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:2603.15412v2 Announce Type: replace Abstract: The mammalian brain, most extensively studied in rodents and bats, solves an enormous variety of non-spatial cognitive tasks using neural circuitry...
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:2608.23889v1 Announce Type: cross Abstract: Plasticity under changing environments is central to both evolutionary biology and continual learning. Motivated by recent work on genotype--phenotyp...
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:2609. 23366v1 Announce Type: new Abstract: Recurrent models must preserve information that changes future behavior while suppressing hidden-state error.