Automatic Chain-of-Thought (Auto-CoT) is an advanced prompt engineering technique designed to enhance the reasoning capabilities of large language models (LLMs). Introduced by Zhang et al. (2022), Auto-CoT addresses the limitations of few-shot Chain-of-Thought (CoT) prompting by eliminating the need for manually curated training examples. This technique has shown promising results across various tasks, including Mathematical Problem Solving, Multi-Hop Reasoning, and Commonsense Reasoning.
Auto-CoT builds upon the Chain-of-Thought prompting method, which encourages LLMs to break down complex problems into intermediate reasoning steps. The key innovation of Auto-CoT lies in its automated approach to generating these reasoning chains, removing the dependency on human-curated examples.
The theoretical foundation of Auto-CoT is based on two main principles:
-
Clustering of Similar Queries: By grouping similar queries together, Auto-CoT can identify representative examples that cover a wide range of problem types within a dataset.
-
Zero-Shot CoT Generation: Using a zero-shot approach to generate reasoning chains for representative queries eliminates the need for manual curation of training examples.
The Auto-CoT algorithm consists of two primary steps:
-
Query Clustering:
- Input: A dataset of queries
- Process: Apply a clustering algorithm (e.g., K-means) to group similar queries
- Output: A set of clusters, each containing similar queries
-
Representative Query Selection and CoT Generation:
- For each cluster:
- Select a representative query (e.g., the query closest to the cluster centroid)
- Generate a zero-shot CoT reasoning chain for the representative query
- Output: A set of representative queries with their corresponding CoT reasoning chains
- For each cluster:
Here's a high-level implementation of the Auto-CoT algorithm in Rust:
- ndarray for multi-dimensional arrays
- rand for random number generation
- linfa for machine learning operations (specifically K-means clustering)
- std::collections::HashMap for storing clustered data
[dependencies]
- ndarray = "0.15.6"
- rand = "0.8.5"
- rand_distr = "0.4.3"
- linfa = "0.6.1"
- linfa-clustering = "0.6.1"
use ndarray::{Array1, Array2};
use rand::seq::SliceRandom;
use rand::thread_rng;
use rand_distr::{Distribution, Uniform};
use linfa::prelude::*;
use linfa_clustering::KMeans;
use std::collections::HashMap;
// Simulating a language model API
struct LanguageModel {
// In a real implementation, this would be a connection to an actual LLM API
}
impl LanguageModel {
fn new() -> Self {
LanguageModel {}
}
fn get_embeddings(&self, queries: &[String]) -> Vec<Array1<f64>> {
let mut rng = thread_rng();
let dist = Uniform::new(0., 1.);
// Simulate embedding generation
queries
.iter()
.map(|_| Array1::from_vec((0..100).map(|_| dist.sample(&mut rng)).collect()))
.collect()
}
fn generate_zero_shot_cot(&self, query: &str) -> String {
// Simulate CoT generation
format!("Reasoning steps for: {}\n1. Step one\n2. Step two\n3. Conclusion", query)
}
}
struct AutoCoT {
n_clusters: usize,
llm: LanguageModel,
}
impl AutoCoT {
fn new(n_clusters: usize, llm: LanguageModel) -> Self {
AutoCoT {
n_clusters,
llm,
}
}
fn cluster_queries(&self, queries: &[String]) -> HashMap<usize, Vec<usize>> {
let embeddings = self.llm.get_embeddings(queries);
let embedding_len = embeddings[0].len();
let data = Array2::from_shape_vec(
(queries.len(), embedding_len),
embeddings.iter().flat_map(|arr| arr.iter().cloned()).collect(),
)
.unwrap();
// Convert Array2 to DatasetBase
let dataset = DatasetBase::from(data)
.with_feature_names((0..embedding_len).map(|i| i.to_string()).collect());
let model = KMeans::params(self.n_clusters)
.max_n_iterations(100)
.tolerance(1e-5)
.fit(&dataset)
.expect("KMeans failed to converge");
let predictions = model.predict(&dataset);
// Group indices by cluster
let mut clusters: HashMap<usize, Vec<usize>> = HashMap::new();
for (idx, &cluster) in predictions.iter().enumerate() {
clusters.entry(cluster as usize).or_default().push(idx);
}
clusters
}
fn select_representative_query(&self, cluster: &[usize], queries: &[String]) -> String {
// Select a random query from the cluster as the representative
cluster
.choose(&mut thread_rng())
.map(|&idx| queries[idx].clone())
.unwrap()
}
fn generate_cot(&self, query: &str) -> String {
self.llm.generate_zero_shot_cot(query)
}
fn run(&self, queries: &[String]) -> Vec<(String, String)> {
let clusters = self.cluster_queries(queries);
let mut representative_queries = Vec::new();
for (_, cluster) in clusters {
let representative_query = self.select_representative_query(&cluster, queries);
let cot = self.generate_cot(&representative_query);
representative_queries.push((representative_query, cot));
}
representative_queries
}
}
fn main() {
let llm = LanguageModel::new();
let auto_cot = AutoCoT::new(3, llm);
let queries = vec![
"Solve 2x + 3 = 7".to_string(),
"What is the capital of France?".to_string(),
"If John has 5 apples and eats 2, how many does he have left?".to_string(),
"What is 15% of 80?".to_string(),
"A train travels 120 km in 2 hours. What is its average speed?".to_string(),
];
let results = auto_cot.run(&queries);
println!("Auto-CoT Results:");
for (query, cot) in results {
println!("Representative Query: {}\nGenerated CoT:\n{}\n", query, cot);
}
}- Query Clustering: Utilizes K-means clustering to group similar queries based on their embeddings.
