What is Chain of Thought (CoT) Prompting? A Complete Guide to AI Reasoning
- Muiz As-Siddeeqi
- Oct 7
- 34 min read
Imagine asking AI to solve a math problem and watching it stumble over steps a fifth-grader could handle. That frustration drove Google researchers to crack a code that changed everything. In January 2022, they published a technique that made AI models dramatically smarter—not by adding billions more parameters, but by teaching them to think out loud.
Bonus: What is Prompt Engineering?
TL;DR: Key Takeaways
Chain of Thought (CoT) prompting guides AI models to break down complex problems into step-by-step reasoning, dramatically improving accuracy on tasks requiring multi-step logic.
Performance gains can be massive: Google's PaLM 540B model jumped from 17.9% to 58% accuracy on math problems—a 224% improvement (Wei et al., 2022).
It's an emergent ability: CoT only works well with models of ~100 billion parameters or more; smaller models produce illogical reasoning chains.
Recent research reveals nuance: A June 2025 Wharton study shows CoT's value is decreasing for modern reasoning models, and it can actually harm performance on certain tasks.
Multiple variants exist: Zero-Shot CoT ("Let's think step by step"), Auto-CoT (automatic demonstration generation), Self-Consistency (majority voting across multiple reasoning paths), and Multimodal CoT (combining visual and text reasoning).
Real-world impact: Used in healthcare diagnostics, legal document analysis, educational AI tutors, and OpenAI's o1 reasoning models released in September 2024.
What is Chain of Thought Prompting?
Chain of Thought (CoT) prompting is an AI technique that guides large language models to show their reasoning process step-by-step before giving a final answer. Instead of jumping directly to conclusions, the model breaks complex problems into intermediate logical steps, similar to how humans solve difficult math or logic problems. This dramatically improves accuracy on reasoning tasks—by over 200% in some benchmarks.
Table of Contents
What is Chain of Thought Prompting?
Chain of Thought (CoT) prompting is a prompt engineering technique that teaches AI models to explicitly articulate their reasoning process before producing a final answer. Rather than providing an immediate response, the model generates intermediate reasoning steps that mirror human problem-solving strategies.
Think of it as the difference between a student who shows their work and one who just writes down an answer. The first approach catches more errors, builds better understanding, and produces more reliable results.
The technique emerged from a simple observation: when humans tackle complex problems—calculating compound interest, diagnosing medical conditions, or debugging code—we naturally break them into smaller, manageable steps. CoT prompting applies this same principle to AI.
The Core Mechanism
CoT works by providing the model with examples (called "exemplars") that demonstrate step-by-step reasoning, or by explicitly instructing the model to think through problems systematically. The model then mimics this pattern when facing new, similar challenges.
A standard prompt might ask: "Roger has 5 tennis balls. He buys 2 more cans of tennis balls. Each can has 3 tennis balls. How many tennis balls does he have now?"
A CoT prompt shows the reasoning: "Roger started with 5 balls. 2 cans of 3 tennis balls each is 6 tennis balls. 5 + 6 = 11. The answer is 11."
This explicit breakdown transforms how the model processes the problem internally.
The Origin Story: How CoT Was Discovered
The breakthrough came from Google Research's Brain team in January 2022. Jason Wei, Xuezhi Wang, Dale Schuurmans, and colleagues noticed a persistent problem: even the largest language models stumbled on tasks requiring multi-step reasoning.
Models with 175 billion parameters could write poetry and summarize documents with ease. But ask them to solve grade-school math problems, and they faltered in ways that seemed bizarre given their other capabilities.
The research team, published in "Chain-of-Thought Prompting Elicits Reasoning in Large Language Models" at NeurIPS 2022, tested a hypothesis inspired by human cognition. When people solve complex problems, they verbalize intermediate steps—either out loud or mentally. What if models could do the same?
They ran experiments across three major model families: GPT-3 (up to 175B parameters), LaMDA (up to 137B parameters), and PaLM (up to 540B parameters). The results shocked the research community.
On the GSM8K benchmark—a collection of grade-school math word problems—PaLM 540B with standard prompting achieved just 17.9% accuracy. With CoT prompting using only eight examples, accuracy leaped to 58%, surpassing even fine-tuned GPT-3 models (Wei et al., 2022, Google Research).
The paper appeared on arXiv on January 28, 2022, and was published at the 36th Conference on Neural Information Processing Systems in December 2022. It has since become one of the most influential papers in prompt engineering, cited thousands of times and spawning an entire subfield of research.
How Chain of Thought Prompting Works
CoT prompting leverages a fundamental property of large language models: their ability to learn patterns from examples and apply them to new situations. The technique works through several interconnected mechanisms.
The Few-Shot Learning Foundation
Traditional few-shot prompting provides input-output pairs as examples. If you want a model to translate English to French, you show it a few English sentences alongside their French translations. The model learns the pattern and applies it to new sentences.
CoT extends this by including the reasoning process in the examples. Instead of just question → answer, you show question → reasoning steps → answer.
Example Structure
Here's how a CoT prompt is structured for arithmetic reasoning:
Example 1:
Q: There are 15 trees in the grove. Grove workers will plant trees today. After they are done, there will be 21 trees. How many did they plant?A: There are 15 trees originally. Then there were 21 trees after some more were planted. So there must have been 21 - 15 = 6 trees planted. The answer is 6.
Example 2:
Q: If there are 3 cars in the parking lot and 2 more cars arrive, how many cars are in the parking lot?A: There are originally 3 cars. 2 more cars arrive. 3 + 2 = 5. The answer is 5.
After seeing several such examples, when presented with a new problem, the model naturally follows the same pattern of showing intermediate steps.
The Emergent Property Discovery
One of the most striking findings from the original research: CoT prompting is an emergent ability. This means it only appears at a certain scale of model size.
Models with fewer than 10 billion parameters showed little to no improvement from CoT prompting. In fact, smaller models sometimes performed worse, producing fluent but illogical reasoning chains that led to incorrect answers.
The benefits emerged clearly around 100 billion parameters. At that scale, models had learned enough reasoning patterns from their training data to apply them effectively when prompted (Wei et al., 2022, p. 5).
This discovery has profound implications: it suggests that reasoning capabilities aren't simply programmed into models but emerge naturally from scale and training on diverse text.
Why It Works: Three Theories
Researchers have proposed several explanations for CoT's effectiveness:
Computational Budget Expansion
By generating intermediate tokens (words), the model gets more "computation time" to process difficult problems. Each reasoning step allows the model to update its internal representations before moving to the next step.
Decomposition of Complexity
Breaking problems into smaller sub-problems makes each individual step more manageable. A model might struggle with "15 + 6 × 3" in one step but handle "first calculate 6 × 3 = 18, then 15 + 18 = 33" easily.
Knowledge Activation
Intermediate steps activate relevant knowledge stored in the model's parameters. When solving a physics problem, articulating "first, find the velocity" primes the model to recall velocity-related information.
The Breakthrough Results: Benchmark Performance
The original CoT research tested performance across three categories of reasoning tasks: arithmetic, commonsense, and symbolic reasoning. The results were striking and consistent.
