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Mechanosensing is a ubiquitous process to translate external mechanical stimuli into biological responses. Piezo1 ion channels are directly gated by mechanical forces and play an essential role in cellular mechanotransduction. However, readouts of Piezo1 activity are mainly examined by invasive or indirect techniques, such as electrophysiological analyses and cytosolic calcium imaging. Here, we introduce GenEPi, a genetically-encoded fluorescent reporter for non-invasive optical monitoring of Piezo1-dependent activity. We demonstrate that GenEPi has high spatiotemporal resolution for Piezo1-dependent stimuli from the single-cell level to that of the entire organism. GenEPi reveals transient, local mechanical stimuli in the plasma membrane of single cells, resolves repetitive contraction-triggered stimulation of beating cardiomyocytes within microtissues, and allows for robust and reliable monitoring of Piezo1-dependent activity in vivo. GenEPi will enable non-invasive optical monitoring of Piezo1 activity in mechanochemical feedback loops during development, homeostatic regulation, and disease.

Object-centric representations form the basis of human perception, and enable us to reason about the world and to systematically generalize to new settings. Currently, most works on unsupervised object discovery focus on slot-based approaches, which explicitly separate the latent representations of individual objects. While the result is easily interpretable, it usually requires the design of involved architectures. In contrast to this, we propose a comparatively simple approach - the Complex AutoEncoder (CAE) - that creates distributed object-centric representations. Following a coding scheme theorized to underlie object representations in biological neurons, its complex-valued activations represent two messages: their magnitudes express the presence of a feature, while the relative phase differences between neurons express which features should be bound together to create joint object representations. In contrast to previous approaches using complex-valued activations for object discovery, we present a fully unsupervised approach that is trained end-to-end - resulting in significant improvements in performance and efficiency. Further, we show that the CAE achieves competitive or better unsupervised object discovery performance on simple multi-object datasets compared to a state-of-the-art slot-based approach while being up to 100 times faster to train., Comment: Published in Transactions on Machine Learning Research (TMLR)

Efficiency and robustness are increasingly needed for applications on 3D point clouds, with the ubiquitous use of edge devices in scenarios like autonomous driving and robotics, which often demand real-time and reliable responses. The paper tackles the challenge by designing a general framework to construct 3D learning architectures with SO(3) equivariance and network binarization. However, a naive combination of equivariant networks and binarization either causes sub-optimal computational efficiency or geometric ambiguity. We propose to locate both scalar and vector features in our networks to avoid both cases. Precisely, the presence of scalar features makes the major part of the network binarizable, while vector features serve to retain rich structural information and ensure SO(3) equivariance. The proposed approach can be applied to general backbones like PointNet and DGCNN. Meanwhile, experiments on ModelNet40, ShapeNet, and the real-world dataset ScanObjectNN, demonstrated that the method achieves a great trade-off between efficiency, rotation robustness, and accuracy. The codes are available at https://github.com/zhuoinoulu/svnet., Accepted in 3DV 2022. 11 pages including the appendix

Stochastic elements in reinforcement learning (RL) have shown promise to improve exploration and handling of uncertainty, such as the utilization of stochastic weights in NoisyNets and stochastic policies in the maximum entropy RL frameworks. Yet effective and general approaches to include such elements in actor-critic models are still lacking. Inspired by the aforementioned techniques, we propose an effective way to inject randomness into actor-critic models to improve general exploratory behavior and reflect environment uncertainty. Specifically, randomness is added at the level of intermediate activations that feed into both policy and value functions to achieve better correlated and more complex perturbations. The proposed framework also features flexibility and simplicity, which allows straightforward adaptation to a variety of tasks. We test several actor-critic models enhanced with stochastic activations and demonstrate their effectiveness in a wide range of Atari 2600 games, a continuous control problem and a car racing task. Lastly, in a qualitative analysis, we present evidence of the proposed model adapting the noise in the policy and value functions to reflect uncertainty and ambiguity in the environment.

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.

Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined by a composition of a continuous distribution (such as a normalizing flow), and an argmax function. To optimize this model, we learn a probabilistic inverse for the argmax that lifts the categorical data to a continuous space. Multinomial Diffusion gradually adds categorical noise in a diffusion process, for which the generative denoising process is learned. We demonstrate that our method outperforms existing dequantization approaches on text modelling and modelling on image segmentation maps in log-likelihood.

