# Improving Protein Optimization with Smoothed Fitness Landscapes

arXiv: https://arxiv.org/abs/2307.00494 · HTML: https://mlsanity.com/paper/2307.00494/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 2 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [Evaluating Protein Transfer Learning with TAPE](https://mlsanity.com/paper/1906.08230/) (2019)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Local Latent Space Bayesian Optimization over Structured Inputs](https://mlsanity.com/paper/2201.11872/) (2022)
- [Tranception: protein fitness prediction with autoregressive transformers and inference-time retrieval](https://mlsanity.com/paper/2205.13760/) (2022)
- [AdaLead: A simple and robust adaptive greedy search algorithm for sequence design](https://mlsanity.com/paper/2010.02141/) (2020)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Protein Discovery with Discrete Walk-Jump Sampling](https://mlsanity.com/paper/2306.12360/) (2023)
- [Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMC](https://mlsanity.com/paper/2212.09925/) (2022)
- [Importance Weighted Expectation-Maximization for Protein Sequence Design](https://mlsanity.com/paper/2305.00386/) (2023)
- [Extrapolative Controlled Sequence Generation via Iterative Refinement](https://mlsanity.com/paper/2303.04562/) (2023)

## Built on by (most cited first, 21 of 21)

- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling](https://mlsanity.com/paper/2504.10612/) (2025)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Robust Optimization in Protein Fitness Landscapes Using Reinforcement Learning in Latent Space](https://mlsanity.com/paper/2405.18986/) (2024)
- [Improved Off-policy Reinforcement Learning in Biological Sequence Design](https://mlsanity.com/paper/2410.04461/) (2024)
- [Steering Generative Models with Experimental Data for Protein Fitness Optimization](https://mlsanity.com/paper/2505.15093/) (2025)
- [Steering Protein Language Models](https://mlsanity.com/paper/2509.07983/) (2025)
- [Variational Search Distributions](https://mlsanity.com/paper/2409.06142/) (2024)
- [Revealing Domain-Spatiality Patterns for Configuration Tuning: Domain Knowledge Meets Fitness Landscapes](https://mlsanity.com/paper/2603.19897/) (2026)
- [Rethinking Performance Analysis for Configurable Software Systems: A Case Study from a Fitness Landscape Perspective](https://mlsanity.com/paper/2412.16888/) (2024)
- [Advances in Protein Representation Learning: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2503.16659/) (2025)
- [ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoods](https://mlsanity.com/paper/2505.22494/) (2025)
- [Protein Circuit Tracing via Cross-layer Transcoders](https://mlsanity.com/paper/2602.12026/) (2026)
- [Speaking the Language of Science: Toward a General-Purpose Generative Foundation Model for the Natural Sciences](https://mlsanity.com/paper/2606.16905/) (2026)
- [GROOT: Effective Design of Biological Sequences with Limited Experimental Data](https://mlsanity.com/paper/2411.11265/) (2024)
- [One protein is all you need](https://mlsanity.com/paper/2411.02109/) (2024)
- [Efficient Protein Optimization via Structure-aware Hamiltonian Dynamics](https://mlsanity.com/paper/2601.11012/) (2026)
- [Repurposing Protein Language Models for Latent Flow-Based Fitness Optimization](https://mlsanity.com/paper/2602.02425/) (2026)
- [Feedback-Calibrated Protein Optimization with Batch-Aligned Tail Arbitration](https://mlsanity.com/paper/2609.37808/) (2026)
- [Structure-aware Reinforcement Learning for Protein Directed Evolution](https://mlsanity.com/paper/2609.39048/) (2026)
- [Generative Models as Adaptive Trust Regions for Discrete Bayesian Optimisation](https://mlsanity.com/paper/2610.16992/) (2026)

## Abstract (arXiv)

The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS