arXiv:2512. 18471v2 Announce Type: replace Abstract: Continual learning systems face a fundamental geometric obstacle: as experience accumulates on a fixed-capacity manifold, covering numbers grow linearly with time, eventually forcing representational overlap and catastrophic interference.
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.
arXiv:2606. 21253v2 Announce Type: replace Abstract: Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally.
We introduce Neural Subspace Reallocation (NSR), which reframes continual learning as memory management over parameter subspaces. Instead of treating Low-Rank Adaptation (LoRA) modules as disposable per-task adapters, NSR manages them as compressible, retrievable memory units on a frozen backbone through a recurring cycle: (1) compress learned LoRAs via SVD, (2) reserve them in a TaskKnowledgeBank, (3) recall related past LoRAs by embedding similarity to warm-start new or returning tasks, and (4) reallocate the active subspace accordingly, with distillation protecting prior tasks.
arXiv:2606. 07598v1 Announce Type: cross Abstract: We propose a topological framework for comparing trained Graph Neural Networks (GNNs) by mapping the Stochastic Block Models (SBMs) induced on the graphon-signal space of a Message Passing Neural Network (MPNN) onto the unit $n$-sphere $\sphere^{n-1}\subset\R^n$.
How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank.
arXiv:2606. 30067v1 Announce Type: cross Abstract: We introduce Neural Subspace Reallocation (NSR), which reframes continual learning as memory management over parameter subspaces.
arXiv:2606. 30512v1 Announce Type: cross Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory.
arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
arXiv:2608. 09572v1 Announce Type: new Abstract: Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities.
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.