Learning Discrete Concepts in Latent Hierarchical Models
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；University of California San Diego（加州大学圣地亚哥分校）
Lingjing Kong, Guangyi Chen, Biwei Huang, Eric P. Xing, Yuejie Chi, Kun Zhang
Learning concepts from natural high-dimensional data (e.g., images) holds potential in building human-aligned and interpretable machine learning models. Despite its encouraging prospect, formalization and theoretical insights into this crucial task are still lacking. In this work, we formalize concepts as discrete latent causal variables that are related via a hierarchical causal model that encodes different abstraction levels of concepts embedded in high-dimensional data (e.g., a dog breed and its eye shapes in natural images). We formulate conditions to facilitate the identification of the proposed causal model, which reveals when learning such concepts from unsupervised data is possible. Our conditions permit complex causal hierarchical structures beyond latent trees and multi-level directed acyclic graphs in prior work and can handle high-dimensional, continuous observed variables, which is well-suited for unstructured data modalities such as images. We substantiate our theoretical claims with synthetic data experiments. Further, we discuss our theory's implications for understanding the underlying mechanisms of latent diffusion models and provide corresponding empirical evidence for our theoretical insights.
Identification of Nonlinear Latent Hierarchical Models
Carnegie Mellon University（卡内基梅隆大学）；University of California San Diego（加州大学圣迭戈分校）；Beijing Technology and Business University（北京工商大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Carnegie Mellon University（卡内基梅隆大学）；Beijing Technology and Business University（北京工商大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some variables are latent and they form a hierarchical graph structure to generate the measured variables; the children of latent variables may still be latent and only leaf nodes are measured, and moreover, there can be multiple paths between every pair of variables (i.e., it is beyond tree structure). We propose an estimation procedure that can efficiently locate…
Variational autoencoders (VAE) combined with hierarchical RNNs have emerged as a powerful framework for conversation modeling. However, they suffer from the notorious degeneration problem, where the decoders learn to ignore latent variables and reduce to vanilla RNNs. We empirically show that this degeneracy occurs mostly due to two reasons. First, the expressive power of hierarchical RNN decoders is often high enough to model the data using only its decoding distributions without relying on the latent variables. Second, the conditional VAE structure whose generation process is conditioned on …
Inria（法国国家信息与自动化技术研究院）；PSL Research University（巴黎社会科学高等研究院）；CMAP（巴黎高等理工学院应用数学与计算科学实验室）；Ecole Polytechnique Palaiseau, France（法国巴黎高等理工学院Palaiseau分校）；Sakana AI Tokyo, Japan（日本东京Sakana AI公司）
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Future Network of Intelligence Institute（未来智能网络研究院）；Radboud University（拉德堡德大学）；Institute for Computing and Information Sciences（计算与信息科学研究所）
Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its latent functions. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness…
Volkswagen Group（大众汽车集团）；Technical University of Munich（慕尼黑工业大学）
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate the learning problem as a constrained optimisation problem by extending the Taming VAEs framework to two-level hierarchical models. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold---and present several examples, where desired propertie…
Differentiable Causal Discovery For Latent Hierarchical Causal Models
University of California San Diego（加利福尼亚大学圣迭戈分校）；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）；Oxford-Man Institute（牛津-曼彻斯特研究所）
Successfully training Variational Autoencoders (VAEs) with a hierarchy of discrete latent variables remains an area of active research. Vector-Quantised VAEs are a powerful approach to discrete VAEs, but naive hierarchical extensions can be unstable when training. Leveraging insights from classical methods of inference we introduce \textit{Relaxed-Responsibility Vector-Quantisation}, a novel way to parameterise discrete latent variables, a refinement of relaxed Vector-Quantisation that gives better performance and more stable training. This enables a novel approach to hierarchical discrete var…
H-LDM: Hierarchical Latent Diffusion Models for Controllable and Interpretable PCG Synthesis from Clinical Metadata
School of Cyber Engineering Xidian University Xi'an, China（电子科技大学信息工程学院西安中国）；School of Telecommunications Engineering Xidian University Xi'an, China（电子科技大学电信工程学院西安中国）
The Variational Autoencoder (VAE) has proven to be an effective model for producing semantically meaningful latent representations for natural data. However, it has thus far seen limited application to sequential data, and, as we demonstrate, existing recurrent VAE models have difficulty modeling sequences with long-term structure. To address this issue, we propose the use of a hierarchical decoder, which first outputs embeddings for subsequences of the input and then uses these embeddings to generate each subsequence independently. This structure encourages the model to utilize its latent cod…
