Tuan Anh Le

Marco Bertolini, Tuan Le, Djork-Arné Clevert

We introduce a novel class of score-based diffusion processes that operate directly in the representation space of Lie groups. Leveraging the framework of Generalized Score Matching, we derive a class of Langevin dynamics that decomposes as a direct sum of Lie algebra representations, enabling the modeling of any target distribution on any (non-Abelian) Lie group. Standard score-matching emerges as a special case of our framework when the Lie group is the translation group. We prove that our generalized generative processes arise as solutions to a new class of paired stochastic differential equations (SDEs), introduced here for the first time. We validate our approach through experiments on diverse data types, demonstrating its effectiveness in real-world applications such as SO(3)-guided molecular conformer generation and modeling ligand-specific global SE(3) transformations for molecular docking, showing improvement in comparison to Riemannian diffusion on the group itself. We show that an appropriate choice of Lie group enhances learning efficiency by reducing the effective dimensionality of the trajectory space and enables the modeling of transitions between complex data distributions.

Robin Winter, Marco Bertolini, Tuan Le et al.

Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and equivariant representation learning to the field of unsupervised deep learning. We propose a general learning strategy based on an encoder-decoder framework in which the latent representation is separated in an invariant term and an equivariant group action component. The key idea is that the network learns to encode and decode data to and from a group-invariant representation by additionally learning to predict the appropriate group action to align input and output pose to solve the reconstruction task. We derive the necessary conditions on the equivariant encoder, and we present a construction valid for any G, both discrete and continuous. We describe explicitly our construction for rotations, translations and permutations. We test the validity and the robustness of our approach in a variety of experiments with diverse data types employing different network architectures.

Vaden Masrani, Tuan Anh Le, Frank Wood

We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We use the TVO to learn both discrete and continuous deep generative models and empirically demonstrate state of the art model and inference network learning.

Tuan Anh Le, Adam R. Kosiorek, N. Siddharth et al.

Stochastic control-flow models (SCFMs) are a class of generative models that involve branching on choices from discrete random variables. Amortized gradient-based learning of SCFMs is challenging as most approaches targeting discrete variables rely on their continuous relaxations---which can be intractable in SCFMs, as branching on relaxations requires evaluating all (exponentially many) branching paths. Tractable alternatives mainly combine REINFORCE with complex control-variate schemes to improve the variance of naive estimators. Here, we revisit the reweighted wake-sleep (RWS) (Bornschein and Bengio, 2015) algorithm, and through extensive evaluations, show that it outperforms current state-of-the-art methods in learning SCFMs. Further, in contrast to the importance weighted autoencoder, we observe that RWS learns better models and inference networks with increasing numbers of particles. Our results suggest that RWS is a competitive, often preferable, alternative for learning SCFMs.

Tuan Anh Le, Maximilian Igl, Tom Rainforth et al.

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models.