### Session

## Oral Session 4

Moderators: Alexey Dosovitskiy · Christian Wolf · Rui Wang

**End-to-end Adversarial Text-to-Speech**

Jeff Donahue · Sander Dieleman · Mikolaj Binkowski · Erich Elsen · Karen Simonyan

Modern text-to-speech synthesis pipelines typically involve multiple processing stages, each of which is designed or learnt independently from the rest. In this work, we take on the challenging task of learning to synthesise speech from normalised text or phonemes in an end-to-end manner, resulting in models which operate directly on character or phoneme input sequences and produce raw speech audio outputs. Our proposed generator is feed-forward and thus efficient for both training and inference, using a differentiable alignment scheme based on token length prediction. It learns to produce high fidelity audio through a combination of adversarial feedback and prediction losses constraining the generated audio to roughly match the ground truth in terms of its total duration and mel-spectrogram. To allow the model to capture temporal variation in the generated audio, we employ soft dynamic time warping in the spectrogram-based prediction loss. The resulting model achieves a mean opinion score exceeding 4 on a 5 point scale, which is comparable to the state-of-the-art models relying on multi-stage training and additional supervision.

**Autoregressive Entity Retrieval**

Nicola De Cao · Gautier Izacard · Sebastian Riedel · Fabio Petroni

Entities are at the center of how we represent and aggregate knowledge. For instance, Encyclopedias such as Wikipedia are structured by entities (e.g., one per Wikipedia article). The ability to retrieve such entities given a query is fundamental for knowledge-intensive tasks such as entity linking and open-domain question answering. One way to understand current approaches is as classifiers among atomic labels, one for each entity. Their weight vectors are dense entity representations produced by encoding entity meta information such as their descriptions. This approach leads to several shortcomings: (i) context and entity affinity is mainly captured through a vector dot product, potentially missing fine-grained interactions between the two; (ii) a large memory footprint is needed to store dense representations when considering large entity sets; (iii) an appropriately hard set of negative data has to be subsampled at training time. In this work, we propose GENRE, the first system that retrieves entities by generating their unique names, left to right, token-by-token in an autoregressive fashion and conditioned on the context. This enables us to mitigate the aforementioned technical issues since: (i) the autoregressive formulation allows us to directly capture relations between context and entity name, effectively cross encoding both; (ii) the memory footprint is greatly reduced because the parameters of our encoder-decoder architecture scale with vocabulary size, not entity count; (iii) the exact softmax loss can be efficiently computed without the need to subsample negative data. We show the efficacy of the approach, experimenting with more than 20 datasets on entity disambiguation, end-to-end entity linking and document retrieval tasks, achieving new state-of-the-art or very competitive results while using a tiny fraction of the memory footprint of competing systems. Finally, we demonstrate that new entities can be added by simply specifying their unambiguous name. Code and pre-trained models at https://github.com/facebookresearch/GENRE.

**Interpreting Graph Neural Networks for NLP With Differentiable Edge Masking**

Michael Schlichtkrull · Nicola De Cao · Ivan Titov

Graph neural networks (GNNs) have become a popular approach to integrating structural inductive biases into NLP models. However, there has been little work on interpreting them, and specifically on understanding which parts of the graphs (e.g. syntactic trees or co-reference structures) contribute to a prediction. In this work, we introduce a post-hoc method for interpreting the predictions of GNNs which identifies unnecessary edges. Given a trained GNN model, we learn a simple classifier that, for every edge in every layer, predicts if that edge can be dropped. We demonstrate that such a classifier can be trained in a fully differentiable fashion, employing stochastic gates and encouraging sparsity through the expected $L_0$ norm. We use our technique as an attribution method to analyze GNN models for two tasks -- question answering and semantic role labeling -- providing insights into the information flow in these models. We show that we can drop a large proportion of edges without deteriorating the performance of the model, while we can analyse the remaining edges for interpreting model predictions.