We make the following striking observation: fully convolutional VAE models trained on 32x32 ImageNet can generalize well, not just to 64x64 but also to far larger photographs, with no changes to the model. We use this property, applying fully convolutional models to lossless compression, demonstrating a method to scale the VAE-based 'Bits-Back with ANS' algorithm for lossless compression to large color photographs, and achieving state of the art for compression of full size ImageNet images. We release Craystack, an open source library for convenient prototyping of lossless compression using pr…
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
We propose a family of novel hierarchical Bayesian deep auto-encoder models capable of identifying disentangled factors of variability in data. While many recent attempts at factor disentanglement have focused on sophisticated learning objectives within the VAE framework, their choice of a standard normal as the latent factor prior is both suboptimal and detrimental to performance. Our key observation is that the disentangled latent variables responsible for major sources of variability, the relevant factors, can be more appropriately modeled using long-tail distributions. The typical Gaussian…
Nagoya Institute of Technology（名古屋工业大学）；Microsoft Development Co., Ltd.（微软开发有限公司）
This paper proposes a hierarchical generative model with a multi-grained latent variable to synthesize expressive speech. In recent years, fine-grained latent variables are introduced into the text-to-speech synthesis that enable the fine control of the prosody and speaking styles of synthesized speech. However, the naturalness of speech degrades when these latent variables are obtained by sampling from the standard Gaussian prior. To solve this problem, we propose a novel framework for modeling the fine-grained latent variables, considering the dependence on an input text, a hierarchical ling…
DeepMind（深度思维）；Microsoft Research New England（微软新英格兰研究院）
Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach add…
University at Buffalo（布法罗大学）；Criteo（Criteo公司）；Duke University（杜克大学）
Variational autoencoders (VAEs) are essential tools in end-to-end representation learning. However, the sequential text generation common pitfall with VAEs is that the model tends to ignore latent variables with a strong auto-regressive decoder. In this paper, we propose a principled approach to alleviate this issue by applying a discretized bottleneck to enforce an implicit latent feature matching in a more compact latent space. We impose a shared discrete latent space where each input is learned to choose a combination of latent atoms as a regularized latent representation. Our model endows …
We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we propose GraphDF, a novel discrete latent variable model for molecular graph generation based on normalizing flow methods. GraphDF uses invertible modulo shift transforms to map discrete latent variables to graph nodes and edges. We show that the use of discrete latent variables reduces computational costs and eliminates the negative effect of dequantization. Comp…
NVIDIA（英伟达）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Denoising diffusion models (DDMs) have shown promising results in 3D point cloud synthesis. To advance 3D DDMs and make them useful for digital artists, we require (i) high generation quality, (ii) flexibility for manipulation and applications such as conditional synthesis and shape interpolation, and (iii) the ability to output smooth surfaces or meshes. To this end, we introduce the hierarchical Latent Point Diffusion Model (LION) for 3D shape generation. LION is set up as a variational autoencoder (VAE) with a hierarchical latent space that combines a global shape latent representation with…
University of Oxford（牛津大学）；DeepMind（深度思维）；Microsoft Research（微软研究院）
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidea…
This paper proposes a hierarchical, fine-grained and interpretable latent variable model for prosody based on the Tacotron 2 text-to-speech model. It achieves multi-resolution modeling of prosody by conditioning finer level representations on coarser level ones. Additionally, it imposes hierarchical conditioning across all latent dimensions using a conditional variational auto-encoder (VAE) with an auto-regressive structure. Evaluation of reconstruction performance illustrates that the new structure does not degrade the model while allowing better interpretability. Interpretations of prosody a…
Generative Modeling of Discrete Data Using Geometric Latent Subspaces
Institute for Mathematics, Heidelberg University（海德堡大学数学研究所）；Mannheim Institute for Intelligent Systems in Medicine, Heidelberg University（海德堡大学曼海姆智能医学系统研究所）；IWR, Heidelberg University（海德堡大学IWR研究所）；Research Station Geometry and Dynamics, Heidelberg University（海德堡大学几何与动力学研究站）
Discrete latent variables are considered important for real world data, which has motivated research on Variational Autoencoders (VAEs) with discrete latents. However, standard VAE training is not possible in this case, which has motivated different strategies to manipulate discrete distributions in order to train discrete VAEs similarly to conventional ones. Here we ask if it is also possible to keep the discrete nature of the latents fully intact by applying a direct discrete optimization for the encoding model. The approach is consequently strongly diverting from standard VAE-training by si…
University of Tübingen（图宾根大学）；IMPRS-IS（马克斯·普朗克智能系统研究所国际马克斯·普朗克研究学院）
