arXiv subjects

Arturs Berzins

Publications and source records attributed to Arturs Berzins.

9 recordsLinked to original sources

arXiv2026

Meltdown: Circuits and Bifurcations in Point-Cloud-Conditioned 3D Diffusion Transformers

Sparse point clouds are a common input modality for 3D surface reconstruction, including in safety-critical settings such as surgical navigation and autonomous perception. Recent point-cloud-conditioned 3D diffusion transformers achieve state-of-the-art results in this regime by leveraging learned priors. We show that these models can fail catastrophically under realistic input variation, and present a mechanistic case study of why. We identify a failure mode we call Meltdown: tiny on-surface perturbations to a sparse input point cloud can fracture the reconstructed output into hundreds of disconnected pieces. Adversarial search recovers Meltdown in 89.9-100% of shapes across the two open-weight state-of-the-art architectures we study (WaLa, Make-a-Shape) on real-world datasets (GSO, SimJEB) and under both DDPM and DDIM sampling. We trace Meltdown along the forward pass: it is governed by how uniformly the points are distributed on the surface, faithfully transduced through the point-cloud encoder, and committed by a single early-denoising cross-attention write in the diffusion backbone. Diffusion-trajectory ensembles exhibit symmetry-breaking near this commit step, consistent with a bifurcation of the reverse process. Through a suite of matched-magnitude controls, we show that the variable on which the model commits is directional, concentrated in a low-rank subspace of the write's perturbation drift. Motivated by this finding, we introduce PowerRemap, a test-time control that reshapes the singular spectrum of the localized write to suppress this drift, with rescue rates of 98.3% on WaLa and 84.6% on Make-a-Shape. Together, these results link a circuit-level cross-attention mechanism to a trajectory-level account of the failure, demonstrating how mechanistic analysis can explain and guide behavior in conditional diffusion transformers.

cs.LG↗

arXiv2026

Gauss-Newton Natural Gradient Descent for Shape Learning

We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning of the underlying differential constraints and the mismatch between the optimization problem in parameter space and the function space where the problem is naturally posed. This leads to significantly faster and more stable convergence than standard first-order methods, while also requiring far fewer iterations. Experiments across benchmark shape optimization tasks demonstrate that the Gauss-Newton method consistently improves both training speed and final solution accuracy.

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arXiv2026

Einstein Fields: A Neural Perspective To Computational General Relativity

We introduce Einstein Fields, a neural representation designed to compress computationally intensive four-dimensional numerical relativity simulations into compact implicit neural network weights. By modeling the metric, the core tensor field of general relativity, Einstein Fields enable the derivation of physical quantities via automatic differentiation. Unlike conventional neural fields (e.g., signed distance, occupancy, or radiance fields), Einstein Fields fall into the class of Neural Tensor Fields with the key difference that, when encoding the spacetime geometry into neural field representations, dynamics emerge naturally as a byproduct. Our novel implicit approach demonstrates remarkable potential, including continuum modeling of four-dimensional spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use. It achieves up to a $4,000$-fold reduction in storage memory compared to discrete representations while retaining a numerical accuracy of five to seven decimal places. Moreover, in single precision, differentiation of the Einstein Fields-parameterized metric tensor is up to five orders of magnitude more accurate compared to naive finite differencing methods. We demonstrate these properties on several canonical test beds of general relativity and numerical relativity simulation data, while also releasing an open-source JAX-based library: \href{https://github.com/AndreiB137/EinFields}{https://github.com/AndreiB137/EinFields}, taking the first steps to studying the potential of machine learning in numerical relativity.

