Theoretical analyses for Generative Adversarial Networks (GANs) generally assume an arbitrarily large family of discriminators and do not consider the characteristics of the architectures used in practice. We show that this framework of analysis is too simplistic to properly analyze GAN training. To tackle this issue, we leverage the theory of infinite-width neural networks to model neural discriminator training for a wide range of adversarial losses via its Neural Tangent Kernel (NTK). Our analytical results show that GAN trainability primarily depends on the discriminator's architecture. We further study the discriminator for specific architectures and losses, and highlight properties providing a new understanding of GAN training. For example, we find that GANs trained with the integral probability metric loss minimize the maximum mean discrepancy with the NTK as kernel. Our conclusions demonstrate the analysis opportunities provided by the proposed framework, which paves the way for better and more principled GAN models. We release a generic GAN analysis toolkit based on our framework that supports the empirical part of our study.

Recent developments in the field of model-based RL have proven successful in a range of environments, especially ones where planning is essential. However, such successes have been limited to deterministic fully-observed environments. We present a new approach that handles stochastic and partially-observable environments. Our key insight is to use discrete autoencoders to capture the multiple possible effects of an action in a stochastic environment. We use a stochastic variant of Monte Carlo tree search to plan over both the agent's actions and the discrete latent variables representing the environment's response. Our approach significantly outperforms an offline version of MuZero on a stochastic interpretation of chess where the opponent is considered part of the environment. We also show that our approach scales to DeepMind Lab, a first-person 3D environment with large visual observations and partial observability.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

Recent advances in Transformer models allow for unprecedented sequence lengths, due to linear space and time complexity. In the meantime, relative positional encoding (RPE) was proposed as beneficial for classical Transformers and consists in exploiting lags instead of absolute positions for inference. Still, RPE is not available for the recent linear-variants of the Transformer, because it requires the explicit computation of the attention matrix, which is precisely what is avoided by such methods. In this paper, we bridge this gap and present Stochastic Positional Encoding as a way to generate PE that can be used as a replacement to the classical additive (sinusoidal) PE and provably behaves like RPE. The main theoretical contribution is to make a connection between positional encoding and cross-covariance structures of correlated Gaussian processes. We illustrate the performance of our approach on the Long-Range Arena benchmark and on music generation.

In the area of customer support, understanding customers' intents is a crucial step. Machine learning plays a vital role in this type of intent classification. In reality, it is typical to collect confirmation from customer support representatives (CSRs) regarding the intent prediction, though it can unnecessarily incur prohibitive cost to ask CSRs to assign existing or new intents to the mis-classified cases. Apart from the confirmed cases with and without intent labels, there can be a number of cases with no human curation. This data composition (Positives + Unlabeled + multiclass Negatives) creates unique challenges for model development. In response to that, we propose a semi-supervised multi-task learning paradigm. In this manuscript, we share our experience in building text-based intent classification models for a customer support service on an E-commerce website. We improve the performance significantly by evolving the model from multiclass classification to semi-supervised multi-task learning by leveraging the negative cases, domain- and task-adaptively pretrained ALBERT on customer contact texts, and a number of un-curated data with no labels. In the evaluation, the final model boosts the average AUC ROC by almost 20 points compared to the baseline finetuned multiclass classification ALBERT model.

Recent studies show a close connection between neural networks (NN) and kernel methods. However, most of these analyses (e.g., NTK) focus on the influence of (infinite) width instead of the depth of NN models. There remains a gap between theory and practical network designs that benefit from the depth. This paper first proposes a novel kernel family named Neural Optimization Kernel (NOK). Our kernel is defined as the inner product between two $T$-step updated functionals in RKHS w.r.t. a regularized optimization problem. Theoretically, we proved the monotonic descent property of our update rule for both convex and non-convex problems, and a $O(1/T)$ convergence rate of our updates for convex problems. Moreover, we propose a data-dependent structured approximation of our NOK, which builds the connection between training deep NNs and kernel methods associated with NOK. The resultant computational graph is a ResNet-type finite width NN. Our structured approximation preserved the monotonic descent property and $O(1/T)$ convergence rate. Namely, a $T$-layer NN performs $T$-step monotonic descent updates. Notably, we show our $T$-layered structured NN with ReLU maintains a $O(1/T)$ convergence rate w.r.t. a convex regularized problem, which explains the success of ReLU on training deep NN from a NN architecture optimization perspective. For the unsupervised learning and the shared parameter case, we show the equivalence of training structured NN with GD and performing functional gradient descent in RKHS associated with a fixed (data-dependent) NOK at an infinity-width regime. For finite NOKs, we prove generalization bounds. Remarkably, we show that overparameterized deep NN (NOK) can increase the expressive power to reduce empirical risk and reduce the generalization bound at the same time. Extensive experiments verify the robustness of our structured NOK blocks.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.

Stochastic simulations such as large-scale, spatiotemporal, age-structured epidemic models are computationally expensive at fine-grained resolution. We propose Interactive Neural Process (INP), an interactive framework to continuously learn a deep learning surrogate model and accelerate simulation. Our framework is based on the novel integration of Bayesian active learning, stochastic simulation and deep sequence modeling. In particular, we develop a novel spatiotemporal neural process model to mimic the underlying process dynamics. Our model automatically infers the latent process which describes the intrinsic uncertainty of the simulator. This also gives rise to a new acquisition function that can quantify the uncertainty of deep learning predictions. We design Bayesian active learning algorithms to iteratively query the simulator, gather more data, and continuously improve the model. We perform theoretical analysis and demonstrate that our approach reduces sample complexity compared with random sampling in high dimension. Empirically, we demonstrate our framework can faithfully imitate the behavior of a complex infectious disease simulator with a small number of examples, enabling rapid simulation and scenario exploration.

Automatic evaluations for natural language generation (NLG) conventionally rely on token-level or embedding-level comparisons with the text references. This is different from human language processing, for which visual imaginations often improve comprehension. In this work, we propose ImaginE, an imagination-based automatic evaluation metric for natural language generation. With the help of CLIP and DALL-E, two cross-modal models pre-trained on large-scale image-text pairs, we automatically generate an image as the embodied imagination for the text snippet and compute the imagination similarity using contextual embeddings. Experiments spanning several text generation tasks demonstrate that adding imagination with our ImaginE displays great potential in introducing multi-modal information into NLG evaluation, and improves existing automatic metrics' correlations with human similarity judgments in many circumstances.

When in a new situation or geographical location, human drivers have an extraordinary ability to watch others and learn maneuvers that they themselves may have never performed. In contrast, existing techniques for learning to drive preclude such a possibility as they assume direct access to an instrumented ego-vehicle with fully known observations and expert driver actions. However, such measurements cannot be directly accessed for the non-ego vehicles when learning by watching others. Therefore, in an application where data is regarded as a highly valuable asset, current approaches completely discard the vast portion of the training data that can be potentially obtained through indirect observation of surrounding vehicles. Motivated by this key insight, we propose the Learning by Watching (LbW) framework which enables learning a driving policy without requiring full knowledge of neither the state nor expert actions. To increase its data, i.e., with new perspectives and maneuvers, LbW makes use of the demonstrations of other vehicles in a given scene by (1) transforming the ego-vehicle's observations to their points of view, and (2) inferring their expert actions. Our LbW agent learns more robust driving policies while enabling data-efficient learning, including quick adaptation of the policy to rare and novel scenarios. In particular, LbW drives robustly even with a fraction of available driving data required by existing methods, achieving an average success rate of 92% on the original CARLA benchmark with only 30 minutes of total driving data and 82% with only 10 minutes.