[Long-term] Investigate and improve cross-platform prediction consistency

[noahho]

Issue Description

When running TabPFN consistency tests across different platforms (e.g., macOS vs Linux, x86 vs ARM), we've observed significant differences in model predictions.

Current Observations:

1. Despite using , regression predictions on diabetes dataset still show differences:

   • On macOS (ARM):
   • On Linux CI:
   • Difference: ~2.34 (about ~1.6% relative difference)

2. Classification predictions seem more stable but still show small variations

Impact:

• Makes it difficult to have reproducible research/benchmarks across platforms
• Requires platform-specific consistency tests (as implemented in PR Add model consistency tests #217)
• Could affect production deployments across different infrastructures

Potential Causes:

• Different CPU architectures (x86 vs. ARM)
• Different BLAS/LAPACK implementations
• OS-specific optimizations
• Compiler-specific floating-point optimizations

Suggested Solutions to Investigate:

1. More aggressive precision control beyond sklearn's 16-decimal option
2. Implementation of deterministic mode that sacrifices some performance for better consistency
3. Platform detection with environment-specific reference values
4. Custom normalization/scaling approaches that are more robust to platform differences

Related PR:

PR #217 worked around this by making consistency tests platform-specific, but we should investigate a more fundamental solution.

Priority:

Medium - This is not breaking functionality but affects reproducibility