### **Multinomial Sampling in Text Generation**

**Multinomial Sampling** (also known as *ancestral sampling*) is a text generation strategy that contrasts with greedy search by allowing randomness in token selection. Instead of always picking the token with the highest probability, multinomial sampling selects the next token based on the entire probability distribution provided by the model. Each token in the vocabulary has a chance to be chosen, with tokens that have a higher probability being more likely to be selected, but any token with a non-zero probability can be selected. This approach introduces variability and can reduce the risk of repetitive outputs.

### **How Multinomial Sampling Works:**
- **Greedy Search** always picks the most probable next token, leading to predictable but often repetitive text.
- **Multinomial Sampling** selects the next token randomly based on the probability distribution, allowing for more varied and creative outputs.

This method is especially useful for tasks where you want diverse, less repetitive text generation, and it can help when the generation should not always follow the most probable sequence.

### **Key Parameters for Multinomial Sampling:**
- **`do_sample=True`**: This enables sampling-based decoding, as opposed to deterministic approaches like greedy search or beam search.
- **`num_beams=1`**: Ensures that beam search is not used, as it would override the sampling mechanism.

### **Example Code for Multinomial Sampling:**

```python
from transformers import AutoTokenizer, AutoModelForCausalLM, set_seed

# Set a seed for reproducibility
set_seed(0)

# Define the checkpoint and tokenizer
checkpoint = "openai-community/gpt2-large"
tokenizer = AutoTokenizer.from_pretrained(checkpoint)
model = AutoModelForCausalLM.from_pretrained(checkpoint)

# Define the prompt and prepare inputs
prompt = "Today was an amazing day because"
inputs = tokenizer(prompt, return_tensors="pt")

# Generate text using multinomial sampling with do_sample=True and num_beams=1
outputs = model.generate(**inputs, do_sample=True, num_beams=1, max_new_tokens=100)

# Decode the generated text
generated_text = tokenizer.batch_decode(outputs, skip_special_tokens=True)
print(generated_text)
```

### **Explanation:**
- **`do_sample=True`**: Enables the sampling mechanism.
- **`num_beams=1`**: Ensures that beam search is not applied, and only a single candidate sequence is considered.
- **`max_new_tokens=100`**: Limits the generated text to 100 tokens beyond the input prompt.
- **Prompt**: `"Today was an amazing day because"` serves as the input for the model to generate a continuation.

### **Generated Output:**
```plaintext
Today was an amazing day because we received these wonderful items by the way of a gift shop. The box arrived on a Thursday and I opened it on Monday afternoon to receive the gifts. Both bags featured pieces from all the previous years!

The box had lots of surprises in it, including some sweet little mini chocolate chips! I don't think I'd eat all of these. This was definitely one of the most expensive presents I have ever got, I actually got most of them for free!

The first package came
```

### **When to Use Multinomial Sampling:**
- **Creativity and Diversity**: Multinomial sampling is useful when you want to introduce more variety in the generated text, especially for creative tasks like storytelling or idea generation.
- **Avoiding Repetition**: Unlike greedy search, this method helps reduce repetitive outputs by allowing tokens with lower probabilities to be selected, making it more suitable for generating long-form, less predictable content.

By enabling **`do_sample=True`** and setting **`num_beams=1`**, multinomial sampling offers a flexible and probabilistic approach to text generation, producing more diverse and engaging results.