arXiv subjects

Przemyslaw Musialski

Publications and source records attributed to Przemyslaw Musialski.

At least 19 recordsLinked to original sources

arXiv2026

The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups

We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $ρ(g)$ carrying it. To our knowledge this is the first attention construction whose tokens are bare matrix Lie group elements: their score is the closed-form algebra norm of the relative pose rather than a learned kernel, and it reaches the affine full-frame groups that every irrep- or surjective-exp-based method must exclude. We call it Lie-Algebra Attention. Once tokens are group elements, the rest follows with none of the usual representation-theoretic machinery. The relative geometry of a pair is canonical, $g_i^{-1} g_j$, so the pairwise invariant $w_{ij} = \log(g_i^{-1} g_j)$ is intrinsic rather than designed; equivariance under the diagonal $G$-action is tautological, and the cocycle condition holds automatically. The attention score is the negative squared algebra norm, $s_{ij} = -\|\log(g_i^{-1} g_j)\|_λ^2/τ$: the canonical proximity kernel under a block-weighted Frobenius inner product, with no irreducible representations, spherical harmonics, Clebsch-Gordan products, or learned kernel. The construction applies to any matrix Lie group on a chosen logarithm chart containing the relative poses, including the non-compact non-abelian affine groups with scale and shear that no vector-token attention method reaches: neither the irrep tradition nor surjective-exp methods. Three sequence-completion experiments, on SE(2), SO(3), and Aff(2), bear this out: the closed-form score matches a learned MLP kernel on the same invariant and outperforms it on SE(2), using 50 to 80x fewer score parameters, while a vector-token baseline breaks invariance by five to twelve orders of magnitude.

cs.LG↗

arXiv2026

StippleDiffusion: Capacity-Constrained Stippling using Controlled Diffusion

Stipple patterns, point sets whose local density tracks a target image, are traditionally produced by per-density iterative optimizers, which are slow, non-differentiable, and must be re-run from scratch for each new target. Learned alternatives have so far addressed only unconditional point generation; capacity-constrained, image-conditioned stippling has remained out of reach. We present the first diffusion-based sampler that simultaneously satisfies a learned local point-distribution prior and a continuous, image-defined capacity constraint at inference. The method is a ControlNet branch built on top of an optimal-transport-grid point-set diffusion baseline, conditioned on the target density map and a high-resolution image. Two design choices make the combination tractable: training and inference are restricted to the late-stage denoising regime, initialized from a density-weighted rejection sample, and the standard zero-convolution injection is replaced with a sigmoid-gated 1x1 projection that preserves the base model's blue-noise structure under hard density signals. A single trained checkpoint accepts arbitrary target densities at inference, generalizes to point budgets that were not seen during training, and produces stipples in time nearly independent of the output point count. On the Icons-50 benchmark, our learned sampler reaches parity with per-density-optimized baselines on every reported metric while remaining differentiable end-to-end.

cs.GR↗

arXiv2026

Pro-DG: Procedural Diffusion Guidance for Architectural Facade Generation

We use hierarchical procedural rules for the generation of control maps within the stable diffusion framework to produce photo-realistic architectural facade images. Starting from a single input image and its segmentation, we apply an inverse procedural module to identify the facade's hierarchical layout. Leveraging this hierarchy and structural features, we introduce a novel ControlNet pipeline that generates new facade imagery guided by procedural transformations. Our method enables various structural edits, including floor duplication and window rearrangement, by integrating hierarchical alignment directly into control maps. This precisely guides the diffusion-based generative process, ensuring local appearance fidelity alongside extensive structural modifications. Comprehensive evaluations, including comparisons with inpainting-based approaches and synthetic benchmarks, confirm our approach's superior capability in preserving architectural identity and achieving accurate, controllable edits. Quantitative results and user feedback validate our method's effectiveness.

cs.GR↗

arXiv2026

Geometric Guidance for Globally Synchronized Deployment of Elastic Geodesic Grids

Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized, time-coupled deformation trajectories. Starting from inverse tracing -- collapsing the deployed structure with a lightweight rod model while recording node paths under a shared parameter -- we obtain feasible node paths and formulate a polyline approximation problem that selects {globally synchronized} time steps and minimizes a robust tail-aggregated deviation measure under monotonicity constraints. {We solve the resulting non-smooth optimization problem via global optimization to obtain compact, synchronized displacement sequences for all paths simultaneously}. We evaluate the method using geometry-centric metrics (deviation versus step count, scaling with trajectory count) and demonstrate its utility by driving finite element deployment simulations that avoid intermediate buckling and capture deployment-induced prestress.