Variational Autoencoders (VAEs) were originally motivated (Kingma & Welling, 2014) as probabilistic generative models in which one performs approximate Bayesian inference. The proposal of $β$-VAEs (Higgins et al., 2017) breaks this interpretation and generalizes VAEs to application domains beyond generative modeling (e.g., representation learning, clustering, or lossy data compression) by introducing an objective function that allows practitioners to trade off between the information content ("bit rate") of the latent representation and the distortion of reconstructed data (Alemi et al., 2018)…
Despite progress in training neural networks for lossy image compression, current approaches fail to maintain both perceptual quality and abstract features at very low bitrates. Encouraged by recent success in learning discrete representations with Vector Quantized Variational Autoencoders (VQ-VAEs), we motivate the use of a hierarchy of VQ-VAEs to attain high factors of compression. We show that the combination of stochastic quantization and hierarchical latent structure aids likelihood-based image compression. This leads us to introduce a novel objective for training hierarchical VQ-VAEs. Ou…
Learning Discrete Latent Variable Structures with Tensor Rank Conditions
School of Computer Science, Guangdong University of Technology（广东工业大学计算机学院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Beijing Technology and Business University（北京工商大学）；Zhejiang University（浙江大学）；Carnegie Mellon University（卡内基梅隆大学）
We propose a hierarchical normalizing flow model for generating molecular graphs. The model produces new molecular structures from a single-node graph by recursively splitting every node into two. All operations are invertible and can be used as plug-and-play modules. The hierarchical nature of the latent codes allows for precise changes in the resulting graph: perturbations in the top layer cause global structural changes, while perturbations in the consequent layers change the resulting molecule marginally. The proposed model outperforms existing generative graph models on the distribution l…
Korea University（高丽大学）；Queen Mary University of London（伦敦玛丽女王大学）；Korea National Open University（韩国国立开放大学）
In recent years, neural network based methods have been proposed as a method that cangenerate representations from music, but they are not human readable and hardly analyzable oreditable by a human. To address this issue, we propose a novel method to learn source-awarelatent representations of music through Vector-Quantized Variational Auto-Encoder(VQ-VAE).We train our VQ-VAE to encode an input mixture into a tensor of integers in a discrete latentspace, and design them to have a decomposed structure which allows humans to manipulatethe latent vector in a source-aware manner. This paper also s…
University of California, Berkeley（加利福尼亚大学伯克利分校）；Google Brain（谷歌大脑）
In this work, we take a representation learning perspective on hierarchical reinforcement learning, where the problem of learning lower layers in a hierarchy is transformed into the problem of learning trajectory-level generative models. We show that we can learn continuous latent representations of trajectories, which are effective in solving temporally extended and multi-stage problems. Our proposed model, SeCTAR, draws inspiration from variational autoencoders, and learns latent representations of trajectories. A key component of this method is to learn both a latent-conditioned policy and …
We address the problem of learning hierarchical deep neural network policies for reinforcement learning. In contrast to methods that explicitly restrict or cripple lower layers of a hierarchy to force them to use higher-level modulating signals, each layer in our framework is trained to directly solve the task, but acquires a range of diverse strategies via a maximum entropy reinforcement learning objective. Each layer is also augmented with latent random variables, which are sampled from a prior distribution during the training of that layer. The maximum entropy objective causes these latent …
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generali…
Columbia University（哥伦比亚大学）；University of Michigan（密歇根大学）
Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints on the configurations of latent attributes. These components encode practitioners' design information and carry important scientific meanings. Despite the popularity of HLAMs, the fundamental identifiability issue remains unaddressed. The existence of the attribute hierarchy gra…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be appropriate. One should instead use effective dimension (Geiger et al. 1996). This paper is concerned with the computation of effective dimension. First we present an upper bound on the effective dimension of a latent class (LC) model. This bound is tight and its computation is eas…
Amsterdam Machine Learning Lab, University of Amsterdam（阿姆斯特丹大学阿姆斯特丹机器学习实验室）
Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent variable inputs to induce predictive distributions. However, the expressiveness of vanilla NPs is limited as they only use a global latent variable, while target specific local variation may be crucial sometimes. To address this challenge, we investigate NPs systematically and present a new variant of NP model that we call Doubly Stochastic Variational Neural Pr…
Towards Identifiability of Hierarchical Temporal Causal Representation Learning
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东技术大学）；University of California San Diego（加州大学圣地亚哥分校）