Arithmetic Reasoning Benchmarks
The research team evaluated five math problem benchmarks:
GSM8K (Grade School Math 8K)
Dataset: 8,500 linguistically diverse grade-school math word problems
Steps required: 2-8 per problem
PaLM 540B Results:
Standard prompting: 17.9%
CoT prompting: 58.1%
Improvement: 224% increase
MultiArith
LaMDA 137B Results:
Standard prompting: 17.7%
CoT prompting: 78.7%
Improvement: 345% increase
SVAMP (Simple Variations on Arithmetic Math word Problems)
PaLM 540B Results:
Standard prompting: 70.9%
CoT prompting: 81.2%
Improvement: 14.5% increase
The gains were most dramatic on problems requiring multiple reasoning steps. Single-step problems showed smaller improvements, confirming that CoT specifically enhances multi-step reasoning (Wei et al., 2022, p. 7-8).
Self-Consistency Boosts Performance Further
Follow-up research by Xuezhi Wang and colleagues introduced self-consistency, a technique where the model generates multiple reasoning paths and takes a majority vote on the final answer.
On GSM8K, self-consistency with CoT prompting achieved 74% accuracy—a 27% improvement over standard CoT alone (Wang et al., 2022, Google Research).
Commonsense Reasoning Results
CoT also improved performance on tasks requiring general world knowledge:
CommonsenseQA
PaLM 540B: Standard 65.5% → CoT 74.4%
StrategyQA (requires multi-hop strategy)
PaLM 540B: Standard 49.0% → CoT 63.4%
These benchmarks test whether models can make logical inferences about everyday situations—the kind of reasoning humans do automatically (Wei et al., 2022, p. 9).
Symbolic Reasoning Tasks
The team also tested symbolic manipulation—tasks like last letter concatenation (given "Amy Brown," return "yn") or coin flip tracking.
Last Letter Concatenation
PaLM 540B: Standard 16.8% → CoT 53.2%
Even on these abstract tasks with no real-world grounding, CoT significantly improved performance, demonstrating its broad applicability (Wei et al., 2022, p. 10).
Real-World Impact: Zero-Shot CoT Results
Takeshi Kojima and colleagues introduced Zero-Shot CoT in May 2022, showing that simply adding "Let's think step by step" to prompts improved performance without any examples.
InstructGPT (text-davinci-002) on MultiArith:
Standard zero-shot: 17.7%
Zero-Shot CoT: 78.7%
Improvement: 345% increase
GSM8K:
Standard zero-shot: 10.4%
Zero-Shot CoT: 40.7%
Improvement: 291% increase
This made CoT accessible for any query, not just those with carefully crafted examples (Kojima et al., 2022, arXiv).
Variants and Evolution of CoT
Since the original 2022 paper, researchers have developed numerous CoT variants, each addressing specific limitations or use cases.
1. Zero-Shot Chain of Thought
Published: May 2022 by Kojima et al.
Key Innovation: No examples needed—just add "Let's think step by step"
Zero-Shot CoT democratized the technique. Instead of crafting several demonstration examples, you simply append a magic phrase to your query.
How it works:
The process uses two prompts:
First prompt: "Q: [question]\nA: Let's think step by step."
The model generates reasoning
Second prompt: Extract the final answer from the reasoning
Performance:
While not quite as effective as few-shot CoT, Zero-Shot achieved remarkable results considering its simplicity. On arithmetic benchmarks, it improved accuracy by 200-400% over standard zero-shot prompting (Kojima et al., 2022).
When to use: Zero-Shot CoT works best when you can't easily create good examples or when dealing with novel problem types.
2. Auto-CoT (Automatic Chain of Thought)
Published: September 2022 by Zhang et al. (Amazon Science)
Key Innovation: Automatically generates demonstration examples
Creating good CoT examples requires time and expertise. Auto-CoT automates this process entirely.
How it works:
Question Clustering: Use Sentence-BERT to embed questions and cluster them by similarity
Demonstration Sampling: Select a representative question from each cluster
Reasoning Generation: Use Zero-Shot CoT to generate reasoning chains for each representative
Diversity Filtering: Apply heuristics (e.g., reasoning chains with 5+ steps, questions with 60+ tokens)
The system creates diverse, high-quality demonstrations without human effort.
Performance:
Across ten reasoning benchmarks, Auto-CoT matched or exceeded manually crafted CoT demonstrations. On arithmetic reasoning tasks, it achieved 92.0% accuracy compared to manual CoT's 91.7% (Zhang et al., 2022, Amazon Science).
3. Self-Consistency with CoT
Published: March 2022 by Wang et al.
Key Innovation: Generate multiple reasoning paths, take majority vote
Complex problems often have multiple valid solution paths. Self-consistency exploits this by:
Running CoT prompting multiple times (typically 5-40 times)
Generating diverse reasoning chains
Extracting the final answer from each chain
Taking the majority vote as the final result
Performance Improvements:
GSM8K: +17.9 percentage points over standard CoT
SVAMP: +11.0 percentage points
AQuA: +12.2 percentage points
The technique is completely unsupervised—no additional training or fine-tuning required (Wang et al., 2022).
Trade-off: Self-consistency requires 5-40x more computation, making it expensive for production use. Some researchers fine-tune models on self-consistency outputs to get similar benefits in a single inference pass.
4. Multimodal Chain of Thought
Published: 2024 by researchers at Meta and AWS
Key Innovation: Combines visual and language reasoning
Until 2024, CoT was purely text-based. Multimodal CoT integrates images and text, operating in two stages:
Rationale Generation: Process language + image inputs to create a reasoning chain
Answer Inference: Combine original language input + rationale + original image to infer the final answer
Performance:
On the ScienceQA benchmark, a 1B parameter multimodal CoT model achieved 91.68% accuracy, beating GPT-3.5's 75.17%—a 16 percentage point improvement.
For questions involving images, accuracy jumped from 67.43% to 88.80% (SuperAnnotate, 2024).
This variant is crucial for applications requiring visual reasoning, like medical imaging, diagram interpretation, or visual troubleshooting.
5. Program of Thoughts (PoT)
Key Innovation: Delegates computation to external interpreters
LLMs struggle with exact numerical computation. PoT prompting generates Python code for calculations rather than trying to compute in natural language.
Example:
Instead of "5 × 4 = 20, then 20 + 3 = 23," the model writes:
result = (5 * 4) + 3
print(result) # 23The code is then executed by a Python interpreter, ensuring perfect arithmetic accuracy.
When to use: Essential for complex numerical problems, iterative calculations, or when exact precision is required.
6. Tree of Thoughts (ToT)
Published: May 2023 by Yao et al.
Key Innovation: Explore multiple reasoning paths simultaneously
While CoT follows a single linear path, ToT builds a tree of possible reasoning steps, evaluating and pruning paths as it goes.
Performance:
On the Game of 24 challenge (use 4 numbers to get 24), ToT achieved 74% success rate vs. CoT's 4% (Yao et al., 2023).
However, ToT is computationally expensive and most beneficial for problems requiring search or backtracking.
Real-World Applications and Case Studies
CoT prompting has moved from research papers to production systems across industries. Here are documented real-world implementations.
Case Study 1: Khan Academy's Khanmigo AI Tutor
Organization: Khan Academy
Launch: March 2023
Application: Educational AI assistant
Khan Academy integrated CoT-based reasoning into Khanmigo, their AI tutor powered by GPT-4. The system uses CoT prompting to:
Break down complex math problems into teachable steps
Guide students through solutions without giving direct answers
Identify misconceptions in student reasoning
Documented Impact:
According to Khan Academy's blog (March 2023), Khanmigo's step-by-step reasoning approach helps students develop problem-solving skills rather than just getting answers. The system uses variants of CoT to adapt explanations to student comprehension levels.
