Paper Citation Record · LEDGER

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought

As of 8 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 1 inbound Pith citation observation for arXiv:2509.04027.

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

pith.paper-citation-record.v1
2509.04027 v4

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T10:31:37.980968Z

measured 54 of 54 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-18T00:02:24.352947Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T00:02:25.420148Z

Reference resolution

53 of 53 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 653d22f5-53a2-4c5d-bd2d-c921f972abc5 · outbound

This paper cites write newline.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.734744Z

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Observation e0ece3d5-b6d2-4ecf-b2e1-086f710063dc · outbound

This paper cites Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.745578Z

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Observation 3a99df52-5d06-4985-9c17-1f152740cc5b · outbound

This paper cites Language models are few-shot learners.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Language models are few-shot learners

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.751394Z

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Observation 7eadecf7-832c-4bab-b6de-39a6d38e2ae3 · outbound

This paper cites Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models

Reference 4

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Observation 1d8dd784-010b-452d-ac80-2bda6dbdfb2a · outbound

This paper cites Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.759551Z

Source-reported events for the cited work

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Observation 0f1e3433-c858-49cf-852f-f44ed4fbd56d · outbound

This paper cites An Empirical Study on Eliciting and Improving R1-like Reasoning Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought An Empirical Study on Eliciting and Improving R1-like Reasoning Models

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.763822Z

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Observation 0469f239-9c70-4708-bb4d-0844b17ddcdc · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Training Verifiers to Solve Math Word Problems

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.768029Z

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Observation 022a69a8-5b54-430b-bcf8-f3e022ec8531 · outbound

This paper cites DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 8

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Observation 8b0b2129-bb5a-4ea7-92e5-788a2ffe8717 · outbound

This paper cites Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.775535Z

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Observation fa980435-17e7-40da-a5ea-0905e43f7941 · outbound

This paper cites Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Rethinking External Slow-Thinking: From Snowball Errors to Probability of Correct Reasoning

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.779402Z

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Observation 9bec0efd-2831-4438-9c99-49d7773451f0 · outbound

This paper cites On distances in uniformly random networks.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought On distances in uniformly random networks

Reference 11

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Observation 758aa007-4123-474a-a24a-2b735e7b363f · outbound

This paper cites Measuring Mathematical Problem Solving With the MATH Dataset.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Measuring Mathematical Problem Solving With the MATH Dataset

Reference 12

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Observation 6dd9e2e9-cabd-40dd-9a55-44c83f72e0ef · outbound

This paper cites REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization

Reference 13

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Observation 295b6ad4-dade-4ed1-8e1a-2143e6727bdb · outbound

This paper cites Survey of hallucination in natural language generation.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Survey of hallucination in natural language generation

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.525058Z

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Observation 0a8439d8-5404-4d31-926f-f181fcc433c4 · outbound

This paper cites Enhancing LLM Reasoning with Reward-guided Tree Search.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Enhancing LLM Reasoning with Reward-guided Tree Search

Reference 15

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Observation ada20603-706a-4c55-be5c-3159391cb56d · outbound

This paper cites On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima

Reference 16

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Observation 0270234c-1444-4e64-a0a9-8a94c501a99b · outbound

This paper cites Decoupled Weight Decay Regularization.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Decoupled Weight Decay Regularization

Reference 17

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Observation cc6366ea-b12b-4c5c-807e-a77ef077744a · outbound

This paper cites Some pac-bayesian theorems.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Some pac-bayesian theorems

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.514186Z

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Observation a7d29796-62ed-4555-b21d-81aadb7bb521 · outbound

This paper cites The Llama 3 Herd of Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought The Llama 3 Herd of Models

Reference 19

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Observation 99b43959-d9de-4c31-8bb8-631a3602bb7c · outbound

This paper cites Nearest neighbor distance in three-dimensional space.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Nearest neighbor distance in three-dimensional space

Reference 20

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Observation 18994fd2-58ee-43b0-8eaf-e72069020449 · outbound

This paper cites Learning to reason with llms, 2024.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Learning to reason with llms, 2024

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.490571Z

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Observation a947c17b-463c-415e-bf3c-2bae4b76115f · outbound

This paper cites Introducing openai o3 and o4-mini, 2025.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Introducing openai o3 and o4-mini, 2025

Reference 22

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Observation a54cd083-fb2f-4c11-8b4a-c49510dbb830 · outbound

This paper cites Qwq: Reflect deeply on the boundaries of the unknown, November 2024.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Qwq: Reflect deeply on the boundaries of the unknown, November 2024

Reference 23

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Observation 6e0006be-46fd-4878-b922-e522d5a14d00 · outbound

This paper cites Qwen2.5 Technical Report.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Qwen2.5 Technical Report

Reference 24

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Observation f30b8c27-7c1d-4049-a9f9-9ec2465ce29f · outbound

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Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Qwen3 Technical Report

Reference 25

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Observation ed7d4204-0de5-4b55-ae19-7960911b9773 · outbound

This paper cites Benchmarking prompt sensitivity in large language models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Benchmarking prompt sensitivity in large language models

