Q-BIOLAT: Binary Latent Protein Fitness Landscapes for QUBO-Based Optimization

Protein fitness optimization is inherently a discrete combinatorial problem, yet most learning-based approaches rely on continuous representations and are primarily evaluated through predictive accuracy. We introduce Q-BIOLAT, a framework for modeling and optimizing protein fitness landscapes in compact binary latent spaces. Starting from pretrained protein language model embeddings, we construct binary latent representations and learn a quadratic unconstrained binary optimization (QUBO) surrogate that captures unary and pairwise interactions. Beyond its formulation, Q-BIOLAT provides a representation-centric perspective on protein fitness modeling. We show that representations with similar predictive performance can induce fundamentally different optimization landscapes. In particular, learned autoencoder-based representations collapse after binarization, producing degenerate latent spaces that fail to support combinatorial search, whereas simple structured representations such as PCA yield high-entropy, decodable, and optimization-friendly latent spaces. Across multiple datasets and data regimes, we demonstrate that classical combinatorial optimization methods, including simulated annealing, genetic algorithms, and greedy hill climbing, are highly effective in structured binary latent spaces. By expressing the objective in QUBO form, our approach connects modern machine learning with discrete and quantum-inspired optimization. Our implementation and dataset are publicly available at: https://github.com/HySonLab/Q-BIOLAT-Extended