#01Nov 6, 2026
eess.SY
Extending Grid Foundation Models for Phasor-Domain Dynamic Simulation
Boyang Zhao, Yifan Zhou, Alban Puech and 2 more
Grid Foundation Models (GridFMs) are emerging as a powerful framework for learning and transferring knowledge across power grids and grid analysis tasks. This work extends GridFMs from steady-state analysis to dynamic simulation. We present DynGridFM, which uses component-wise tokenization and a structured latent operator to learn shared dynamic representations across heterogeneous grids and enable transfer to unseen systems. Pretrained on nine grids, DynGridFM is adapted to a held-out 48-machine grid, where fine-tuning on 64 trajectories achieves accuracy comparable to training from scratch on 128. On a single GPU, it achieves 924x to 1232x speedup over numerical simulators on one CPU core.
#02Nov 6, 2026
math.ST
Reweighting for Transfer Classification: Exact Risk Conversion and Minimax Adaptation
Aoran Chen, Yang Feng
A source can make a training mixture easier to learn while making its accuracy less valuable for the target. We study how the training problem a source creates and the finite-sample error of learning it jointly determine target-risk guarantees under reweighting. For binary classification, for each pair of laws and each positive target weight, we derive the sharpest target excess hinge-risk bound implied by mixture excess alone, uniformly over clipped predictors. This exact conversion curve is determined by density-weighted local votes. A two-sample oracle inequality for weighted support vector machines supplies the mixture excess, and the composition becomes explicit for Gaussian kernels. On a tilted-boundary class, we establish the all-procedure minimax classification rate $[n+s_+^2/(m^{-1}+τ^2)]^{-1}$ in the transferable strength $s_+$ and the tilt $τ$, separating source sampling uncertainty ($m^{-1}$) from relation uncertainty ($τ^2$). A target-checked Gaussian-SVM selector adapts to unknown $s_+$ and $τ$ up to a logarithmic factor for fixed dimension, and retains the target-only rate up to the same factor against arbitrary independent sources under the stated target model. On a separate smooth opposition class, the minimax risk within the family of exact Gaussian SVMs fitted to the original labels with nonnegative weights is exponentially larger than the unrestricted minimax risk whenever the target sample is at most half the source sample, despite arbitrary data-dependent weighting and tuning. The value of a source thus depends on the training problem it creates, on what accuracy there means for the target, and on whether the permitted use of the source can implement the needed correction.
#03Nov 6, 2026
cs.LG
Accuracy Is Not Value: Choosing Weak Supervisors by What the Student Inherits
Romano Li, Xunfan Cai
Weak supervisors are usually judged by their own errors, but what matters is what a student learns from them. For squared loss and any linear learner shared by all supervisors, we show that a supervisor's value is determined by its errors after they pass through the student's learning operator. Consequently, the inner products of the supervisors' raw errors can be compatible with every feasible value of the student's risk, and weighting supervisors by them can be arbitrarily worse than the best weighting in relative excess risk. This student-relative value is not identifiable from unlabeled data, but what is missing is small: one finite-dimensional projection of the target decides whether training on a weak aggregate helps, another decides how to weight the supervisors. Known teacher training rules, or a label-model condition stated in student-relative form, shrink it further. Clean labels close the remaining gap at a cost set by the geometry of the unresolved directions rather than by the dimension of the student's representation, with matching worst-case lower bounds. In Gaussian designs we also quantify when exact teacher structure beats ordinary stacking and when weak supervisors, combined with clean labels, beat every procedure that uses the clean labels alone. The guarantees extend to fitted ridge students and finite unlabeled data.
#04Nov 6, 2026
stat.ML
Beyond the Lower-Star Filtration: Alternative Filtration Methods for Persistent Homology
Innocent Abaa, Umar Islambekov
In the lower-star filtration (LSF), simplices are assigned filtration values according to the maximum-vertex rule, with each simplex entering the filtration when its highest-valued vertex appears. A limitation of this construction is that some higher-dimensional simplices may enter simultaneously with their boundary faces, causing certain topological features to be filled immediately upon formation and thus not appear in the resulting persistence diagram. To address this limitation, we propose three alternative filtration methods: the \(\varepsilon\)-lower-star filtration (ELSF), the \(L_p\) filtration (LpF), and the softmax filtration (SMF). {ELSF introduces a dimension-dependent delay to the maximum-vertex rule,} allowing higher-dimensional simplices to enter the filtration after their boundary faces, whereas {LpF and SMF use aggregation functions that depend on all vertex values rather} than solely on their maximum. By modifying how filtration values are assigned, these methods allow simplices to enter the filtration more progressively, so that topological features such as loops and voids may persist over longer filtration intervals rather than being filled immediately. Consequently, the resulting persistence diagrams may include persistence features that are not observed under LSF, potentially providing useful information for distinguishing data populations. Experimental results on simulated and real-world datasets demonstrate that the proposed filtration methods are computationally efficient and can provide greater sensitivity to structural differences in the data than LSF.
#05Nov 5, 2026
cs.LG
TopoSHAP: Shapley for Explainable and Efficient Topological Deep Learning
Mathilde Papillon, Nina Miolane
Topological deep learning (TDL) extends learning on graphs, such as molecules or social networks, to higher-order structures, such as rings in a molecule or groups in a social network. Explaining which of these structures drive a model's predictions, and which architectural components matter most for its performance, remains challenging. We introduce TopoSHAP, an efficient and general explanation framework that addresses both questions across topological domains and model architectures. TopoSHAP-cell assigns Shapley values to topological data cells and extracts compact explanations. These explanations match or outperform graph-based counterparts on GraphXAI benchmark data while running up to 112$\times$ faster. They also reveal advantageous topological feature design, leading to measured improvements in explanation recovery and predictive accuracy. On the architecture side, TopoSHAP-neighbor explains how neighborhoods contribute to model performance, and turns these evaluations into a backward-elimination search that identifies smaller, competitive architectures early in training. This is up to $11.3\times$ cheaper than traditional TDL training sweeps.