1. Chain-of-Thought (CoT): Showing Their Work

As math teachers insist on showing every step, Chain-of-Thought prompting guides the model through a coherent sequence of logical stages, improving transparency and accuracy.

Simple Example: If asked "If John has 15 apples and gives 7 to Sarah, how many does he have left?", a CoT-enabled model would reason:

• "John starts with 15 apples"
• "He gives away 7 apples"
• "The operation needed is subtraction: 15 - 7 = 8"
• "Therefore, John has 8 apples left"

This transparency dramatically improves accuracy on tasks involving logic and common sense reasoning. By guiding the model to "think aloud," CoT improves accuracy, especially in tasks involving logic, math, and complex decision-making.

2. Tree-of-Thought (ToT): Exploring Every Path

Whereas Chain-of-Thought follows one line of reasoning, Tree-of-Thoughts explores branching paths of intermediate steps. Akin to a chess grandmaster considering multiple moves simultaneously.

ToT expands the traditional "left-to-right" token generation reasoning process into a "tree structure exploration," where each node represents a thought unit. This supports multi-path attempts, backtracking, forward reasoning, and self-evaluation within the reasoning process.

The model can:

• Generate multiple solution paths
• Evaluate the potential of each path
• Backtrack from dead ends
• Choose the most promising route

3. Logical Inference: The AI Detective

This is more like the classic Sherlock Holmes style reasoning. The model draws conclusions based on given information and rules. For example:

• Rule: All cats are mammals
• Fact: Fluffy is a cat
• Conclusion: Therefore, Fluffy is a mammal

However, this is also where limitations appear. If the initial rules are flawed, the AI can make incorrect logical leaps.

Methodical Exploration: Smart Search

When facing problems with clear goals and defined rules, reasoning models use algorithms like A* Search. The model:

• Builds a mental map of explored paths
• Makes educated guesses about promising directions
• Prioritizes the most efficient routes
• Avoids revisiting dead ends

This allows AI to find optimal solutions without exploring every possibility—much like how you'd navigate a maze by being systematic rather than random.

Adaptive Learning: Reinforcement Learning

In reinforcement learning, the model earns positive rewards for correct reasoning and penalties for errors. Through millions of practice runs, the model:

• Tries different approaches
• Receives rewards for good moves
• Gets penalties for mistakes
• Gradually develops winning strategies

Most recent systems use policy-gradient methods such as Proximal Policy Optimization (PPO) because PPO constrains each policy update with a clipped objective, which stabilizes training for very large policies.

1. The Hallucination Problem

Benchmarks record hallucination rates of 33% for o3 and 48% for o4-mini on PersonQA, higher than those of non-reasoning models highlighting the need for stronger factual grounding.

Reasoning requires an element of creativity, and errors that go undetected as part of that process could compound while a model works through a problem.

2. The Black Box of Thought

Even with Chain-of-Thought making reasoning more transparent, understanding why an AI arrived at a particular conclusion can still be challenging. As models become more complex, the "thought process" becomes a tangled web, making it difficult to:

• Debug errors
• Identify biases
• Build trust in the AI's reasoning

3. Beyond the Training Data

Current models struggle with truly novel problems that fall outside their training distribution. Hallucination is defined as inconsistencies between a computable LLM and a computable ground truth function, and there is ongoing research to eliminate hallucination in LLMs. True intelligence requires reasoning and learning in completely new contexts, a capability that remains elusive.

4. Getting Stuck in Local Solutions

In planning tasks, models face the challenge of balancing exploration (trying new strategies) with exploitation (sticking to known good strategies). They can get stuck in "local optima" good but not optimal solutions.