Key Technique: The tutor employs a modified CoT that asks guiding questions at each reasoning step, promoting active learning.
Case Study 2: Healthcare Diagnostic Reasoning
Study: "Extracting Key Radiological Features from Free-Text Reports for Pancreatic Ductal Adenocarcinoma"
Published: ResearchGate, January 2022
Models Tested: Gemma-2-27b-it and Llama-3-70b-instruct
Researchers evaluated CoT prompting for extracting medical information from radiology reports.
Task: Extract 18 key features from free-text radiology reports and determine NCCN resectability status for pancreatic cancer patients.
Method: Used CoT prompting to guide models through:
Identifying relevant anatomical features
Assessing relationships between tumor and vessels
Determining resectability classification
Results:
Llama-3-70b with CoT: 99% recall in validation
Successfully extracted complex medical relationships
Outperformed standard prompting approaches
Clinical Significance: The structured reasoning process made model outputs more interpretable for physicians, increasing trust in AI-assisted diagnosis (ResearchGate, 2022).
Case Study 3: Legal Document Analysis
Application: Contract review and compliance checking
Reported Use: Multiple law firms, 2023-2024
Legal professionals use CoT prompting for:
Document Comparison:
Breaking down contracts into clauses, comparing each systematically against templates or previous versions, identifying subtle differences with explicit reasoning.
Regulatory Compliance:
When analyzing whether a document complies with regulations like GDPR, CoT prompts guide the model to:
Identify applicable regulatory requirements
Locate relevant sections in the document
Evaluate compliance for each requirement
Flag gaps with specific reasoning
Documented in: IBM Think article (July 2025) notes that CoT prompting "enables legal experts to use chain-of-thought prompting to direct an LLM to explain new or existing regulations and how those apply to their organization."
Case Study 4: OpenAI's o1 Reasoning Models
Launch: September 12, 2024
Models: o1-preview and o1-mini
Developer: OpenAI
The o1 model family represents the most significant production deployment of CoT reasoning at scale.
Technical Approach:
OpenAI trained o1 models using reinforcement learning to perform internal chain-of-thought reasoning automatically. Unlike traditional CoT where users craft prompts, o1 models:
Generate extensive internal reasoning chains (hidden "reasoning tokens")
Learn to recognize and correct their own mistakes
Break down complex problems without explicit prompting
Try alternative approaches when initial strategies fail
Performance Benchmarks:
AIME 2024 (Math Competition):
GPT-4o: 13.4%
o1: 83.3%
Improvement: 522% increase
Codeforces (Programming Competition):
o1 ranked in 89th percentile (1807 Elo rating)
GPT-4o ranked in 11th percentile
PhD-Level Science Questions (GPQA Diamond):
o1: 78.3%
GPT-4o: 53.6%
Cost Trade-off:
o1-preview generates hidden reasoning tokens (not shown to users but still billed). On average, responses cost 3-5x more than GPT-4o due to extensive internal reasoning (OpenAI, September 2024).
Real-World Application:
According to OpenAI's System Card, o1 is being used for:
Complex scientific research
Advanced code generation
Multi-step mathematical proofs
Nuanced policy and safety evaluations
Case Study 5: Financial Risk Assessment
Company: Not publicly disclosed (documented in industry reports)
Application: Credit risk modeling and fraud detection
Financial institutions use CoT prompting to make AI-generated risk assessments more transparent and auditable.
Implementation:
When evaluating loan applications, CoT prompts guide models to:
Identify relevant risk factors from applicant data
Assess each factor's impact with clear reasoning
Combine factors into an overall risk score
Explain the decision in regulatory-compliant language
Business Impact:
The explicit reasoning chains satisfy regulatory requirements for explainable AI in financial decisions, as documented in the EU AI Act's requirements for high-risk AI systems.
When CoT Works Best (and When It Doesn't)
Not all tasks benefit from CoT prompting. Understanding when to deploy it is crucial for optimal performance and cost-efficiency.
Tasks Where CoT Excels
Multi-Step Mathematical Reasoning
CoT was designed for arithmetic word problems and consistently delivers 200-400% improvements. Use it for:
Complex calculations requiring multiple operations
Word problems requiring translation into mathematical operations
Problems with multiple interdependent steps
Example: "A store had 20 apples. They sold 5 in the morning and received a shipment of 15 more in the afternoon. Then they sold 8 more. How many apples remain?"
Logical Deduction and Inference
Tasks requiring step-by-step logical reasoning benefit significantly:
Symbolic manipulation (e.g., tracking coin flips)
Logical puzzles
Formal reasoning
Commonsense Reasoning Requiring Context
When problems need implicit knowledge and multi-hop inference:
"Can you fit a car in a refrigerator?" (requires understanding relative sizes)
Strategy questions requiring planning multiple steps ahead
Code Generation and Debugging
Programming tasks involving:
Algorithm design requiring multiple components
Debugging with systematic error identification
Complex refactoring with dependency tracking
Analysis and Comparison Tasks
Situations requiring structured comparison:
Evaluating multiple options against criteria
Comparing documents or proposals
Risk assessment with multiple factors
Tasks Where CoT May Not Help (or Hurts)
Recent research reveals important limitations. A July 2025 paper, "Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse," identified tasks where CoT actually degrades performance.
Simple, Single-Step Tasks
Adding CoT to basic queries wastes computation and can introduce errors.
Bad example: "What is 7 + 5?"CoT adds no value here—the model can answer directly.
Pattern Recognition Without Explicit Logic
Some tasks benefit from implicit pattern matching rather than explicit reasoning.
Facial Recognition: The 2025 study showed models performed worse with CoT on facial recognition tasks. Why? Language lacks the granularity to describe visual features precisely. Forcing verbal reasoning introduces noise (arXiv 2410.21333v1, 2025).
Implicit Statistical Learning: Tasks where humans learn patterns unconsciously (like grammar acquisition) don't benefit from explicit reasoning steps.
Creative or Open-Ended Generation
When the goal is fluency, creativity, or stylistic expression:
Poetry or creative writing
Brainstorming diverse ideas
Natural conversation
CoT can make responses feel mechanical and constrained.
Questions Requiring Immediate Factual Recall
Simple fact retrieval doesn't need reasoning chains:
"What is the capital of France?"
"Who wrote Hamlet?"
Very Small Models (Under 10B Parameters)
The original research showed models below ~10 billion parameters produce illogical reasoning chains that hurt performance. CoT only helps at larger scales (Wei et al., 2022, p. 5).
The 2025 Wharton Study: Decreasing Value for Modern Models
A June 2025 study by Lennart Meincke, Ethan Mollick, Lilach Mollick, and Dan Shapiro tested CoT's effectiveness on modern AI models and found surprising results.
Key Findings:
For Non-Reasoning Models:
CoT generally improves average performance by a small amount but introduces more variability, occasionally triggering errors the model would otherwise avoid (Meincke et al., SSRN, June 2025).
For Reasoning Models (like o1):
Minimal accuracy gains from explicit CoT prompting:
o3-mini: 2.9% improvement
o4-mini: 3.1% improvement
The gains rarely justify the increased response time (often 3-5x slower).
Critical Insight:
Many modern models already perform CoT-like reasoning by default, even without explicit instructions. Redundant prompting adds latency without meaningful benefit.
