Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods.
This paper explores the connections between optimal transport and variational inference, with a focus on forward and reverse time stochastic differential equations and Girsanov transformations.We present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of a novel score-based annealed flow technique (with connections to Jarzynski and Crooks identities from statistical physics) and a regularised iterative proportional fitting (IPF)-type objective, departing from the sequential nature of standard IPF. Through a series of generative modelling examples and a double-well-based rare event task, we showcase the potential of the proposed methods.
Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into a Gaussian. Samples from the generative model are then obtained by simulating an approximation of the time reversal of this diffusion initialized by Gaussian samples. Recent research has explored adapting diffusion models for sampling and inference tasks. In this paper, we leverage known connections to stochastic control akin to the F\"ollmer drift to extend established neural network approximation results for the F\"ollmer drift to denoising diffusion models and samplers.
Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation, noise reduction and efficient downstream processing of the data. In this work, we introduce the ProbDR variational framework, which interprets a wide range of classical DR algorithms as probabilistic inference algorithms in this framework. ProbDR encompasses PCA, CMDS, LLE, LE, MVU, diffusion maps, kPCA, Isomap, (t-)SNE, and UMAP. In our framework, a low-dimensional latent variable is used to construct a covariance, precision, or a graph Laplacian matrix, which can be used as part of a generative model for the data. Inference is done by optimizing an evidence lower bound. We demonstrate the internal consistency of our framework and show that it enables the use of probabilistic programming languages (PPLs) for DR. Additionally, we illustrate that the framework facilitates reasoning about unseen data and argue that our generative models approximate Gaussian processes (GPs) on manifolds. By providing a unified view of DR, our framework facilitates communication, reasoning about uncertainties, model composition, and extensions, particularly when domain knowledge is present.
Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution. Samples from the generative model are then obtained by simulating an approximation of the time-reversal of this diffusion initialized by Gaussian samples. Practically, the intractable score terms appearing in the time-reversed process are approximated using score matching techniques. We explore here a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. We consider a process where the target density diffuses towards a Gaussian. Denoising Diffusion Samplers (DDS) are obtained by approximating the corresponding time-reversal. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling. Existing theoretical results from denoising diffusion models also provide theoretical guarantees for DDS. We discuss the connections between DDS, optimal control and Schr\"odinger bridges and finally demonstrate DDS experimentally on a variety of challenging sampling tasks.
The representation space of neural models for textual data emerges in an unsupervised manner during training. Understanding how human-interpretable concepts, such as gender, are encoded in these representations would improve the ability of users to \emph{control} the content of these representations and analyze the working of the models that rely on them. One prominent approach to the control problem is the identification and removal of linear concept subspaces -- subspaces in the representation space that correspond to a given concept. While those are tractable and interpretable, neural network do not necessarily represent concepts in linear subspaces. We propose a kernalization of the linear concept-removal objective of [Ravfogel et al. 2022], and show that it is effective in guarding against the ability of certain nonlinear adversaries to recover the concept. Interestingly, our findings suggest that the division between linear and nonlinear models is overly simplistic: when considering the concept of binary gender and its neutralization, we do not find a single kernel space that exclusively contains all the concept-related information. It is therefore challenging to protect against \emph{all} nonlinear adversaries at once.
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control. We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.
Deep neural networks have a wide range of applications across multiple domains such as computer vision and medicine. In many cases, the input of a model at inference time can consist of sensitive user data, which raises questions concerning the levels of privacy and trust guaranteed by such services. Much existing work has leveraged homomorphic encryption (HE) schemes that enable computation on encrypted data to achieve private inference for multi-layer perceptrons and CNNs. An early work along this direction was CryptoNets, which takes 250 seconds for one MNIST inference. The main limitation of such approaches is that of compute, which is due to the costly nature of the NTT (number theoretic transform)operations that constitute HE operations. Others have proposed the use of model pruning and efficient data representations to reduce the number of HE operations required. In this paper, we focus on improving upon existing work by proposing changes to the representations of intermediate tensors during CNN inference. We construct and evaluate private CNNs on the MNIST and CIFAR-10 datasets, and achieve over a two-fold reduction in the number of operations used for inferences of the CryptoNets architecture.
The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schr\"odinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.
Bolukbasi et al. (2016) presents one of the first gender bias mitigation techniques for word embeddings. Their method takes pre-trained word embeddings as input and attempts to isolate a linear subspace that captures most of the gender bias in the embeddings. As judged by an analogical evaluation task, their method virtually eliminates gender bias in the embeddings. However, an implicit and untested assumption of their method is that the bias sub-space is actually linear. In this work, we generalize their method to a kernelized, non-linear version. We take inspiration from kernel principal component analysis and derive a non-linear bias isolation technique. We discuss and overcome some of the practical drawbacks of our method for non-linear gender bias mitigation in word embeddings and analyze empirically whether the bias subspace is actually linear. Our analysis shows that gender bias is in fact well captured by a linear subspace, justifying the assumption of Bolukbasi et al. (2016).