# Q1 (2 marks)

Subject: Natural Language Processing

Exam: M2

Reader: https://deep-learning-study-room.vercel.app/nlp/#m2/mocks/mock-b/q1

Canonical: https://deep-learning-study-room.vercel.app/read/nlp/m2/mocks/mock-b--q1/

M2 · confirmed 2 + 2 + any two of 3 + 3 + 3 · worked practice

### Q1

A language model gives a test sequence probability of 0.0016 across four predicted tokens. Calculate perplexity. (2 marks)

**Given**

P=0.0016; N=4.

**To find**

PP.

### Formula and why it applies



$$
PP=P^{-1/N}=\left(\frac1P\right)^{1/N}
$$



Use the number of predicted events, not an unrelated training token count.

### Solution

#### Step 1. Reciprocal



$$
\frac1{0.0016}=625
$$



#### Step 2. Fourth root



$$
PP=625^{1/4}=5
$$



Perplexity=5.