Implement Batch-Level Parallelism for Multiscale Processing #161

Problem

The current implementation processes each element in a batch sequentially during the multiscale decomposition and mixing phases. This approach doesn't leverage modern GPU architecture effectively, resulting in suboptimal training performance.

Impact

• Training is slower than it could be
• Inefficient GPU utilization
• Limited scaling to larger batch sizes

Proposed Solution

Refactor the multiscale processing operations to support true batch-level parallelism:

1. Rewrite the __multi_scale_process_inputs method to operate on entire batches simultaneously
2. Optimize the mixing operations in MultiScaleSeasonMixing and MultiScaleTrendMixing classes
3. Vectorize operations where possible to avoid sequential processing

Technical Details

The issue is primarily in models/TimeMixer.py where several functions process batch elements one at a time:

# Current approach (pseudocode)
for i in range(B):  # Process each sample in batch sequentially
    # Process sample i
    ...

# Proposed approach (pseudocode)
# Process entire batch at once with tensor operations
...

Specific attention should be given to:

• The __multi_scale_process_inputs method
• future_multi_mixing implementation
• Batch handling in PastDecomposableMixing

Expected Outcome

• Significant speedup in training time (estimated 30-50%)
• Better GPU utilization
• Ability to scale to larger batch sizes with near-linear performance

Implementation Complexity

Medium - requires careful refactoring of core model operations while maintaining numerical equivalence.