Normalising flows (NFs) for discrete data are challenging because parameterising bijective transformations of discrete variables requires predicting discrete/integer parameters. Having a neural network architecture predict discrete parameters takes a non-differentiable activation function (eg, the step function) which precludes gradient-based learning. To circumvent this non-differentiability, previous work has employed biased proxy gradients, such as the straight-through estimator. We present an unbiased alternative where rather than deterministically parameterising one transformation, we predict a distribution over latent transformations. With stochastic transformations, the marginal likelihood of the data is differentiable and gradient-based learning is possible via score function estimation. To test the viability of discrete-data NFs we investigate performance on binary MNIST. We observe great challenges with both deterministic proxy gradients and unbiased score function estimation. Whereas the former often fails to learn even a shallow transformation, the variance of the latter could not be sufficiently controlled to admit deeper NFs.
Hasso Plattner Institute for Digital Engineering（哈索·普拉特纳数字工程研究所）；University of Kaiserslautern-Landau（凯泽斯劳滕-兰道大学）；Hasso Plattner Institute for Digital Health at the Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院哈索·普拉特纳数字健康研究所）
Hasso Plattner Institute for Digital Engineering（哈索·普拉特纳数字工程学院）；University of Kaiserslautern-Landau（凯泽斯劳滕-兰道大学）；Hasso Plattner Institute for Digital Health at the Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院哈索·普拉特纳数字健康研究所）
We introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that evolve non-linearly through time. Due to the complexity and non-linearity inherent in DSSMs, previous works on DSSMs typically produced latent variables that are very difficult to interpret. Our paper focus on producing interpretable latent parameters with two key modifications. First, we simplify the predictive decoder by restricting the response variables …
Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However, few flow models have been able to strike a good balance among all these properties. Realising that the integral of a convex sum of sinusoidal functions squared leads to a bijective residual transformation, we propose Sinusoidal Flow, a new type of normalising flows that inherits the expressive power and triangular Jacobian from fully autoregressive flows while…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be further improved based on insights from robust (in particular, resistant) statistics. Specifically, we propose to endow flow-based models with fat-tailed latent distributions such as multivariate Student's $t$, as a simple drop-in replacement for the Gaussian distribution used by conventional normalising flows. While robustness brings many advantages, this …
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying latent structure in the data. In this work, we incorporate a generative manifold model into the latent space of an autoencoder in order to learn the low-dimensional manifold structure from the data and adapt the latent space to accommodate this structure. In particular, we focus on …
Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the transformed space, while preserving the topological properties of the original space, and investigate the effect of the latent space transformation on learning generative models and denoising corrupted data. The experimental results demonstrate that our generative and denoising models based on the proposed framework can provide better performance than convention…
The University of Sydney（悉尼大学）；NVIDIA USA（NVIDIA美国）
Sampling-based motion planning is the predominant paradigm in many real-world robotic applications, but its performance is immensely dependent on the quality of the samples. The majority of traditional planners are inefficient as they use uninformative sampling distributions as opposed to exploiting structures and patterns in the problem to guide better sampling strategies. Moreover, most current learning-based planners are susceptible to posterior collapse or mode collapse due to the sparsity and highly varying nature of C-Space and motion plan configurations. In this work, we introduce a con…
We extend the framework of variational autoencoders to represent transformations explicitly in the latent space. In the family of hierarchical graphical models that emerges, the latent space is populated by higher order objects that are inferred jointly with the latent representations they act on. To explicitly demonstrate the effect of these higher order objects, we show that the inferred latent transformations reflect interpretable properties in the observation space. Furthermore, the model is structured in such a way that in the absence of transformations, we can run inference and obtain ge…
Data61, CSIRO（联邦科学与工业研究组织数据61研究所）；Australian National University（澳大利亚国立大学）
Principal Component Analysis (PCA) and its exponential family extensions have three components: observations, latents and parameters of a linear transformation. We consider a generalised setting where the canonical parameters of the exponential family are a nonlinear transformation of the latents. We show explicit relationships between particular neural network architectures and the corresponding statistical models. We find that deep equilibrium models -- a recently introduced class of implicit neural networks -- solve maximum a-posteriori (MAP) estimates for the latents and parameters of the …
Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variational bound to efficiently train with Boltzmann machine priors. Using this bound, we develop DVAE++, a generative model with a global discrete prior and a hierarchy of convolutional continuous variables. …
Deep latent variable models are powerful tools for representation learning. In this paper, we adopt the deep information bottleneck model, identify its shortcomings and propose a model that circumvents them. To this end, we apply a copula transformation which, by restoring the invariance properties of the information bottleneck method, leads to disentanglement of the features in the latent space. Building on that, we show how this transformation translates to sparsity of the latent space in the new model. We evaluate our method on artificial and real data.
