Maksim Zhdanov, Lisa Randolph, Thomas Kluge et al.
Grazing-Incidence Small-Angle X-ray Scattering (GISAXS) is a modern imaging technique used in material research to study nanoscale materials. Reconstruction of the parameters of an imaged object imposes an ill-posed inverse problem that is further complicated when only an in-plane GISAXS signal is available. Traditionally used inference algorithms such as Approximate Bayesian Computation (ABC) rely on computationally expensive scattering simulation software, rendering analysis highly time-consuming. We propose a simulation-based framework that combines variational auto-encoders and normalizing flows to estimate the posterior distribution of object parameters given its GISAXS data. We apply the inference pipeline to experimental data and demonstrate that our method reduces the inference cost by orders of magnitude while producing consistent results with ABC.
Functional connectivity plays an essential role in modern neuroscience. The modality sheds light on the brain's functional and structural aspects, including mechanisms behind multiple pathologies. One such pathology is schizophrenia which is often followed by auditory verbal hallucinations. The latter is commonly studied by observing functional connectivity during speech processing. In this work, we have made a step toward an in-depth examination of functional connectivity during a dichotic listening task via deep learning for three groups of people: schizophrenia patients with and without auditory verbal hallucinations and healthy controls. We propose a graph neural network-based framework within which we represent EEG data as signals in the graph domain. The framework allows one to 1) predict a brain mental disorder based on EEG recording, 2) differentiate the listening state from the resting state for each group and 3) recognize characteristic task-depending connectivity. Experimental results show that the proposed model can differentiate between the above groups with state-of-the-art performance. Besides, it provides a researcher with meaningful information regarding each group's functional connectivity, which we validated on the current domain knowledge.
Machine learning has been applied to the problem of X-ray diffraction phase prediction with promising results. In this paper, we describe a method for using machine learning to predict crystal structure phases from X-ray diffraction data of transition metals and their oxides. We evaluate the performance of our method and compare the variety of its settings. Our results demonstrate that the proposed machine learning framework achieves competitive performance. This demonstrates the potential for machine learning to significantly impact the field of X-ray diffraction and crystal structure determination. Open-source implementation: https://github.com/maxnygma/NeuralXRD.
Electroencephalography produces high-dimensional, stochastic data from which it might be challenging to extract high-level knowledge about the phenomena of interest. We address this challenge by applying the framework of variational auto-encoders to 1) classify multiple pathologies and 2) recover the neurological mechanisms of those pathologies in a data-driven manner. Our framework learns generative factors of data related to pathologies. We provide an algorithm to decode those factors further and discover how different pathologies affect observed data. We illustrate the applicability of the proposed approach to identifying schizophrenia, either followed or not by auditory verbal hallucinations. We further demonstrate the ability of the framework to learn disease-related mechanisms consistent with current domain knowledge. We also compare the proposed framework with several benchmark approaches and indicate its classification performance and interpretability advantages.
Pedro M. P. Curvo, Maksim Zhdanov, Floor Eijkelboom et al.
Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.
Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on standard convolutions with $G$-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group $G$, implementing a kernel basis does not generalize to other symmetry transformations, complicating the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize $G$-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group $G$ for which a $G$-equivariant MLP can be built. We prove the effectiveness of our method on multiple tasks, including N-body simulations, point cloud classification and molecular property prediction.
Machine Learning Interatomic Potentials (MLIPs) achieve near ab initio accuracy at a fraction of the cost of quantum-mechanical simulations, yet they remain prone to silent failures on out-of-distribution configurations, making principled uncertainty quantification (UQ) essential for error-aware simulations and active learning. Existing non-ensemble UQ methods for MLIPs rely either on variational inference or on parametric distributional assumptions, both of which add architectural complexity and hyper-parameters that must be tuned per task. Inspired by recent advances in probabilistic weather forecasting, we propose a simpler alternative: turn a deterministic MLIP into a probabilistic one through learned functional perturbations and finetune it end-to-end with the Continuous Ranked Probability Score (CRPS), a proper scoring rule. We validate the approach with an equivariant GNN (P-EGNN) trained from scratch and by finetuning the foundation model the Orb-v3 for silica. On the N-body charged particle benchmark, P-EGNN improves CRPS over the state-of-the-art Bayesian MLIP method BLIP by 19-32% across all training sizes; on silica, P-Orb raises the Spearman correlation between predicted uncertainty and actual error from 0.75 (BLIP-Orb) to 0.84.
We present Clifford-Steerable Convolutional Neural Networks (CS-CNNs), a novel class of $\mathrm{E}(p, q)$-equivariant CNNs. CS-CNNs process multivector fields on pseudo-Euclidean spaces $\mathbb{R}^{p,q}$. They cover, for instance, $\mathrm{E}(3)$-equivariance on $\mathbb{R}^3$ and Poincaré-equivariance on Minkowski spacetime $\mathbb{R}^{1,3}$. Our approach is based on an implicit parametrization of $\mathrm{O}(p,q)$-steerable kernels via Clifford group equivariant neural networks. We significantly and consistently outperform baseline methods on fluid dynamics as well as relativistic electrodynamics forecasting tasks.
The concepts of overfitting and generalization are vital for evaluating machine learning models. In this work, we show that the popular Recall@K metric depends on the number of classes in the dataset, which limits its ability to estimate generalization. To fix this issue, we propose a new metric, which measures retrieval performance, and, unlike Recall@K, estimates generalization. We apply the proposed metric to popular image retrieval methods and provide new insights about deep metric learning generalization.
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.
Maksim Zhdanov, Stanislav Dereka, Sergey Kolesnikov
Uncertainty estimation is crucial in safety-critical applications, where robust out-of-distribution (OOD) detection is essential. Traditional Bayesian methods, though effective, are often hindered by high computational demands. As an alternative, Laplace approximation offers a more practical and efficient approach to uncertainty estimation. In this paper, we introduce the Identity Curvature Laplace Approximation (ICLA), a novel method that challenges the conventional posterior covariance formulation by using identity curvature and optimizing prior precision. This innovative design significantly enhances OOD detection performance on well-known datasets such as CIFAR-10, CIFAR-100, and ImageNet, while maintaining calibration scores. We attribute this improvement to the alignment issues between typical feature embeddings and curvature as measured by the Fisher information matrix. Our findings are further supported by demonstrating that incorporating Fisher penalty or sharpness-aware minimization techniques can greatly enhance the uncertainty estimation capabilities of standard Laplace approximation.