arXiv subjects

Daniel Franzen

Publications and source records attributed to Daniel Franzen.

7 recordsLinked to original sources

arXiv2026

Tensor Channel Equivariant Graph Neural Networks for Molecular Polarizability Prediction

We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2 tensor channels aligned with the decomposition of polarizability into isotropic and anisotropic components. In contrast to approaches that construct tensor outputs only at readout, our model propagates tensor structure throughout message passing using geometrically motivated tensor bases. This yields a target-aligned architecture for tensor-valued molecular prediction. On optimized QM7-X geometries, the proposed model achieves lower full-tensor and anisotropic error than both a PaiNN-style readout baseline and a dielectric MACE baseline under matched training conditions and at nearly identical parameter count. In this controlled setting, it also outperforms MACE while remaining substantially faster at inference. Ablation studies show that the gain does not arise from increased capacity alone, but from the combination of explicit tensor propagation and a traceless target parameterization matched to the anisotropic part of the polarizability tensor. Among the tensor bases considered, the strongest results are obtained from interactions between learned directional features, indicating that these are particularly effective for modeling molecular polarizability. Rotational equivariance tests further confirm that all compared models are numerically equivariant, so the observed improvements are attributable to better learning of the target tensor itself. Overall, our results show that for structured tensor-valued targets, propagating target-aligned tensor features can outperform both readout-only tensor construction and a more general higher-order equivariant model in the present training setting.

cs.LG↗

arXiv2026

Discretizing Group-Convolutional Neural Networks for 3D Geometry in Feature Space

Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and filters in different poses (with suitable anti-aliasing for steerable GCNNs) to maintain equivariance with respect to $G$. Unfortunately, applying filters to many data items resulting from this sampling is expensive (even for translations alone, i.e., in ordinary CNNs), and costs grow exponentially with increasing degrees of freedom (such as translations and rotations in 3D), which often hinders practical applications. In this paper, we propose sampling in feature space, i.e., replacing geometrically dense samples with representative samples selected by feature similarity. This decouples geometric resolution from memory and processing costs during training and inference, providing a novel way to trade off computational effort and accuracy. Our main empirical finding is that a coarse feature-space sampling already preserves classification accuracy remarkably well, which permits precomputation based on geometric similarity, accelerating the training of equivariant 3D classifiers substantially.

cs.CV↗

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↗

arXiv2023

Machine learning-based spin structure detection

One of the most important magnetic spin structure is the topologically stabilised skyrmion quasi-particle. Its interesting physical properties make them candidates for memory and efficient neuromorphic computation schemes. For the device operation, detection of the position, shape, and size of skyrmions is required and magnetic imaging is typically employed. A frequently used technique is magneto-optical Kerr microscopy where depending on the samples material composition, temperature, material growing procedures, etc., the measurements suffer from noise, low-contrast, intensity gradients, or other optical artifacts. Conventional image analysis packages require manual treatment, and a more automatic solution is required. We report a convolutional neural network specifically designed for segmentation problems to detect the position and shape of skyrmions in our measurements. The network is tuned using selected techniques to optimize predictions and in particular the number of detected classes is found to govern the performance. The results of this study shows that a well-trained network is a viable method of automating data pre-processing in magnetic microscopy. The approach is easily extendable to other spin structures and other magnetic imaging methods.

cs.LG↗

arXiv2022

"Am I Private and If So, how Many?" - Communicating Privacy Guarantees of Differential Privacy with Risk Communication Formats

Decisions about sharing personal information are not trivial, since there are many legitimate and important purposes for such data collection, but often the collected data can reveal sensitive information about individuals. Privacy-preserving technologies, such as differential privacy (DP), can be employed to protect the privacy of individuals and, furthermore, provide mathematically sound guarantees on the maximum privacy risk. However, they can only support informed privacy decisions, if individuals understand the provided privacy guarantees. This article proposes a novel approach for communicating privacy guarantees to support individuals in their privacy decisions when sharing data. For this, we adopt risk communication formats from the medical domain in conjunction with a model for privacy guarantees of DP to create quantitative privacy risk notifications. We conducted a crowd-sourced study with 343 participants to evaluate how well our notifications conveyed the privacy risk information and how confident participants were about their own understanding of the privacy risk. Our findings suggest that these new notifications can communicate the objective information similarly well to currently used qualitative notifications, but left individuals less confident in their understanding. We also discovered that several of our notifications and the currently used qualitative notification disadvantage individuals with low numeracy: these individuals appear overconfident compared to their actual understanding of the associated privacy risks and are, therefore, less likely to seek the needed additional information before an informed decision. The promising results allow for multiple directions in future research, for example, adding visual aids or tailoring privacy risk communication to characteristics of the individuals.

cs.HC↗

arXiv2022

"Am I Private and If So, how Many?" -- Using Risk Communication Formats for Making Differential Privacy Understandable

Mobility data is essential for cities and communities to identify areas for necessary improvement. Data collected by mobility providers already contains all the information necessary, but privacy of the individuals needs to be preserved. Differential privacy (DP) defines a mathematical property which guarantees that certain limits of privacy are preserved while sharing such data, but its functionality and privacy protection are difficult to explain to laypeople. In this paper, we adapt risk communication formats in conjunction with a model for the privacy risks of DP. The result are privacy notifications which explain the risk to an individual's privacy when using DP, rather than DP's functionality. We evaluate these novel privacy communication formats in a crowdsourced study. We find that they perform similarly to the best performing DP communications used currently in terms of objective understanding, but did not make our participants as confident in their understanding. We also discovered an influence, similar to the Dunning-Kruger effect, of the statistical numeracy on the effectiveness of some of our privacy communication formats and the DP communication format used currently. These results generate hypotheses in multiple directions, for example, toward the use of risk visualization to improve the understandability of our formats or toward adaptive user interfaces which tailor the risk communication to the characteristics of the reader.

cs.HC↗

arXiv2021

Nonlinearities in Steerable SO(2)-Equivariant CNNs

Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have emerged as the standard solution. An inherent problem of steerable representations is that general nonlinear layers break equivariance, thus restricting architectural choices. Our paper applies harmonic distortion analysis to illuminate the effect of nonlinearities on Fourier representations of SO(2). We develop a novel FFT-based algorithm for computing representations of non-linearly transformed activations while maintaining band-limitation. It yields exact equivariance for polynomial (approximations of) nonlinearities, as well as approximate solutions with tunable accuracy for general functions. We apply the approach to build a fully E(3)-equivariant network for sampled 3D surface data. In experiments with 2D and 3D data, we obtain results that compare favorably to the state-of-the-art in terms of accuracy while permitting continuous symmetry and exact equivariance.

cs.LG↗