The paper introduces the DLP curve, a metric that quantifies how well nonlinear embeddings like t‑SNE and UMAP preserve local and global structure by measuring the share of each point’s k‑nearest neighbors retained in the map. Corrected for chance, the curve yields local fidelity (L) at k=10 and global fidelity (G) over 30–50% of the data, with the midpoint provably equivalent to a rank correlation of distances. The authors also present the LG reversal test to compare two maps and the entity fidelity (E) to predict which entities a map loses, demonstrating strong agreement with established global scores on twelve large datasets.
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)...
The paper introduces Smooth Rank t‑SNE (SR‑tSNE), a variant of t‑SNE that incorporates a differentiable rank term using a sigmoid approximation to preserve the ordering of neighbors in the embedding. It also proposes Ordinal DLP (O‑DLP), a metric that rewards neighbors only when they appear at their original rank. Across eight diverse benchmarks, SR‑tSNE outperforms 12 baselines in rank preservation, neighborhood overlap, and downstream tasks such as label transfer, cell‑type discovery, and intraday trading.
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:2604.02535v2 Announce Type: replace Abstract: Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure....
arXiv:2510.01335v2 Announce Type: replace Abstract: The manifold hypothesis suggests that data lies on manifolds with smaller intrinsic dimension (ID) than their ambient dimension. However there is n...
arXiv:2608. 06809v1 Announce Type: new Abstract: How can an analyst decide whether a nonlinear dimensionality reduction embedding can be trusted?
arXiv:2610.35411v1 Announce Type: new Abstract: We measure the emotion geometry of six LLMs spanning Google's Gemma 2 family. Using an extraction pipeline established by Sofroniew et al. (2026) on Cl...
arXiv:2607. 26278v1 Announce Type: new Abstract: It is common for two-dimensional embeddings of high-dimensional data to be read far beyond what they can support.
arXiv:2610.05518v1 Announce Type: cross Abstract: The Fr\'echet distance is a de facto standard for evaluating generative models across domains, appearing as FID for images and FVD for videos. It sum...
arXiv:2605. 11428v2 Announce Type: replace Abstract: Exploratory analysis of high-dimensional data rarely stops at a single embedding.
arXiv:2511. 11041v2 Announce Type: replace-cross Abstract: We find that current sentence-embedding models produce outputs with a consistent bias: every embedding $e$ decomposes as $\tilde e + \mu$, where the mean $\mu$ is near-identical across all sentences.
arXiv:2603.04317v2 Announce Type: replace-cross Abstract: A growing literature shows that variables can be linearly decoded from the activations of large language models (LLMs). These range from prop...