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained to predict edges from example solutions. We evaluate our framework on the travelling salesman problem (TSP), the vehicle routing problem (VRP) and TSP with time windows (TSPTW) and show that the neural policy improves the performance of (restricted) DP algorithms, making them competitive to strong alternatives such as LKH, while also outperforming most other 'neural approaches' for solving TSPs, VRPs and TSPTWs with 100 nodes., 21 pages

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

In healthcare applications, predictive uncertainty has been used to assess predictive accuracy. In this paper, we demonstrate that predictive uncertainty estimated by the current methods does not highly correlate with prediction error by decomposing the latter into random and systematic errors, and showing that the former is equivalent to the variance of the random error. In addition, we observe that current methods unnecessarily compromise performance by modifying the model and training loss to estimate the target and uncertainty jointly. We show that estimating them separately without modifications improves performance. Following this, we propose a novel method that estimates the target labels and magnitude of the prediction error in two steps. We demonstrate this method on a large-scale MRI reconstruction task, and achieve significantly better results than the state-of-the-art uncertainty estimation methods.

In today’s clinical practice, magnetic resonance imaging (MRI) is routinely accelerated through subsampling of the associated Fourier domain. Currently, the construction of these subsampling strategies - known as experimental design - relies primarily on heuristics. We propose to learn experimental design strategies for accelerated MRI with policy gradient methods. Unexpectedly, our experiments show that a simple greedy approximation of the objective leads to solutions nearly on-par with the more general non-greedy approach. We offer a partial explanation for this phenomenon rooted in greater variance in the non-greedy objective's gradient estimates, and experimentally verify that this variance hampers non-greedy models in adapting their policies to individual MR images. We empirically show that this adaptivity is key to improving subsampling designs.

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.

In this work, we propose a new Transformer-based survival model which estimates the patient-specific survival distribution. Our contributions are twofold. First, to the best of our knowledge, existing deep survival models use either fully connected or recurrent networks, and we are the first to apply the Transformer in survival analysis. In addition, we use ordinal regression to optimize the survival probabilities over time, and penalize randomized discordant pairs. Second, many survival models are evaluated using only the ranking metrics such as the concordance index. We propose to also use the absolute error metric that evaluates the precise duration predictions on observed subjects. We demonstrate our model on two publicly available real-world datasets, and show that our mean absolute error results are significantly better than the current models, meanwhile, it is challenging to determine the best model under the concordance index.

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D., Comment: Accepted at Neural Information Processing Systems (NeurIPS 2021)

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation, and stochastic in the reverse direction -- hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.

Standard causal discovery methods must fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information - for instance, the dynamics describing the effects of causal relations - which is lost when following this approach. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with different underlying causal graphs, and thus makes use of the information that is shared. We demonstrate experimentally that this approach, implemented as a variational model, leads to significant improvements in causal discovery performance, and show how it can be extended to perform well under hidden confounding.

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $\mathcal{O}(D^3)$ to $\mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while training more quickly and surpassing the performance of functionally constrained counterparts.

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich transformations on high-dimensional data. As building blocks for IDFs, we introduce a flexible transformation layer called integer discrete coupling. Our experiments show that IDFs are competitive with other flow-based generative models. Furthermore, we demonstrate that IDF based compression achieves state-of-the-art lossless compression rates on CIFAR10, ImageNet32, and ImageNet64. To the best of our knowledge, this is the first lossless compression method that uses invertible neural networks.

This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been proposed. We introduce COMBO, a new Gaussian Process (GP) BO. COMBO quantifies “smoothness” of functions on combinatorial search spaces by utilizing a combinatorial graph. The vertex set of the combinatorial graph consists of all possible joint assignments of the variables, while edges are constructed using the graph Cartesian product of the sub-graphs that represent the individual variables. On this combinatorial graph, we propose an ARD diffusion kernel with which the GP is able to model high-order interactions between variables leading to better performance. Moreover, using the Horseshoe prior for the scale parameter in the ARD diffusion kernel results in an effective variable selection procedure, making COMBO suitable for high dimensional problems. Computationally, in COMBO the graph Cartesian product allows the Graph Fourier Transform calculation to scale linearly instead of exponentially. We validate COMBO in a wide array of realistic benchmarks, including weighted maximum satisfiability problems and neural architecture search. COMBO outperforms consistently the latest state-of-the-art while maintaining computational and statistical efficiency

