Deep neural networks (DNNs) and optimization techniques are increasingly used in the search for approximation methods for high-dimensional problems in scientific computing. In the case of a partial differential equation (PDE), the approximation of the solution is challenging, since grid based approaches are burdened by the so called curse of dimension [2]. By this we mean that in order to achieve an accuracy ε 0, the computational cost has asymptotically an exponential dependence with respect to the dimension of the spatial domain of the PDE. As a result practical computations on dimensions larger than 4 or 6 become already very computationally intensive. A particularly relevant example of high dimensional PDEs are Hamilton-Jacobi-Bellman (HJB) equations associated with stochastic optimal control problems which are relevant for example in engineering and financial modelling.

One of the central features of deep learning is the generalization abilities of neural networks, which seem to improve relentlessly with over-parametrization. In this work, we investigate how properties of data impact the test error as a function of the number of training examples and number of training parameters; in other words, how the structure of data shapes the "generalization phase space". We first focus on the random features model trained in the teacher-student scenario. The synthetic input data is composed of independent blocks, which allow us to tune the saliency of low-dimensional structures and their relevance with respect to the target function. Using methods from statistical physics, we obtain an analytical expression for the train and test errors for both regression and classification tasks in the high-dimensional limit. The derivation allows us to show that noise in the labels and strong anisotropy of the input data play similar roles on the test error. Both promote an asymmetry of the phase space where increasing the number of training examples improves generalization further than increasing the number of training parameters. Our analytical insights are confirmed by numerical experiments involving fully-connected networks trained on MNIST and CIFAR10.

The design of recurrent neural networks (RNNs) to accurately process sequential inputs with long-time dependencies is very challenging on account of the exploding and vanishing gradient problem. To overcome this, we propose a novel RNN architecture which is based on a structure preserving discretization of a Hamiltonian system of second-order ordinary differential equations that models networks of oscillators. The resulting RNN is fast, invertible (in time), memory efficient and we derive rigorous bounds on the hidden state gradients to prove the mitigation of the exploding and vanishing gradient problem. A suite of experiments are presented to demonstrate that the proposed RNN provides state of the art performance on a variety of learning tasks with (very) long time-dependencies.

We introduce active testing: a new framework for sample-efficient model evaluation. While approaches like active learning reduce the number of labels needed for model training, existing literature largely ignores the cost of labeling test data, typically unrealistically assuming large test sets for model evaluation. This creates a disconnect to real applications where test labels are important and just as expensive, e.g. for optimizing hyperparameters. Active testing addresses this by carefully selecting the test points to label, ensuring model evaluation is sample-efficient. To this end, we derive theoretically-grounded and intuitive acquisition strategies that are specifically tailored to the goals of active testing, noting these are distinct to those of active learning. Actively selecting labels introduces a bias; we show how to remove that bias while reducing the variance of the estimator at the same time. Active testing is easy to implement, effective, and can be applied to any supervised machine learning method. We demonstrate this on models including WideResNet and Gaussian processes on datasets including CIFAR-100.

Stochastic generative models enable us to capture the geometric structure of a data manifold lying in a high dimensional space through a Riemannian metric in the latent space. However, its practical use is rather limited mainly due to inevitable complexity. In this work we propose a surrogate conformal Riemannian metric in the latent space of a generative model that is simple, efficient and robust. This metric is based on a learnable prior that we propose to learn using a basic energy-based model. We theoretically analyze the behavior of the proposed metric and show that it is sensible to use in practice. We demonstrate experimentally the efficiency and robustness, as well as the behavior of the new approximate metric. Also, we show the applicability of the proposed methodology for data analysis in the life sciences.

