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Discrete Solution Operator Learning for Geometry-Dependent PDEs

arXiv:2601.09143v3 Announce Type: replace Abstract: Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological changes, abrupt changes in boundary conditions or…

Subspace Geometry Governs Catastrophic Forgetting in Low-Rank Adaptation

arXiv:2603.02224v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) has emerged as a parameter-efficient approach for adapting large pre-trained models, yet its behavior under continual learning remains poorly understood. We present a geometric theory characterizing catastrophic forgetting in LoRA through the…

Scaling Reward Modeling without Human Supervision

arXiv:2603.02225v1 Announce Type: new Abstract: Learning from feedback is an instrumental process for advancing the capabilities and safety of frontier models, yet its effectiveness is often constrained by cost and scalability. We present a pilot study that explores scaling reward…

Efficient Sparse Selective-Update RNNs for Long-Range Sequence Modeling

arXiv:2603.02226v1 Announce Type: new Abstract: Real-world sequential signals, such as audio or video, contain critical information that is often embedded within long periods of silence or noise. While recurrent neural networks (RNNs) are designed to process such data efficiently, they…

Infinite dimensional generative sensing

arXiv:2603.03196v1 Announce Type: cross Abstract: Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces, creating a gap when the physical…