cs.LG↗

arXiv2025

Neural surrogates for designing gravitational wave detectors

Physics simulators are essential in science and engineering, enabling the analysis, control, and design of complex systems. In experimental sciences, they are increasingly used to automate experimental design, often via combinatorial search and optimization. However, as the setups grow more complex, the computational cost of traditional, CPU-based simulators becomes a major limitation. Here, we show how neural surrogate models can significantly reduce reliance on such slow simulators while preserving accuracy. Taking the design of interferometric gravitational wave detectors as a representative example, we train a neural network to surrogate the gravitational wave physics simulator Finesse, which was developed by the LIGO community. Despite that small changes in physical parameters can change the output by orders of magnitudes, the model rapidly predicts the quality and feasibility of candidate designs, allowing an efficient exploration of large design spaces. Our algorithm loops between training the surrogate, inverse designing new experiments, and verifying their properties with the slow simulator for further training. Assisted by auto-differentiation and GPU parallelism, our method proposes high-quality experiments much faster than direct optimization. Solutions that our algorithm finds within hours outperform designs that take five days for the optimizer to reach. Though shown in the context of gravitational wave detectors, our framework is broadly applicable to other domains where simulator bottlenecks hinder optimization and discovery.

cs.LG↗

arXiv2025

Geometry-Informed Neural Networks

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

cs.LG↗

arXiv2025

Diverse Topology Optimization using Modulated Neural Fields

Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the exploration of alternative designs. To address this limitation, we introduce Topology Optimization using Modulated Neural Fields (TOM) - a data-free method that trains a neural network to generate structurally compliant shapes and explores diverse solutions through an explicit diversity constraint. The network is trained with a solver-in-the-loop, optimizing the material distribution in each iteration. The trained model produces diverse shapes that closely adhere to the design requirements. We validate TOM on 2D and 3D TO problems. Our results show that TOM generates more diverse solutions than any previous method, all while maintaining near-optimality and without relying on a dataset. These findings open new avenues for engineering and design, offering enhanced flexibility and innovation in structural optimization.

cs.LG↗

arXiv2025

Shape Generation via Weight Space Learning

Foundation models for 3D shape generation have recently shown a remarkable capacity to encode rich geometric priors across both global and local dimensions. However, leveraging these priors for downstream tasks can be challenging as real-world data are often scarce or noisy, and traditional fine-tuning can lead to catastrophic forgetting. In this work, we treat the weight space of a large 3D shape-generative model as a data modality that can be explored directly. We hypothesize that submanifolds within this high-dimensional weight space can modulate topological properties or fine-grained part features separately, demonstrating early-stage evidence via two experiments. First, we observe a sharp phase transition in global connectivity when interpolating in conditioning space, suggesting that small changes in weight space can drastically alter topology. Second, we show that low-dimensional reparameterizations yield controlled local geometry changes even with very limited data. These results highlight the potential of weight space learning to unlock new approaches for 3D shape generation and specialized fine-tuning.

cs.CV↗

arXiv2023

Polyhedral Complex Extraction from ReLU Networks using Edge Subdivision

A neural network consisting of piecewise affine building blocks, such as fully-connected layers and ReLU activations, is itself a piecewise affine function supported on a polyhedral complex. This complex has been previously studied to characterize theoretical properties of neural networks, but, in practice, extracting it remains a challenge due to its high combinatorial complexity. A natural idea described in previous works is to subdivide the regions via intersections with hyperplanes induced by each neuron. However, we argue that this view leads to computational redundancy. Instead of regions, we propose to subdivide edges, leading to a novel method for polyhedral complex extraction. A key to this are sign-vectors, which encode the combinatorial structure of the complex. Our approach allows to use standard tensor operations on a GPU, taking seconds for millions of cells on a consumer grade machine. Motivated by the growing interest in neural shape representation, we use the speed and differentiability of our method to optimize geometric properties of the complex. The code is available at https://github.com/arturs-berzins/relu_edge_subdivision .

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arXiv2023

Neural Implicit Shape Editing using Boundary Sensitivity

Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however, neural representations do not allow the user to exert intuitive control over the shape. Motivated by this, we leverage boundary sensitivity to express how perturbations in parameters move the shape boundary. This allows to interpret the effect of each learnable parameter and study achievable deformations. With this, we perform geometric editing: finding a parameter update that best approximates a globally prescribed deformation. Prescribing the deformation only locally allows the rest of the shape to change according to some prior, such as semantics or deformation rigidity. Our method is agnostic to the model its training and updates the NN in-place. Furthermore, we show how boundary sensitivity helps to optimize and constrain objectives (such as surface area and volume), which are difficult to compute without first converting to another representation, such as a mesh.

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