Program of Thoughts: Quantifying Code Structure and Logic for Improving Model Reasoning

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First things first what is code structure? Well, it’s like the bones in your body. Just kidding, but sorta! Code structure refers to how lines of code are organized into functions or blocks, which can make them easier for humans (and models) to understand and reason about. For example:

# This function calculates the sum of a list of numbers
def calculate_sum(numbers):
    # Initialize a variable to store the total sum
    total = 0
    # Loop through each number in the list
    for num in numbers:
        # Add the current number to the total sum
        total += num
    # Return the total sum
    return total

This code has a clear structure with functions, variables, and loops that make it easy to follow along. On the other hand, this code is like a tangled mess of spaghetti:

# This code has a clear structure with functions, variables, and loops that make it easy to follow along.
# On the other hand, this code is like a tangled mess of spaghetti.



# Define variables x, y, and z and assign values to them
x = 1
y = 2
z = x + y

# Check if z is greater than 5
if z > 5:
    # If z is greater than 5, print "z is greater than 5"
    print("z is greater than 5")
else:
    # If z is not greater than 5, print "z is not greater than 5"
    print("z is not greater than 5")

It’s still technically correct, but it’s harder to reason about because the structure isn’t as clear.

Now code logic this refers to how lines of code are connected and what they do. For example:

# This script checks if the value of x is greater than 5 and prints a corresponding message.

# First, we define the variable x and assign it a value of 6.
x = 6

# Next, we use an if statement to check if x is greater than 5.
if x > 5:
    # If x is greater than 5, the following code block will be executed.
    # The print() function is used to display a message to the user.
    print("x is greater than 5")
else:
    # If x is not greater than 5, the following code block will be executed.
    # The print() function is used to display a different message to the user.
    print("x is not greater than 5")

This code has clear logic with an if statement that checks whether `x` is greater than 5, and then prints a message based on the result. On the other hand, this code doesn’t have as much logical structure:

# This code has clear logic with an if statement that checks whether x is greater than 5, and then prints a message based on the result.
# On the other hand, this code doesn't have as much logical structure.



# First, we define the variable x and assign it a value of 6.
x = 6

# Next, we use an if statement to check if x is greater than 5.
if x > 5:
    # If x is greater than 5, we print a message stating that x is greater than 5.
    print("x is greater than 5")
# If x is not greater than 5, we move on to the next line of code.
else:
    # Here, we define the variable y and assign it a value of 10.
    y = 10
    # Then, we define the variable z and assign it a value of y + 2.
    z = y + 2

It still works, but it’s not as clear what the logic is because there are two different actions happening in response to `x`.

So how does this relate to model reasoning? Well, according to a recent study called “Program of Thoughts,” quantifying code structure and logic can help improve model reasoning performance. By assigning scores based on these factors, researchers were able to create prompts with varying levels of complexity that could be used to train models to reason more effectively.

For example:

# This function calculates the sum of a list of numbers
def calculate_sum(numbers):
    # Initialize a variable to store the total sum
    total = 0
    # Loop through each number in the list
    for num in numbers:
        # Add the current number to the total sum
        total += num
    # Return the final total sum
    return total

This code has a high structure score and a medium logic score, making it an ideal candidate for training models to reason about. On the other hand:

# This code has a high structure score and a medium logic score, making it an ideal candidate for training models to reason about. On the other hand:

# Here is the script:
# The following code assigns values to variables x, y, and z, and checks if z is greater than 5.
# The original code is missing proper indentation and a colon after the if statement.
# Additionally, it is not clear what the purpose of the code is without proper annotations.

x = 1 # Assigns the value 1 to variable x
y = 2 # Assigns the value 2 to variable y
z = x + y # Assigns the sum of x and y to variable z
if z > 5: # Checks if z is greater than 5
    print("z is greater than 5") # Prints a message if z is greater than 5
else: # Executes if z is not greater than 5
    print("z is not greater than 5") # Prints a message if z is not greater than 5

This code has a high structure score and a medium logic score, but it’s still more complex than the previous example. It could be used to train models that need to reason about more complicated scenarios.

Overall, “Program of Thoughts” offers an exciting new approach for improving model reasoning performance by quantifying code structure and logic. By creating prompts with varying levels of complexity, researchers can help models learn how to think like humans or at least, like a well-organized program!

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