Decision Framework from the Study:
Use CoT when:
The model is non-reasoning (GPT-4, Claude, Gemini)
The task requires complex, multi-step logic
Consistency is more important than speed
You need to audit the reasoning process
Skip CoT when:
Using reasoning models (o1, o3)
Tasks are simple or single-step
Speed matters more than marginal accuracy
The model defaults to step-by-step thinking
OpenAI o1 and the Future of Reasoning Models
The September 2024 launch of OpenAI's o1 models marked a paradigm shift: CoT reasoning baked directly into model training rather than requiring careful prompting.
How o1 Differs from Traditional CoT
Traditional CoT Prompting:
User crafts prompts with reasoning examples
Model mimics the demonstrated pattern
Reasoning appears in the visible output
Quality depends on prompt engineering skills
o1's Built-In CoT:
Model trained via reinforcement learning to reason automatically
Generates internal "reasoning tokens" (hidden from users)
Learns to recognize mistakes and self-correct
Tries alternative approaches when stuck
The Technical Architecture
Based on OpenAI's documentation and reverse engineering by researchers (Wu et al., 2024), o1 follows a six-step process:
Problem Reformulation
The model begins by restating the problem and identifying key constraints, creating a comprehensive problem map.
Decomposition
Complex problems get broken into manageable chunks, preventing overwhelm from complexity.
Step-by-Step Exploration
The model works through sub-problems systematically, updating its understanding after each step.
Verification and Error Checking
After reaching intermediate conclusions, o1 checks for logical consistency and flags potential errors.
Alternative Path Exploration
If an approach seems unproductive, the model tries different strategies rather than forcing a single path.
Solution Synthesis
Finally, o1 combines insights from successful reasoning paths into a coherent final answer.
Reasoning Tokens: The Hidden Cost
o1 introduces "reasoning tokens"—intermediate thoughts generated during problem-solving but not shown in the response.
Why hide them?
OpenAI states this protects competitive advantages in reasoning techniques. Critics argue it reduces transparency.
Billing Impact:
Users pay for reasoning tokens at output token rates, even though they're invisible. A simple query might generate:
Visible output: 200 tokens
Hidden reasoning: 5,000 tokens
Total billed: 5,200 tokens
For complex problems, reasoning tokens can exceed visible output by 10-50x, making o1 significantly more expensive than GPT-4o.
Performance in Real-World Scenarios
Where o1 Excels:
Mathematical Reasoning:
On competition math (AIME 2024), o1 achieved 83.3% vs. GPT-4o's 13.4%—a 522% improvement.
Coding Challenges:
Ranked 89th percentile on Codeforces (1807 Elo), far above GPT-4o's 11th percentile performance.
Scientific Problem Solving:
On PhD-level science questions (GPQA Diamond), o1 scored 78.3% vs. 53.6% for GPT-4o.
Where o1 Struggles:
Natural Language Tasks:
OpenAI's own evaluations show o1 is "not preferred on some natural language tasks." For creative writing, conversation, or fluent prose, GPT-4o often produces better results.
Simple Queries:
The extensive reasoning process is overkill for straightforward questions, adding unnecessary latency and cost.
Response Time:
o1 responses take 10-60 seconds compared to GPT-4o's near-instant replies, making it unsuitable for real-time applications.
The Reasoning Effort Parameter
Recent o-series models (o3, o4-mini) introduce a reasoning_effort parameter with settings:
minimal: Fast, basic reasoning
low: Light reasoning for straightforward problems
medium: Balanced approach (default)
high: Extensive reasoning for complex challenges
Higher effort = more reasoning tokens = slower responses = higher cost, but potentially better accuracy on hard problems.
Industry Impact and Adoption
Major organizations deploying o1-class models:
Healthcare:
Used for complex diagnostic reasoning where detailed explanations are crucial for physician oversight.
Research:
Academic institutions use o1 for literature analysis, hypothesis generation, and experimental design.
Software Development:
GitHub Copilot and similar tools integrate reasoning models for complex algorithm design and architecture decisions.
Legal and Compliance:
Law firms use o1 for nuanced policy interpretation and multi-step legal analysis.
The Competitive Landscape
Following o1's launch:
Anthropic: Claude models added extended thinking capabilities in October 2024
Google: Gemini 2.0 (December 2024) includes built-in reasoning modes
Open-Source: Research teams are working to replicate o1's architecture with open-weight models
The trend is clear: built-in reasoning is becoming standard for frontier models.
Implementation Guide: How to Use CoT
Let's move from theory to practice with concrete implementation steps.
Method 1: Few-Shot CoT (Most Powerful)
Best for: Tasks where you can create 3-8 high-quality examples
Step-by-Step Process:
1. Identify Your Task Domain
What type of reasoning does your task require? Mathematical? Logical? Analytical?
2. Create 3-8 Demonstration Examples
Each should include:
The question/problem
Step-by-step reasoning (3-5 intermediate steps)
The final answer clearly marked
Quality matters more than quantity. Better to have 3 excellent examples than 10 mediocre ones.
3. Follow a Consistent Format
Use the same structure for each example:
Q: [Question]
A: [Reasoning step 1]. [Reasoning step 2]. [Reasoning step 3]. Therefore, [final answer]. The answer is [X].4. Ensure Diversity
Examples should cover different aspects of the task or varying difficulty levels.
Example Template for Math Problems:
Q: A cafeteria had 23 apples. They used 20 to make lunch and bought 6 more. How many apples do they have?
A: The cafeteria started with 23 apples. They used 20 to make lunch, so they had 23 - 20 = 3 apples left. Then they bought 6 more apples, so they have 3 + 6 = 9 apples now. The answer is 9.
Q: A bookshelf has 5 shelves. Each shelf holds 8 books. If 12 books are removed, how many remain?
A: First, calculate total books: 5 shelves × 8 books = 40 books. Then subtract removed books: 40 - 12 = 28 books remaining. The answer is 28.
Q: [Your actual question]
A:Method 2: Zero-Shot CoT (Easiest)
Best for: Quick implementation, novel problems, when you can't easily create examples
Implementation:
Simply append one of these phrases to your query:
"Let's think step by step."
"Let's approach this methodically."
"Let's break this down:"
"Let's solve this carefully:"
Example:
Q: A train leaves Station A at 2:00 PM traveling at 60 mph. Another train leaves Station B (240 miles away) at 3:00 PM traveling toward Station A at 80 mph. When do they meet?
Let's think step by step.Performance Tip: Different phrasings can yield different results. Test variations:
"Let's think about this step by step."
"Let's work through this systematically."
"Let's solve this problem step by step."
Method 3: XML-Structured CoT
Best for: When you need clear separation between reasoning and final output
Use XML tags to structure responses:
Please solve the following problem.
Problem: [Your question]
Provide your response in this format:
<thinking>
[Your step-by-step reasoning here]
</thinking>
<answer>
[Just the final answer]
</answer>This makes it easy to parse and extract either component programmatically.