We develop ancestral Gumbel-Top-k sampling: a generic and efficient method for sampling without replacement from discrete-valued Bayesian networks, which includes multivariate discrete distributions, Markov chains and sequence models. The method uses an extension of the Gumbel-Max trick to sample without replacement by finding the top k of perturbed log-probabilities among all possible configurations of a Bayesian network. Despite the exponentially large domain, the algorithm has a complexity linear in the number of variables and sample size k. Our algorithm allows to set the number of parallel processors m, to trade off the number of iterations versus the total cost (iterations times m) of running the algorithm. For m=1 the algorithm has minimum total cost, whereas for m=k the number of iterations is minimized, and the resulting algorithm is known as Stochastic Beam Search. We provide extensions of the algorithm and discuss a number of related algorithms. We analyze the properties of ancestral Gumbel-Top-k sampling and compare against alternatives on randomly generated Bayesian networks with different levels of connectivity. In the context of (deep) sequence models, we show its use as a method to generate diverse but high-quality translations and statistical estimates of translation quality and entropy.

We introduce deep scale-spaces (DSS), a generalization of convolutional neural networks, exploiting the scale symmetry structure of conventional image recognition tasks. Put plainly, the class of an image is invariant to the scale at which it is viewed. We construct scale equivariant cross-correlations based on a principled extension of convolutions, grounded in the theory of scale-spaces and semigroups. As a very basic operation, these cross-correlations can be used in almost any modern deep learning architecture in a plug-and-play manner. We demonstrate our networks on the Patch Camelyon and Cityscapes datasets, to prove their utility and perform introspective studies to further understand their properties.

The removal of phosphorus (P) from fields in the harvested seeds of staple crops is a major driver of the global P cycle, and consequently, there is interest in breeding grain crops with lower seed P concentrations. While it is expected that a reduction in seed total P would result in lower concentrations of the P-rich anti-nutrient phytate, the potential consequences for starch lysophospholipids (LPLs), which affect rice grain quality and health outcomes in humans, are unknown. We examined the accumulation of phytate and starch LPLs in developing indica (cv. IR64) and japonica (cv. Nipponbare) rice grains as well as the stability of starch LPLs and phytate under varying P supply treatments in hydroponics. Source-sink relationships during grain filling (drought and floret abortion) were also investigated in a pot study. Accumulation of phytate and starch LPLs in seeds continued until 18 days after anthesis (DAA) in cv. Nipponbare and 21 DAA in cv. IR64, which mirrored the accumulation of biomass in seeds. In the hydroponic study, permanent withdrawal of P from the nutrient solution at anthesis (until maturity) led to significant reductions in both phytate and starch LPLs with a similar trend observed when P was withdrawn at 8 DAA. In the pot study using soil, alteration of source-sink systems through drought stress during grain filling or floret abortion (manual removal of the top half of each panicle) also led to significant reductions in grain phytate and starch LPLs compared to control plants. These results indicate that in addition to affecting phytate concentrations, reduced P supply to rice plants during grain filling and alteration of source-sink relationships also impacts starch LPL concentrations. Given these complexities, breeding and selection for reduced seed P concentration in rice and other cereals should be undertaken with caution.

A structured understanding of our world in terms of objects, relations, and hierarchies is an important component of human cognition. Learning such a structured world model from raw sensory data remains a challenge. As a step towards this goal, we introduce Contrastively-trained Structured World Models (C-SWMs). C-SWMs utilize a contrastive approach for representation learning in environments with compositional structure. We structure each state embedding as a set of object representations and their relations, modeled by a graph neural network. This allows objects to be discovered from raw pixel observations without direct supervision as part of the learning process. We evaluate C-SWMs on compositional environments involving multiple interacting objects that can be manipulated independently by an agent, simple Atari games, and a multi-object physics simulation. Our experiments demonstrate that C-SWMs can overcome limitations of models based on pixel reconstruction and outperform typical representatives of this model class in highly structured environments, while learning interpretable object-based representations.

Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of performance, we introduce a differentiable quantization procedure. Differentiability can be achieved by transforming continuous distributions over the weights and activations of the network to categorical distributions over the quantization grid. These are subsequently relaxed to continuous surrogates that can allow for efficient gradient-based optimization. We further show that stochastic rounding can be seen as a special case of the proposed approach and that under this formulation the quantization grid itself can also be optimized with gradient descent. We experimentally validate the performance of our method on MNIST, CIFAR 10 and Imagenet classification. © 7th International Conference on Learning Representations, ICLR 2019. All Rights Reserved.

Deep neural networks are almost universally trained with reverse-mode automatic differentiation (a.k.a. backpropagation). Biological networks, on the other hand, appear to lack any mechanism for sending gradients back to their input neurons, and thus cannot be learning in this way. In response to this, Scellier & Bengio (2017) proposed Equilibrium Propagation - a method for gradient-based train- ing of neural networks which uses only local learning rules and, crucially, does not rely on neurons having a mechanism for back-propagating an error gradient. Equilibrium propagation, however, has a major practical limitation: inference involves doing an iterative optimization of neural activations to find a fixed-point, and the number of steps required to closely approximate this fixed point scales poorly with the depth of the network. In response to this problem, we propose Initialized Equilibrium Propagation, which trains a feedforward network to initialize the iterative inference procedure for Equilibrium propagation. This feed-forward network learns to approximate the state of the fixed-point using a local learning rule. After training, we can simply use this initializing network for inference, resulting in a learned feedforward network. Our experiments show that this network appears to work as well or better than the original version of Equilibrium propagation. This shows how we might go about training deep networks without using backpropagation.

Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder aggregated posterior and the prior in latent space, plus a reconstruction error. We also identify the role of its trade-off hyperparameter as the capacity of the generator: its Lipschitz constant. Moreover, we prove that optimizing the encoder over any class of universal approximators, such as deterministic neural networks, is enough to come arbitrarily close to the optimum. We therefore advertise this framework, which holds for any metric space and prior, as a sweet-spot of current generative autoencoding objectives. We then introduce the Sinkhorn auto-encoder (SAE), which approximates and minimizes the p-Wasserstein distance in latent space via backprogation through the Sinkhorn algorithm. SAE directly works on samples, i.e. it models the aggregated posterior as an implicit distribution, with no need for a reparameterization trick for gradients estimations. SAE is thus able to work with different metric spaces and priors with minimal adaptations. We demonstrate the flexibility of SAE on latent spaces with different geometries and priors and compare with other methods on benchmark data sets.

We consider the problem of domain generalization, namely, how to learn representations given data from a set of domains that generalize to data from a previously unseen domain. We propose the Domain Invariant Variational Autoencoder (DIVA), a generative model that tackles this problem by learning three independent latent subspaces, one for the domain, one for the class, and one for any residual variations. We highlight that due to the generative nature of our model we can also incorporate unlabeled data from known or previously unseen domains. To the best of our knowledge this has not been done before in a domain generalization setting. This property is highly desirable in fields like medical imaging where labeled data is scarce. We experimentally evaluate our model on the rotated MNIST benchmark and a malaria cell images dataset where we show that (i) the learned subspaces are indeed complementary to each other, (ii) we improve upon recent works on this task and (iii) incorporating unlabelled data can boost the performance even further., Comment: Code available at https://github.com/AMLab-Amsterdam/DIVA

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a linear combination of a complete steerable kernel basis, which is derived analytically in this paper. We prove that equivariant convolutions are the most general equivariant linear maps between fields over R^3. Our experimental results confirm the effectiveness of 3D Steerable CNNs for the problem of amino acid propensity prediction and protein structure classification, both of which have inherent SE(3) symmetry.

Generative flows are attractive because they admit exact likelihood optimization and efficient image synthesis. Recently, Kingma & Dhariwal (2018) demonstrated with Glow that generative flows are capable of generating high quality images. We generalize the 1 x 1 convolutions proposed in Glow to invertible d x d convolutions, which are more flexible since they operate on both channel and spatial axes. We propose two methods to produce invertible convolutions that have receptive fields identical to standard convolutions: Emerging convolutions are obtained by chaining specific autoregressive convolutions, and periodic convolutions are decoupled in the frequency domain. Our experiments show that the flexibility of d x d convolutions significantly improves the performance of generative flow models on galaxy images, CIFAR10 and ImageNet., Accepted at International Conference on Machine Learning (ICML) 2019

