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 (logits or predictions or loss values)

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

Problem Statement:

In dialogue evaluation, these metrics assess the quality and effectiveness of responses within dialogue systems. Here are the typical mathematical formulations:

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### 1. **Dialogue Coherence Score**  
Dialogue Coherence Score generally measures the logical consistency and relevance of a response within the context of previous dialogue turns. Coherence is often human-evaluated on a scale (e.g., from 1 to 5), but can also be estimated using machine-learned models trained on coherent/incoherent dialogue examples. Since this score is generally a scaled value, it’s represented as:
\[
\text{Dialogue Coherence Score} = \frac{1}{B} \sum_{i=1}^{B} \text{Coherence}(r_i)
\]
where:
- \( B \) is the batch size (number of dialogues in the batch).
- \( \text{Coherence}(r_i) \) is the coherence rating (human-evaluated or model-predicted) for response \( r_i \) in each dialogue.

---

### 2. **Next-Response Relevance**  
Next-Response Relevance measures the probability or score indicating how well the predicted response \( r \) aligns with the next expected response in context. This can be derived from models trained on a next-response prediction task, such as by using softmax probabilities over a vocabulary.

The relevance score for each response is computed as:
\[
\text{Next-Response Relevance} = \frac{1}{B} \sum_{i=1}^{B} P(r_i | c_i)
\]
where:
- \( P(r_i | c_i) \) is the probability assigned by the model for response \( r_i \) given the context \( c_i \).
- \( B \) is the batch size (number of dialogue contexts).

This probability is often derived from the softmax output over a vocabulary or selection of candidate responses, indicating the likelihood of the predicted response being the most contextually relevant.

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### 3. **User Satisfaction**  
User Satisfaction aims to quantify the perceived quality or effectiveness of responses in fulfilling user needs within a dialogue. Satisfaction scores are often obtained through human evaluations or predicted via machine learning models trained on satisfaction-labeled data.

For user satisfaction score, the average score over the batch is calculated as:
\[
\text{User Satisfaction} = \frac{1}{B} \sum_{i=1}^{B} \text{Satisfaction}(r_i)
\]
where:
- \( B \) is the batch size (number of dialogues).
- \( \text{Satisfaction}(r_i) \) is the satisfaction rating or score (human-evaluated or model-predicted) for response \( r_i \) within each dialogue.

This metric provides insight into the overall effectiveness of the dialogue system, often reflecting factors like helpfulness, engagement, and appropriateness of responses.

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These metrics are crucial for evaluating the quality of dialogue systems in terms of coherence, response relevance, and user experience.