The paper introduces the Intersection Euler Characteristic Profile, a topological metric for measuring class overlap in neural representations, and provides exact permutation and sign‑flip tests to assess disentanglement across layers. Using this statistic, the authors analyze 111 networks and 52,650 measurements, finding that disentanglement is depth‑graded, occurs early, and is influenced by training choices such as augmentation and weight decay. The study also demonstrates that the unnormalized mass of the profile predicts test accuracy, while the dimensionless quotient does not outperform simple linear probes.
arXiv:2609.08561v1 Announce Type: new Abstract: Class disentanglement (the separation of a representation's class-conditional point clouds along depth and over training) is usually read off descripti...
arXiv:2605.06240v2 Announce Type: replace-cross Abstract: Forward-Forward (FF) training lets each layer learn from a local goodness criterion. In cumulative-goodness variants, later layers can inheri...
arXiv:2607. 12501v3 Announce Type: replace Abstract: The Forward-Forward algorithm trains each layer locally, so that a scalar goodness - the sum of squared activations - is high on real inputs and low on contrastive ones.
arXiv:2608.29702v1 Announce Type: new Abstract: A token-embedding table holds a hub of short rows near its origin, and we show that this cluster biases what nearest-neighbor intrinsic-dimension (ID)...
arXiv:2607. 24797v1 Announce Type: cross Abstract: In the literate human brain, reading and writing are two doubly-dissociable systems: a ventral decoding route (impaired in pure alexia) and a fronto-parietal encoding route (impaired in pure agraphia), sharing a partial orthographic core.
arXiv:2606. 31856v1 Announce Type: new Abstract: We study layered models, including feedforward networks, ResNets, and transformers, by limiting each layer to a width of $d = 3$, i.
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2609.16183v1 Announce Type: new Abstract: Fixed-state recurrences--linear attention and state-space models--are reported to lag behind attention on associative recall, but whole-architecture co...
A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable.
arXiv:2601. 09173v5 Announce Type: replace Abstract: Representational similarity analysis and related methods compare the internal geometries of neural networks, but they measure only alignment between spaces, leaving a blind spot -- whether a representation's structure is reliably recoverable, not merely similar.
Approximate machine unlearning seeks to remove the influence of a forget set from a trained model without full retraining. Existing gradient-based methods require data-dependent hyperparameter search,...
The paper introduces Unmerge, an efficient machine unlearning algorithm that treats unlearning as the inverse of task arithmetic. By representing the forget component as a low‑rank basis at each layer, Unmerge optimizes three goals—matching the merged vector, suppressing leakage, and bounding correction size—to limit forget leakage and retain damage. Experiments on ResNet‑50, ViT‑S/16, and Llama‑3.2‑3B show significant performance gains over existing methods while maintaining privacy and feature‑distribution fidelity.