Following this instruction :
1. Strictly adhere to PEP-8 standards, ensuring code is clean, well-structured, and follows Python's style guide for readability.
2. Use appropriate modules like `typing` for type hints, ensuring code clarity, maintainability, and leveraging Python's standard libraries effectively.
3. Focus on time, space, robustness, scalability; write optimized, efficient code that can handle large datasets and scale seamlessly.
4. Implement comprehensive error handling, catching exceptions gracefully, providing meaningful error messages, and ensuring code robustness under unexpected conditions.
5. Ensure the developer agent writes advanced, maintainable Python code, balancing performance and readability while adhering to best practices.

TASK : Generalised robustness metrics Pipeline , 

NOTE : using the only torch module,  we have implement below scratch 

Problem Statement:

I'll explain Byte-Pair Encoding (BPE) tokenization step by step with mathematical details.

1) Initial Setup:

Let's start with a corpus of text C consisting of words W = {w₁, w₂, ..., wₙ}
Each word is initially split into individual characters/bytes plus a special end-of-word token '_'

2) Vocabulary Initialization:

Base vocabulary V₀ = {all unique characters/bytes in corpus}
Set of merged tokens M = {}
Target vocabulary size k

3) Frequency Counting:

For each word w in corpus:
   Split into characters: c₁c₂...cₘ
   Count frequency of all adjacent pairs (c₁,c₂), (c₂,c₃), ..., (cₘ₋₁,cₘ)

Mathematically:
freq(x,y) = Σ count((x,y) ∈ w) for all w ∈ W
where (x,y) is a pair of adjacent tokens

4) Merge Operation:

While |V₀ ∪ M| < k:
    1. Find most frequent pair (x,y):
       (x*,y*) = argmax(x,y) freq(x,y)
    
    2. Create new token z = x*+y*
    
    3. Add to merge set:
       M = M ∪ {z}
    
    4. Update corpus by replacing all occurrences of (x*,y*) with z

5) Mathematical Formalization of Merge:

For a word w = t₁t₂...tₙ (where tᵢ are current tokens):
If pair (tᵢ,tᵢ₊₁) = (x*,y*):
   Replace tᵢtᵢ₊₁ with z
   New word length = n-1

6) Tokenization Algorithm:

Input: word w
Output: sequence of tokens T

Algorithm:
1. Initialize w as character sequence: w = c₁c₂...cₘ
2. For each merge operation (x,y) → z in M (in order):
   Apply w = replace_all(w, xy, z)
3. Return resulting tokens T

7) Probability Model:

P(w) = P(t₁,t₂,...,tₖ) where w is tokenized as t₁t₂...tₖ

For subword tokenization:
P(w) = Π P(tᵢ|t₁...tᵢ₋₁)

8) Vocabulary Growth:

|V| = |V₀| + |M|
where |V₀| is initial vocabulary size
and |M| is number of merges

9) Compression Rate:

Compression Rate = Original text size / Tokenized text size
                = Σ|w| / Σ|T(w)|
where |w| is character length of word
and |T(w)| is token length after tokenization

10) Implementation Details:

a) Data Structure for storing frequencies:
   freq_dict = {(token1, token2): count}

b) Priority queue for merge operations:
   queue = PriorityQueue(key=freq_dict)

c) Token replacement:
   For each word:
       current_tokens = list(word)
       for merge_rule in merge_rules:
           apply_merge(current_tokens, merge_rule)

Example Python-like pseudocode:

```python
def train_bpe(corpus, num_merges):
    # Initialize vocabulary with characters
    vocab = set(char for word in corpus for char in word)
    
    # Initialize frequencies
    freq = defaultdict(int)
    for word in corpus:
        chars = list(word)
        for i in range(len(chars)-1):
            freq[(chars[i], chars[i+1])] += 1
    
    # Perform merges
    merges = []
    for i in range(num_merges):
        best_pair = max(freq.items(), key=lambda x: x[1])[0]
        merges.append(best_pair)
        update_frequencies(freq, best_pair)
        
    return vocab, merges

def tokenize(word, merges):
    tokens = list(word)
    for (x, y) in merges:
        tokens = apply_merge(tokens, x, y)
    return tokens
```

This algorithm provides a data-driven approach to building a subword vocabulary that balances vocabulary size with token frequency and meaningful subword units.