**Expressive Power of Invariant and Equivariant Graph Neural Networks**

Waïss Azizian · marc lelarge

Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power of these GNN architectures. The current universality theorems only apply to intractable classes of GNNs. Here, we prove the first approximation guarantees for practical GNNs, paving the way for a better understanding of their generalization. Our theoretical results are proved for invariant GNNs computing a graph embedding (permutation of the nodes of the input graph does not affect the output) and equivariant GNNs computing an embedding of the nodes (permutation of the input permutes the output). We show that Folklore Graph Neural Networks (FGNN), which are tensor based GNNs augmented with matrix multiplication are the most expressive architectures proposed so far for a given tensor order. We illustrate our results on the Quadratic Assignment Problem (a NP-Hard combinatorial problem) by showing that FGNNs are able to learn how to solve the problem, leading to much better average performances than existing algorithms (based on spectral, SDP or other GNNs architectures). On a practical side, we also implement masked tensors to handle batches of graphs of varying sizes.

**Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs**

Pim De Haan · Maurice Weiler · Taco Cohen · Max Welling

A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs). Such GCNs utilize isotropic kernels and are therefore insensitive to the relative orientation of vertices and thus to the geometry of the mesh as a whole. We propose Gauge Equivariant Mesh CNNs which generalize GCNs to apply anisotropic gauge equivariant kernels. Since the resulting features carry orientation information, we introduce a geometric message passing scheme defined by parallel transporting features over mesh edges. Our experiments validate the significantly improved expressivity of the proposed model over conventional GCNs and other methods.

**Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator**

Max B Paulus · Chris Maddison · Andreas Krause

Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple function evaluations, or use learned, input-dependent baselines. Thus, there is a need for estimators that require minimal tuning, are computationally cheap, and have low mean squared error. In this paper, we show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization without increasing the number of function evaluations. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.

**Scalable Learning and MAP Inference for Nonsymmetric Determinantal Point Processes**

Mike Gartrell · Insu Han · Elvis Dohmatob · Jennifer Gillenwater · Victor-Emmanuel Brunel

Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work shows that nonsymmetric DPP (NDPP) kernels have significant advantages over symmetric kernels in terms of modeling power and predictive performance. However, for an item collection of size $M$, existing NDPP learning and inference algorithms require memory quadratic in $M$ and runtime cubic (for learning) or quadratic (for inference) in $M$, making them impractical for many typical subset selection tasks. In this work, we develop a learning algorithm with space and time requirements linear in $M$ by introducing a new NDPP kernel decomposition. We also derive a linear-complexity NDPP maximum a posteriori (MAP) inference algorithm that applies not only to our new kernel but also to that of prior work. Through evaluation on real-world datasets, we show that our algorithms scale significantly better, and can match the predictive performance of prior work.

**Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows**

Kashif Rasul · Abdul-Saboor Sheikh · Ingmar Schuster · Urs Bergmann · Roland Vollgraf

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multi-variate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multi-variate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.

**Noise against noise: stochastic label noise helps combat inherent label noise**

Pengfei Chen · Guangyong Chen · Junjie Ye · jingwei zhao · Pheng-Ann Heng

The noise in stochastic gradient descent (SGD) provides a crucial implicit regularization effect, previously studied in optimization by analyzing the dynamics of parameter updates. In this paper, we are interested in learning with noisy labels, where we have a collection of samples with potential mislabeling. We show that a previously rarely discussed SGD noise, induced by stochastic label noise (SLN), mitigates the effects of inherent label noise. In contrast, the common SGD noise directly applied to model parameters does not. We formalize the differences and connections of SGD noise variants, showing that SLN induces SGD noise dependent on the sharpness of output landscape and the confidence of output probability, which may help escape from sharp minima and prevent overconfidence. SLN not only improves generalization in its simplest form but also boosts popular robust training methods, including sample selection and label correction. Specifically, we present an enhanced algorithm by applying SLN to label correction. Our code is released.