University of Tübingen（图宾根大学）；Max-Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Potsdam（波茨坦大学）
Humans can make predictions on various time scales and hierarchical levels. Thereby, the learning of event encodings seems to play a crucial role. In this work we model the development of hierarchical predictions via autonomously learned latent event codes. We present a hierarchical recurrent neural network architecture, whose inductive learning biases foster the development of sparsely changing latent state that compress sensorimotor sequences. A higher level network learns to predict the situations in which the latent states tend to change. Using a simulated robotic manipulator, we demonstra…
This paper addresses the issue of detecting hierarchical changes in latent variable models (HCDL) from data streams. There are three different levels of changes for latent variable models: 1) the first level is the change in data distribution for fixed latent variables, 2) the second one is that in the distribution over latent variables, and 3) the third one is that in the number of latent variables. It is important to detect these changes because we can analyze the causes of changes by identifying which level a change comes from (change interpretability). This paper proposes an information-th…
The Hong Kong University of Science and Technology（香港科技大学）
We propose a novel document generation process based on hierarchical latent tree models (HLTMs) learned from data. An HLTM has a layer of observed word variables at the bottom and multiple layers of latent variables on top. For each document, we first sample values for the latent variables layer by layer via logic sampling, then draw relative frequencies for the words conditioned on the values of the latent variables, and finally generate words for the document using the relative word frequencies. The motivation for the work is to take word counts into consideration with HLTMs. In comparison w…
In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically meant for search: rich enough to specify the desired output but compact enough to make search more efficient. Discrete latent codes are appealing for this purpose, as they naturally allow sophisticated combinatorial search strategies. The latent codes are learned using a self-supervised learning principle, in which first a discrete autoencoder is trained on the …
Hierarchical Latent Structure Learning through Online Inference
Center for Theoretical Neuroscience and Zuckerman Institute（理论神经科学中心和Zuckerman研究所）；Columbia University（哥伦比亚大学）；Department of Psychiatry, Columbia University Irving Medical Center（精神病学系，哥伦比亚大学伊万杰琳医学中心）；New York State Psychiatric Institute（纽约州精神医学研究所）；Columbia Data Science Institute（哥伦比亚数据科学研究所）
Université de Montréal（蒙特利尔大学）；Maluuba Inc（Maluuba公司）；McGill University（麦吉尔大学）
Sequential data often possesses a hierarchical structure with complex dependencies between subsequences, such as found between the utterances in a dialogue. In an effort to model this kind of generative process, we propose a neural network-based generative architecture, with latent stochastic variables that span a variable number of time steps. We apply the proposed model to the task of dialogue response generation and compare it with recent neural network architectures. We evaluate the model performance through automatic evaluation metrics and by carrying out a human evaluation. The experimen…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.
Informatics Institute, University of Amsterdam（阿姆斯特丹大学信息学研究所）
We present a novel hierarchical model for human activity recognition. In contrast to approaches that successively recognize actions and activities, our approach jointly models actions and activities in a unified framework, and their labels are simultaneously predicted. The model is embedded with a latent layer that is able to capture a richer class of contextual information in both state-state and observation-state pairs. Although loops are present in the model, the model has an overall linear-chain structure, where the exact inference is tractable. Therefore, the model is very efficient in bo…
The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong Institute of Education（香港教育学院）
Hierarchical latent tree analysis (HLTA) is recently proposed as a new method for topic detection. It differs fundamentally from the LDA-based methods in terms of topic definition, topic-document relationship, and learning method. It has been shown to discover significantly more coherent topics and better topic hierarchies. However, HLTA relies on the Expectation-Maximization (EM) algorithm for parameter estimation and hence is not efficient enough to deal with large datasets. In this paper, we propose a method to drastically speed up HLTA using a technique inspired by recent advances in the m…
For robots operating in the real world, it is desirable to learn reusable behaviours that can effectively be transferred and adapted to numerous tasks and scenarios. We propose an approach to learn abstract motor skills from data using a hierarchical mixture latent variable model. In contrast to existing work, our method exploits a three-level hierarchy of both discrete and continuous latent variables, to capture a set of high-level behaviours while allowing for variance in how they are executed. We demonstrate in manipulation domains that the method can effectively cluster offline data into d…
