mlsanityData to 7 Oct 2026

Efficiently Scaling LLM Reasoning with Certaindex

arXiv 2412.20993 ↗First posted 30 Dec 2024cs.LG cs.CLcited by 56

On the map: LLM reasoning → Test-time compute and efficient thinking

also in 1 more
Abstract (arXiv)

Test-time reasoning algorithms such as chain-of-thought, self-consistency, and MCTS enhance LLM problem-solving but can wastefully generate many tokens without improving accuracy. At the same time, we observe that these algorithms exhibit answer stabilization: their intermediate solutions often cease to change after a certain point, and further investment of compute does not change their final answer. To quantify this phenomenon, we introduce Certaindex, an algorithm-agnostic metric measuring this evolving stability, signaling when further computation is unlikely to alter the final result. Certaindex is lightweight, can accelerate reasoning program inference via early exit, and further enables dynamic token allocation, gang scheduling, and many opportunities when integrated with real-world LLM serving systems. To quantify real-world benefits, we built Certaindex as a scheduler into Dynasor, our reasoning-aware LLM serving system, and demonstrate up to 50% compute savings and 3.3x higher throughput in real workloads with no accuracy drop. Our code is available at https://github.com/hao-ai-lab/Dynasor.git

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 47 of its 80 references that are in the map. First posted on arXiv 30 Dec 2024.

Builds on

47 of 80 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Token-Budget-Aware LLM Reasoning24 Dec
  2. 2024Adaptive Inference-Time Compute: LLMs Can Predict if They Can Do Better, Even Mid-Generation3 Oct
  3. 2024Reasoning Aware Self-Consistency: Leveraging Reasoning Paths for Efficient LLM Sampling30 Aug
  4. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters6 Aug
  5. 2024Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning19 Jan
  6. 2023Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training29 Sep
  7. 2023Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs19 May
  8. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
  9. 2023Self-Evaluation Guided Beam Search for Reasoning1 May
  10. 2022Language Models (Mostly) Know What They Know11 Jul

Other references · 37

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2021Training Verifiers to Solve Math Word Problemscited by 9,743
  3. 2019Sentence-BERT: Sentence Embeddings using Siamese BERT-Networkscited by 9,049
  4. 2022ReAct: Synergizing Reasoning and Acting in Language Modelscited by 8,355
  5. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  6. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  7. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  8. 2023Let's Verify Step by Stepcited by 3,598
  9. 2024Qwen2 Technical Reportcited by 2,076
  10. 2024Gemma 2: Improving Open Language Models at a Practical Sizecited by 1,928
  11. 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 1,906
  12. 2024Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phonecited by 1,883
25 more
  1. 2023SGLang: Efficient Execution of Structured Language Model Programscited by 1,107
  2. 2023Teaching Large Language Models to Self-Debugcited by 963
  3. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 946
  4. 2023Reasoning with Language Model is Planning with World Modelcited by 846
  5. 2023Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generationcited by 795
  6. 2024DistServe: Disaggregating Prefill and Decoding for Goodput-optimized Large Language Model Servingcited by 595
  7. 2023Splitwise: Efficient generative LLM inference using phase splittingcited by 536
  8. 2022CodeT: Code Generation with Generated Testscited by 369
  9. 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 314
  10. 2023LEVER: Learning to Verify Language-to-Code Generation with Executioncited by 228
  11. 2023SARATHI: Efficient LLM Inference by Piggybacking Decodes with Chunked Prefillscited by 187
  12. 2024Generative Reward Modelscited by 148
  13. 2023Fast Distributed Inference Serving for Large Language Modelscited by 143
  14. 2024From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Modelscited by 136
  15. 2024Fast Best-of-N Decoding via Speculative Rejectioncited by 112
  16. 2024DeepSpeed-FastGen: High-throughput Text Generation for LLMs via MII and DeepSpeed-Inferencecited by 106
  17. 2024Parrot: Efficient Serving of LLM-based Applications with Semantic Variablecited by 96
  18. 2024Efficient LLM Scheduling by Learning to Rankcited by 83
  19. 2023Rewarding Chatbots for Real-World Engagement with Millions of Userscited by 58
  20. 2023The Curious Case of Hallucinatory (Un)answerability: Finding Truths in the Hidden States of Over-Confident Large Language Modelscited by 54
  21. 2024Do LLMs Know about Hallucination? An Empirical Investigation of LLM's Hidden Statescited by 50
  22. 2024Self-Consistency Preference Optimizationcited by 50
  23. 2024Distinguishing the Knowable from the Unknowable with Language Modelscited by 45
  24. 2019Themis: Fair and Efficient GPU Cluster Schedulingcited by 43
  25. 2024DOCE: Finding the Sweet Spot for Execution-Based Code Generationcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 33; 2026: 23.

56 papers.