Reference 26

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Observation 2571ea31-6b53-4441-9afc-b0e244fadcb5 · outbound

This paper cites How much does your data exploration overfit? controlling bias via information usage.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought How much does your data exploration overfit? controlling bias via information usage

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.438143Z

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Observation e3cad880-d189-4e67-bcf5-def90fd559b8 · outbound

This paper cites Proximal Policy Optimization Algorithms.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Proximal Policy Optimization Algorithms

Reference 28

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Observation c3121a39-00b2-46a5-a1ab-654f921f914f · outbound

This paper cites Scaling Test-Time Compute Without Verification or RL is Suboptimal.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Scaling Test-Time Compute Without Verification or RL is Suboptimal

Reference 29

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Observation 70d53b55-92e9-418f-8b2e-2d0617b2bff0 · outbound

This paper cites Spurious Rewards: Rethinking Training Signals in RLVR.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Spurious Rewards: Rethinking Training Signals in RLVR

Reference 30

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This paper cites DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Reference 31

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Observation a67f407a-8b36-4419-adf6-781640bcc753 · outbound

This paper cites A bayesian perspective on generalization and stochastic gradient descent.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought A bayesian perspective on generalization and stochastic gradient descent

Reference 32

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Observation 21dc2f48-eff6-498b-8b74-69cc9287bd3b · outbound

This paper cites Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Reference 33

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Observation b671102f-5d38-4cf1-801e-336e7c3bd280 · outbound

This paper cites Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models

Reference 34

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Observation b5bd238d-19cf-4f4f-afa0-29c1ecc4ad53 · outbound

This paper cites Understanding Chain-of-Thought in LLMs through Information Theory.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Understanding Chain-of-Thought in LLMs through Information Theory

Reference 35

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Observation fcb68915-e810-4f07-9ce4-755df89ed3d5 · outbound

This paper cites Alphazero-like tree-search can guide large language model decoding and training.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Alphazero-like tree-search can guide large language model decoding and training

Reference 36

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Observation f9dfb13e-8c84-4749-abd2-807892557a2e · outbound

This paper cites Self-Consistency Improves Chain of Thought Reasoning in Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Self-Consistency Improves Chain of Thought Reasoning in Language Models

Reference 37

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Observation 4f90a21e-332b-47fe-8db8-77670c608173 · outbound

This paper cites Emergent Abilities of Large Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Emergent Abilities of Large Language Models

Reference 38

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Observation 5f0d9a22-a300-49fa-b531-53970135c7ae · outbound

This paper cites Chain-of-thought prompting elicits reasoning in large language models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Chain-of-thought prompting elicits reasoning in large language models

Reference 39

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Observation d155c5de-8c81-4195-a9f0-170c5792b7e6 · outbound

This paper cites Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models

Reference 40

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This paper cites Information-theoretic analysis of generalization capability of learning algorithms.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Information-theoretic analysis of generalization capability of learning algorithms

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.398678Z

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Observation f010506b-53ab-4da0-8a04-855bf8c5800b · outbound

This paper cites Tree of thoughts: Deliberate problem solving with large language models.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Tree of thoughts: Deliberate problem solving with large language models

Reference 42

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Observation 25fff4de-bd51-413e-97d0-775fd7de3d63 · outbound

This paper cites DAPO: An Open-Source LLM Reinforcement Learning System at Scale.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought DAPO: An Open-Source LLM Reinforcement Learning System at Scale

Reference 43

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Observation 5c9667f0-812e-4e67-8d41-0e8f7003c117 · outbound

This paper cites What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought What's Behind PPO's Collapse in Long-CoT? Value Optimization Holds the Secret

Reference 44

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Observation c7f1001c-2bab-4f60-8465-b46f3d0069de · outbound

This paper cites Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?

Reference 45

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Observation 97bdd282-cc34-4964-b295-0a99b8da6273 · outbound

This paper cites VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks

Reference 46

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Observation 1d10c2c0-d047-4c30-b3ad-a1a73d9121db · outbound

This paper cites Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-05T10:31:37.951774Z

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Observation 6174444d-a37b-45bc-95a6-2838c75b832c · outbound

This paper cites Rest-mcts*: Llm self-training via process reward guided tree search.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Rest-mcts*: Llm self-training via process reward guided tree search

Reference 48

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Observation cbe4cbfe-156e-46e5-874d-4a5c2542018f · outbound

This paper cites Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining

Reference 49

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Observation 238330f5-2f6a-4340-aa8c-b4321bac6f44 · outbound

This paper cites Prosa: Assessing and understanding the prompt sensitivity of llms.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Prosa: Assessing and understanding the prompt sensitivity of llms

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:31:38.367597Z

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This paper cites @esa (Ref.

Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought @esa (Ref

Reference 51

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Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Unresolved cited work

Reference 52

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Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought Unresolved cited work

Reference 53

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Pith citing papers

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A Survey of Reinforcement Learning for Large Reasoning Models cites this paper.

A Survey of Reinforcement Learning for Large Reasoning Models Why Does Reasoning Length Converge? Unveiling the Underfitting-Overfitting Trade-off in Chain-of-Thought

Reference 152

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