cs.GR↗

arXiv2026

STEP-Parts: Geometric Partitioning of Boundary Representations for Large-Scale CAD Processing

Many CAD learning pipelines discretize Boundary Representations (B-Reps) into triangle meshes, discarding analytic surface structure and topological adjacency and thereby weakening consistent instance-level analysis. We present STEP-Parts, a deterministic CAD-to-supervision toolchain that extracts geometric instance partitions directly from raw STEP B-Reps and transfers them to tessellated carriers through retained source-face correspondence, yielding instance labels and metadata for downstream learning and evaluation. The construction merges adjacent B-Rep faces only when they share the same analytic primitive type and satisfy a near-tangent continuity criterion. On ABC, same-primitive dihedral angles are strongly bimodal, yielding a threshold-insensitive low-angle regime for part extraction. Because the partition is defined on intrinsic B-Rep topology rather than on a particular triangulation, the resulting boundaries remain stable under changes in tessellation. Applied to the DeepCAD subset of ABC, the pipeline processes approximately 180{,}000 models in under six hours on a consumer CPU. We release code and precomputed labels, and show that STEP-Parts serves both as a tessellation-robust geometric reference and as a useful supervision source in two downstream probes: an implicit reconstruction--segmentation network and a dataset-level point-based backbone.

cs.GR↗

arXiv2026

INST-Align: Implicit Neural Alignment for Spatial Transcriptomics via Canonical Expression Fields

Spatial transcriptomics (ST) measures mRNA expression while preserving spatial organization, but multi-slice analysis faces two coupled difficulties: large non-rigid deformations across slices and inter-slice batch effects when alignment and integration are treated independently. We present INST-Align, an unsupervised pairwise framework that couples a coordinate-based deformation network with a shared Canonical Expression Field, an implicit neural representation mapping spatial coordinates to expression embeddings, for joint alignment and reconstruction. A two-phase training strategy first establishes a stable canonical embedding space and then jointly optimizes deformation and spatial-feature matching, enabling mutually constrained alignment and representation learning. Cross-slice parameter sharing of the canonical field regularizes ambiguous correspondences and absorbs batch variation. Across nine datasets, INST-Align achieves state-of-the-art mean OT Accuracy (0.702), NN Accuracy (0.719), and Chamfer distance, with Chamfer reductions of up to 94.9\% on large-deformation sections relative to the strongest baseline. The framework also yields biologically meaningful spatial embeddings and coherent 3D tissue reconstruction. The code will be released after review phase.

cs.CV↗

arXiv2026

Beyond Segmentation: Structurally Informed Facade Parsing from Imperfect Images

Standard object detectors typically treat architectural elements independently, often resulting in facade parsings that lack the structural coherence required for downstream procedural reconstruction. We address this limitation by augmenting the YOLOv8 training objective with a custom lightweight alignment loss. This regularization encourages grid-consistent arrangements of bounding boxes during training, effectively injecting geometric priors without altering the standard inference pipeline. Experiments on the CMP dataset demonstrate that our method successfully improves structural regularity, correcting alignment errors caused by perspective and occlusion while maintaining a controllable trade-off with standard detection accuracy.

cs.CV↗

arXiv2026

What a Comfortable World: Ergonomic Principles Guided Apartment Layout Generation

Current data-driven floor plan generation methods often reproduce the ergonomic inefficiencies found in real-world training datasets. To address this, we propose a novel approach that integrates architectural design principles directly into a transformer-based generative process. We formulate differentiable loss functions based on established architectural standards from literature to optimize room adjacency and proximity. By guiding the model with these ergonomic priors during training, our method produces layouts with significantly improved livability metrics. Comparative evaluations show that our approach outperforms baselines in ergonomic compliance while maintaining high structural validity.

cs.GR↗

arXiv2026

HOSC: A Periodic Activation with Saturation Control for High-Fidelity Implicit Neural Representations

