Paper Citation Record · LEDGER

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

As of 7 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 2 inbound Pith citation observations for arXiv:2507.21040.

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

pith.paper-citation-record.v1
2507.21040 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T13:07:29.303917Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-11T02:17:32.226166Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T05:00:55.095597Z

Reference resolution

15 of 15 outbound references displayed

verified exact2
verified fuzzy2
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d13fb353-c5b6-4077-a4d3-87ee04128d36 · outbound

This paper cites Learning to Optimize: A Primer and A Benchmark.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Learning to Optimize: A Primer and A Benchmark

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T13:07:29.464617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation fcfc5fc1-28d0-4688-ba88-61363ff35730 · outbound

This paper cites Exploring Simple Siamese Representation Learning.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Exploring Simple Siamese Representation Learning

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.265680Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ee8b431-5ba9-42d4-9ab3-0aa957581e41 · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.275496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bffb6a7-8bf1-40e1-855b-a02b8819cdc3 · outbound

This paper cites Semi-Supervised Classification with Graph Convolutional Networks.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Semi-Supervised Classification with Graph Convolutional Networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.278848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34bc18ae-2cec-4d82-ac70-d109f085d9a5 · outbound

This paper cites Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:07:29.505432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4d96c6ce-b423-40ce-aeb0-9104158f4ac2 · outbound

This paper cites Yaodong Yu, Sam Buchanan, Druv Pai, Tianzhe Chu, Ziyang Wu, Shengbang Tong, Benjamin D.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Yaodong Yu, Sam Buchanan, Druv Pai, Tianzhe Chu, Ziyang Wu, Shengbang Tong, Benjamin D

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:07:29.495844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4120858b-98ee-4243-908f-6de4db8209d7 · outbound

This paper cites White-Box Transformers via Sparse Rate Reduction.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements White-Box Transformers via Sparse Rate Reduction

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-06T13:07:29.353702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation abc32348-9235-4c1e-b283-593083bc8a28 · outbound

This paper cites doi: 10.1007/s11263-015-0816-y.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements doi: 10.1007/s11263-015-0816-y

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.289481Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79e7297d-e4ff-4bf8-95eb-2d0f1d036307 · outbound

This paper cites A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.269047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfaf3add-e18b-4950-b00e-f76c295d88d6 · outbound

This paper cites Graph Attention Networks.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Graph Attention Networks

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.296567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aeb1c040-23ce-435d-a682-47abf07164f2 · outbound

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

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.272423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 364f4d71-9a4b-4fe3-9654-b3c6e40ebc5c · outbound

This paper cites wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.254741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 816f2f11-3cd8-486c-b101-adb0c9f36515 · outbound

This paper cites Transformer Interpretability Beyond Attention Visualization.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Transformer Interpretability Beyond Attention Visualization

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.258665Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4c4f451-e873-4976-b6ef-8c7b968a98f4 · outbound

This paper cites Dimensionality Reduction as Probabilistic Inference.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Dimensionality Reduction as Probabilistic Inference

Reference 2023

Resolution: verified exact; local_arxiv, observed 2026-08-06T13:07:29.379797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 36d539bb-f6ed-4105-90ca-33f9215d64f3 · outbound

This paper cites Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE.

Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T13:07:29.282080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation cabe0242-351e-46ee-8f59-8b5a6bfc806d · inbound

Uncovering and Shaping the Latent Representation of 3D Scene Topology in Vision-Language Models cites this paper.

Uncovering and Shaping the Latent Representation of 3D Scene Topology in Vision-Language Models Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:00:55.098204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation fb788890-7832-4c3a-80ba-a58c3112ee3c · inbound

Revisiting Transformer Layer Parameterization Through Causal Energy Minimization cites this paper.

Revisiting Transformer Layer Parameterization Through Causal Energy Minimization Transformers as Unrolled Inference in Probabilistic Laplacian Eigenmaps: An Interpretation and Potential Improvements

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:45:59.059692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.