arXiv subjects

Michal Jan Wlodarczyk

Publications and source records attributed to Michal Jan Wlodarczyk.

4 recordsLinked to original sources

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

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↗