Periodic activations such as sine preserve high-frequency information in implicit neural representations (INRs) through their oscillatory structure, but often suffer from gradient instability and limited control over multi-scale behavior. We introduce the Hyperbolic Oscillator with Saturation Control (HOSC) activation, $\text{HOSC}(x) = \tanh\bigl(β\sin(ω_0 x)\bigr)$, which exposes an explicit parameter $β$ that controls the Lipschitz bound of the activation by $βω_0$. This provides a direct mechanism to tune gradient magnitudes while retaining a periodic carrier. We provide a mathematical analysis and conduct a comprehensive empirical study across images, audio, video, NeRFs, and SDFs using standardized training protocols. Comparative analysis against SIREN, FINER, and related methods shows where HOSC provides substantial benefits and where it achieves competitive parity. Results establish HOSC as a practical periodic activation for INR applications, with domain-specific guidance on hyperparameter selection. For code visit the project page https://hosc-nn.github.io/ .

cs.LG↗

arXiv2025

A Finite Difference Approximation of Second Order Regularization of Neural-SDFs

We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Others reduced this overhead by avoiding explicit Hessian assembly, but still required higher-order differentiation. In contrast, our method replaces these operations with lightweight finite-difference stencils that approximate second derivatives using the well known Taylor expansion with a truncation error of O(h^2), and can serve as drop-in replacements for Gaussian curvature and rank-deficiency losses. Experiments demonstrate that our finite-difference variants achieve reconstruction fidelity comparable to their automatic-differentiation counterparts, while reducing GPU memory usage and training time by up to a factor of two. Additional tests on sparse, incomplete, and non-CAD data confirm that the proposed formulation is robust and general, offering an efficient and scalable alternative for curvature-aware SDF learning.

cs.GR↗

arXiv2025

Scheduling the Off-Diagonal Weingarten Loss of Neural SDFs for CAD Models

Neural signed distance functions (SDFs) have become a powerful representation for geometric reconstruction from point clouds, yet they often require both gradient- and curvature-based regularization to suppress spurious warp and preserve structural fidelity. FlatCAD introduced the Off-Diagonal Weingarten (ODW) loss as an efficient second-order prior for CAD surfaces, approximating full-Hessian regularization at roughly half the computational cost. However, FlatCAD applies a fixed ODW weight throughout training, which is suboptimal: strong regularization stabilizes early optimization but suppresses detail recovery in later stages. We present scheduling strategies for the ODW loss that assign a high initial weight to stabilize optimization and progressively decay it to permit fine-scale refinement. We investigate constant, linear, quintic, and step interpolation schedules, as well as an increasing warm-up variant. Experiments on the ABC CAD dataset demonstrate that time-varying schedules consistently outperform fixed weights. Our method achieves up to a 35% improvement in Chamfer Distance over the FlatCAD baseline, establishing scheduling as a simple yet effective extension of curvature regularization for robust CAD reconstruction.

cs.GR↗

arXiv2025

Joint Neural SDF Reconstruction and Semantic Segmentation for CAD Models

We propose a simple, data-efficient pipeline that augments an implicit reconstruction network based on neural SDF-based CAD parts with a part-segmentation head trained under PartField-generated supervision. Unlike methods tied to fixed taxonomies, our model accepts meshes with any number of parts and produces coherent, geometry-aligned labels in a single pass. We evaluate on randomly sampled CAD meshes from the ABC dataset with intentionally varied part cardinalities, including over-segmented shapes, and report strong performance across reconstruction (CDL1/CDL2, F1-micro, NC) and segmentation (mIoU, Accuracy), together with a new Segmentation Consistency metric that captures local label smoothness. We attach a lightweight segmentation head to the Flat-CAD SDF trunk; on a paired evaluation it does not alter reconstruction while providing accurate part labels for meshes with any number of parts. Even under degraded reconstructions on thin or intricate geometries, segmentation remains accurate and label-coherent, often preserving the correct part count. Our approach therefore offers a practical route to semantically structured CAD meshes without requiring curated taxonomies or exact palette matches. We discuss limitations in boundary precision, partly due to per-face supervision, and outline paths toward boundary-aware training and higher resolution labels.

cs.GR↗

arXiv2025

FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models

Neural signed-distance fields (SDFs) are a versatile backbone for neural geometry representation, but enforcing CAD-style developability usually requires Gaussian-curvature penalties with full Hessian evaluation and second-order differentiation, which are costly in memory and time. We introduce an off-diagonal Weingarten loss that regularizes only the mixed shape operator term that represents the gap between principal curvatures and flattens the surface. We present two variants: a finite-difference version using six SDF evaluations plus one gradient, and an auto-diff version using a single Hessian-vector product. Both converge to the exact mixed term and preserve the intended geometric properties without assembling the full Hessian. On the ABC benchmarks the losses match or exceed Hessian-based baselines while cutting GPU memory and training time by roughly a factor of two. The method is drop-in and framework-agnostic, enabling scalable curvature-aware SDF learning for engineering-grade shape reconstruction. Our code is available at https://flatcad.github.io/.

