The dynamics between agents and the environment are an important component of multi-agent Reinforcement Learning (RL), and learning them provides a basis for decision making. However, a major challenge in optimizing a learned dynamics model is the accumulation of error when predicting multiple steps into the future. Recent advances in variational inference provide model based solutions that predict complete trajectory segments, and optimize over a latent representation of trajectories. For single-agent scenarios, several recent studies have explored this idea, and showed its benefits over conventional methods. In this work, we extend this approach to the multi-agent case, and effectively optimize over a latent space that encodes multi-agent strategies. We discuss the challenges in optimizing over a latent variable model for multiple agents, both in the optimization algorithm and in the model representation, and propose a method for both cooperative and competitive settings based on risk-sensitive optimization. We evaluate our method on tasks in the multi-agent particle environment and on a simulated RoboCup domain.

The design of activation functions is a growing research area in the field of neural networks. In particular, instead of using fixed point-wise functions (e.g., the rectified linear unit), several authors have proposed ways of learning these functions directly from the data in a non-parametric fashion. In this paper we focus on the kernel activation function (KAF), a recently proposed framework wherein each function is modeled as a one-dimensional kernel model, whose weights are adapted through standard backpropagation-based optimization. One drawback of KAFs is the need to select a single kernel function and its eventual hyper-parameters. To partially overcome this problem, we motivate an extension of the KAF model, in which multiple kernels are linearly combined at every neuron, inspired by the literature on multiple kernel learning. We provide an application of the resulting multi-KAF on a realistic use case, specifically handwritten Latin OCR, on a large dataset collected in the context of the `In Codice Ratio' project. Results show that multi-KAFs can improve the accuracy of the convolutional networks previously developed for the task, with faster convergence, even with a smaller number of overall parameters.

We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show that any block-switch invariant function has a PEN-like representation. The DeepSets architecture is a special case of PEN and we can therefore also target fully exchangeable data. We employ PENs to learn summary statistics in approximate Bayesian computation (ABC). When comparing PENs to previous deep learning methods for learning summary statistics, our results are highly competitive, both considering time series and static models. Indeed, PENs provide more reliable posterior samples even when using less training data.

To understand the dynamics of optimization in deep neural networks, we develop a tool to study the evolution of the entire Hessian spectrum throughout the optimization process. Using this, we study a number of hypotheses concerning smoothness, curvature, and sharpness in the deep learning literature. We then thoroughly analyze a crucial structural feature of the spectra: in non-batch normalized networks, we observe the rapid appearance of large isolated eigenvalues in the spectrum, along with a surprising concentration of the gradient in the corresponding eigenspaces. In batch normalized networks, these two effects are almost absent. We characterize these effects, and explain how they affect optimization speed through both theory and experiments. As part of this work, we adapt advanced tools from numerical linear algebra that allow scalable and accurate estimation of the entire Hessian spectrum of ImageNet-scale neural networks; this technique may be of independent interest in other applications.

In the early history of positive-unlabeled (PU) learning, the sample selection approach, which heuristically selects negative (N) data from U data, was explored extensively. However, this approach was later dominated by the importance reweighting approach, which carefully treats all U data as N data. May there be a new sample selection method that can outperform the latest importance reweighting method in the deep learning age? This paper is devoted to answering this question affirmatively---we propose to label large-loss U data as P, based on the memorization properties of deep networks. Since P data selected in such a way are biased, we develop a novel learning objective that can handle such biased P data properly. Experiments confirm the superiority of the proposed method.

Polluting fine dusts in South Korea which are mainly consisted of biomass burning and fugitive dust blown from dust belt is significant problem these days. Predicting concentrations of fine dust particles in Seoul is challenging because they are product of complicate chemical reactions among gaseous pollutants and also influenced by dynamical interactions between pollutants and multiple climate variables. Elaborating state-of-art time series analysis techniques using deep learning, non-linear interactions between multiple variables can be captured and used to predict future dust concentration. In this work, we propose the LSTM based model to predict hourly concentration of fine dust at target location in Seoul based on previous concentration of pollutants, dust concentrations and climate variables in surrounding area. Our results show that proposed model successfully predicts future dust concentrations at 25 target districts(Gu) in Seoul.

