property is particularly important in bimodal scenarios, where rarity cannot be accurately inferred from target values alone. Experimental results demonstrate that the InHaR correctly identifies rare regions under bimodal distributions and, when used to guide resampling strategies such as Random Oversampling (RO) and Gaussian Noise (GN), leads to significant improvements in predictive performance compared to traditional relevance-based approaches. The code, dataset, and further details about the proposed method are publicly available at https://github.com/VitorLeitao/instance-hardness-Imbalanced-regression.
#05Jul 22, 2026
cs.LG
On Optimization Complexity of Second-Order Certified Unlearning
Nikita Doikov, Anastasia Koloskova
We study machine unlearning: the removal of memorized training data from a trained model. Specifically, we investigate the algorithmic complexity of certified unlearning from an optimization perspective. We formalize the goal of an unlearning algorithm as simultaneously achieving certified unlearning and optimization accuracy. Utilizing the notion of uniformly convex regularizers, we prove new bounds on the distance between initial and unlearned models using a novel substitute for generalization error. Thus we theoretically demonstrate that if the removed data is well-predicted by the unlearned model, the corresponding optimization problem is simple. Furthermore, we develop a new second-order unlearning algorithm with an anisotropic Gaussian mechanism and state-of-the-art global convergence. We prove fast rates for our method in achieving certified unlearning for linear models with quasi-self-concordant losses. As a direct application, our theory covers unlearning for logistic and exponential regressions and shows a provable benefit of utilizing second-order information compared to first-order unlearning methods.