Due to its low storage cost and fast search speed, cross-modal retrieval based on hashing has attracted widespread attention and is widely used in real-world applications of social media search.

Unlike single-objective optimization, which aggregates objectives into a scalar through weighted sums, MOPs focus on generating specific or diverse Pareto solutions and learning the entire Pareto set directly.

Mathematical reasoning is an important capability of large language models (LLMs) for real-world applications.

Despite the development of several deep learning methods for predicting amino acid sequences (peptides) responsible for generating the observed mass spectra, training data biases hinder further advancements of de novo peptide sequencing. Firstly, prior methods struggle to identify amino acids with Post-Translational Modifications (PTMs) due to their lower frequency in training data compared to canonical amino acids, further resulting in unsatisfactory peptide sequencing performance. Secondly, various noise and missing peaks in mass spectra reduce the reliability of training data (Peptide-Spectrum Matches, PSMs).