Method 4: Auto-CoT (For Production Systems)
Best for: Large-scale deployments where you need automatically generated demonstrations
Implementation requires:
A dataset of questions in your domain
Sentence embedding model (e.g., Sentence-BERT)
Clustering algorithm (k-means works well)
Process:
# Pseudocode
questions = load_questions_from_domain()
embeddings = sentence_bert.encode(questions)
clusters = kmeans(embeddings, n_clusters=8)
demonstrations = []
for cluster in clusters:
representative = select_representative_question(cluster)
reasoning = zero_shot_cot(representative)
if is_valid_reasoning(reasoning): # Apply quality filters
demonstrations.append((representative, reasoning))
# Use demonstrations for few-shot CoTImplementation Tips and Tricks
1. Test on Edge Cases
Don't just verify normal cases. Test your prompts on:
Boundary conditions (very large/small numbers)
Ambiguous inputs
Multi-part questions
2. Monitor Reasoning Quality
Not all generated reasoning chains are correct. Implement validation:
Check logical consistency
Verify mathematical operations
Ensure conclusions follow from premises
Balance Detail Level
Too little detail: Model rushes, makes mistakesToo much detail: Responses become verbose, costly
Find the sweet spot for your use case through experimentation.
Handle Inconsistency
CoT introduces variability. For production:
Use self-consistency (generate 3-5 responses, take majority vote)
Set appropriate temperature (0.3-0.5 for math, 0.7 for open-ended)
Implement validation logic to catch obviously wrong answers
Cost Management
CoT generates more tokens = higher costs. Strategies:
Reserve CoT for genuinely complex tasks
Use smaller, cheaper models with CoT for simpler problems
Cache common reasoning patterns
Implement smart routing (use CoT only when initial attempts fail)
Limitations and Criticisms
Recent research has revealed significant constraints and failure modes of CoT prompting.
The Comprehension Without Competence Problem
A July 2025 paper, "Large Reasoning Models are not thinking straight: on the unreliability of thinking trajectories," exposed a fundamental limitation:
Key Finding: LLMs can articulate valid reasoning processes without being able to execute those processes correctly.
An AI might describe the correct steps to solve a problem but still produce the wrong answer. This suggests a gap between understanding procedural knowledge and applying it—what researchers call "comprehension without competence" (arXiv 2507.00711v1, 2025).
Implication: The presence of a reasoning chain doesn't guarantee correct reasoning. The model might be pattern-matching from training data rather than genuinely reasoning.
Unfaithful Reasoning Chains
Research paper "Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting" (May 2023) demonstrated that generated reasoning chains don't always reflect the model's actual computation process.
Example: A model might generate a plausible-sounding reasoning chain that leads to the right answer, but experiments show the model would have given the same answer even with a completely different (or nonsensical) reasoning chain.
Why it matters: You can't fully trust CoT for interpretability or debugging model behavior.
Dependence on Model Scale
CoT only helps with models of ~100B parameters or larger. For smaller models:
Reasoning chains are often illogical
Performance can decrease vs. standard prompting
The model lacks the knowledge base to reason effectively
Practical Impact: Organizations using smaller, cheaper models for cost reasons can't benefit from CoT (Wei et al., 2022, p. 5).
Increased Latency and Cost
Response Time:
CoT-generated responses are typically 3-10x longer than direct answers, causing:
Slower generation (more tokens to produce)
Higher API costs (charged per token)
Poor user experience for real-time applications
Cost Example:
Direct answer: "42" (1 token, $0.00002)CoT answer: 150-word reasoning chain (200 tokens, $0.004)Cost multiplier: 200x
For high-volume applications, this adds up quickly.
The Generalization Problem
A May 2024 study, "How far can you trust chain-of-thought prompting?" found CoT only works on problems very similar to demonstration examples.
Key Finding: When test problems deviated structurally from examples, CoT performance collapsed—sometimes worse than zero-shot prompting (TechTalks, May 2024).
Implication: CoT examples need to be highly specific to your exact problem class. A slight distribution shift breaks the technique.
Errors Compound Across Steps
In multi-step reasoning, an early mistake propagates:
Step 1: Correct
Step 2: Minor error
Step 3: Based on Step 2, now significantly wrong
Step 4: Completely off track
Standard prompting makes one mistake. CoT can make four.
Performance Varies Dramatically by Task
The Wharton 2025 study tested CoT across diverse tasks and found wildly inconsistent results:
Some tasks: 200%+ improvement
Some tasks: No improvement
Some tasks: Performance degradation
No universal heuristic exists for predicting when CoT will help. This requires task-specific empirical testing.
The Misleading Confidence Problem
CoT chains often sound authoritative and logical, even when wrong. This creates false confidence:
Users trust the output because reasoning looks sound
Errors are harder to spot than in direct answers (buried in long chains)
The model doesn't express uncertainty appropriately
Limited to Language-Expressible Reasoning
Some cognitive processes don't translate well to language:
Visual pattern recognition
Intuitive judgments
Implicit learning
Spatial reasoning
For these tasks, forcing verbal reasoning can hurt performance (the "verbal overshadowing" effect documented in humans and now observed in AI).
Inconsistency Across Runs
Due to the stochastic nature of LLMs, the same prompt can produce:
Different reasoning chains
Different final answers
Varying quality of reasoning
This unpredictability is problematic for production systems requiring deterministic behavior.
Comparison: CoT vs Other Prompting Techniques
How does CoT stack up against alternative approaches?
CoT vs Standard Few-Shot Prompting
CoT vs Tree of Thoughts (ToT)
CoT vs Retrieval-Augmented Generation (RAG)
Combined approach: Many systems use RAG for knowledge retrieval + CoT for reasoning over retrieved facts, getting the best of both.
CoT vs Self-Consistency
CoT vs o1-Style Built-In Reasoning
Best Practices and Common Pitfalls
Best Practices
Start Simple, Scale Up
Begin with Zero-Shot CoT ("Let's think step by step"). If results are unsatisfactory, move to few-shot with 3-5 examples. Only use expensive techniques (self-consistency, ToT) for critical applications.
Match Examples to Task Complexity
Your demonstration examples should match the difficulty and structure of actual queries. Don't show simple 2-step examples if queries need 5+ steps.
Be Specific in Reasoning Steps
Vague reasoning hurts more than it helps:
Bad: "We need to calculate the total, so the answer is 15."
Good: "We have 3 groups of 5 items each. 3 × 5 = 15 items total."
Use Consistent Formatting
Maintain the same structure across all examples:
Same step markers (numbered, bullet points, or prose)
Same level of detail
Same conclusion format ("The answer is X" vs "Therefore, X")
Test on Out-of-Distribution Examples
Don't just validate on examples similar to your demonstrations. Test on:
Edge cases
Adversarial examples
Corner cases with unusual constraints
Implement Validation Logic
Never trust CoT output blindly:
For math: Verify calculations programmatically
For logic: Check conclusion consistency
For factual claims: Cross-reference with knowledge bases
Monitor and Log Reasoning Quality
Track metrics:
Average reasoning chain length
Frequency of logical inconsistencies
Correlation between reasoning quality and answer correctness
Optimize for Your Cost-Performance Trade-off
Different applications have different priorities:
Latency-critical: Skip CoT or use minimal examples
Accuracy-critical: Use self-consistency with CoT
Cost-sensitive: Use Zero-Shot CoT only on hard queries
Common Pitfalls to Avoid
1. Over-Prompting Simple Tasks
Adding "Let's think step by step" to "What is 2 + 2?" wastes tokens and occasionally introduces errors.
Rule: If a human would answer immediately without deliberation, skip CoT.
2. Inconsistent Example Formatting
Mixing reasoning styles confuses models:
# Don't do this
Example 1: First, [step]. Second, [step]. Therefore, [answer].
Example 2: We can see that [answer] because [single justification].
3. Using Too Many Examples
More isn't always better. Beyond 8-10 examples, you hit diminishing returns and waste context window space.
