#01Nov 4, 2026
cs.LG
Message-passing graph persistence
Jorge Luiz Franco, Arthur Queiroz Moura, Moacir Ponti and 1 more
Message-passing graph neural networks (GNNs) are limited in expressive power by the one-dimensional Weisfeiler-Leman test. Persistent homology (PH) provides topological descriptors that can complement GNN representations, but existing approaches typically compute persistence separately from the representation learning process. In this paper, we introduce Message-Passing Graph Persistence (MGP), a family of topological descriptors that incorporates message passing into graph filtrations. At each filtration step, node embeddings are updated using the current subgraph and associated with persistence events. These embeddings also determine the representatives of connected components during persistence computation. We prove that MGP is invariant under graph isomorphism and that it is strictly more expressive than the PH-based descriptors it extends. We evaluate MGP on an expressivity benchmark and on several graph classification and regression datasets. Experiments show that MGP outperforms other PH-based descriptors on most of these datasets.
#02Nov 4, 2026
quant-ph
GFlowQEC: Generative Flow Networks that Learn to Sample Quantum LDPC Codes
Nuno Batista, Gabriel Falcao, Penousal Machado
Choosing a quantum error-correcting code for a real device means scoring candidates with circuit-level simulations so slow that only a few hundred can be run. So every evaluation counts, and a search is judged by how many good codes it finds per paid evaluation. Quantum LDPC codes built from a few group elements protect many logical qubits, but good ones are rare in a huge space. We introduce GFlowQEC, to our knowledge the first generative flow network (GFlowNet) for quantum code design. It builds a code one group element at a time and learns to propose codes in proportion to a power of their score. We train it once on scores from earlier searches, freeze it, and let it propose lifted-product codes with 180 physical qubits, scored by their distances. Ranking ten of its draws per paid call, it finds more than twice as many new top-scoring codes (inequivalent to any it was trained on) as tuned parallel tempering, even when tempering starts from GFlowQEC's training codes. It finds more than three and a half times as many as a supervised screen ranking ten random candidates per call. When both rank a hundred, the screen beats GFlowQEC, and does best ranking GFlowQEC's draws. Soft Q-learning, which shares the GFlowNet's optimal policy, does as well at one noise bias and better at the other, so the gain does not depend on the GFlowNet's training loss. Trained proposers can make a budget of expensive evaluations go further when good codes are rare.
#03Nov 4, 2026
cs.LG
Continual Classification Beyond the Kernel Regime: Harnessing the Sparsity Bias of L2 Regularization in Diagonal Linear Networks
Gilad Karpel, Itay Evron, Ron Meir and 1 more
We study logistic regression for continual learning with linear predictors in a high-dimensional statistical setting. Existing theoretical work has largely focused on continual linear regression with variants of L2 regularization, motivated by their analytical simplicity and connection to the kernel regime of neural networks. We first derive the optimal L2 regularization strength for continual linear classification and characterize its generalization performance, recovering behavior analogous to prior results for continual linear regression. Next, we examine the effect of L2 regularization in deeper models using a minimal two-layer diagonal linear network. In the single-task setting, L2 regularization on the weights of such models is known to promote sparsity in the resulting predictor, yielding a rich, sparse feature-learning regime beyond the kernel regime (a similar effect arises in two-layer ReLU networks). However, in continual learning, where L2 regularization is typically centered on previous-task weights, this sparsity bias is no longer preserved. We therefore propose a weighted variant of L2 regularization that extends this beneficial sparsity bias to continual learning. We show theoretically and empirically that, for a sufficiently sparse teacher, our variant converges substantially faster than directly learning a linear predictor with conventional continual L2 or L1 regularization, trading some long-horizon bias for markedly improved performance over moderate task horizons.
#04Nov 4, 2026
cond-mat.mtrl-sci
Thermally Conditioned Time-Series Forecasting of Grain Growth in Polycrystalline Materials
Eliane Younes, Elie Hachem, Marc Bernacki
Grain growth during heat treatment strongly affects the microstructure of polycrystalline materials and, consequently, their mechanical properties. Although numerical methods such as front-tracking or front-capturing simulations can accurately describe grain growth, their high computational cost limits their use for long or non-isothermal thermal cycles. In previous work, grain growth was successfully predicted under isothermal conditions by treating grain size distributions as time series and forecasting their evolution using recurrent neural networks, allowing complete grain growth trajectories to be generated in seconds rather than through costly PDE-based simulations. In the present work, this forecasting framework is reformulated to handle non-isothermal conditions by explicitly incorporating thermal information into the model architecture. Grain size distributions are encoded using a convolutional neural network, thermal descriptors are embedded through a dedicated multilayer perceptron, and temporal evolution is predicted using a recurrent network. Instantaneous temperature and thermal rate are provided at each time step, allowing the model to adapt its predictions to changing thermal conditions. The framework is trained and evaluated on datasets generated from validated front-tracking simulations across a wide range of non-isothermal thermal paths. The results show that the thermally conditioned model accurately reproduces grain growth dynamics under complex thermal histories, achieving, in k-fold cross-validation over all simulations, mean relative errors of 2.99% (one-hour cycles) and 4.51% (four-hour cycles) with coefficients of determination exceeding 0.99, and mean relative errors between 1.91% and 14.66% on ten simulations following four unseen thermal histories of increasing complexity.
#05Nov 4, 2026
cond-mat.mtrl-sci
Evolutionary Design of Interpretable Spatial Descriptors for Structure-Property Relationship Discovery
Aditya Raghavan, Sergei V Kalinin
Structure property prediction is a classical task in machine learning, ranging from molecular activity and materials properties to local functional responses measured in microscopy. For image-based regression, two choices define the information available to the predictor: the size of the image neighborhood and the spatial resolution retained within it. A small neighborhood can omit relevant surrounding structure, whereas a large, finely sampled neighborhood can introduce redundant or irrelevant information. Here, we develop a framework for constructing spatial descriptors for prediction of local spectra and hysteresis loops. We benchmark regression models, use SHAP maps to examine their spatial attribution, and explore the effect of the patch size and compression to establish the relationship between predictive accuracy and descriptor dimensionality. We then use a genetic algorithm to optimize spatial partitions and the assignment of mean, minimum, and maximum pooling operations. Each retained region contributes an explicit measurement of the image, allowing the search to balance prediction error against the number of descriptor values. Cartesian and polar constructions provide complementary ways to organize this information. The resulting descriptors make it possible to examine where spatial detail is needed, where regional summaries are sufficient, and how these choices depend on the predictor and the measured response. The same approach can be used for molecules and solids once the genetic algorithm rules for these are established.