ICLR 2025 Papers

We propose practical deep Gaussian process models on Riemannian manifolds, similar in spirit to residual neural networks. With manifold-to-manifold hidden layers and an arbitrary last layer, they can model manifold- and scalar-valued functions, as well as vector fields. We target data inherently supported on manifolds, which is too complex for shallow Gaussian processes thereon. For example, while the latter perform well on high-altitude wind data, they struggle with the more intricate, nonstationary patterns at low altitudes. Our models significantly improve performance in these settings, enhancing prediction quality and uncertainty calibration, and remain robust to overfitting, reverting to shallow models when additional complexity is unneeded. We further showcase our models on Bayesian optimisation problems on manifolds, using stylised examples motivated by robotics, and obtain substantial improvements in later stages of the optimisation process. Finally, we show our models to have potential for speeding up inference for non-manifold data, when, and if, it can be mapped to a proxy manifold well enough.

Generative Flow Networks (GFlowNets) are an emerging class of sampling methods for distributions over discrete and compositional objects, e.g., graphs. In spite of their remarkable success in problems such as drug discovery and phylogenetic inference, the question of when and whether GFlowNets learn to sample from the target distribution remains underexplored. To tackle this issue, we first assess the extent to which a violation of the detailed balance of the underlying flow network might hamper the correctness of GFlowNet's sampling distribution. In particular, we demonstrate that the impact of an imbalanced edge on the model's accuracy is influenced by the total amount of flow passing through it and, as a consequence, is unevenly distributed across the network. We also argue that, depending on the parameterization, imbalance may be inevitable. In this regard, we consider the problem of sampling from distributions over graphs with GFlowNets parameterized by graph neural networks (GNNs) and show that the representation limits of GNNs delineate which distributions these GFlowNets can approximate. Lastly, we address these limitations by proposing a theoretically sound and computationally tractable metric for assessing GFlowNets, experimentally showing it is a better proxy for correctness than popular evaluation protocols.

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable terms. To tackle this issue, state-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior and decompose its scores into two terms: the prior score and an intractable guidance term. While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated. In this paper, we propose a novel approach that utilises a decomposition of the transitions which, in contrast to previous methods, allows a trade-off between the complexity of the intractable guidance term and that of the prior transitions. We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems, including challenging cases with latent diffusion models as priors, and demonstrate its effectiveness in reconstructing electrocardiogram (ECG) from partial measurements for accurate cardiac diagnosis.

Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar loss function but instead correspond to solving a variational inequality (VI) problem. This difference in setting has caused many practical challenges as naive gradient-based approaches from supervised learning tend to diverge and cycle in the VI case. In this work, we propose a principled surrogate-based approach compatible with deep learning to solve VIs. We show that our surrogate-based approach has three main benefits: (1) under assumptions that are realistic in practice (when hidden monotone structure is present, interpolation, and sufficient optimization of the surrogates), it guarantees convergence, (2) it provides a unifying perspective of existing methods, and (3) is amenable to existing deep learning optimizers like ADAM. Experimentally, we demonstrate our surrogate-based approach is effective in min-max optimization and minimizing projected Bellman error. Furthermore, in the deep reinforcement learning case, we propose a novel variant of TD(0) which is more compute and sample efficient.

Stein variational gradient descent (SVGD) (Liu & Wang, 2016) performs approximate Bayesian inference by representing the posterior with a set of particles. However, SVGD suffers from variance collapse, i.e. poor predictions due to underestimating uncertainty (Ba et al., 2021), even for moderately-dimensional models such as small Bayesian neural networks (BNNs). To address this issue, we generalize SVGD by letting each particle parameterize a component distribution in a mixture model. Our method, Stein Mixture Inference (SMI), optimizes a lower bound to the evidence (ELBO) and introduces user-specified guides parameterized by particles. SMI extends the Nonlinear SVGD framework (Wang & Liu, 2019) to the case of variational Bayes. SMI effectively avoids variance collapse, judging by a previously described test developed for this purpose, and performs well on standard data sets. In addition, SMI requires considerably fewer particles than SVGD to accurately estimate uncertainty for small BNNs. The synergistic combination of NSVGD, ELBO optimization and user-specified guides establishes a promising approach towards variational Bayesian inference in the case of tall and wide data.

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.

The success of deep learning requires large datasets and extensive training, which can create significant computational challenges. To address these challenges, pseudo-coresets, small learnable datasets that mimic the entire data, have been proposed. Bayesian Neural Networks, which offer predictive uncertainty and probabilistic interpretation for deep neural networks, also face issues with large-scale datasets due to their high-dimensional parameter space. Prior works on Bayesian Pseudo-Coresets (BPC) attempt to reduce the computational load for computing weight posterior distribution by a small number of pseudo-coresets but suffer from memory inefficiency during BPC training and sub-optimal results. To overcome these limitations, we propose Variational Bayesian Pseudo-Coreset (VBPC), a novel approach that utilizes variational inference to efficiently approximate the posterior distribution, reducing memory usage and computational costs while improving performance across benchmark datasets.