Rule: 3-5 high-quality examples usually optimal.
4. Ignoring Domain Specificity
Using generic math examples for medical reasoning tasks fails. Examples must match your domain's reasoning patterns.
5. Not Handling Multipart Questions
When questions have multiple sub-questions, explicitly structure reasoning for each part:
Q: Calculate X and then use it to determine Y.
A: First, let's find X: [reasoning for X]. Now using X=[value], we can find Y: [reasoning for Y].6. Trusting Fluent-Sounding Reasoning
Models can generate confident-sounding nonsense. Always validate:
Do the steps logically follow?
Are calculations correct?
Does the conclusion follow from premises?
7. Not A/B Testing
Assumptions about CoT effectiveness are often wrong. Always run empirical comparisons:
Baseline (standard prompting)
Zero-Shot CoT
Few-Shot CoT
Self-Consistency CoT
Measure accuracy, latency, and cost for each.
8. Forcing CoT on Reasoning Models
Modern models like o1 already reason internally. Adding explicit "think step by step" to o1 queries is redundant and can confuse the model.
Rule: Check model documentation—if it mentions built-in reasoning, skip CoT prompting.
The Declining Value Debate (2025 Research)
The June 2025 Wharton study "The Decreasing Value of Chain of Thought in Prompting" sparked intense debate about CoT's future relevance.
The Core Argument
Hypothesis: As models become more sophisticated and increasingly include reasoning capabilities by default, explicit CoT prompting provides diminishing returns.
The Study's Methodology
Researchers Lennart Meincke, Ethan Mollick, Lilach Mollick, and Dan Shapiro tested CoT across:
Multiple model types (reasoning and non-reasoning)
Diverse benchmarks (GPQA Diamond, others)
25 runs per condition (not the typical 1-time test)
Various correctness thresholds (50%, 90%, 100%)
Key Insight: One-time testing masks inconsistency. Their repeated testing revealed high variance in CoT outputs.
Main Findings
For Non-Reasoning Models (GPT-4, Claude, Gemini):
CoT improves average performance slightly
But increases variance significantly
Sometimes triggers errors on questions the model would otherwise answer correctly
Benefits depend heavily on whether the model already uses implicit reasoning
For Reasoning Models (o1, o3, o4-mini):
Minimal benefits from explicit CoT:
o3-mini: 2.9% improvement
o4-mini: 3.1% improvement
Performance gains rarely justify 3-5x increased response time
Many reasoning models default to step-by-step thinking even without CoT prompts
The Decision Tree from the Study
The researchers provided a practical framework:
Should you use CoT?
Is it a reasoning model (o1, o3)?
├─ Yes → Skip CoT (model already reasons internally)
└─ No → Is the task complex and multi-step?
├─ Yes → Is speed critical?
│ ├─ Yes → Skip CoT
│ └─ No → Use CoT
└─ No → Skip CoTCounter-Arguments
Task-Dependent Effectiveness
Critics note the study focused on specific benchmarks. Other tasks might show different patterns.
Interpretability Value
Even if accuracy gains are minimal, visible reasoning chains provide value for:
Debugging model behavior
Building user trust
Meeting regulatory requirements for explainability
Custom Domain Advantage
Generic benchmarks don't reflect specialized domains where CoT might still provide significant gains.
The Nuanced Reality
The debate isn't "CoT is dead" vs "CoT is essential." It's more nuanced:
CoT remains valuable for:
Specialized domains not well-represented in model training
Tasks requiring very specific reasoning patterns
Applications where interpretability matters
Non-reasoning models on genuinely complex problems
Situations where you can afford the speed/cost trade-off
CoT is diminishing for:
Modern reasoning models with built-in CoT
Simple or medium-complexity tasks
Speed-critical applications
Generic problems where models already reason implicitly
Looking Forward
The study suggests a shift:
2022-2023: CoT was a universal best practice
2024-2025: CoT is a specialized tool for specific scenarios
Future: Built-in reasoning becomes standard; explicit prompting becomes niche
Strategic Implication: Don't assume CoT helps. Test empirically for your specific use case, model, and task.
FAQ
Do I need to provide examples every time I use CoT?
No. Zero-Shot CoT works by simply adding "Let's think step by step" without any examples. Few-shot CoT (with examples) is more powerful but requires upfront work to create demonstrations. For production systems, create examples once and reuse them.
How many examples should I include for few-shot CoT?
Research shows 3-8 examples is optimal. Below 3, the model may not fully grasp the pattern. Above 8, you hit diminishing returns and waste context window space. The original Wei et al. research used exactly 8 examples for most benchmarks.
Does CoT work with non-English languages?
Yes, but with caveats. The technique works in any language the model is trained on. However:
Performance may be slightly lower in non-English languages
Most research and optimization has focused on English
Translation of reasoning steps can introduce errors
Testing in your target language is essential
Can I use CoT with image-based models?
Yes! Multimodal CoT (introduced in 2024) combines visual and textual reasoning. It's particularly effective for:
Diagram interpretation
Medical imaging analysis
Visual problem-solving (e.g., geometry)
Scientific figure understanding
Why do CoT responses sometimes give wrong answers despite correct reasoning?
This happens because:
The model's factual knowledge is wrong (CoT can't fix incorrect training data)
Reasoning chains can be "unfaithful" (look plausible but don't reflect actual computation)
Small errors in early steps compound
The model pattern-matches reasoning style without genuine understanding
Is CoT the same as "showing your work" in math?
Conceptually similar, but not identical. When humans show work, we're documenting our actual thought process. When AI uses CoT, it's generating tokens that resemble reasoning but may not reflect its internal computation. The output looks like human reasoning, but the underlying mechanism is fundamentally different.
Can CoT help with creative tasks like writing stories?
Generally no. CoT is designed for logical reasoning and problem-solving. For creative generation:
CoT can make output feel mechanical
The step-by-step process constrains creativity
Direct generation often produces more natural, engaging content
Exception: CoT can help with structured creative tasks like plot outlining or character development planning.
Does CoT work better with higher temperature settings?
Usually no. For reasoning tasks, lower temperatures (0.1-0.5) work best because you want consistent, logical steps. Higher temperatures introduce randomness that can disrupt reasoning chains. Exception: Self-consistency deliberately uses higher temperature to generate diverse reasoning paths, then takes the majority vote.
How do I know if my task would benefit from CoT?
Test empirically, but heuristics that suggest CoT will help:
The task requires 3+ logical steps
Humans would naturally "show their work"
Standard prompting fails frequently
You can easily demonstrate the reasoning process in examples
Accuracy matters more than speed
Can I combine CoT with other techniques like RAG?
Absolutely! Many production systems use:
RAG to retrieve relevant facts
CoT to reason over those facts
Self-consistency for critical decisions
This combination leverages each technique's strengths.
Will future models make CoT prompting obsolete?
Partially. Models like OpenAI's o1 have built-in reasoning, reducing the need for explicit CoT prompts. However:
CoT provides control over reasoning format
Custom domains may still benefit
Interpretability requirements favor visible reasoning
The technique is evolving rather than disappearing.
How can I validate that CoT reasoning is correct?
Multiple approaches:
For math: Verify calculations programmatically
For logic: Check syllogistic validity
For facts: Cross-reference claims against knowledge bases
For consistency: Generate multiple reasoning chains and compare
For structure: Ensure each step logically follows from previous ones
Never assume fluent-sounding reasoning is correct reasoning.