cs.GR↗

arXiv2025

Beyond Blur: A Fluid Perspective on Generative Diffusion Models

We propose a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion processes which generalizes existing PDE-based approaches. Our forward pass formulates image corruption via a physically motivated PDE that couples directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless numbers (Peclet, Fourier). We implement this PDE numerically through a GPU-accelerated custom Lattice Boltzmann solver for fast evaluation. To induce realistic turbulence, we generate stochastic velocity fields that introduce coherent motion and capture multi-scale mixing. In the generative process, a neural network learns to reverse the advection-diffusion operator thus constituting a novel generative model. We discuss how previous methods emerge as specific cases of our operator, demonstrating that our framework generalizes prior PDE-based corruption techniques. We illustrate how advection improves the diversity and quality of the generated images while keeping the overall color palette unaffected. This work bridges fluid dynamics, dimensionless PDE theory, and deep generative modeling, offering a fresh perspective on physically informed image corruption processes for diffusion-based synthesis.

cs.GR↗

arXiv2025

Neural Surface Priors for Editable Gaussian Splatting

In computer graphics and vision, recovering easily modifiable scene appearance from image data is crucial for applications such as content creation. We introduce a novel method that integrates 3D Gaussian Splatting with an implicit surface representation, enabling intuitive editing of recovered scenes through mesh manipulation. Starting with a set of input images and camera poses, our approach reconstructs the scene surface using a neural signed distance field. This neural surface acts as a geometric prior guiding the training of Gaussian Splatting components, ensuring their alignment with the scene geometry. To facilitate editing, we encode the visual and geometric information into a lightweight triangle soup proxy. Edits applied to the mesh extracted from the neural surface propagate seamlessly through this intermediate structure to update the recovered appearance. Unlike previous methods relying on the triangle soup proxy representation, our approach supports a wider range of modifications and fully leverages the mesh topology, enabling a more flexible and intuitive editing process. The complete source code for this project can be accessed at: https://github.com/WJakubowska/NeuralSurfacePriors.

cs.CV↗

arXiv2024

Optimizing 3D Geometry Reconstruction from Implicit Neural Representations

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary as the zero-level set of the learned continuous function and learns a mapping from a low-dimensional latent space to the space of all possible shapes represented by its signed distance function. However, most INRs struggle to retain high-frequency details, which are crucial for accurate geometric depiction, and they are computationally expensive. To address these limitations, we present a novel approach that both reduces computational expenses and enhances the capture of fine details. Our method integrates periodic activation functions, positional encodings, and normals into the neural network architecture. This integration significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

cs.CV↗

arXiv2024

Shrinking: Reconstruction of Parameterized Surfaces from Signed Distance Fields

We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching Cubes extract discrete meshes that lose the continuous and differentiable properties of INRs, our approach iteratively contracts a parameterized initial sphere to conform to the target SDF shape, preserving differentiability and surface parameterization throughout. This enables downstream applications such as texture mapping, geometry processing, animation, and finite element analysis. Evaluated on the typical geometric shapes and parts of the ABC dataset, our method achieves competitive reconstruction quality, maintaining smoothness and differentiability crucial for advanced computer graphics and geometric deep learning applications.

cs.GR↗

arXiv2024

FaçAID: A Transformer Model for Neuro-Symbolic Facade Reconstruction

We introduce a neuro-symbolic transformer-based model that converts flat, segmented facade structures into procedural definitions using a custom-designed split grammar. To facilitate this, we first develop a semi-complex split grammar tailored for architectural facades and then generate a dataset comprising of facades alongside their corresponding procedural representations. This dataset is used to train our transformer model to convert segmented, flat facades into the procedural language of our grammar. During inference, the model applies this learned transformation to new facade segmentations, providing a procedural representation that users can adjust to generate varied facade designs. This method not only automates the conversion of static facade images into dynamic, editable procedural formats but also enhances the design flexibility, allowing for easy modifications.

cs.GR↗