University of Edinburgh（爱丁堡大学）；University of Amsterdam（阿姆斯特丹大学）
Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their flow is a neural network (NN) whose parameters are predicted by another NN. The latter grows quadratically with the size of the former and thus an efficient technique for parametrization is needed. We propose block neural autoregressive flow (B-NAF), a much more compact universal a…
In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transformation associated with the assigned label. Generated pseudo observation-label pairs are subsequently used to train a neural network with Auto-clustering Output Layer (ACOL) that introduces multiple softmax nodes for each pseudo parent-class. Due to the unsupervised objective based …
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous results on Riemannian metrics. We show how a class of heuristic measures gives more flexibility in finding meaningful, problem-specific distances, and how it can be applied to diverse generator types such as autoregressive generators commonly used in e.g. language and other sequence modeling. We further demonstrate how a diffusion-inspired transformation previ…
The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold. Variational Autoencoders (VAEs) approximate this manifold by learning mappings from low-dimensional latent vectors to high-dimensional data while encouraging a global structure in the latent space through the use of a specified prior distribution. When this prior does not match the structure of the true data manifold, it can lead to a less accurate model of the data. To resolve this mismatch, we introduce the Variational Autoencoder with Learned Latent Structure (…
Machine learning models have demonstrated vulnerability to adversarial attacks, more specifically misclassification of adversarial examples. In this paper, we investigate an attack-agnostic defense against adversarial attacks on high-resolution images by detecting suspicious inputs. The intuition behind our approach is that the essential characteristics of a normal image are generally consistent with non-essential style transformations, e.g., slightly changing the facial expression of human portraits. In contrast, adversarial examples are generally sensitive to such transformations. In our app…
Simplifying Flow Matching Transformations with Low-Rank Mixture Models
Stanford Intelligent Systems Laboratory in the Department of Aeronautics and Astronautics at Stanford University（斯坦福大学航空航天系智能系统实验室）；Industrial and Systems Engineering Department at King Fahd University of Petroleum and Minerals（科威特石油矿物大学工业与系统工程系）
Collaborative Robotics and Intelligent Systems (CoRIS) Institute（协作机器人与智能系统（CoRIS）研究所）；Oregon State University（俄勒冈州立大学）
CounterFactual (CF) visual explanations try to find images similar to the query image that change the decision of a vision system to a specified outcome. Existing methods either require inference-time optimization or joint training with a generative adversarial model which makes them time-consuming and difficult to use in practice. We propose a novel approach, Cycle-Consistent Counterfactuals by Latent Transformations (C3LT), which learns a latent transformation that automatically generates visual CFs by steering in the latent space of generative models. Our method uses cycle consistency betwe…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be computationally cheap while still achieving high approximation quality. The concept, which we call Laplace Matching, involves closed-form, approximate, bi-directional transformations between the parameter spaces of exponential families. These are constructed from Laplace approximations under custom-designed basis transformations. The mappings can then be leveraged to …
Ben-Gurion University of the Negev（内盖夫本-古里安大学）；NEC Corporation（日本电气股份有限公司）
Model agnostic feature attribution algorithms (such as SHAP and LIME) are ubiquitous techniques for explaining the decisions of complex classification models, such as deep neural networks. However, since complex classification models produce superior performance when trained on low-level (or encoded) features, in many cases, the explanations generated by these algorithms are neither interpretable nor usable by humans. Methods proposed in recent studies that support the generation of human-interpretable explanations are impractical, because they require a fully invertible transformation functio…
Korea University（高丽大学）；Korea National Open University（韩国国立开放大学）
