LLM scaling laws in Prompt Engineering / GenAI - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the relationship between model size and performance

Which statement best describes the general trend observed in LLM scaling laws regarding model size and performance?

A Performance improves as a power-law function of the number of parameters in the model.

B Performance improves logarithmically with the number of parameters in the model.

C Performance improves linearly with the number of parameters in the model.

D Performance remains constant regardless of the number of parameters.

💡 Hint

Think about how small increases in size can lead to significant improvements, but not in a simple linear way.

LLM scaling laws show that performance improves following a power-law relationship with model size, meaning gains are significant but not linear or logarithmic.

❓ Metrics

intermediate

Evaluating loss behavior with increased compute

According to LLM scaling laws, how does the training loss typically change as the amount of compute used for training increases?

A Training loss remains unchanged regardless of compute.

B Training loss decreases following a power-law with increased compute.

C Training loss decreases exponentially with increased compute.

D Training loss increases as compute increases.

💡 Hint

Consider how more compute allows better fitting but with diminishing returns.

Training loss decreases following a power-law as compute increases, showing diminishing returns but consistent improvement.

❓ Model Choice

advanced

Choosing model size for fixed compute budget

Given a fixed compute budget, which strategy aligns best with LLM scaling laws to minimize training loss?

A Train multiple small models independently and average their outputs.

B Train a smaller model for more training steps.

C Train a very large model with fewer training steps.

D Balance model size and training steps to optimize compute usage.

💡 Hint

Think about how compute is split between model size and training duration.

LLM scaling laws suggest an optimal balance between model size and training steps to best use compute and minimize loss.

🔧 Debug

advanced

Identifying incorrect interpretation of scaling laws

Which of the following interpretations of LLM scaling laws is incorrect?

A Loss decreases smoothly as model size and compute increase.

B Compute-efficient training requires balancing model size and data.

C Doubling model parameters always halves the training loss.

D Increasing dataset size improves performance up to a point.

💡 Hint

Consider if the relationship between parameters and loss is linear or not.

Doubling parameters does not halve loss; improvements follow a power-law with diminishing returns, so this interpretation is incorrect.

❓ Predict Output

expert

Predicting training loss from scaling law formula

Given the scaling law formula for training loss:
loss = a * (N)^-b + c where N is the number of parameters, a=10, b=1/3, and c=0.1. What is the training loss when N=1000000?

Prompt Engineering / GenAI

a = 10
b = 1/3
c = 0.1
N = 1000000
loss = a * (N)**(-b) + c
print(round(loss, 4))

A 0.2

B 0.4

C 0.3

D 0.5

💡 Hint

Calculate N to the power of -b first, then multiply by a and add c.

1000000 = 10^6, so (10^6)^{-1/3} = 10^{-6/3} = 10^{-2} = 0.01 exactly. Then 10 * 0.01 = 0.1, plus c = 0.1 gives loss = 0.2 exactly. round(0.2, 4) outputs 0.2000, corresponding to 0.2.