Enhanced matrix inference with Seq2seq models via diagonal sorting

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Mathematics

Background:

• Sequence-to-sequence (seq2seq) models excel in natural language processing.
• Extending seq2seq models to mathematical computing shows promise, treating tasks as machine translation.
• Generic sorting strategies limit seq2seq models in inferring on matrices of unseen rank.

Purpose of the Study:

• To address the limitations of generic sorting in seq2seq models for matrix-based tasks.
• To propose a novel diagonal-based sorting method for the matrix-to-sequence process.
• To enhance the inference capabilities of seq2seq models for matrices with varying ranks.

Main Methods:

• Developed a diagonal-based sorting approach to create stable element ordering for principal submatrices.
• Constructed stable ordering structures for shared leading principal submatrix sections.
• Compared seq2seq models with generic sorting against the proposed diagonal-based sorting.

Main Results:

• The proposed diagonal-based sorting significantly improves seq2seq model inference on matrices of unseen rank.
• Experiments involving maximal independent sets and Sudoku laws validated the method's effectiveness.
• The diagonal-based sorting overcomes the suboptimal performance of generic methods.

Conclusions:

• Diagonal-based sorting enhances seq2seq model suitability for matrix inclusion law investigations.
• The novel method expands the application of seq2seq models to complex matrix-related computational tasks.
• This approach offers a more robust solution for matrix inference problems using seq2seq architectures.