Recent deep-learning approaches have shown that Frequency Transformation (FT) blocks can significantly improve spectrogram-based single-source separation models by capturing frequency patterns. The goal of this paper is to extend the FT block to fit the multi-source task. We propose the Latent Source Attentive Frequency Transformation (LaSAFT) block to capture source-dependent frequency patterns. We also propose the Gated Point-wise Convolutional Modulation (GPoCM), an extension of Feature-wise Linear Modulation (FiLM), to modulate internal features. By employing these two novel methods, we ex…
We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST dig…
University of Basel（巴塞尔大学）；National Centre for Computational Design and Discovery of Novel Materials MARVEL（新型材料计算设计与发现国家中心（MARVEL））；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation with a model consisting of two latent subspaces, where the first subspace captures the target and the second subspace the remaining invariant information. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Unl…
Yandex Skolkovo Institute of Science Technology (Skoltech)（亚斯科尔科沃科学技术研究所（斯科尔科沃科技学院））；National Research University Higher School of Economics（俄罗斯国家研究型高等经济大学）
Recent advances in high-fidelity semantic image editing heavily rely on the presumably disentangled latent spaces of the state-of-the-art generative models, such as StyleGAN. Specifically, recent works show that it is possible to achieve decent controllability of attributes in face images via linear shifts along with latent directions. Several recent methods address the discovery of such directions, implicitly assuming that the state-of-the-art GANs learn the latent spaces with inherently linearly separable attribute distributions and semantic vector arithmetic properties. In our work, we show…
Wuhan University（武汉大学）；The Hong Kong University of Science and Technology（香港科技大学）
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a transformer network is trained to predict the velocity field of the transformation from a standard normal distribution to the target latent distribution. Our error analysis demonstrates the effectiveness of this approach, showing that the distribution of samples generated via estimated ODE flow converges to the target distribution in the Wasserstein-2 distance under …
Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Princeton University（普林斯顿大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes…
L-GTA: Latent Generative Modeling for Time Series Augmentation
Faculdade de Engenharia da Universidade do Porto（葡萄牙波尔图大学工程学院）；Fraunhofer Portugal AICOS（德国弗劳恩霍夫葡萄牙AICOS研究所）；University of Coimbra（科英布拉大学）；Dalhousie University（达尔豪斯大学）
CSIRO（澳大利亚联邦科学与工业研究组织）；National University of Singapore（新加坡国立大学）
Previous robustness approaches for deep learning models such as data augmentation techniques via data transformation or adversarial training cannot capture real-world variations that preserve the semantics of the input, such as a change in lighting conditions. To bridge this gap, we present NaTra, an adversarial training scheme that is designed to improve the robustness of image classification algorithms. We target attributes of the input images that are independent of the class identification, and manipulate those attributes to mimic real-world natural transformations (NaTra) of the inputs, w…
Emotion detection in text is an important task in NLP and is essential in many applications. Most of the existing methods treat this task as a problem of single-label multi-class text classification. To predict multiple emotions for one instance, most of the existing works regard it as a general Multi-label Classification (MLC) problem, where they usually either apply a manually determined threshold on the last output layer of their neural network models or train multiple binary classifiers and make predictions in the fashion of one-vs-all. However, compared to labels in the general MLC datase…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose a composable framework for latent space image augmentation that allows for easy combination of multiple augmentations. Image augmentation has been shown to be an effective technique for improving the performance of a wide variety of image classification and generation tasks. Our framework is based on the Variational Autoencoder architecture and uses a novel approach for augmentation via linear transformation within the latent space itself. We explore losses and augmentation latent geometry to enforce the transformations to be composable and involuntary, thus allowing the transformat…
Structured Contrastive Learning for Interpretable Latent Representations
Department of Electrical and Electronic Engineering, Imperial College London（帝国理工学院伦敦电子与电气工程系）；Institute of Biomedical Engineering, Department of Engineering Science, University of Oxford（牛津大学生物医学工程研究所）
