# Make Every Penny Count: Difficulty-Adaptive Self-Consistency for Cost-Efficient Reasoning

arXiv: https://arxiv.org/abs/2408.13457 · HTML: https://mlsanity.com/paper/2408.13457/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 24 Aug 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Specializing Smaller Language Models towards Multi-Step Reasoning](https://mlsanity.com/paper/2301.12726/) (2023)
- [Let's Sample Step by Step: Adaptive-Consistency for Efficient Reasoning and Coding with LLMs](https://mlsanity.com/paper/2305.11860/) (2023)
- [Escape Sky-high Cost: Early-stopping Self-Consistency for Multi-step Reasoning](https://mlsanity.com/paper/2401.10480/) (2024)
- [Batch Prompting: Efficient Inference with Large Language Model APIs](https://mlsanity.com/paper/2301.08721/) (2023)
- [Large Language Models Can Self-Correct with Key Condition Verification](https://mlsanity.com/paper/2405.14092/) (2024)
- [Multi-Task Inference: Can Large Language Models Follow Multiple Instructions at Once?](https://mlsanity.com/paper/2402.11597/) (2024)
- [Integrate the Essence and Eliminate the Dross: Fine-Grained Self-Consistency for Free-Form Language Generation](https://mlsanity.com/paper/2407.02056/) (2024)
- [CliqueParcel: An Approach For Batching LLM Prompts That Jointly Optimizes Efficiency And Faithfulness](https://mlsanity.com/paper/2402.14833/) (2024)

## Built on by (most cited first, 30 of 63)

- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?](https://mlsanity.com/paper/2503.24235/) (2025)
- [Reasoning Models Know When They're Right: Probing Hidden States for Self-Verification](https://mlsanity.com/paper/2504.05419/) (2025)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [Between Underthinking and Overthinking: An Empirical Study of Reasoning Length and correctness in LLMs](https://mlsanity.com/paper/2505.00127/) (2025)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Efficient Reasoning Models: A Survey](https://mlsanity.com/paper/2504.10903/) (2025)
- [Efficient Inference for Large Reasoning Models: A Survey](https://mlsanity.com/paper/2503.23077/) (2025)
- [Harnessing the Reasoning Economy: A Survey of Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.24377/) (2025)
- [Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens](https://mlsanity.com/paper/2505.18237/) (2025)
- [Reasoning on a Budget: A Survey of Adaptive and Controllable Test-Time Compute in LLMs](https://mlsanity.com/paper/2507.02076/) (2025)
- [Think Smarter not Harder: Adaptive Reasoning with Inference Aware Optimization](https://mlsanity.com/paper/2501.17974/) (2025)
- [BudgetThinker: Empowering Budget-aware LLM Reasoning with Control Tokens](https://mlsanity.com/paper/2508.17196/) (2025)
- [The LLM Already Knows: Estimating LLM-Perceived Question Difficulty via Hidden Representations](https://mlsanity.com/paper/2509.12886/) (2025)
- [From Medprompt to o1: Exploration of Run-Time Strategies for Medical Challenge Problems and Beyond](https://mlsanity.com/paper/2411.03590/) (2024)
- [Route to Reason: Adaptive Routing for LLM and Reasoning Strategy Selection](https://mlsanity.com/paper/2505.19435/) (2025)
- [An Empirical Study of LLM Reasoning Ability Under Strict Output Length Constraint](https://mlsanity.com/paper/2504.14350/) (2025)
- [Automatic Curriculum Expert Iteration for Reliable LLM Reasoning](https://mlsanity.com/paper/2410.07627/) (2024)
- [Generative AI Act II: Test Time Scaling Drives Cognition Engineering](https://mlsanity.com/paper/2504.13828/) (2025)
- [Parallel-Probe: Towards Efficient Parallel Thinking via 2D Probing](https://mlsanity.com/paper/2602.03845/) (2026)
- [Adaptive GoGI-Skip: Coupling Goal-Gradient Importance with Dynamic Uncertainty for Efficient Reasoning](https://mlsanity.com/paper/2505.08392/) (2025)
- [Certified Self-Consistency: Statistical Guarantees and Test-Time Training for Reliable Reasoning in LLMs](https://mlsanity.com/paper/2510.17472/) (2025)
- [Revisiting Self-Consistency from Dynamic Distributional Alignment Perspective on Answer Aggregation](https://mlsanity.com/paper/2502.19830/) (2025)
- [Reversal of Thought: Enhancing Large Language Models with Preference-Guided Reverse Reasoning Warm-up](https://mlsanity.com/paper/2410.12323/) (2024)
- [Exploring the System 1 Thinking Capability of Large Reasoning Models](https://mlsanity.com/paper/2504.10368/) (2025)
- [LLMs Improving LLMs: Agentic Discovery for Test-Time Scaling](https://mlsanity.com/paper/2605.08083/) (2026)
- [AdaBoN: Adaptive Best-of-N Alignment](https://mlsanity.com/paper/2505.12050/) (2025)
- [Optimal Self-Consistency for Efficient Reasoning with Large Language Models](https://mlsanity.com/paper/2511.12309/) (2025)
- [VLA-ATTC: Adaptive Test-Time Compute for VLA Models with Relative Action Critic Model](https://mlsanity.com/paper/2605.01194/) (2026)

## Abstract (arXiv)

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants, Adaptive self-consistency (ASC) and Early-stopping self-consistency (ESC), dynamically adjust the number of samples based on the posterior distribution of a set of pre-samples, reducing the cost of SC with minimal impact on performance. Both methods, however, do not exploit the prior information about question difficulty. It often results in unnecessary repeated sampling for easy questions that could be accurately answered with just one attempt, wasting resources. To tackle this problem, we propose Difficulty-Adaptive Self-Consistency (DSC), which leverages the difficulty information of batch queries from both prior and posterior perspectives to adaptively allocate inference resources, further reducing the overall cost of SC. To demonstrate the effectiveness of DSC, we conduct extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning on six benchmarks. The empirical results show that DSC consistently surpasses the strong baseline ASC and ESC in terms of costs by a significant margin, while attaining comparable performances.