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

arXiv: https://arxiv.org/abs/2603.27526 · HTML: https://mlsanity.com/paper/2603.27526/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 29 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Multiresolution Equivariant Graph Variational Autoencoder](https://mlsanity.com/paper/2106.00967/) (2021)
- [Multi-Objective Latent Space Optimization of Generative Molecular Design Models](https://mlsanity.com/paper/2203.00526/) (2022)
- [COIL: Constrained Optimization in Learned Latent Space: Learning Representations for Valid Solutions](https://mlsanity.com/paper/2202.02163/) (2022)
- [Quantum Annealing for Combinatorial Optimization: A Benchmarking Study](https://mlsanity.com/paper/2504.06201/) (2025)
- [Effectiveness of Binary Autoencoders for QUBO-Based Optimization Problems](https://mlsanity.com/paper/2602.10037/) (2026)

## Abstract (arXiv)

Protein fitness optimization is a discrete search problem, and the representation used for prediction also determines the neighborhood graph traversed by an optimizer. We introduce Q-BioLat, a framework that maps pretrained protein-language-model embeddings to compact binary codes and fits a quadratic unconstrained binary optimization (QUBO) surrogate with unary and pairwise latent interactions. Our central contribution is an optimization-aware view of representation: binary encodings that are similar in pointwise predictive accuracy can induce different Hamming neighborhoods, local optima, and search trajectories. We formalize when a recoding is only a Hamming-isometric reparameterization and give a constructive example showing that exact pointwise agreement does not imply optimization equivalence. We study experimentally measured GFP and AAV fitness landscapes from ProteinGym. The internal QUBO surrogate is evaluated against labels withheld from QUBO fitting. A conservative retrieval analysis maps optimized codes to measured variants and reports their experimental fitness, while neural decoding of potentially unmeasured sequences is evaluated separately with an experiment-trained sequence surrogate and is interpreted only as model-based candidate prioritization. Across the reported comparisons, PCA followed by per-coordinate median thresholding yields a more balanced and decodable binary space than the post-hoc-zero-threshold AE/VAE baselines, despite the latter's low continuous reconstruction error. In the measured-library retrieval analysis, simulated annealing, genetic algorithms, and greedy hill climbing frequently return high-percentile variants; decoded candidates are reported separately using surrogate-predicted scores.