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Asking LLMs to Verify First is Almost Free Lunch

Shiguang Wu, Quanming Yao

TL;DR

The paper tackles the high costs of improving LLM reasoning by introducing Verification-First prompting, which asks models to verify a candidate answer before solving, leveraging a reverse reasoning path that complements forward chain-of-thought. It generalizes this idea into Iter-VF for test-time scaling, enabling sequential verification that maintains a compact context window. Across diverse benchmarks and model families, VF with random/trivial answers consistently outperforms standard CoT, and Iter-VF outperforms existing test-time strategies with minimal overhead. The approach proves robust in real-world, open-ended tasks and under thought-hidden LLM services, offering a training-free, cost-effective path to stronger reasoning.

Abstract

To enhance the reasoning capabilities of Large Language Models (LLMs) without high costs of training, nor extensive test-time sampling, we introduce Verification-First (VF), a strategy that prompts models to verify a provided candidate answer, even a trivial or random one, before generating a solution. This approach triggers a "reverse reasoning" process that is cognitively easier and complementary to standard forward Chain-of-Thought (CoT), effectively invoking the model's critical thinking to reduce logical errors. We further generalize the VF strategy to Iter-VF, a sequential test-time scaling (TTS) method that iteratively cycles the verification-generation process using the model's previous answer. Extensive experiments across various benchmarks (from mathematical reasoning to coding and agentic tasks) and various LLMs (from open-source 1B to cutting-edge commercial ones) confirm that VF with random answer consistently outperforms standard CoT with minimal computational overhead, and Iter-VF outperforms existing TTS strategies.

Asking LLMs to Verify First is Almost Free Lunch

TL;DR

The paper tackles the high costs of improving LLM reasoning by introducing Verification-First prompting, which asks models to verify a candidate answer before solving, leveraging a reverse reasoning path that complements forward chain-of-thought. It generalizes this idea into Iter-VF for test-time scaling, enabling sequential verification that maintains a compact context window. Across diverse benchmarks and model families, VF with random/trivial answers consistently outperforms standard CoT, and Iter-VF outperforms existing test-time strategies with minimal overhead. The approach proves robust in real-world, open-ended tasks and under thought-hidden LLM services, offering a training-free, cost-effective path to stronger reasoning.

Abstract

To enhance the reasoning capabilities of Large Language Models (LLMs) without high costs of training, nor extensive test-time sampling, we introduce Verification-First (VF), a strategy that prompts models to verify a provided candidate answer, even a trivial or random one, before generating a solution. This approach triggers a "reverse reasoning" process that is cognitively easier and complementary to standard forward Chain-of-Thought (CoT), effectively invoking the model's critical thinking to reduce logical errors. We further generalize the VF strategy to Iter-VF, a sequential test-time scaling (TTS) method that iteratively cycles the verification-generation process using the model's previous answer. Extensive experiments across various benchmarks (from mathematical reasoning to coding and agentic tasks) and various LLMs (from open-source 1B to cutting-edge commercial ones) confirm that VF with random answer consistently outperforms standard CoT with minimal computational overhead, and Iter-VF outperforms existing TTS strategies.

Paper Structure

This paper contains 22 sections, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. LLM Reasoning
  4. Reverse Reasoning and Critical Thinking
  5. Proposed Method
  6. Understanding VF Prompting by Random Answer
  7. Deriving the General Method
  8. Comparison with Existing Works
  9. Experiments
  10. VF Prompting with Random/Trivial Answer
  11. Performance and Cost Comparison.
  12. Sensitivity on Provided Answer to Verify.
  13. Iter-VF for Test-Time Scaling
  14. Performance Comparison and Analysis.
  15. Discussion.
  16. ...and 7 more sections

Figures (6)

  • Figure 1: A reverse reasoning path (verification process) could be easier to find and contain complementary information to forward-reasoning path (standard CoT).
  • Figure 2: VF prompting with random/trivial answer (Right), comparing with standard CoT prompting (Left)
  • Figure 3: Illustration of (a) VF prompting with previously generated answer, and iterating such process as (b) Iter-VF for test-time scaling.
  • Figure 4: VF prompting consistently outperforms standard CoT prompting.
  • Figure 5: Providing different answers to VF for verification.
  • ...and 1 more figures