Paper Citation Record · LEDGER

Shrink the longest: improving latent space isotropy with symplicial geometry

As of 17 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2501.05502.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.05502 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:18:31.269440Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

verified exact0
verified fuzzy14
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation beb7de16-357f-45c6-9707-5c17eb9aee21 · outbound

This paper cites Persistent entropy for separating topo- logical features from noise in Vietoris-rips complexes.

Shrink the longest: improving latent space isotropy with symplicial geometry Persistent entropy for separating topo- logical features from noise in Vietoris-rips complexes

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.704296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8c393914-6a7b-434c-986b-8cc608a5d199 · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:32.569284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 228fd064-df49-466b-b8ba-51e182feaf61 · outbound

This paper cites J., & Downey, D.

Shrink the longest: improving latent space isotropy with symplicial geometry J., & Downey, D

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.556265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 950a1219-b9e6-42be-8732-650d14791914 · outbound

This paper cites BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding.

Shrink the longest: improving latent space isotropy with symplicial geometry BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.459283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2d00172d-553c-4b57-856e-226655ef12e1 · outbound

This paper cites On Isotropy Calibration of Transformer Models.

Shrink the longest: improving latent space isotropy with symplicial geometry On Isotropy Calibration of Transformer Models

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.363495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 103e4086-9ee9-42a2-b65a-52800c1c9cc8 · outbound

This paper cites How Contextual are Contextualized Word Representations? Com- paring the Geometry of BERT, ELMo, and GPT-2 Embeddings.

Shrink the longest: improving latent space isotropy with symplicial geometry How Contextual are Contextualized Word Representations? Com- paring the Geometry of BERT, ELMo, and GPT-2 Embeddings

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.349851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 96fc77ba-5e56-4c4f-8468-60368e3918bb · outbound

This paper cites Representation Degenera- tion Problem in Training Natural Language Generation Models.

Shrink the longest: improving latent space isotropy with symplicial geometry Representation Degenera- tion Problem in Training Natural Language Generation Models

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.239106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0f2ce34a-f309-49c5-b457-0c6d7b381283 · outbound

This paper cites Anisotropy Is Inherent to Self- Attention in Transformers.

Shrink the longest: improving latent space isotropy with symplicial geometry Anisotropy Is Inherent to Self- Attention in Transformers

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.151889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 3dbe009b-1a1c-4d38-b97e-cd2e490d647d · outbound

This paper cites WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach.

Shrink the longest: improving latent space isotropy with symplicial geometry WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.137277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 30fd4d0c-f297-4622-8d23-3b21027097ff · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Shrink the longest: improving latent space isotropy with symplicial geometry Adam: A Method for Stochastic Optimization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T21:18:31.058598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4299e567-e708-4521-8b50-444de612b6a8 · outbound

This paper cites A Framework for Differential Calculus on Persistence Barcodes.

Shrink the longest: improving latent space isotropy with symplicial geometry A Framework for Differential Calculus on Persistence Barcodes

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.089372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c79475e6-efeb-4cef-834b-f9bca6ef423d · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:32.015802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2d742bb0-165c-4dd8-8b00-49e09bfc58c1 · outbound

This paper cites G., Cao, R., Zheng, J., Ren, J., & Gao, L.

Shrink the longest: improving latent space isotropy with symplicial geometry G., Cao, R., Zheng, J., Ren, J., & Gao, L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:32.001750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2c7faab6-7f8d-4d81-a0a9-a77d2ca9f937 · outbound

This paper cites RoBERTa: A Robustly Optimized BERT Pretraining Approach.

Shrink the longest: improving latent space isotropy with symplicial geometry RoBERTa: A Robustly Optimized BERT Pretraining Approach

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T21:18:31.075021Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0056332b-1701-48a4-b888-8eba8fd3889e · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.911752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 546ee7f4-d327-4d35-8e7d-c9e13d069494 · outbound

This paper cites (2017) Using the Output Embedding to Improve Language Mod- els In Proc.

Shrink the longest: improving latent space isotropy with symplicial geometry (2017) Using the Output Embedding to Improve Language Mod- els In Proc

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:31.804616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 42e82e29-4426-402d-9a0f-843c5defd4a6 · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.662416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4fd009ff-f05c-47b2-987e-e4aed7e276f2 · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.649549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f8e28349-2cd6-41be-8d18-02b8e692c8c0 · outbound

This paper cites Learning topology-preserving data representations.

Shrink the longest: improving latent space isotropy with symplicial geometry Learning topology-preserving data representations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:31.604207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e75278b4-c193-4c2d-bbbc-358fa3ea8814 · outbound

This paper cites NN., Kaiser, L., & Polosukhin, I.

Shrink the longest: improving latent space isotropy with symplicial geometry NN., Kaiser, L., & Polosukhin, I

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:31.505789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 396d9f4c-4d10-4e5b-978d-a7659909bfc7 · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.492436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c4608bfd-0503-48d5-a510-107d1d14c689 · outbound

This paper cites Improving Neural Language Generation with Spectrum Control.

Shrink the longest: improving latent space isotropy with symplicial geometry Improving Neural Language Generation with Spectrum Control

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:18:31.478897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 652209ac-52ab-4fcc-a2f1-8bcb598ebe22 · outbound

This paper cites Understanding and Improving Layer Normalization.

Shrink the longest: improving latent space isotropy with symplicial geometry Understanding and Improving Layer Normalization

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T21:18:31.260191Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebb6ba0a-9140-4f14-a4a2-dac047123976 · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.403415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9ddce372-544a-4429-81bc-4e4cfdc90a0a · outbound

This paper cites an unresolved cited work.

Shrink the longest: improving latent space isotropy with symplicial geometry Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:18:31.391052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.