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. 17961v1 Announce Type: cross Abstract: Positional encoding is a fundamental component of Transformer architectures, as it injects information about the spatial or sequential arrangement of inputs.
arXiv:2607. 02386v1 Announce Type: cross Abstract: While Vision Transformers have achieved remarkable success across computer vision and language applications, the geometric evolution of their internal representations throughout training remains insufficiently understood.
Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason...
arXiv:2511. 09432v2 Announce Type: replace Abstract: Machine learning (ML) models achieve remarkable performance but remain hard to interpret due to their scale and complexity.
COMPLEX is a closed‑form, training‑free embedding for multiparameter persistence modules that provides both an upper and a lower Lipschitz bound, enabling faithful feature representations. By slicing modules along a near‑diagonal net and embedding each slice with the certified PLACE/PALACE landmark map, the method guarantees that separated modules remain separated in the embedding. On Orbit benchmarks and molecular graph tasks, COMPLEX achieves state‑of‑the‑art accuracy, outperforming existing landmark, transformer, and graph‑based approaches.
arXiv:2609.27988v1 Announce Type: cross Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent work finds only weak pointwise similarity between mo...
arXiv:2609.24209v1 Announce Type: new Abstract: The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent wor...
The paper investigates how neural representations maintain the structure of input changes, linking representation analysis with internal interventions. It characterises when transformations can be applied through an encoder, providing linear settings where defects depend on discarded information and detailing failure modes for rectifiers and harmonic carriers. Using colour as a case study, the authors show that hue orbits in frozen visual features concentrate most energy in the first two harmonics, that this structure is inherited from input and architecture, and that a compact, fixed‑action interface can read hue zero‑shot with low error on unseen shapes.
arXiv:2606. 00124v1 Announce Type: cross Abstract: Positional embeddings (PEs) in Vision Transformers (ViTs) are known to impact performance and robustness, but their role in shaping internal spatial representations is not well understood.
arXiv:2606. 10824v1 Announce Type: new Abstract: The Euler Characteristic Curve (ECC) records the Euler characteristic of a linearly embedded cell complex as a function of filtration height in a given direction, and the Euler Characteristic Transform (ECT) is the injective shape descriptor obtained by collecting ECCs over many directions.
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.