arXiv subjects

Jan Disselhoff

Publications and source records attributed to Jan Disselhoff.

3 recordsLinked to original sources

arXiv2026

Reconstruction of spin structures from topological charge distributions via generative neural network systems

Localized topological defects inherently possess a multiscale character. While their microstructure configuration depends on the specific physical system, their topological features and mutual interactions can be described on the macroscale in terms of a particle representation. However, determining the physical properties associated with a given defect pattern often requires knowledge of the underlying microscopic structure. In this work, we extend a Wasserstein generative adversarial neural network by incorporating physical constraints and Fourier-space information to generate microscopic spin configurations consistent with prescribed macroscopic patterns and thermodynamic parameters. Using the two-dimensional XY model as a test case, where vortex-antivortex pairs act as long-range interacting defects, we show that the model generates spin configurations that accurately reproduce magnetization, susceptibility, helicity modulus, and spin-spin correlations over a wide range of temperatures below the Kosterlitz-Thouless transition. At the same time, deviations in the specific heat reveal limitations in reproducing higher order energy fluctuations. A complementary analysis based on topological data analysis uncovers subtle differences in global spin-correlation structures at near critical temperatures that are not apparent from conventional correlation functions alone. These results demonstrate both the promise and current limitations of generative approaches for multiscale studies of defect-dominated spin systems and at the same time highlight topological methods as valuable tools for characterizing critical behavior.

cond-mat.stat-mech↗

arXiv2025

Product of Experts with LLMs: Boosting Performance on ARC Is a Matter of Perspective

The Abstraction and Reasoning Corpus (ARC-AGI) poses a significant challenge for large language models (LLMs), exposing limitations in their abstract reasoning abilities. In this work, we leverage task-specific data augmentations throughout the training, generation, and scoring phases, and employ a depth-first search algorithm to generate diverse, high-probability candidate solutions. Furthermore, we utilize the LLM not only as a generator but also as a scorer, using its output probabilities to select the most promising solutions. Our method achieves a score of 71.6% (286.5/400 solved tasks) on the public ARC-AGI evaluation set, demonstrating state-of-the-art performance among publicly available approaches. While concurrent closed-source work has reported higher scores, our method distinguishes itself through its transparency, reproducibility, and remarkably low inference cost, averaging only around 2ct per task on readily available hardware (we assume a price of 36ct/hour for a Nvidia 4090 GPU).

cs.CL↗

arXiv2022

Nonlinear Advantage: Trained Networks Might Not Be As Complex as You Think

We perform an empirical study of the behaviour of deep networks when fully linearizing some of its feature channels through a sparsity prior on the overall number of nonlinear units in the network. In experiments on image classification and machine translation tasks, we investigate how much we can simplify the network function towards linearity before performance collapses. First, we observe a significant performance gap when reducing nonlinearity in the network function early on as opposed to late in training, in-line with recent observations on the time-evolution of the data-dependent NTK. Second, we find that after training, we are able to linearize a significant number of nonlinear units while maintaining a high performance, indicating that much of a network's expressivity remains unused but helps gradient descent in early stages of training. To characterize the depth of the resulting partially linearized network, we introduce a measure called average path length, representing the average number of active nonlinearities encountered along a path in the network graph. Under sparsity pressure, we find that the remaining nonlinear units organize into distinct structures, forming core-networks of near constant effective depth and width, which in turn depend on task difficulty.

cs.LG↗