Paper Citation Record · LEDGER

Neural Thermodynamic Laws for Large Language Model Training

As of 15 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2505.10559.

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

pith.paper-citation-record.v1
2505.10559 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:16:10.422836Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:59:05.518604Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-16T07:00:43.273983Z

Reference resolution

34 of 34 outbound references displayed

verified exact1
verified fuzzy13
unresolved19
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d212e579-4736-4103-b4d3-8542c19ba52b · outbound

This paper cites Bayesian learning via stochastic gradient langevin dynamics.

Neural Thermodynamic Laws for Large Language Model Training Bayesian learning via stochastic gradient langevin dynamics

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.276576Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a950008-b592-48e9-b839-c497e6d402ee · outbound

This paper cites Thermodynamics-inspired explanations of artificial intelli- gence.

Neural Thermodynamic Laws for Large Language Model Training Thermodynamics-inspired explanations of artificial intelli- gence

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.854755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eb823f02-bcc2-435c-b0db-c5cca54d8faa · outbound

This paper cites Statistical mechanics of learning.

Neural Thermodynamic Laws for Large Language Model Training Statistical mechanics of learning

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.841719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4b77da36-8744-449b-9ffa-0d35359d4f31 · outbound

This paper cites Statistical mechanics of deep learning.

Neural Thermodynamic Laws for Large Language Model Training Statistical mechanics of deep learning

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.829349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c0f021a9-d8f0-4eab-8225-95664e1e90bc · outbound

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

Neural Thermodynamic Laws for Large Language Model Training Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.293933Z

Source-reported events for the cited work

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Observation 11e2a7b6-6bce-48d9-8fae-5acc1ef8208e · outbound

This paper cites How noise affects the Hessian spectrum in overparameterized neural networks.

Neural Thermodynamic Laws for Large Language Model Training How noise affects the Hessian spectrum in overparameterized neural networks

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.299041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5705197c-17c9-408b-b4a5-fb1d4f50b76b · outbound

This paper cites FOCUS: First Order Concentrated Updating Scheme.

Neural Thermodynamic Laws for Large Language Model Training FOCUS: First Order Concentrated Updating Scheme

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.303679Z

Source-reported events for the cited work

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Observation 3c1eea92-38df-4956-89e6-2fc88a336a71 · outbound

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

Neural Thermodynamic Laws for Large Language Model Training MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.308075Z

Source-reported events for the cited work

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Observation be573704-5082-4bfe-8460-94297b5b5030 · outbound

This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Neural Thermodynamic Laws for Large Language Model Training Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.312287Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a58f5b92-0d8c-46dd-a841-f45d69571120 · outbound

This paper cites Scaling laws and compute-optimal training beyond fixed training durations.

Neural Thermodynamic Laws for Large Language Model Training Scaling laws and compute-optimal training beyond fixed training durations

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.817150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 54d121ff-1a49-4fc7-bda8-ba7003fa8064 · outbound

This paper cites an unresolved cited work.

Neural Thermodynamic Laws for Large Language Model Training Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.320808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b9dbac8-217c-4ea7-8ed3-ea12abddc571 · outbound

This paper cites A multi-power law for loss curve prediction across learning rate schedules.

Neural Thermodynamic Laws for Large Language Model Training A multi-power law for loss curve prediction across learning rate schedules

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.795287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation adb2480a-b973-45ce-8c44-4d3486f0c5e2 · outbound

This paper cites modded-nanogpt.

Neural Thermodynamic Laws for Large Language Model Training modded-nanogpt

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.781648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e10bec04-7f0f-4a15-9eab-f4feff0a122d · outbound

This paper cites Implicit Gradient Regularization.

Neural Thermodynamic Laws for Large Language Model Training Implicit Gradient Regularization

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.333148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 975e5bbb-1674-458d-926f-1134ba17a91b · outbound

This paper cites The limiting dynamics of sgd: Modified loss, phase-space oscillations, and anomalous diffusion.

Neural Thermodynamic Laws for Large Language Model Training The limiting dynamics of sgd: Modified loss, phase-space oscillations, and anomalous diffusion

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.770762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3fa17f3c-0219-4868-9251-f6ded64f650d · outbound

This paper cites Stochastic collapse: How gra- dient noise attracts sgd dynamics towards simpler subnetworks.Advances in Neural Information Processing Systems, 36:35027–35063, 2023.

Neural Thermodynamic Laws for Large Language Model Training Stochastic collapse: How gra- dient noise attracts sgd dynamics towards simpler subnetworks.Advances in Neural Information Processing Systems, 36:35027–35063, 2023

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.757806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 710f4bf1-39bc-443b-93ce-34b437911117 · outbound

This paper cites Stochastic gradient descent as approximate bayesian inference.

Neural Thermodynamic Laws for Large Language Model Training Stochastic gradient descent as approximate bayesian inference

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.744777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3e756cd0-1ae7-49aa-b88d-f3b250cec91c · outbound

This paper cites A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima.

Neural Thermodynamic Laws for Large Language Model Training A Diffusion Theory For Deep Learning Dynamics: Stochastic Gradient Descent Exponentially Favors Flat Minima

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.351351Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d89849d2-59be-42e7-80ce-2cfc42587224 · outbound

This paper cites Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate.

Neural Thermodynamic Laws for Large Language Model Training Direction Matters: On the Implicit Bias of Stochastic Gradient Descent with Moderate Learning Rate

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-15T21:16:10.538298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation dbec16f3-8046-48dd-9e77-15f4b5af7ac0 · outbound

This paper cites Gradient Descent Maximizes the Margin of Homogeneous Neural Networks.

Neural Thermodynamic Laws for Large Language Model Training Gradient Descent Maximizes the Margin of Homogeneous Neural Networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.360638Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d8dc6a4-c009-475a-a7e6-526b7fd195d4 · outbound

This paper cites The implicit bias for adaptive optimization algorithms on homogeneous neural networks.

Neural Thermodynamic Laws for Large Language Model Training The implicit bias for adaptive optimization algorithms on homogeneous neural networks

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.732032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5bf4fd29-7f62-4325-bc6a-6971e63bb0e1 · outbound

This paper cites An overview of condensation phenomenon in deep learning.

Neural Thermodynamic Laws for Large Language Model Training An overview of condensation phenomenon in deep learning

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.369421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d30cc1f6-f2d3-4bec-8fef-f587ab01b983 · outbound

This paper cites Loss surfaces, mode connectivity, and fast ensembling of dnns.

Neural Thermodynamic Laws for Large Language Model Training Loss surfaces, mode connectivity, and fast ensembling of dnns

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.373316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e6fee98e-5454-4dfd-98ee-63807f5f9ac9 · outbound

This paper cites Linear mode connectivity and the lottery ticket hypothesis.

Neural Thermodynamic Laws for Large Language Model Training Linear mode connectivity and the lottery ticket hypothesis

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.378385Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14003317-7996-4b1c-aa40-4bcd29f84b95 · outbound

This paper cites SGDR: Stochastic Gradient Descent with Warm Restarts.

Neural Thermodynamic Laws for Large Language Model Training SGDR: Stochastic Gradient Descent with Warm Restarts

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.382408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9c19445-75c5-4c60-b43b-ed7169e8d14d · outbound

This paper cites Cyclical learning rates for training neural networks.

Neural Thermodynamic Laws for Large Language Model Training Cyclical learning rates for training neural networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.703872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation cae9e569-d9fb-44df-8f14-d605328e46c4 · outbound

This paper cites Attention is all you need.

Neural Thermodynamic Laws for Large Language Model Training Attention is all you need

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.391341Z

Source-reported events for the cited work

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Observation 389cbea2-8c0b-46ca-a545-57a66aebce39 · outbound

This paper cites The information bottleneck method.

Neural Thermodynamic Laws for Large Language Model Training The information bottleneck method

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.395835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf45d999-1565-418a-abed-41956b681423 · outbound

This paper cites Entropy-sgd: Biasing gradient descent into wide valleys.

Neural Thermodynamic Laws for Large Language Model Training Entropy-sgd: Biasing gradient descent into wide valleys

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.681046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0221e432-621f-4859-9a46-591124545197 · outbound

This paper cites A learning algorithm for boltzmann machines.

Neural Thermodynamic Laws for Large Language Model Training A learning algorithm for boltzmann machines

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:16:10.667575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 98bdeea6-d6e2-4d6d-96de-4eb885ceffae · outbound

This paper cites Hopfield Networks is All You Need.

Neural Thermodynamic Laws for Large Language Model Training Hopfield Networks is All You Need

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.410063Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c2a8453-6e38-4eb4-804f-834e09498e3a · outbound

This paper cites Deep unsuper- vised learning using nonequilibrium thermodynamics.

Neural Thermodynamic Laws for Large Language Model Training Deep unsuper- vised learning using nonequilibrium thermodynamics

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.414092Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30cca370-659f-4db5-9d77-e0379a008b63 · outbound

This paper cites Score-Based Generative Modeling through Stochastic Differential Equations.

Neural Thermodynamic Laws for Large Language Model Training Score-Based Generative Modeling through Stochastic Differential Equations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T21:16:10.417979Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8430a16a-5d30-48c7-a45d-43a0ab8ab73c · outbound

This paper cites edge of stability.

Neural Thermodynamic Laws for Large Language Model Training edge of stability

Reference 34

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T21:16:10.647787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

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

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

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

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Unavailable: canonical work link unavailable.

Observation b88f9cc7-7416-4d8d-b8e8-91e37a2868d3 · inbound

Falcon-H1: A Family of Hybrid-Head Language Models Redefining Efficiency and Performance cites this paper.

Falcon-H1: A Family of Hybrid-Head Language Models Redefining Efficiency and Performance Neural Thermodynamic Laws for Large Language Model Training

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-06T11:44:05.058346Z

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Unavailable: canonical work link unavailable.

Observation 4617356d-24ea-480a-be5f-e57e497bff5e · inbound

Theory of Optimal Learning Rate Schedules and Scaling Laws for a Random Feature Model cites this paper.

Theory of Optimal Learning Rate Schedules and Scaling Laws for a Random Feature Model Neural Thermodynamic Laws for Large Language Model Training

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-16T07:00:43.275595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.