- Language Model Integration: Assumes the existence of a
LanguageModelstruct that can generate embeddings and zero-shot CoT reasoning. - Representative Query Selection: Simplifies the selection process by choosing the first query in each cluster.
- CoT Generation: Uses the language model to generate zero-shot CoT reasoning for representative queries.
Auto-CoT offers several advantages over traditional few-shot CoT:
- Automation: Eliminates the need for manual curation of training examples.
- Scalability: Can handle large and diverse datasets efficiently.
- Adaptability: Automatically adjusts to different types of queries within a dataset.
Performance-wise, Auto-CoT has shown promising results:
- Matches or outperforms few-shot CoT across various tasks.
- Particularly effective in Mathematical Problem Solving, Multi-Hop Reasoning, and Commonsense Reasoning tasks.
- Reduces the risk of biases introduced by manually selected examples.
Auto-CoT represents a significant advancement in prompt engineering techniques for LLMs. By automating the process of generating Chain-of-Thought reasoning, it offers a more scalable and adaptable approach to enhancing LLM performance on complex reasoning tasks. The implementation in Rust demonstrates the feasibility of integrating this technique into existing NLP pipelines.
Future research directions may include:
- Exploring more sophisticated clustering algorithms
- Investigating the impact of different representative query selection methods
- Combining Auto-CoT with other prompting techniques for further performance improvements
To better understand how Auto-CoT works in practice, let's consider a theoretical example using a small dataset of mathematical word problems.
Given Dataset:
- "If John has 5 apples and eats 2, how many apples does he have left?"
- "What is 15% of 80?"
- "A train travels 120 km in 2 hours. What is its average speed?"
- "If a rectangle has a length of 10 cm and a width of 6 cm, what is its area?"
- "Sarah is twice as old as Tom. If Tom is 15, how old is Sarah?"
- "A shop offers a 20% discount on a $50 shirt. What is the final price?"
- "If 3x + 7 = 22, what is the value of x?"
Step 1: Query Clustering The Auto-CoT algorithm would first cluster these questions based on their similarity. Let's assume it creates three clusters:
Cluster 1 (Basic Arithmetic): Questions 1, 5 Cluster 2 (Percentages and Discounts): Questions 2, 6 Cluster 3 (Algebra and Formulas): Questions 3, 4, 7
Step 2: Representative Query Selection and CoT Generation The algorithm would then select a representative query from each cluster and generate a zero-shot CoT for it:
Cluster 1 Representative: Query: "If John has 5 apples and eats 2, how many apples does he have left?" Generated CoT:
- Understand the initial quantity: John has 5 apples
- Identify the change: John eats 2 apples
- Calculate the remaining apples: 5 - 2 = 3
- Conclusion: John has 3 apples left
Cluster 2 Representative: Query: "What is 15% of 80?" Generated CoT:
- Convert the percentage to a decimal: 15% = 0.15
- Multiply the decimal by the whole number: 0.15 × 80
- Perform the calculation: 0.15 × 80 = 12
- Conclusion: 15% of 80 is 12
Cluster 3 Representative: Query: "If 3x + 7 = 22, what is the value of x?" Generated CoT:
- Identify the equation: 3x + 7 = 22
- Subtract 7 from both sides: 3x = 15
- Divide both sides by 3: x = 5
- Verify: 3(5) + 7 = 22 (correct)
- Conclusion: The value of x is 5
These generated CoTs can then be used as prompts for solving similar problems within each cluster. For example, when faced with the question "Sarah is twice as old as Tom. If Tom is 15, how old is Sarah?", the model can refer to the CoT generated for Cluster 1, adapting the step-by-step reasoning process to this new but similar problem.
This example demonstrates how Auto-CoT automatically generates diverse and relevant Chain-of-Thought examples without manual curation, covering a range of problem types within the dataset.