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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).

Jonas Weidner, Michal Balcerak, Ivan Ezhov et al.

Glioblastoma, the most aggressive primary brain tumor, poses a severe clinical challenge due to its diffuse microscopic infiltration, which remains largely undetected on standard MRI. As a result, current radiotherapy planning employs a uniform 15 mm margin around the resection cavity, failing to capture patient-specific tumor spread. Tumor growth modeling offers a promising approach to reveal this hidden infiltration. However, methods based on partial differential equations or physics-informed neural networks tend to be computationally intensive or overly constrained, limiting their clinical adaptability to individual patients. In this work, we propose a lightweight, rapid, and robust optimization framework that estimates the 3D tumor concentration by fitting it to MRI tumor segmentations while enforcing a smooth concentration landscape. This approach achieves superior tumor recurrence prediction on 192 brain tumor patients across two public datasets, outperforming state-of-the-art baselines while reducing runtime from 30 minutes to less than one minute. Furthermore, we demonstrate the framework's versatility and adaptability by showing its ability to seamlessly integrate additional imaging modalities or physical constraints.