We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the challenges that arise when trying to learn an (almost arbitrary) latent neural SDE from large-scale data, such as efficient gradient computation, we take a step back and study a specific subclass instead. In our case, the SDE evolves on a homogeneous latent space and is induced by stochastic dynamics of the corresponding (matrix) Lie group. In learning problems, SDEs on the unit $n$-sphere are arguably the most relevant incarnation of this setup. Notably, for variational inference, the sphere not only facilitates using a truly uninformative prior SDE, but we also obtain a particularly simple and intuitive expression for the Kullback-Leibler divergence between the approximate posterior and prior process in the evidence lower bound. Experiments demonstrate that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less diverse class of SDEs, we achieve competitive or even state-of-the-art performance on various time series interpolation and classification benchmarks.
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It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single forward-pass models do not sample weights during inference and often make assumptions about the target distribution, such as assuming it is Gaussian. This can be restrictive in regression tasks, where the mean and standard deviation are inadequate to model the target distribution accurately. This paper proposes a deep Bayesian quantile regression model that can estimate the quantiles of a continuous target distribution without the Gaussian assumption. The proposed method is based on evidential learning, which allows the model to capture aleatoric and epistemic uncertainty with a single deterministic forward-pass model. This makes the method efficient and scalable to large models and datasets. We demonstrate that the proposed method achieves calibrated uncertainties on non-Gaussian distributions, disentanglement of aleatoric and epistemic uncertainty, and robustness to out-of-distribution samples.
We analysis performance of semantic segmentation models wrt. adversarial attacks, and observe that the adversarial examples generated from a source model fail to attack the target models. i.e The conventional attack methods, such as PGD and FGSM, do not transfer well to target models, making it necessary to study the transferable attacks, especially transferable attacks for semantic segmentation. We find two main factors to achieve transferable attack. Firstly, the attack should come with effective data augmentation and translation-invariant features to deal with unseen models. Secondly, stabilized optimization strategies are needed to find the optimal attack direction. Based on the above observations, we propose an ensemble attack for semantic segmentation to achieve more effective attacks with higher transferability. The source code and experimental results are publicly available via our project page: //github.com/anucvers/TASS.
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional distributions. Based on this result, we propose a novel conditional generation algorithm where conditional distributions are fully characterized by a metric space defined by a statistical distance. We employ optimal transport theory to propose the \textit{Wasserstein geodesic generator}, a new conditional generator that learns the Wasserstein geodesic. The proposed method learns both conditional distributions for observed domains and optimal transport maps between them. The conditional distributions given unobserved intermediate domains are on the Wasserstein geodesic between conditional distributions given two observed domain labels. Experiments on face images with light conditions as domain labels demonstrate the efficacy of the proposed method.
We construct conforming finite element elasticity complexes on Worsey-Farin splits in three dimensions. Spaces for displacement, strain, stress, and the load are connected in the elasticity complex through the differential operators representing deformation, incompatibility, and divergence. For each of these component spaces, a corresponding finite element space on Worsey-Farin meshes is exhibited. Unisolvent degrees of freedom are developed for these finite elements, which also yields commuting (cochain) projections on smooth functions. A distinctive feature of the spaces in these complexes is the lack of extrinsic supersmoothness at subsimplices of the mesh. Notably, the complex yields the first (strongly) symmetric stress finite element with no vertex or edge degrees of freedom in three dimensions. Moreover, the lowest order stress space uses only piecewise linear functions which is the lowest feasible polynomial degree for the stress space.
Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the causal effect. In this work, we consider the problem of designing the collection of interventions with the minimum cost to identify the desired effect. First, we prove that this problem is NP-hard, and subsequently propose an algorithm that can either find the optimal solution or a logarithmic-factor approximation of it. This is done by establishing a connection between our problem and the minimum hitting set problem. Additionally, we propose several polynomial-time heuristic algorithms to tackle the computational complexity of the problem. Although these algorithms could potentially stumble on sub-optimal solutions, our simulations show that they achieve small regrets on random graphs.
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By carefully combining a focalized variant of call-by-push-value, bidirectional typing, and our novel technique of value-determined indexes, our system generates solvable SMT constraints without existential (unification) variables. We design a polarized subtyping relation allowing us to prove our logically focused typing algorithm is sound, complete, and decidable. We prove type soundness of our declarative system with respect to an elementary domain-theoretic denotational semantics. Type soundness implies, relatively simply, the total correctness and logical consistency of our system. The relative ease with which we obtain both algorithmic and semantic results ultimately stems from the proof-theoretic technique of focalization.
Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
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