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TASK: The challenge is to develop a hybrid advanced decoding strategy for natural language generation (NLG) that combines multiple methods, including beam search, sampling, and contrastive techniques, to balance diversity, coherence, and efficiency while minimizing repetition and adhering to constraints for generating high-quality, contextually relevant sequences.
(only torch module)

idea 1
Algorithm: Hybrid Advanced Decoding with Multi-Strategy Control

Input: 
  - Model (M)
  - Input Sequence (X)
  - Decoding Parameters: 
      * beam_width (b),
      * top_k (k),
      * top_p (p),
      * temperature (T),
      * repetition_penalty (r),
      * length_penalty (l),
      * forced_sequence (F),
      * constraints (C),
      * max_length (L)

Output:
  - Decoded Sequence (Y)

1. Initialize:
    a. Candidate Sequences (S) ← [Start Token]
    b. Beam Probabilities (P) ← [1.0]  // For Beam Search initialization
    c. Best Sequence (Y_best) ← []
    d. Max Utility (U_max) ← -∞  // For MBR Decoding utility calculations

2. FOR step t from 1 to max_length (L) DO:
    
    3. IF using Beam Search THEN:
        a. Expand each beam (S) using model predictions P_t ← M(X, S)
        b. Apply length_penalty to adjust scores: P_t ← P_t / (t^l)
        c. Select top b beams using Beam Search:
            i. For each candidate beam, calculate overall probability.
            ii. Prune low-probability beams.
    
    4. IF using Diverse Beam Search THEN:
        a. Penalize similarity between beams to improve diversity:
            i. For each beam pair, compute similarity penalty.
            ii. Adjust probabilities accordingly.
    
    5. IF using Sampling-based decoding THEN:
        a. Apply Top-k Sampling: Limit token set to top k candidates by probability.
        b. Apply Top-p Sampling: Select tokens whose cumulative probability ≥ p.
        c. Apply Temperature Scaling: Adjust logits P_t ← P_t / T.
        d. Sample next token based on modified probabilities.

    6. Apply Repetition Penalty:
        a. Penalize logit scores of repeated tokens in the sequence.

    7. Apply Constraints (IF applicable):
        a. Constrained Decoding: Restrict next token to allowable set defined by constraints C.
    
    8. IF using Forced Decoding THEN:
        a. Force the next token in the sequence to follow predefined token F if at the corresponding position.
    
    9. IF using Minimum Bayes Risk (MBR) Decoding THEN:
        a. Evaluate expected risk for each candidate sequence.
        b. Update the Best Sequence (Y_best) based on minimized risk utility (U).
    
    10. IF using Contrastive Search THEN:
        a. Combine greedy selection of high-probability tokens with contrastive token selection for diversity.
    
    11. Check stopping criteria:
        a. IF all beams end with an End Token or reach max_length (L) THEN:
            BREAK loop.
    
12. Return the Best Sequence (Y_best) or highest-scoring beam.