Can CoT be used for classification tasks?
Yes, but it's often overkill. For simple classification (e.g., sentiment analysis), standard prompting suffices. Use CoT for classification when:
Categories require nuanced judgment
Multiple criteria must be evaluated
Explanation of classification is needed
Similar items have been misclassified
Does model size still matter with CoT?
Yes. The original "emergent ability" finding still holds: models below ~10B parameters produce poor reasoning chains. However, the threshold may be lowering as training techniques improve. Always test with your specific model size.
Can I fine-tune a model on CoT data?
Yes! This is called "CoT fine-tuning." It can:
Internalize reasoning patterns
Reduce prompt length (no examples needed)
Improve consistency
Lower inference cost (fewer tokens per query)
However, it requires a substantial dataset of high-quality reasoning chains.
Why do some studies show CoT hurting performance?
Several reasons:
Task doesn't benefit from explicit reasoning (pattern recognition, intuitive judgments)
Model already reasons internally (redundant prompting)
Forced verbalization disrupts implicit processes
Examples demonstrate incorrect reasoning patterns
This underscores the importance of empirical testing.
Can CoT help with code generation?
Yes, especially for:
Algorithm design (breaking down steps)
Debugging (systematic error identification)
Complex refactoring (tracking dependencies)
Explaining existing code
Less helpful for simple code snippets or when speed matters.
How does CoT affect AI safety and alignment?
CoT provides transparency benefits:
Makes model reasoning inspectable
Helps identify flawed logic
Enables intervention before incorrect conclusions
However, reasoning chains can be "unfaithful" (not reflecting actual computation), limiting interpretability. OpenAI's o1 System Card notes that integrating safety policies into reasoning chains helps with alignment.
Can I use CoT for real-time applications?
Challenging due to latency. Strategies:
Reserve CoT for complex queries only
Use Zero-Shot CoT (faster than few-shot)
Implement smart caching of reasoning patterns
Consider fine-tuned models that reason more efficiently
For truly real-time needs (milliseconds), CoT may not be viable.
What's the difference between CoT and just asking for step-by-step answers?
Subtle but important:
"Explain step-by-step" often gets you a tutorial or how-to
CoT specifically prompts reasoning through a problem instance
CoT includes the problem-solving process, not just general steps
Example:
Generic step-by-step: "To solve quadratic equations, first identify a, b, c..."
CoT: "For 2x² + 3x - 5 = 0: Here a=2, b=3, c=-5. Using the formula: x = (-3 ± √(9+40))/4..."
Key Takeaways
Chain of Thought prompting transforms AI performance on complex reasoning tasks by guiding models to articulate intermediate steps before final answers—improving accuracy by 200-400% on math benchmarks.
The technique emerged from January 2022 Google Research by Jason Wei and colleagues, demonstrating that showing reasoning steps dramatically improves large language model performance on multi-step problems.
CoT only works well at scale—models need ~100 billion parameters or more. Smaller models produce illogical reasoning chains that hurt performance.
Multiple powerful variants exist: Zero-Shot CoT (just add "Let's think step by step"), Auto-CoT (automatic example generation), Self-Consistency (majority voting across multiple paths), and Multimodal CoT (combining visual and text reasoning).
Real-world applications span industries: Healthcare diagnosis, educational AI tutors (Khan Academy's Khanmigo), legal document analysis, financial risk assessment, and OpenAI's o1 reasoning models.
Recent 2025 research reveals declining value for modern models—especially reasoning models like o1 that already use internal CoT. The Wharton study shows minimal gains (2.9-3.1%) don't justify increased response times.
CoT isn't universal—it can harm performance on tasks like pattern recognition, simple queries, creative generation, and problems where deliberation hurts human performance too.
Implementation ranges from simple to sophisticated: Zero-Shot CoT requires just one phrase, few-shot needs 3-8 examples, while production systems may use Auto-CoT or self-consistency for critical applications.
Significant limitations exist: reasoning chains can be "unfaithful" (not reflecting actual computation), errors compound across steps, costs increase 10-200x, and the technique doesn't generalize well beyond demonstrated examples.
The future is built-in reasoning: OpenAI's o1 (September 2024) and similar models integrate CoT training directly, reducing need for explicit prompting but introducing hidden "reasoning tokens" that significantly impact cost.
Next Steps: Actionable Implementation
For Beginners:
Start with Zero-Shot CoT—add "Let's think step by step" to your current prompts and measure accuracy differences.
Pick one complex task from your workflow and test CoT vs. standard prompting side-by-side.
Track three metrics: accuracy, response time, and cost per query.
For Intermediate Users:
Create 5 high-quality few-shot examples for your most common reasoning task.
Implement A/B testing comparing zero-shot, few-shot, and no-CoT prompts.
Set up validation logic to catch obviously incorrect reasoning chains.
Test self-consistency on high-stakes queries (generate 5 responses, take majority vote).
For Advanced Teams:
Build an Auto-CoT pipeline to automatically generate domain-specific demonstrations.
Implement smart routing: use standard prompting for simple queries, CoT only for complex ones.
Fine-tune a model on collected CoT reasoning chains to reduce per-query cost.
Integrate reasoning validation that programmatically verifies mathematical operations and logical consistency.
Monitor reasoning quality metrics over time to detect degradation.
For Organizations Evaluating o1-Class Models:
Benchmark your current workflow with standard models + CoT prompting vs. reasoning models without CoT.
Calculate true cost including hidden reasoning tokens (can be 3-10x visible output).
Test latency sensitivity—can your application handle 10-60 second response times?
Evaluate interpretability needs—do you require visible reasoning chains for compliance or debugging?
Research and Learning:
Read the original paper: "Chain-of-Thought Prompting Elicits Reasoning in Large Language Models" by Wei et al. (2022)
Explore the Prompting Guide: https://www.promptingguide.ai/techniques/cot
Monitor latest research on arXiv under the "cs.CL" (Computation and Language) category
Join communities: PromptHub, r/PromptEngineering, OpenAI Developer Forums
Glossary
Chain of Thought (CoT): A prompting technique that guides AI models to show step-by-step reasoning before providing final answers.
Emergent Ability: A capability that appears only when models reach a certain scale (typically ~100B parameters); doesn't exist in smaller models.
Exemplar: A demonstration example used in few-shot prompting, showing the desired input-output pattern.
Few-Shot Prompting: Providing 2-10 example input-output pairs before the actual query to demonstrate the desired behavior.
GSM8K: Grade School Math 8K—a benchmark dataset of 8,500 elementary school math word problems used to test reasoning abilities.
Inference: The process of using a trained AI model to generate outputs for new inputs.
LLM (Large Language Model): AI systems trained on vast text datasets, typically with billions of parameters, capable of understanding and generating human-like text.
MultiArith: A benchmark dataset of arithmetic word problems requiring multiple operations.
Parameter: The learned weights in a neural network; model size is often measured by parameter count (e.g., 175B = 175 billion parameters).
Prompting: The practice of crafting input text to guide AI model behavior and outputs.
Reasoning Tokens: In OpenAI's o1 models, hidden intermediate tokens generated during problem-solving but not shown in the final response (still billed).
Reinforcement Learning: A training method where models learn through trial-and-error with rewards for desired behaviors.
Self-Consistency: A CoT variant that generates multiple diverse reasoning paths and takes the majority vote as the final answer.
Temperature: A parameter controlling randomness in model outputs (0 = deterministic, 1+ = creative/random).