The accurate estimation of predictive uncertainty carries importance in medical scenarios such as lung node segmentation. Unfortunately, most existing works on predictive uncertainty do not return calibrated uncertainty estimates, which could be used in practice. In this work we exploit multi-grader annotation variability as a source of ‘groundtruth’ aleatoric uncertainty, which can be treated as a target in a supervised learning problem. We combine this groundtruth uncertainty with a Probabilistic U-Net and test on the LIDC-IDRI lung nodule CT dataset and MICCAI2012 prostate MRI dataset. We find that we are able to improve predictive uncertainty estimates. We also find that we can improve sample accuracy and sample diversity. In real-world applications, our method could inform doctors about the confidence of the segmentation results.

Backpropagation is almost universally used to train artificial neural networks. However, there are several reasons that backpropagation could not be plausibly implemented by biological neurons. Among these are the facts that (1) biological neurons appear to lack any mechanism for sending gradients backwards across synapses, and (2) biological “spiking” neurons emit binary signals, whereas back-propagation requires that neurons communicate continuous values between one another. Recently, Scellier and Bengio [2017], demonstrated an alternative to backpropagation, called Equilibrium Propagation, wherein gradients are implicitly computed by the dynamics of the neural network, so that neurons do not need an internal mechanism for backpropagation of gradients. This provides an interesting solution to problem (1). In this paper, we address problem (2) by proposing a way in which Equilibrium Propagation can be implemented with neurons which are constrained to just communicate binary values at each time step. We show that with appropriate step-size annealing, we can converge to the same fixed-point as a real-valued neural network, and that with predictive coding, we can make this convergence much faster. We demonstrate that the resulting model can be used to train a spiking neural network using the update scheme from Equilibrium propagation.

High-risk domains require reliable confidence estimates from predictive models. Deep latent variable models provide these, but suffer from the rigid variational distributions used for tractable inference, which err on the side of overconfidence. We propose Stochastic Quantized Activation Distributions (SQUAD), which imposes a flexible yet tractable distribution over discretized latent variables. The proposed method is scalable, self-normalizing and sample efficient. We demonstrate that the model fully utilizes the flexible distribution, learns interesting non-linearities, and provides predictive uncertainty of competitive quality.

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal formulation to learn a flexible inference mechanism and to create an optimal approximate coupling between the data distribution and the generative model. In order to learn the generative model, we use the dual formulation and train the decoder adversarially through a critic network that is regularized by the approximate coupling obtained from the primal. Unlike previous methods that violate various properties of the optimal critic, we regularize the norm and the direction of the gradients of the critic function. Our model shares many of the desirable properties of auto-encoding models in terms of mode coverage and latent structure, while avoiding their undesirable averaging properties, e.g. their inability to capture sharp visual features when modeling real images. We compare our algorithm with several other generative modeling techniques that utilize Wasserstein distances on Frechet Inception Distance (FID) and Inception Scores (IS).

Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder aggregated posterior and the prior in latent space, plus a reconstruction error. We also identify the role of its trade-off hyperparameter as the capacity of the generator: its Lipschitz constant. Moreover, we prove that optimizing the encoder over any class of universal approximators, such as deterministic neural networks, is enough to come arbitrarily close to the optimum. We therefore advertise this framework, which holds for any metric space and prior, as a sweet-spot of current generative autoencoding objectives. We then introduce the Sinkhorn auto-encoder (SAE), which approximates and minimizes the p-Wasserstein distance in latent space via backprogation through the Sinkhorn algorithm. SAE directly works on samples, i.e. it models the aggregated posterior as an implicit distribution, with no need for a reparameterization trick for gradients estimations. SAE is thus able to work with different metric spaces and priors with minimal adaptations. We demonstrate the flexibility of SAE on latent spaces with different geometries and priors and compare with other methods on benchmark data sets., Comment: Accepted for oral presentation at UAI19

Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.

Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We introduce two novelties in this paper: 1) we use hierarchical priors to prune nodes instead of individual weights, and 2) we use the posterior uncertainties to determine the optimal fixed point precision to encode the weights. Both factors significantly contribute to achieving the state of the art in terms of compression rates, while still staying competitive with methods designed to optimize for speed or energy efficiency.

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single-unit bottleneck from planar flows, making a single transformation much more flexible. We compare the performance of Sylvester normalizing flows against planar flows and inverse autoregressive flows and demonstrate that they compare favorably on several datasets.

