LLM scaling laws in Prompt Engineering / GenAI - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the total number of parameters in a transformer model.

Prompt Engineering / GenAI

total_params = num_layers * num_heads * [1]

Drag options to blanks, or click blank then click option'

Ahidden_size

Bbatch_size

Csequence_length

Dlearning_rate

Attempts:

3 left

💡 Hint

Common Mistakes

Using batch size instead of hidden size

Confusing sequence length with parameter count

The total number of parameters depends on the hidden size, number of layers, and heads.

2fill in blank

medium

Complete the code to compute the loss decay rate over training steps.

Prompt Engineering / GenAI

loss = initial_loss * (step)[1]decay_rate

Drag options to blanks, or click blank then click option'

A*

B**

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of exponentiation

Using addition or subtraction incorrectly

Loss typically decays as a power law, so we use the power operator.

3fill in blank

hard

Fix the error in the code to calculate the optimal model size given compute budget.

Prompt Engineering / GenAI

optimal_size = compute_budget [1] (training_steps * batch_size)

Drag options to blanks, or click blank then click option'

A/

B*

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division

Adding or subtracting compute budget incorrectly

Optimal size is compute budget divided by total training tokens (steps * batch size).

4fill in blank

hard

Fill both blanks to create a dictionary of loss values over epochs where loss decreases.

Prompt Engineering / GenAI

losses = {epoch: initial_loss * (decay_rate [1] epoch) for epoch in range(1, num_epochs + 1) if epoch [2] max_epoch}

Drag options to blanks, or click blank then click option'

A**

B<=

C>

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of exponentiation

Using '>' instead of '<=' for filtering epochs

Loss decreases exponentially with epochs (using '**'), and we include epochs up to max_epoch (using '<=').

5fill in blank

hard

Fill all three blanks to create a dictionary mapping model sizes to their expected loss if loss decreases with size.

Prompt Engineering / GenAI

expected_losses = {size: base_loss [1] (size [2] scale_factor) [3] 2 for size in model_sizes if size [2] scale_factor}

Drag options to blanks, or click blank then click option'

A-

B/

C**

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction instead of division

Using wrong operator for power

Confusing division with multiplication

Loss decreases with size: base_loss / ((size / scale_factor) ** 2).

Practice

1. What do LLM scaling laws primarily describe in language model training?

easy

A. The syntax rules for writing code in AI frameworks

B. How model size, data amount, and compute resources affect performance

C. The best way to label data for supervised learning

D. How to deploy models on mobile devices

Solution

1. Step 1: Understand the purpose of scaling laws

   LLM scaling laws explain the relationship between model size, data, and compute with model performance.

2. Step 2: Match the description to options

   Only How model size, data amount, and compute resources affect performance correctly describes this relationship, while others talk about unrelated topics.

3. Final Answer:

   How model size, data amount, and compute resources affect performance -> Option B

4. Quick Check:

   Scaling laws = model size, data, compute impact [OK]

Hint: Focus on model size, data, and compute impact keywords [OK]

Common Mistakes:

• Confusing scaling laws with coding syntax
• Thinking scaling laws are about data labeling
• Assuming scaling laws relate to deployment

2. Which of the following is the correct formula representing a simplified LLM scaling law for loss L as a function of model parameters N and dataset size D?

easy

A. L = a / (N + D)

B. L = a + b * N + c * D

C. L = a * log(N) + b * log(D)

D. L = a * N^(-b) + c * D^(-d)

Solution

1. Step 1: Recall the typical scaling law form

   Scaling laws often show loss decreases as power laws of model size and data, like L = a * N^(-b) + c * D^(-d).

2. Step 2: Compare options to this form

   L = a * N^(-b) + c * D^(-d) matches the power law form; others use linear or logarithmic forms which are incorrect.

3. Final Answer:

   L = a * N^(-b) + c * D^(-d) -> Option D

4. Quick Check:

   Loss decreases as power laws of N and D [OK]

Hint: Look for power law (exponent) form in the formula [OK]

Common Mistakes:

• Choosing linear formulas instead of power laws
• Confusing logarithmic with power law forms
• Ignoring the negative exponents for loss decrease

3. Consider this Python code simulating a simplified LLM loss calculation:

def loss(N, D, a=1.0, b=0.5, c=1.0, d=0.3):
    return a * N**(-b) + c * D**(-d)

print(round(loss(1000, 10000), 4))

What is the output?

medium

A. 0.0947

B. 0.1265

C. 0.0316

D. 1.0000

Solution

1. Step 1: Calculate each term separately

   N=1000, b=0.5: 1000**(-0.5) = 1/sqrt(1000) ≈ 0.0316
   D=10000, d=0.3: 10000**(-0.3) ≈ 0.0631

2. Step 2: Sum the terms and round to 4 decimals

   1.0 * 0.0316 + 1.0 * 0.0631 = 0.0947

3. Final Answer:

   0.0947 -> Option A

4. Quick Check:

   N**(-0.5) + D**(-0.3) ≈ 0.0316 + 0.0631 = 0.0947 [OK]

Hint: Calculate each power term separately, then sum [OK]

Common Mistakes:

• Calculating only one term instead of sum
• Mixing up exponents or signs
• Rounding too early causing errors

4. The following code aims to compute loss using LLM scaling laws but has a bug:

def loss(N, D, a=1.0, b=0.5, c=1.0, d=0.3):
    return a * N**b + c * D**d

print(round(loss(1000, 10000), 4))

What is the main error?

medium

A. Function should return a tuple, not a single value

B. Missing multiplication operator between variables

C. Exponents should be negative to show loss decreases with size

D. Parameters a and c should be integers only

Solution

1. Step 1: Identify the intended formula

   LLM scaling laws show loss decreases as model size and data increase, so exponents must be negative.

2. Step 2: Check the code exponents

   The code uses positive exponents (N**b and D**d), which incorrectly increase loss with size.

3. Final Answer:

   Exponents should be negative to show loss decreases with size -> Option C

4. Quick Check:

   Negative exponents mean loss decreases as size grows [OK]

Hint: Remember loss decreases, so exponents must be negative [OK]

Common Mistakes:

• Thinking multiplication is missing
• Believing return type must be tuple
• Assuming parameter types must be integers

5. You want to reduce the loss of a large language model efficiently. According to LLM scaling laws, which strategy is best if you have limited compute but can increase data or model size?

hard

A. Increase dataset size moderately while keeping model size fixed

B. Increase model size drastically without adding data

C. Keep both model size and data fixed and train longer

D. Reduce dataset size to speed up training

Solution

1. Step 1: Understand compute constraints and scaling laws

   Scaling laws show loss improves with both model size and data, but compute limits large model increases.

2. Step 2: Choose strategy fitting limited compute

   Increasing data moderately is cheaper than drastically increasing model size, so Increase dataset size moderately while keeping model size fixed is best.

3. Final Answer:

   Increase dataset size moderately while keeping model size fixed -> Option A

4. Quick Check:

   Limited compute favors data increase over big model growth [OK]

Hint: With limited compute, grow data before model size [OK]

Common Mistakes:

• Thinking bigger model always better regardless of compute
• Ignoring compute limits and training time
• Reducing data harms performance