The increasing interest in user privacy is leading to new privacy preserving machine learning paradigms. In the Federated Learning paradigm, a master machine learning model is distributed to user clients, the clients use their locally stored data and model for both inference and calculating model updates. The model updates are sent back and aggregated on the server to update the master model then redistributed to the clients. In this paradigm, the user data never leaves the client, greatly enhancing the user' privacy, in contrast to the traditional paradigm of collecting, storing and processing user data on a backend server beyond the user's control. In this paper we introduce, as far as we are aware, the first federated implementation of a Collaborative Filter. The federated updates to the model are based on a stochastic gradient approach. As a classical case study in machine learning, we explore a personalized recommendation system based on users' implicit feedback and demonstrate the method's applicability to both the MovieLens and an in-house dataset. Empirical validation confirms a collaborative filter can be federated without a loss of accuracy compared to a standard implementation, hence enhancing the user's privacy in a widely used recommender application while maintaining recommender performance.

Quantization can improve the execution latency and energy efficiency of neural networks on both commodity GPUs and specialized accelerators. The majority of existing literature focuses on training quantized DNNs, while this work examines the less-studied topic of quantizing a floating-point model without (re)training. DNN weights and activations follow a bell-shaped distribution post-training, while practical hardware uses a linear quantization grid. This leads to challenges in dealing with outliers in the distribution. Prior work has addressed this by clipping the outliers or using specialized hardware. In this work, we propose outlier channel splitting (OCS), which duplicates channels containing outliers, then halves the channel values. The network remains functionally identical, but affected outliers are moved toward the center of the distribution. OCS requires no additional training and works on commodity hardware. Experimental evaluation on ImageNet classification and language modeling shows that OCS can outperform state-of-the-art clipping techniques with only minor overhead.

The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group-equivariant non-expansive operators (GENEOs), which are maps between function spaces associated with groups of transformations. We study the topological and metric properties of the space of GENEOs to evaluate their approximating power and set the basis for general strategies to initialise and compose operators. We begin by defining suitable pseudo-metrics for the function spaces, the equivariance groups, and the set of non-expansive operators. Basing on these pseudo-metrics, we prove that the space of GENEOs is compact and convex, under the assumption that the function spaces are compact and convex. These results provide fundamental guarantees in a machine learning perspective. We show examples on the MNIST and fashion-MNIST datasets. By considering isometry-equivariant non-expansive operators, we describe a simple strategy to select and sample operators, and show how the selected and sampled operators can be used to perform both classical metric learning and an effective initialisation of the kernels of a convolutional neural network.

Shallow supervised 1-hidden layer neural networks have a number of favorable properties that make them easier to interpret, analyze, and optimize than their deep counterparts, but lack their representational power. Here we use 1-hidden layer learning problems to sequentially build deep networks layer by layer, which can inherit properties from shallow networks. Contrary to previous approaches using shallow networks, we focus on problems where deep learning is reported as critical for success. We thus study CNNs on image classification tasks using the large-scale ImageNet dataset and the CIFAR-10 dataset. Using a simple set of ideas for architecture and training we find that solving sequential 1-hidden-layer auxiliary problems lead to a CNN that exceeds AlexNet performance on ImageNet. Extending this training methodology to construct individual layers by solving 2-and-3-hidden layer auxiliary problems, we obtain an 11-layer network that exceeds several members of the VGG model family on ImageNet, and can train a VGG-11 model to the same accuracy as end-to-end learning. To our knowledge, this is the first competitive alternative to end-to-end training of CNNs that can scale to ImageNet. We illustrate several interesting properties of these models theoretically and conduct a range of experiments to study the properties this training induces on the intermediate layers.