Advances in reinforcement learning (RL) have resulted in recent breakthroughs in the application of artificial intelligence (AI) across many different domains. An emerging landscape of development environments is making powerful RL techniques more accessible for a growing community of researchers. However, most existing frameworks do not directly address the problem of learning in complex operating environments, such as dense urban settings or defense-related scenarios, that incorporate distributed, heterogeneous teams of agents. To help enable AI research for this important class of applications, we introduce the AI Arena: a scalable framework with flexible abstractions for distributed multi-agent reinforcement learning. The AI Arena extends the OpenAI Gym interface to allow greater flexibility in learning control policies across multiple agents with heterogeneous learning strategies and localized views of the environment. To illustrate the utility of our framework, we present experimental results that demonstrate performance gains due to a distributed multi-agent learning approach over commonly-used RL techniques in several different learning environments.

Facial expressions play a fundamental role in human communication. Indeed, they typically reveal the real emotional status of people beyond the spoken language. Moreover, the comprehension of human affect based on visual patterns is a key ingredient for any human-machine interaction system and, for such reasons, the task of Facial Expression Recognition (FER) draws both scientific and industrial interest. In the recent years, Deep Learning techniques reached very high performance on FER by exploiting different architectures and learning paradigms. In such a context, we propose a multi-resolution approach to solve the FER task. We ground our intuition on the observation that often faces images are acquired at different resolutions. Thus, directly considering such property while training a model can help achieve higher performance on recognizing facial expressions. To our aim, we use a ResNet-like architecture, equipped with Squeeze-and-Excitation blocks, trained on the Affect-in-the-Wild 2 dataset. Not being available a test set, we conduct tests and models selection by employing the validation set only on which we achieve more than 90\% accuracy on classifying the seven expressions that the dataset comprises.

A common need for mobile application development by end-users or in computing education is to transform a sketch of a user interface into wireframe code using App Inventor, a popular block-based programming environment. As this task is challenging and time-consuming, we present the Sketch2aia approach that automates this process. Sketch2aia employs deep learning to detect the most frequent user interface components and their position on a hand-drawn sketch creating an intermediate representation of the user interface and then automatically generates the App Inventor code of the wireframe. The approach achieves an average user interface component classification accuracy of 87,72% and results of a preliminary user evaluation indicate that it generates wireframes that closely mirror the sketches in terms of visual similarity. The approach has been implemented as a web tool and can be used to support the end-user development of mobile applications effectively and efficiently as well as the teaching of user interface design in K-12.

Training machine learning (ML) models typically involves expensive iterative optimization. Once the model's final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters were indeed the result of this optimization procedure. Such a mechanism would support security of ML applications in several ways. For instance, it would simplify ownership resolution when multiple parties contest ownership of a specific model. It would also facilitate the distributed training across untrusted workers where Byzantine workers might otherwise mount a denial-of-service by returning incorrect model updates. In this paper, we remediate this problem by introducing the concept of proof-of-learning in ML. Inspired by research on both proof-of-work and verified computations, we observe how a seminal training algorithm, stochastic gradient descent, accumulates secret information due to its stochasticity. This produces a natural construction for a proof-of-learning which demonstrates that a party has expended the compute require to obtain a set of model parameters correctly. In particular, our analyses and experiments show that an adversary seeking to illegitimately manufacture a proof-of-learning needs to perform *at least* as much work than is needed for gradient descent itself. We also instantiate a concrete proof-of-learning mechanism in both of the scenarios described above. In model ownership resolution, it protects the intellectual property of models released publicly. In distributed training, it preserves availability of the training procedure. Our empirical evaluation validates that our proof-of-learning mechanism is robust to variance induced by the hardware (ML accelerators) and software stacks.

Many healthcare decisions involve navigating through a multitude of treatment options in a sequential and iterative manner to find an optimal treatment pathway with the goal of an optimal patient outcome. Such optimization problems may be amenable to reinforcement learning. A reinforcement learning agent could be trained to provide treatment recommendations for physicians, acting as a decision support tool. However, a number of difficulties arise when using RL beyond benchmark environments, such as specifying the reward function, choosing an appropriate state representation and evaluating the learned policy.