Iterative Erasure Count Is Not an Affine-Invariant Concept Dimension
arXiv:2608. 10566v1 Announce Type: cross Abstract: How many directions does a neural representation use to encode a concept?
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:2608. 10566v1 Announce Type: cross Abstract: How many directions does a neural representation use to encode a concept?
arXiv:2608. 11661v1 Announce Type: cross Abstract: A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings.
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.
arXiv:2606. 05957v1 Announce Type: new Abstract: Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate.
arXiv:2508. 04227v3 Announce Type: replace-cross Abstract: Vision-language models (VLMs), spanning predictive architectures to generative Multimodal Large Language Models (MLLMs), have revolutionized artificial intelligence through powerful cross-modal alignment and zero-shot generalization.
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:2606. 27242v1 Announce Type: new Abstract: Training-free source selection for LLM families with shared vocabularies arises in scientific string domains such as SMILES, protein, and genomic sequences, where candidate corpora share a tokenizer but differ in prediction targets.
arXiv:2602. 24264v2 Announce Type: replace-cross Abstract: Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems.
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:2605. 13352v2 Announce Type: replace Abstract: Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support).
arXiv:2605. 20282v3 Announce Type: replace-cross Abstract: Machine unlearning in Vertical Federated Learning (VFL) has attracted growing interest, yet existing methods certify forgetting solely using output-level metrics.
arXiv:2606. 32022v1 Announce Type: new Abstract: Residual-stream analysis asks how language-model computation evolves across depth, but intermediate decoding requires comparable readout coordinates across layers.