**Mutual Information State Intrinsic Control**

Rui Zhao · Yang Gao · Pieter Abbeel · Volker Tresp · Wei Xu

Reinforcement learning has been shown to be highly successful at many challenging tasks. However, success heavily relies on well-shaped rewards. Intrinsically motivated RL attempts to remove this constraint by defining an intrinsic reward function. Motivated by the self-consciousness concept in psychology, we make a natural assumption that the agent knows what constitutes itself, and propose a new intrinsic objective that encourages the agent to have maximum control on the environment. We mathematically formalize this reward as the mutual information between the agent state and the surrounding state under the current agent policy. With this new intrinsic motivation, we are able to outperform previous methods, including being able to complete the pick-and-place task for the first time without using any task reward. A video showing experimental results is available at https://youtu.be/AUCwc9RThpk.

**Learning Incompressible Fluid Dynamics from Scratch - Towards Fast, Differentiable Fluid Models that Generalize**

Nils Wandel · Michael Weinmann · Reinhard Klein

Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of incompressible fluids is a challenging task and traditional numerical approximation schemes come at high computational costs. Recent deep learning based approaches promise vast speed-ups but do not generalize to new fluid domains, require fluid simulation data for training, or rely on complex pipelines that outsource major parts of the fluid simulation to traditional methods.

In this work, we propose a novel physics-constrained training approach that generalizes to new fluid domains, requires no fluid simulation data, and allows convolutional neural networks to map a fluid state from time-point t to a subsequent state at time t+dt in a single forward pass. This simplifies the pipeline to train and evaluate neural fluid models. After training, the framework yields models that are capable of fast fluid simulations and can handle various fluid phenomena including the Magnus effect and Kármán vortex streets. We present an interactive real-time demo to show the speed and generalization capabilities of our trained models. Moreover, the trained neural networks are efficient differentiable fluid solvers as they offer a differentiable update step to advance the fluid simulation in time. We exploit this fact in a proof-of-concept optimal control experiment. Our models significantly outperform a recent differentiable fluid solver in terms of computational speed and accuracy.

**Identifying nonlinear dynamical systems with multiple time scales and long-range dependencies**

Dominik Schmidt · Georgia Koppe · Zahra Monfared · Max Beutelspacher · Daniel Durstewitz

A main theoretical interest in biology and physics is to identify the nonlinear dynamical system (DS) that generated observed time series. Recurrent Neural Networks (RNN) are, in principle, powerful enough to approximate any underlying DS, but in their vanilla form suffer from the exploding vs. vanishing gradients problem. Previous attempts to alleviate this problem resulted either in more complicated, mathematically less tractable RNN architectures, or strongly limited the dynamical expressiveness of the RNN. Here we address this issue by suggesting a simple regularization scheme for vanilla RNN with ReLU activation which enables them to solve long-range dependency problems and express slow time scales, while retaining a simple mathematical structure which makes their DS properties partly analytically accessible. We prove two theorems that establish a tight connection between the regularized RNN dynamics and their gradients, illustrate on DS benchmarks that our regularization approach strongly eases the reconstruction of DS which harbor widely differing time scales, and show that our method is also en par with other long-range architectures like LSTMs on several tasks.

Adiabatic quantum computation is a form of computation that acts by slowly interpolating a quantum system between an easy to prepare initial state and a final state that represents a solution to a given computational problem. The choice of the interpolation schedule is critical to the performance: if at a certain time point, the evolution is too rapid, the system has a high probability to transfer to a higher energy state, which does not represent a solution to the problem. On the other hand, an evolution that is too slow leads to a loss of computation time and increases the probability of failure due to decoherence. In this work, we train deep neural models to produce optimal schedules that are conditioned on the problem at hand. We consider two types of problem representation: the Hamiltonian form, and the Quadratic Unconstrained Binary Optimization (QUBO) form. A novel loss function that scores schedules according to their approximated success probability is introduced. We benchmark our approach on random QUBO problems, Grover search, 3-SAT, and MAX-CUT problems and show that our approach outperforms, by a sizable margin, the linear schedules as well as alternative approaches that were very recently proposed.