Dmitry Laptev

V. Slavin, O. Kryvchikov, D. Laptev

We present a graph-based deep learning framework for predicting the magnetic properties of quasi-one-dimensional Ising spin systems. The lattice geometry is encoded as a graph and processed by a graph neural network (GNN) followed by fully connected layers. The model is trained on Monte Carlo simulation data and accurately reproduces key features of the magnetization curve, including plateaus, critical transition points, and the effects of geometric frustration. It captures both local motifs and global symmetries, demonstrating that GNNs can infer magnetic behavior directly from structural connectivity. The proposed approach enables efficient prediction of magnetization without the need for additional Monte Carlo simulations.

Dmitry Laptev, Nikolay Savinov, Joachim M. Buhmann et al.

In this paper we present a deep neural network topology that incorporates a simple to implement transformation invariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in the data, such as rotation or scale changes. Most current methods usually make use of dataset augmentation to address this issue, but this requires larger number of model parameters and more training data, and results in significantly increased training time and larger chance of under- or overfitting. The main reason for these drawbacks is that the learned model needs to capture adequate features for all the possible transformations of the input. On the other hand, we formulate features in convolutional neural networks to be transformation-invariant. We achieve that using parallel siamese architectures for the considered transformation set and applying the TI-POOLING operator on their outputs before the fully-connected layers. We show that this topology internally finds the most optimal "canonical" instance of the input image for training and therefore limits the redundancy in learned features. This more efficient use of training data results in better performance on popular benchmark datasets with smaller number of parameters when comparing to standard convolutional neural networks with dataset augmentation and to other baselines.