We consider matrix completion for recommender systems from the point of view of link prediction on graphs. Interaction data such as movie ratings can be represented by a bipartite user-item graph with labeled edges denoting observed ratings. Building on recent progress in deep learning on graph-structured data, we propose a graph auto-encoder framework based on differentiable message passing on the bipartite interaction graph. Our model shows competitive performance on standard collaborative filtering benchmarks. In settings where complimentary feature information or structured data such as a social network is available, our framework outperforms recent state-of-the-art methods.

The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows while still allowing for local reparametrizations and a tractable lower bound. In experiments we show that with this new approximation we can significantly improve upon classical mean field for Bayesian neural networks on both predictive accuracy as well as predictive uncertainty., Comment: Appearing at the International Conference on Machine Learning (ICML) 2017

Summary Embryonic stem cells (ESCs) are pluripotent stem cells derived from the inner cell mass (ICM) of blastocyst embryos. Although first characterized over 30 years ago, the ontology of these cells remains elusive. Identifying the in vivo counterpart of murine ESCs will be essential for the derivation of stable ESC lines from other species. Several hypotheses exist concerning the ontology of murine ESCs. Recent data demonstrate that ESCs emerge from a subpopulation of ICM cells that transit through a Blimp1-positive state, suggesting that perhaps a germ cell developmental program underlies ESC derivation and maintenance. Alternatively, the common dependence of ESCs and diapause embryos on the cytokine LIF (leukemia inhibitory factor) has been thought to signify that murine ESCs employ a diapause-like program for their maintenance of pluripotency. Here we review different hypotheses regarding the nature of murine ESCs and discuss their implications for human pluripotent stem cell biology.

We introduce an algorithm to do backpropagation on a spiking network. Our network is "spiking" in the sense that our neurons accumulate their activation into a potential over time, and only send out a signal (a "spike") when this potential crosses a threshold and the neuron is reset. Neurons only update their states when receiving signals from other neurons. Total computation of the network thus scales with the number of spikes caused by an input rather than network size. We show that the spiking Multi-Layer Perceptron behaves identically, during both prediction and training, to a conventional deep network of rectified-linear units, in the limiting case where we run the spiking network for a long time. We apply this architecture to a conventional classification problem (MNIST) and achieve performance very close to that of a conventional Multi-Layer Perceptron with the same architecture. Our network is a natural architecture for learning based on streaming event-based data, and is a stepping stone towards using spiking neural networks to learn efficiently on streaming data.

n our research at the University of Amsterdam we have married two types of models into a single comprehensive framework which we have called “Variational Auto Encoders”. The two types of models are: 1) generative models where the data generation process is modelled, and 2) discriminative models, such as deep learning, where measurements are directly mapped to class labels.

We develop a privatised stochastic variational inference method for Latent Dirichlet Allocation (LDA). The iterative nature of stochastic variational inference presents challenges: multiple iterations are required to obtain accurate posterior distributions, yet each iteration increases the amount of noise that must be added to achieve a reasonable degree of privacy. We propose a practical algorithm that overcomes this challenge by combining: (1) an improved composition method for differential privacy, called the moments accountant, which provides a tight bound on the privacy cost of multiple variational inference iterations and thus significantly decreases the amount of additive noise; and (2) privacy amplification resulting from subsampling of large-scale data. Focusing on conjugate exponential family models, in our private variational inference, all the posterior distributions will be privatised by simply perturbing expected sufficient statistics. Using Wikipedia data, we illustrate the effectiveness of our algorithm for large-scale data.

Latent Dirichlet analysis, or topic modeling, is a flexible latent variable framework for modeling high-dimensional sparse count data. Various learning algorithms have been developed in recent years, including collapsed Gibbs sampling, variational inference, and maximum a posteriori estimation, and this variety motivates the need for careful empirical comparisons. In this paper, we highlight the close connections between these approaches. We find that the main differences are attributable to the amount of smoothing applied to the counts. When the hyperparameters are optimized, the differences in performance among the algorithms diminish significantly. The ability of these algorithms to achieve solutions of comparable accuracy gives us the freedom to select computationally efficient approaches. Using the insights gained from this comparative study, we show how accurate topic models can be learned in several seconds on text corpora with thousands of documents., Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)