Protein Design with Guided Discrete Diffusion

A popular approach to protein design is to combine a generative model with a discriminative model for conditional sampling. The generative model samples plausible sequences while the discriminative model guides a search for sequences with high fitness. Given its broad success in conditional sampling, classifier-guided diffusion modeling is a promising foundation for protein design, leading many to develop guided diffusion models for structure with inverse folding to recover sequences. In this work, we propose diffusioN Optimized Sampling (NOS), a guidance method for discrete diffusion models that follows gradients in the hidden states of the denoising network. NOS makes it possible to perform design directly in sequence space, circumventing significant limitations of structure-based methods, including scarce data and challenging inverse design. Moreover, we use NOS to generalize LaMBO, a Bayesian optimization procedure for sequence design that facilitates multiple objectives and edit-based constraints. The resulting method, LaMBO-2, enables discrete diffusions and stronger performance with limited edits through a novel application of saliency maps. We apply LaMBO-2 to a real-world protein design task, optimizing antibodies for higher expression yield and binding affinity to a therapeutic target under locality and liability constraints, with 97% expression rate and 25% binding rate in exploratory in vitro experiments.

Bayesian Optimization with Conformal Coverage Guarantees

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.

PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence design

Bayesian optimization offers a sample-efficient framework for navigating the exploration-exploitation trade-off in the vast design space of biological sequences. Whereas it is possible to optimize the various properties of interest jointly using a multi-objective acquisition function, such as the expected hypervolume improvement (EHVI), this approach does not account for objectives with a hierarchical dependency structure. We consider a common use case where some regions of the Pareto frontier are prioritized over others according to a specified $\textit{partial ordering}$ in the objectives. For instance, when designing antibodies, we would like to maximize the binding affinity to a target antigen only if it can be expressed in live cell culture -- modeling the experimental dependency in which affinity can only be measured for antibodies that can be expressed and thus produced in viable quantities. In general, we may want to confer a partial ordering to the properties such that each property is optimized conditioned on its parent properties satisfying some feasibility condition. To this end, we present PropertyDAG, a framework that operates on top of the traditional multi-objective BO to impose this desired ordering on the objectives, e.g. expression $\rightarrow$ affinity. We demonstrate its performance over multiple simulated active learning iterations on a penicillin production task, toy numerical problem, and a real-world antibody design task.

Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders

Bayesian optimization is a gold standard for query-efficient continuous optimization. However, its adoption for drug and antibody sequence design has been hindered by the discrete, high-dimensional nature of the decision variables. We develop a new approach (LaMBO) which jointly trains a denoising autoencoder with a discriminative multi-task Gaussian process head, enabling gradient-based optimization of multi-objective acquisition functions in the latent space of the autoencoder. These acquisition functions allow LaMBO to balance the explore-exploit trade-off over multiple design rounds, and to balance objective tradeoffs by optimizing sequences at many different points on the Pareto frontier. We evaluate LaMBO on a small-molecule task based on the ZINC dataset and introduce a new large-molecule task targeting fluorescent proteins. In our experiments, LaMBO outperforms genetic optimizers and does not require a large pretraining corpus, demonstrating that Bayesian optimization is practical and effective for biological sequence design.

Deconstructing the Inductive Biases of Hamiltonian Neural Networks

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world systems, such as those that don't conserve energy or contain contacts, a common setting for robotics and reinforcement learning. In this paper, we examine the inductive biases that make physics-inspired models successful in practice. We show that, contrary to conventional wisdom, the improved generalization of HNNs is the result of modeling acceleration directly and avoiding artificial complexity from the coordinate system, rather than symplectic structure or energy conservation. We show that by relaxing the inductive biases of these models, we can match or exceed performance on energy-conserving systems while dramatically improving performance on practical, non-conservative systems. We extend this approach to constructing transition models for common Mujoco environments, showing that our model can appropriately balance inductive biases with the flexibility required for model-based control.

Conditioning Sparse Variational Gaussian Processes for Online Decision-making

With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least $\mathcal{O}(n^2)$ computations for $n$ training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does not require re-training through the evidence lower bound with the addition of new data. OVC enables the pairing of SVGPs with advanced look-ahead acquisition functions for black-box optimization, even with non-Gaussian likelihoods. We show OVC provides compelling performance in a range of applications including active learning of malaria incidence, and reinforcement learning on MuJoCo simulated robotic control tasks.

Does Knowledge Distillation Really Work?

Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not typically work as it is commonly understood: there often remains a surprisingly large discrepancy between the predictive distributions of the teacher and the student, even in cases when the student has the capacity to perfectly match the teacher. We identify difficulties in optimization as a key reason for why the student is unable to match the teacher. We also show how the details of the dataset used for distillation play a role in how closely the student matches the teacher -- and that more closely matching the teacher paradoxically does not always lead to better student generalization.

Kernel Interpolation for Scalable Online Gaussian Processes

Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $O(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently recycle computations for constant-time $O(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting. Code is available at https://github.com/wjmaddox/online_gp.

On the model-based stochastic value gradient for continuous reinforcement learning

Model-based reinforcement learning approaches add explicit domain knowledge to agents in hopes of improving the sample-efficiency in comparison to model-free agents. However, in practice model-based methods are unable to achieve the same asymptotic performance on challenging continuous control tasks due to the complexity of learning and controlling an explicit world model. In this paper we investigate the stochastic value gradient (SVG), which is a well-known family of methods for controlling continuous systems which includes model-based approaches that distill a model-based value expansion into a model-free policy. We consider a variant of the model-based SVG that scales to larger systems and uses 1) an entropy regularization to help with exploration, 2) a learned deterministic world model to improve the short-horizon value estimate, and 3) a learned model-free value estimate after the model's rollout. This SVG variation captures the model-free soft actor-critic method as an instance when the model rollout horizon is zero, and otherwise uses short-horizon model rollouts to improve the value estimate for the policy update. We surpass the asymptotic performance of other model-based methods on the proprioceptive MuJoCo locomotion tasks from the OpenAI gym, including a humanoid. We notably achieve these results with a simple deterministic world model without requiring an ensemble.

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.