Paper Citation Record · LEDGER

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models

As of 18 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2506.16550.

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

pith.paper-citation-record.v1
2506.16550 v3

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:31:29.504053Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T22:40:30.304801Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T22:40:30.714811Z

Reference resolution

29 of 29 outbound references displayed

verified exact1
verified fuzzy16
unresolved10
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 32a610e8-a554-448e-8c07-b04a45fbb174 · outbound

This paper cites Large Language Models: A Deep Dive: Bridging Theory and Practice.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Large Language Models: A Deep Dive: Bridging Theory and Practice

Reference 1

Resolution: verified exact; doi, observed 2026-08-15T19:31:29.536918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c4a62795-b74c-40a4-a374-3b6b0e1030fb · outbound

This paper cites Attention is all you need.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Attention is all you need

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.813292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 35542756-eb1f-4814-b9de-602dbe254030 · outbound

This paper cites Lan- guage models are unsupervised multitask learners.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Lan- guage models are unsupervised multitask learners

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.806869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5bfc5869-fd2a-4e94-a878-5cf9f582710b · outbound

This paper cites Deep evidential regres- sion.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Deep evidential regres- sion

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.799542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2b48a120-8702-4396-a3f5-82040da8ef77 · outbound

This paper cites Bayesian attention modules.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Bayesian attention modules

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.793018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b8404583-e1e7-43e0-af7c-82b69ffe893c · outbound

This paper cites Probabilistic transformer: A probabilistic dependency model for contextual word representation.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Probabilistic transformer: A probabilistic dependency model for contextual word representation

Reference 6

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T19:31:29.785411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5ab0a8a-4bfd-4810-b5c3-3c1b46efc3d2 · outbound

This paper cites Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Uncertainty-Aware Out-of-Distribution Detection with Gaussian Processes

Reference 7

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Source-reported events for the cited work

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Observation e47ca81b-fa8d-4025-8b97-36b0fdf30892 · outbound

This paper cites Detecting hallucinations in large language models using semantic entropy.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Detecting hallucinations in large language models using semantic entropy

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.451528Z

Source-reported events for the cited work

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Observation a3bb92fa-57b3-4246-aa94-9be269cd6207 · outbound

This paper cites Foundations of non-commutative probability theory.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Foundations of non-commutative probability theory

Reference 9

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bb505ff5-1796-4b96-9506-d763326e5042 · outbound

This paper cites Limit laws for random matrices and free products.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Limit laws for random matrices and free products

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.778446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation eea1b7e3-ee58-4f20-a5b3-5750967957c4 · outbound

This paper cites Nonlinear random matrix theory for deep learning.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Nonlinear random matrix theory for deep learning

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.771662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 67e9c86e-41e5-43a4-9a0e-83e6a1c5fa14 · outbound

This paper cites The singular values and vectors of low rank perturbations of large rectangular random matrices.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models The singular values and vectors of low rank perturbations of large rectangular random matrices

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.765147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 94ccc7dd-3a2d-4c8e-a3ed-4fd3b61efdf2 · outbound

This paper cites Free probability for predicting the per- formance of feed-forward fully connected neural networks.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Free probability for predicting the per- formance of feed-forward fully connected neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.757944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5d5a725a-a8b7-4347-ad03-c8844199c45e · outbound

This paper cites Anderson, Alice Guionnet, and Ofer Zeitouni.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Anderson, Alice Guionnet, and Ofer Zeitouni

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.750817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e5700173-74ae-442e-943b-65384d5b113c · outbound

This paper cites Empirical margin distributions and bounding the generalization error of combined classifiers.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Empirical margin distributions and bounding the generalization error of combined classifiers

Reference 15

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55c3e825-29a7-4e69-8318-7934e1b596b1 · outbound

This paper cites Computing nonvacuous generalization bounds for deep (stochastic) neural networks with many more parameters than training data.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Computing nonvacuous generalization bounds for deep (stochastic) neural networks with many more parameters than training data

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.743667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 026616c2-d0a3-4157-b512-33a7d272602d · outbound

This paper cites A Primer on the Inner Workings of Transformer-based Language Models.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models A Primer on the Inner Workings of Transformer-based Language Models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.473545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf78382a-27c1-4299-945d-04667e7fdde3 · outbound

This paper cites Large language models are zero-shot time series forecasters.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Large language models are zero-shot time series forecasters

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.736506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9a2b43bb-4dbf-4830-b097-2cce0526a068 · outbound

This paper cites Language through a prism: A spectral approach for multiscale language representations.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Language through a prism: A spectral approach for multiscale language representations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.729152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c1eb5e1b-626a-4bc2-a679-f5dc65c453f5 · outbound

This paper cites Mind the Gap: a Spectral Analysis of Rank Collapse and Signal Propagation in Attention Layers.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Mind the Gap: a Spectral Analysis of Rank Collapse and Signal Propagation in Attention Layers

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.480841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3aad3d7-a037-4afd-aebf-7b80fc86866a · outbound

This paper cites Detecting subtle differences between human and model languages using spectrum of relative likelihood.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Detecting subtle differences between human and model languages using spectrum of relative likelihood

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.484401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 723e0bee-bd06-40f0-a356-442a790be142 · outbound

This paper cites Fourier Head: Helping Large Language Models Learn Complex Probability Distributions.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Fourier Head: Helping Large Language Models Learn Complex Probability Distributions

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.486963Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afb2093b-0134-4f42-b062-7ab5350ddacd · outbound

This paper cites Proba- bilistic predictions of people perusing: Evaluating metrics of language model performance for psycholinguistic modeling.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Proba- bilistic predictions of people perusing: Evaluating metrics of language model performance for psycholinguistic modeling

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T19:31:29.489698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f38b588-9bbb-4beb-9a88-114cca5e8c2f · outbound

This paper cites Lectures on the Combinatorics of Free Probability.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Lectures on the Combinatorics of Free Probability

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.721614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8faa947c-7534-4fa9-b625-aee45fc44211 · outbound

This paper cites an unresolved cited work.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:31:29.713972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f09bd167-c6fd-4a69-8c7e-31cd5c999c06 · outbound

This paper cites an unresolved cited work.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:31:29.706304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ac4c621e-b3f9-4a43-a85d-22b2c6e10316 · outbound

This paper cites Free probability and non-crossing partitions.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Free probability and non-crossing partitions

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.698721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 89dff730-f9ee-4143-afe0-950195623590 · outbound

This paper cites Convergence rate of expected spectral distributions of large random matrices.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Convergence rate of expected spectral distributions of large random matrices

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.691013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5de471d7-c271-429f-8eee-974e23a5bb58 · outbound

This paper cites Methodologies in spectral estimation and convergence rates of spectral distribu- tions of large-dimensional random matrices—a review.

A Free Probabilistic Framework for Analyzing the Transformer-based Language Models Methodologies in spectral estimation and convergence rates of spectral distribu- tions of large-dimensional random matrices—a review

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:31:29.683361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 4a6ca5dc-8601-4ce5-929a-a02f1f39227e · inbound

Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift cites this paper.

Zero-Direction Probing: A Linear-Algebraic Framework for Deep Analysis of Large-Language-Model Drift A Free Probabilistic Framework for Analyzing the Transformer-based Language Models

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:40:30.790965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.