# Variational Search Distributions

arXiv: https://arxiv.org/abs/2409.06142 · HTML: https://mlsanity.com/paper/2409.06142/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 93 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 30 of 49)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Implicit Gradient Regularization](https://mlsanity.com/paper/2009.11162/) (2020)
- [On the linearity of large non-linear models: when and why the tangent kernel is constant](https://mlsanity.com/paper/2010.01092/) (2020)
- [A Survey of Controllable Text Generation using Transformer-based Pre-trained Language Models](https://mlsanity.com/paper/2201.05337/) (2022)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Infinite attention: NNGP and NTK for deep attention networks](https://mlsanity.com/paper/2006.10540/) (2020)
- [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)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS](https://mlsanity.com/paper/2009.10683/) (2020)
- [Formal Algorithms for Transformers](https://mlsanity.com/paper/2207.09238/) (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)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterization](https://mlsanity.com/paper/2210.10199/) (2022)

## Built on by (most cited first, 6 of 6)

- [Generalists vs. Specialists: Evaluating LLMs on Highly-Constrained Biophysical Sequence Optimization Tasks](https://mlsanity.com/paper/2410.22296/) (2024)
- [Generative Bayesian Optimization: Generative Models as Acquisition Functions](https://mlsanity.com/paper/2510.25240/) (2025)
- [Variational Transdimensional Inference](https://mlsanity.com/paper/2506.04749/) (2025)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)
- [Kernel-based guarantees for nonlinear parametric models in Bayesian optimization](https://mlsanity.com/paper/2605.13160/) (2026)
- [Sample-Efficient Optimisation over the Outputs of Generative Models](https://mlsanity.com/paper/2509.23800/) (2025)

## Abstract (arXiv)

We develop VSD, a method for conditioning a generative model of discrete, combinatorial designs on a rare desired class by efficiently evaluating a black-box (e.g. experiment, simulation) in a batch sequential manner. We call this task active generation; we formalize active generation's requirements and desiderata, and formulate a solution via variational inference. VSD uses off-the-shelf gradient based optimization routines, can learn powerful generative models for desirable designs, and can take advantage of scalable predictive models. We derive asymptotic convergence rates for learning the true conditional generative distribution of designs with certain configurations of our method. After illustrating the generative model on images, we empirically demonstrate that VSD can outperform existing baseline methods on a set of real sequence-design problems in various protein and DNA/RNA engineering tasks.