Paper Citation Record · LEDGER

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning

As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2506.05447.

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

pith.paper-citation-record.v1
2506.05447 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:31:20.550988Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:02:05.516512Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

43 of 43 outbound references displayed

verified exact3
verified fuzzy2
unresolved38
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation a381240c-4449-458e-9476-d0579b6f0a85 · outbound

This paper cites online" 'onlinestring :=.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning online" 'onlinestring :=

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T10:31:20.306883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 673f7902-411a-4e2f-bc9f-3480e903d649 · outbound

This paper cites write newline.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning write newline

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T10:31:20.314438Z

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Observation 187ee80c-5b8b-4d2e-bde7-363c5159e6eb · outbound

This paper cites Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T10:31:20.328935Z

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Observation 94b2fce2-c6d0-47c3-86a8-d3e2020a40b2 · outbound

This paper cites Atanasov, Jacob A.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Atanasov, Jacob A

Reference 4

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Observation 28757c54-f468-4906-b66d-be7fa4b406f8 · outbound

This paper cites an unresolved cited work.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 5

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Observation 03619f5c-1633-405e-a256-803fcd2d4e81 · outbound

This paper cites an unresolved cited work.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 6

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Observation bfa26d7c-1cd2-4395-9cd4-0e91a68d634d · outbound

This paper cites Broken Neural Scaling Laws.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Broken Neural Scaling Laws

Reference 7

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Observation 6c24d1c1-a387-45a4-ab02-9f5023e092bc · outbound

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

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 8

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Observation f225e47c-d49a-40d2-8c6e-9d2916046295 · outbound

This paper cites Scaling Exponents Across Parameterizations and Optimizers.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Scaling Exponents Across Parameterizations and Optimizers

Reference 9

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Observation ab140c9e-642f-4dae-939a-209b848441b4 · outbound

This paper cites The Pile: An 800GB Dataset of Diverse Text for Language Modeling.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning The Pile: An 800GB Dataset of Diverse Text for Language Modeling

Reference 10

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Source-reported events for the cited work

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Observation 3bb8d72f-b197-4dc5-883b-01621b12d273 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 11

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Observation 2988fb8e-629f-48d4-ace9-b76f3659ff9c · outbound

This paper cites Why do small language models underperform? Studying Language Model Saturation via the Softmax Bottleneck.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Why do small language models underperform? Studying Language Model Saturation via the Softmax Bottleneck

Reference 12

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Observation 1027a3ea-4290-441e-9d5e-0e74972add43 · outbound

This paper cites OLMo: Accelerating the Science of Language Models.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning OLMo: Accelerating the Science of Language Models

Reference 13

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Observation c9652438-c0eb-450e-aaa4-e0fe3a553bd3 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Rae, and Laurent Sifre

Reference 14

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Observation 7fbdc2cd-c03f-4aed-8ad7-76703561d66d · outbound

This paper cites Learning Curve Theory.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Learning Curve Theory

Reference 15

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 16

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Observation 4de56d0a-b8f0-4b67-ba50-8e5e6a1e5294 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 17

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Observation 190826fb-ace0-4549-bb0a-34db1785d24c · outbound

This paper cites an unresolved cited work.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 18

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Source-reported events for the cited work

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Observation ffb6496d-3839-474e-ad3d-49ff68b8cb74 · outbound

This paper cites Scaling Laws for Neural Language Models.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Scaling Laws for Neural Language Models

Reference 19

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 20

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Observation cb665d93-206a-4ac8-b17e-ec2bffb28845 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 21

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 22

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Observation 8e99f216-4cb2-4585-a3ea-18661cbc1fa2 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 23

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Observation b5d9cf26-1b55-47ec-b814-6e278a268e92 · outbound

This paper cites Paloma: A Benchmark for Evaluating Language Model Fit.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Paloma: A Benchmark for Evaluating Language Model Fit

Reference 24

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Observation 64bb2aec-abbc-4d16-aafe-645de5f60d18 · outbound

This paper cites When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale

Reference 25

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 26

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Observation 736de624-1040-4b06-a353-90424ceda43e · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 27

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Observation f894a601-7ebb-4e98-9e4d-ad84dd5733de · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning In-context Learning and Induction Heads

Reference 28

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This paper cites The AdEMAMix Optimizer: Better, Faster, Older.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning The AdEMAMix Optimizer: Better, Faster, Older

Reference 29

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 30

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Observation 77df1296-b4a4-4f56-962b-3c7e4e1842d9 · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 31

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Observation 07729239-587b-4a1a-ae67-0d987caa8ced · outbound

This paper cites Mixture-of-Depths: Dynamically allocating compute in transformer-based language models.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Mixture-of-Depths: Dynamically allocating compute in transformer-based language models

Reference 32

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Outliers with Opposing Signals Have an Outsized Effect on Neural Network Optimization

Reference 33

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Observation 6162da8a-0c80-4923-bf02-e979cd7c508b · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 34

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 35

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Observation e74392e0-56ae-4ef1-9ee2-b5fde6cddedc · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Unresolved cited work

Reference 36

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Gemma 2: Improving Open Language Models at a Practical Size

Reference 37

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Observation 8b1f55d0-2325-4943-aadd-c42eb35e4330 · outbound

This paper cites Scaling Law with Learning Rate Annealing.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Scaling Law with Learning Rate Annealing

Reference 38

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning The Shape of Learning Curves: a Review

Reference 39

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

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Understanding Warmup-Stable-Decay Learning Rates: A River Valley Loss Landscape Perspective

Reference 40

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Observation a13dbdef-d570-432a-b52a-5c9b2282293a · outbound

This paper cites Data-Dependence of Plateau Phenomenon in Learning with Neural Network --- Statistical Mechanical Analysis.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Data-Dependence of Plateau Phenomenon in Learning with Neural Network --- Statistical Mechanical Analysis

Reference 41

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Source-reported events for the cited work

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Observation 380618aa-20e5-4ba1-9f0c-1ad070b497d9 · outbound

This paper cites Opacus: User-Friendly Differential Privacy Library in PyTorch.

Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Opacus: User-Friendly Differential Privacy Library in PyTorch

Reference 42

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Observation 62f9b0f3-c2ac-4530-842f-51ca8ffb82cf · outbound

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Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning Gradient Surgery for Multi-Task Learning

Reference 43

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Pith citing papers

Observation 21d0767b-bbd7-44ae-b12e-a8508b3d6055 · inbound

Bridging Compute- and Data-Optimal Pretraining cites this paper.

Bridging Compute- and Data-Optimal Pretraining Training Dynamics Underlying Language Model Scaling Laws: Loss Deceleration and Zero-Sum Learning

Reference 80

Resolution: verified exact; local_arxiv, observed 2026-08-01T03:08:36.328547Z

Source-reported events for the cited work

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