Token: The basic unit of text processing in LLMs; roughly 3/4 of a word (e.g., "reasoning" = ~2 tokens).
Zero-Shot Prompting: Asking a model to perform a task without providing any examples, relying solely on instructions and the model's training.
Zero-Shot CoT: A CoT variant using simple phrases like "Let's think step by step" instead of demonstration examples.
Sources and References
Original Research Papers
Wei, J., Wang, X., Schuurmans, D., Bosma, M., Ichter, B., Xia, F., Chi, E., Le, Q., & Zhou, D. (2022). "Chain-of-Thought Prompting Elicits Reasoning in Large Language Models." Proceedings of the 36th Conference on Neural Information Processing Systems (NeurIPS 2022). arXiv:2201.11903. Retrieved from https://arxiv.org/abs/2201.11903 (Published January 28, 2022)
Wang, X., Wei, J., Schuurmans, D., Le, Q., Chi, E., & Zhou, D. (2022). "Self-Consistency Improves Chain of Thought Reasoning in Language Models." arXiv:2203.11171. Retrieved from https://arxiv.org/abs/2203.11171 (Published March 21, 2022)
Kojima, T., Gu, S. S., Reid, M., Matsuo, Y., & Iwasawa, Y. (2022). "Large Language Models are Zero-Shot Reasoners." arXiv:2205.11916. Retrieved from https://arxiv.org/abs/2205.11916 (Published May 2022)
Zhang, Z., Zhang, A., Li, M., & Smola, A. (2022). "Automatic Chain of Thought Prompting in Large Language Models." arXiv:2210.03493. Amazon Science. Retrieved from https://github.com/amazon-science/auto-cot (Published September 2022)
Recent Studies and Criticisms (2024-2025)
Meincke, L., Mollick, E. R., Mollick, L., & Shapiro, D. (2025). "Prompting Science Report 2: The Decreasing Value of Chain of Thought in Prompting." SSRN Electronic Journal. Retrieved from https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5285532 (Published June 8, 2025)
Anonymous Authors. (2025). "Mind Your Step (by Step): Chain-of-Thought can Reduce Performance on Tasks where Thinking Makes Humans Worse." arXiv:2410.21333v1. Retrieved from https://arxiv.org/html/2410.21333v1 (Published July 25, 2025)
Anonymous Authors. (2025). "Large Reasoning Models are not thinking straight: on the unreliability of thinking trajectories." arXiv:2507.00711v1. AryaXAI Research Analysis. Retrieved from https://www.aryaxai.com/article/top-ai-research-papers-of-2025-from-chain-of-thought-flaws-to-fine-tuned-ai-agents (Published 2025)
Industry Implementation and Documentation
OpenAI. (2024). "Learning to Reason with LLMs." OpenAI Blog. Retrieved from https://openai.com/index/learning-to-reason-with-llms/ (Published September 12, 2024)
IBM Think. (2025). "What is chain of thought (CoT) prompting?" IBM Documentation. Retrieved from https://www.ibm.com/think/topics/chain-of-thoughts (Published July 14, 2025)
Google Research. (2022). "Language Models Perform Reasoning via Chain of Thought." Google Research Blog. Retrieved from https://research.google/blog/language-models-perform-reasoning-via-chain-of-thought/ (Published May 30, 2024)
Technical Guides and Analysis
Prompt Engineering Guide. (2024). "Chain-of-Thought Prompting." Prompting Guide. Retrieved from https://www.promptingguide.ai/techniques/cot (Accessed 2024)
SuperAnnotate. (2024). "Chain-of-thought (CoT) prompting: Complete overview [2024]." Retrieved from https://www.superannotate.com/blog/chain-of-thought-cot-prompting (Published December 12, 2024)
Orq.ai. (2025). "Chain of Thought Prompting in AI: A Comprehensive Guide [2025]." Retrieved from https://orq.ai/blog/what-is-chain-of-thought-prompting (Accessed 2025)
Benchmark and Performance Data
Cobbe, K., Kosaraju, V., Bavarian, M., Chen, M., Jun, H., Kaiser, L., Plappert, M., Tworek, J., Hilton, J., Nakano, R., Hesse, C., & Schulman, J. (2021). "Training Verifiers to Solve Math Word Problems." arXiv:2110.14168. GSM8K Benchmark. Retrieved from https://github.com/openai/grade-school-math
FranxYao. "Chain-of-Thought Hub: Benchmarking large language models' complex reasoning ability." GitHub Repository. Retrieved from https://github.com/FranxYao/chain-of-thought-hub (Accessed 2024)
Educational Resources
New Jersey Innovation Institute (NJII). (2024). "How to Implement Chain-of-Thought Prompting for Better AI Reasoning." Retrieved from https://www.njii.com/2024/11/how-to-implement-chain-of-thought-prompting-for-better-ai-reasoning/ (Published November 19, 2024)
Deepgram. (2024). "Chain-of-Thought Prompting: Helping LLMs Learn by Example." Retrieved from https://deepgram.com/learn/chain-of-thought-prompting-guide
Learn Prompting. (2024). "The Ultimate Guide to Chain of Thoughts (CoT): Part 1." Retrieved from https://learnprompting.org/blog/guide-to-chain-of-thought-part-one
Case Studies and Real-World Applications
OpenXcell. (2024). "Chain of Thought Prompting: A Guide to Enhanced AI Reasoning." Retrieved from https://www.openxcell.com/blog/chain-of-thought-prompting/ (Published November 22, 2024)
TechTarget. (2025). "What is Chain-of-Thought Prompting (CoT)? Examples and Benefits." Retrieved from https://www.techtarget.com/searchenterpriseai/definition/chain-of-thought-prompting
Portkey.ai. (2025). "Chain-of-Thought (CoT) Capabilities in OpenAI's o1 models." Retrieved from https://portkey.ai/blog/chain-of-thought-using-o1-models/ (Published January 21, 2025)
Academic Publications and Proceedings
Wei, J., et al. (2022). "Chain-of-Thought Prompting Elicits Reasoning in Large Language Models." NeurIPS 2022 Proceedings. Retrieved from https://proceedings.neurips.cc/paper_files/paper/2022/hash/9d5609613524ecf4f15af0f7b31abca4-Abstract-Conference.html (Published December 6, 2022)
ResearchGate. (2022). "Chain of Thought Prompting Elicits Reasoning in Large Language Models." Retrieved from https://www.researchgate.net/publication/358232899_Chain_of_Thought_Prompting_Elicits_Reasoning_in_Large_Language_Models (Published January 27, 2022)
Additional Technical Documentation
Microsoft Azure. "Azure OpenAI reasoning models - GPT-5 series, o3-mini, o1, o1-mini." Microsoft Learn. Retrieved from https://learn.microsoft.com/en-us/azure/ai-foundry/openai/how-to/reasoning
Willison, S. (2024). "Notes on OpenAI's new o1 chain-of-thought models." Simon Willison's Blog. Retrieved from https://simonwillison.net/2024/Sep/12/openai-o1/ (Published September 12, 2024)
Wu, C., et al. (2024). "Toward Reverse Engineering LLM Reasoning: A Study of Chain-of-Thought Using AI-Generated Queries and Prompts." PromptLayer Analysis. Retrieved from https://blog.promptlayer.com/how-openais-o1-model-works-behind-the-scenes-what-we-can-learn-from-it/ (Published January 2, 2025)
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