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  1. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Modelscited by 456
  2. 2025Deep Think with Confidencecited by 199
  3. 2025Reasoning Models Can Be Effective Without Thinkingcited by 182
  4. 2025Reasoning Models Know When They're Right: Probing Hidden States for Self-Verificationcited by 154
  5. 2025THOUGHTTERMINATOR: Benchmarking, Calibrating, and Mitigating Overthinking in Reasoning Modelscited by 34
  6. 2025Retro-Search: Exploring Untaken Paths for Deeper and Efficient Reasoningcited by 32
  7. 2025Mitigating Overthinking in Large Reasoning Models via Manifold Steeringcited by 32
  8. 2025Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Modelscited by 30
  9. 2025Metacognitive Reuse: Turning Recurring LLM Reasoning Into Concise Behaviorscited by 28
  10. 2025BudgetThinker: Empowering Budget-aware LLM Reasoning with Control Tokenscited by 27
  11. 2025The Geometry of Reasoning: Flowing Logics in Representation Spacecited by 21
  12. 2025HAPO: Training Language Models to Reason Concisely via History-Aware Policy Optimizationcited by 18
38 more
  1. 2025LIMOPro: Reasoning Refinement for Efficient and Effective Test-time Scalingcited by 15
  2. 2025Generative AI Act II: Test Time Scaling Drives Cognition Engineeringcited by 14
  3. 2025Hawkeye:Efficient Reasoning with Model Collaborationcited by 11
  4. 2025Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Modelscited by 11
  5. 2025Kinetics: Rethinking Test-Time Scaling Lawscited by 11
  6. 2025Exploring the System 1 Thinking Capability of Large Reasoning Modelscited by 10
  7. 2025Understanding and Steering the Cognitive Behaviors of Reasoning Models at Test-Timecited by 10
  8. 2026Conformal Thinking: Risk Control for Reasoning on a Compute Budgetcited by 9
  9. 2025How Far Are We from Optimal Reasoning Efficiency?cited by 8
  10. 2026Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Modelscited by 7
  11. 2025PATS: Process-Level Adaptive Thinking Mode Switchingcited by 6
  12. 2026TERMINATOR: Learning Optimal Exit Points for Early Stopping in Chain-of-Thought Reasoningcited by 6
  13. 2025PREMISE: Scalable and Strategic Prompt Optimization for Efficient Mathematical Reasoning in Large Modelscited by 5
  14. 2025Fantastic Reasoning Behaviors and Where to Find Them: Unsupervised Discovery of the Reasoning Processcited by 5
  15. 2026Early Stopping for Large Reasoning Models via Confidence Dynamicscited by 5
  16. 2025Queueing, Predictions, and LLMs: Challenges and Open Problemscited by 4
  17. 2025Less is More: Improving LLM Reasoning with Minimal Test-Time Interventioncited by 4
  18. 2026Unveiling the Entropy Dynamics of Chain-of-Thought Reasoningcited by 4
  19. 2025FastTTS: Accelerating Test-Time Scaling for Edge LLM Reasoningcited by 3
  20. 2025Stop Before You Fail: Operational Capability Boundaries for Mitigating Unproductive Reasoning in Large Reasoning Modelscited by 3
  21. 2025ThinkPilot: Steering Reasoning Models via Automated Think-prefixes Optimizationcited by 3
  22. 2026SPORK: Self-Speculative Forking to Accelerate Agentic LLM Inferencecited by 3
  23. 2025GTAlign: Game-Theoretic Alignment of LLM Assistants for Social Welfarecited by 2
  24. 2025Mitigating Overthinking through Reasoning Shapingcited by 2
  25. 2025Distractor Injection Attacks on Large Reasoning Models: Characterization and Defensecited by 2
  26. 2025Justitia: Fair and Efficient Scheduling of Task-parallel LLM Agents with Selective Pamperingcited by 2
  27. 2026Predictive Scheduling for Efficient Inference-Time Reasoning in Large Language Modelscited by 2
  28. 2026interwhen: A Generalizable Framework for Steering Reasoning Models with Test-time Verificationcited by 2
  29. 2026PETS: A Principled Framework Towards Optimal Trajectory Allocation for Efficient Test-Time Self-Consistencycited by 2
  30. 2026ForkKV: Scaling Multi-LoRA Agent Serving via Copy-on-Write Disaggregated KV Cachecited by 2
  31. 2026Efficient Test-Time Scaling via Temporal Reasoning Aggregationcited by 2
  32. 2026Agentic AI Systems Should Be Designed as Marginal Token Allocatorscited by 2
  33. 2026ExpThink: Experience-Guided Reinforcement Learning for Adaptive Chain-of-Thought Compressioncited by 2
  34. 2026Stop When Further Reasoning Won't Help: Attention-State Adaptive Generation in Reasoning Modelscited by 2
  35. 2025GPUs, CPUs, and... NICs: Rethinking the Network's Role in Serving Complex AI Pipelinescited by 1
  36. 2026BFS-PO: Best-First Search for Large Reasoning Modelscited by 1
  37. 2026HyPER: Bridging Exploration and Exploitation for Scalable LLM Reasoning with Hypothesis Path Expansion and Reductioncited by 0
  38. 2026Adaptive Parallel Monte Carlo Tree Search for Efficient Test-time Compute Scalingcited by 0

50 most cited of 56 All 56 (JSON)

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  1. 2026Taming Speculative Search for Test-Time Scaling in LLM Serving
  2. 2026ThinkBooster: A Unified Framework for Seamless Test-Time Scaling of LLM Reasoning
  3. 2026OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation
  4. 2025Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs
  5. 2026Refining Over Resampling: Test-Time Self-Correction for LLM Reasoning
  6. 2025Don't Overthink it. Preferring Shorter Thinking Chains for Improved LLM Reasoning
  7. 2025Scalable LLM Reasoning Acceleration with Low-rank Distillation
  8. 2025Slim-SC: Thought Pruning for Efficient Scaling with Self-Consistency