Florian A. Hölzl

Florian A. Hölzl, Daniel Rueckert, Georgios Kaissis

Machine learning with formal privacy-preserving techniques like Differential Privacy (DP) allows one to derive valuable insights from sensitive medical imaging data while promising to protect patient privacy, but it usually comes at a sharp privacy-utility trade-off. In this work, we propose to use steerable equivariant convolutional networks for medical image analysis with DP. Their improved feature quality and parameter efficiency yield remarkable accuracy gains, narrowing the privacy-utility gap.

Florian A. Hölzl, Daniel Rueckert, Georgios Kaissis

Differentially Private Stochastic Gradient Descent (DP-SGD) limits the amount of private information deep learning models can memorize during training. This is achieved by clipping and adding noise to the model's gradients, and thus networks with more parameters require proportionally stronger perturbation. As a result, large models have difficulties learning useful information, rendering training with DP-SGD exceedingly difficult on more challenging training tasks. Recent research has focused on combating this challenge through training adaptations such as heavy data augmentation and large batch sizes. However, these techniques further increase the computational overhead of DP-SGD and reduce its practical applicability. In this work, we propose using the principle of sparse model design to solve precisely such complex tasks with fewer parameters, higher accuracy, and in less time, thus serving as a promising direction for DP-SGD. We achieve such sparsity by design by introducing equivariant convolutional networks for model training with Differential Privacy. Using equivariant networks, we show that small and efficient architecture design can outperform current state-of-the-art models with substantially lower computational requirements. On CIFAR-10, we achieve an increase of up to $9\%$ in accuracy while reducing the computation time by more than $85\%$. Our results are a step towards efficient model architectures that make optimal use of their parameters and bridge the privacy-utility gap between private and non-private deep learning for computer vision.

Julian McGinnis, Florian A. Hölzl, Suprosanna Shit et al.

Implicit Neural Representations (INRs) based on vanilla Multi-Layer Perceptrons (MLPs) are widely believed to be incapable of representing high-frequency content. This has directed research efforts towards architectural interventions, such as coordinate embeddings or specialized activation functions, to represent high-frequency signals. In this paper, we challenge the notion that the low-frequency bias of vanilla MLPs is an intrinsic, architectural limitation to learn high-frequency content, but instead a symptom of stable rank degradation during training. We empirically demonstrate that regulating the network's rank during training substantially improves the fidelity of the learned signal, rendering even simple MLP architectures expressive. Extensive experiments show that using optimizers like Muon, with high-rank, near-orthogonal updates, consistently enhances INR architectures even beyond simple ReLU MLPs. These substantial improvements hold across a diverse range of domains, including natural and medical images, and novel view synthesis, with up to 9 dB PSNR improvements over the previous state-of-the-art. Our project page, which includes code and experimental results, is available at: (https://muon-inrs.github.io).

Florian A. Hölzl, Daniel Rueckert, Georgios Kaissis

Robust validation metrics remain essential in contemporary deep learning, not only to detect overfitting and poor generalization, but also to monitor training dynamics. In the supervised classification setting, we investigate whether interactions between training data and model weights can yield such a metric that both tracks generalization during training and attributes performance to individual training samples. We introduce Gradient-Weight Alignment (GWA), quantifying the coherence between per-sample gradients and model weights. We show that effective learning corresponds to coherent alignment, while misalignment indicates deteriorating generalization. GWA is efficiently computable during training and reflects both sample-specific contributions and dataset-wide learning dynamics. Extensive experiments show that GWA accurately predicts optimal early stopping, enables principled model comparisons, and identifies influential training samples, providing a validation-set-free approach for model analysis directly from the training data.