Paper Citation Record · LEDGER

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model

As of 10 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2507.04206.

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

pith.paper-citation-record.v1
2507.04206 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:59:06.021532Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T08:04:06.432613Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy7
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4cf05d37-47c2-4ac6-9b1c-93477e120c7e · outbound

This paper cites MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T19:59:05.115154Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46ec7f39-826e-43f3-ad28-e178f90c2d64 · outbound

This paper cites Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T19:59:05.216957Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5b58d3f-becb-42e6-8659-1b47594e9bf5 · outbound

This paper cites FOCUS: First Order Concentrated Updating Scheme.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model FOCUS: First Order Concentrated Updating Scheme

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T19:59:05.396551Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52d8cbf4-a455-4428-b670-c19fcb8309d5 · outbound

This paper cites Neural Thermodynamic Laws for Large Language Model Training.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Neural Thermodynamic Laws for Large Language Model Training

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T19:59:05.518604Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cff97b3-c0e2-4bb3-9cb2-190188754944 · outbound

This paper cites Nonequilibrium thermodynamics of the markovian mpemba effect and its inverse.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Nonequilibrium thermodynamics of the markovian mpemba effect and its inverse

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:07.184869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e5b96d5b-d2a8-448f-b998-e1d83a34acaa · outbound

This paper cites Mpemba index and anomalous relaxation.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Mpemba index and anomalous relaxation

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:07.093283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c7c9f9b5-f3a5-4cc0-8977-b2f191fee7c4 · outbound

This paper cites Speedups in nonequilibrium thermal relaxation: Mpemba and related effects.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Speedups in nonequilibrium thermal relaxation: Mpemba and related effects

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T19:59:05.755041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7123ae6c-5701-4eb4-9fc2-dad18be8ad8e · outbound

This paper cites Precooling strategy allows exponentially faster heating.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Precooling strategy allows exponentially faster heating

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:06.945544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation eaf1d537-f2e9-41ce-9000-fcb7351cf080 · outbound

This paper cites Shortcuts of freely relaxing systems using equilibrium physical observables.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Shortcuts of freely relaxing systems using equilibrium physical observables

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:06.817123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation af8d4fb4-6ceb-48bc-9cd6-5e16548c12ca · outbound

This paper cites Stochastic gradient descent introduces an effective landscape-dependent regularization favoring flat solutions.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Stochastic gradient descent introduces an effective landscape-dependent regularization favoring flat solutions

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:06.714162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e64ce85d-9390-418e-9228-5598d797d7cc · outbound

This paper cites Analyzing & reducing the need for learning rate warmup in gpt training.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model Analyzing & reducing the need for learning rate warmup in gpt training

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:06.545824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 15a7b24f-10fe-45ba-b736-8e028fc9f911 · outbound

This paper cites temperature.

Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model temperature

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:59:06.294133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 5519170b-8034-4edf-8eb0-c05edc37795f · inbound

WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training cites this paper.

WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training Mpemba Effect in Large-Language Model Training Dynamics: A Minimal Analysis of the Valley-River model

Reference 59

Resolution: unresolved; no resolver link, observed 2026-07-14T08:04:06.432613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.