In principle then, chemistry is easy. All you have to do is write down the Schrodinger equation for the reactants and solve it. In practice, this isn't possible because multi-body Schrodinger equations are very difficult to solve. In fact, the only atom we can solve exactly is the Hydrogen atom with one proton and one electron. All other atoms are solved by approximations called perturbation techniques.

Recently, self-supervised learning has proved to be effective to learn representations of events in image sequences, where events are understood as sets of temporally adjacent images that are semantically perceived as a whole. However, although this approach does not require expensive manual annotations, it is data hungry and suffers from domain adaptation problems. As an alternative, in this work, we propose a novel approach for learning event representations named Dynamic Graph Embedding (DGE). The assumption underlying our model is that a sequence of images can be represented by a graph that encodes both semantic and temporal similarity. The key novelty of DGE is to learn jointly the graph and its graph embedding. At its core, DGE works by iterating over two steps: 1) updating the graph representing the semantic and temporal structure of the data based on the current data representation, and 2) updating the data representation to take into account the current data graph structure. The main advantage of DGE over state-of-the-art self-supervised approaches is that it does not require any training set, but instead learns iteratively from the data itself a low-dimensional embedding that reflects their temporal and semantic structure. Experimental results on two benchmark datasets of real image sequences captured at regular intervals demonstrate that the proposed DGE leads to effective event representations. In particular, it achieves robust temporal segmentation on the EDUBSeg and EDUBSeg-Desc benchmark datasets, outperforming the state of the art.

We show how complexity theory can be introduced in machine learning to help bring together apparently disparate areas of current research. We show that this new approach requires less training data and is more generalizable as it shows greater resilience to random attacks. We investigate the shape of the discrete algorithmic space when performing regression or classification using a loss function parametrized by algorithmic complexity, demonstrating that the property of differentiation is not necessary to achieve results similar to those obtained using differentiable programming approaches such as deep learning. In doing so we use examples which enable the two approaches to be compared (small, given the computational power required for estimations of algorithmic complexity). We find and report that (i) machine learning can successfully be performed on a non-smooth surface using algorithmic complexity; (ii) that parameter solutions can be found using an algorithmic-probability classifier, establishing a bridge between a fundamentally discrete theory of computability and a fundamentally continuous mathematical theory of optimization methods; (iii) a formulation of an algorithmically directed search technique in non-smooth manifolds can be defined and conducted; (iv) exploitation techniques and numerical methods for algorithmic search to navigate these discrete non-differentiable spaces can be performed; in application of the (a) identification of generative rules from data observations; (b) solutions to image classification problems more resilient against pixel attacks compared to neural networks; (c) identification of equation parameters from a small data-set in the presence of noise in continuous ODE system problem, (d) classification of Boolean NK networks by (1) network topology, (2) underlying Boolean function, and (3) number of incoming edges.

Healthcare data suffers from both noise and lack of ground truth. The cost of data increases as it is cleaned and annotated in healthcare. Unlike other data sets, medical data annotation, which is critical to accurate ground truth, requires medical domain expertise for a better patient outcome. In this work, we report on the use of reinforcement learning to mimic the decision making process of annotators for medical events, to automate annotation and labelling. The reinforcement agent learns to annotate alarm data based on annotations done by an expert. Our method shows promising results on medical alarm data sets. We trained DQN and A2C agents using the data from monitoring devices annotated by an expert. Initial results from these RL agents learning the expert annotation behavior are promising. The A2C agent performs better in terms of learning the sparse events in a given state, thereby choosing more right actions compared to DQN agent. To the best of our knowledge, this is the first reinforcement learning application for the automation of medical events annotation, which has far-reaching practical use.

We design a classifier for transactional datasets with application in malware detection. We build the classifier based on the minimum description length (MDL) principle. This involves selecting a model that best compresses the training dataset for each class considering the MDL criterion. To select a model for a dataset, we first use clustering followed by closed frequent pattern mining to extract a subset of closed frequent patterns (CFPs). We show that this method acts as a pattern summarization method to avoid pattern explosion; this is done by giving priority to longer CFPs, and without requiring to extract all CFPs. We then use the MDL criterion to further summarize extracted patterns, and construct a code table of patterns. This code table is considered as the selected model for the compression of the dataset. We evaluate our classifier for the problem of static malware detection in portable executable (PE) files. We consider API calls of PE files as their distinguishing features. The presence-absence of API calls forms a transactional dataset. Using our proposed method, we construct two code tables, one for the benign training dataset, and one for the malware training dataset. Our dataset consists of 19696 benign, and 19696 malware samples, each a binary sequence of size 22761. We compare our classifier with deep neural networks providing us with the state-of-the-art performance. The comparison shows that our classifier performs very close to deep neural networks. We also discuss that our classifier is an interpretable classifier. This provides the motivation to use this type of classifiers where some degree of explanation is required as to why a sample is classified under one class rather than the other class.

Deep neural networks are susceptible to adversarial manipulations in the input domain. The extent of vulnerability has been explored intensively in cases of $\ell_p$-bounded and $\ell_p$-minimal adversarial perturbations. However, the vulnerability of DNNs to adversarial perturbations with specific statistical properties or frequency-domain characteristics has not been sufficiently explored. In this paper, we study the smoothness of perturbations and propose SmoothFool, a general and computationally efficient framework for computing smooth adversarial perturbations. Through extensive experiments, we validate the efficacy of the proposed method for both the white-box and black-box attack scenarios. In particular, we demonstrate that: (i) there exist extremely smooth adversarial perturbations for well-established and widely used network architectures, (ii) smoothness significantly enhances the robustness of perturbations against state-of-the-art defense mechanisms, (iii) smoothness improves the transferability of adversarial perturbations across both data points and network architectures, and (iv) class categories exhibit a variable range of susceptibility to smooth perturbations. Our results suggest that smooth APs can play a significant role in exploring the vulnerability extent of DNNs to adversarial examples.

Deep convolutional networks have spectacular applications to classification and regression (LeCun et al., 2015), but they are a black box which are hard to analyze mathematically because of their architecture Despite its simplicity, it applies to complex image classification and reaches a higher accuracy than AlexNet (Krizhevsky et al., 2012) over ImageNet ILSVRC2012. It is implemented with a deep convolutional network architecture. Dictionary learning for classification was introduced in Mairal et al. (2009) and implemented with deep A major issue is to compute the sparse code with a small network. We introduce a new architecture based on homotopy continuation, which leads to exponential convergence. The ALIST A (Liu et al., 2019) sparse code is incorporated in We explain the implementation and mathematical properties of each element of the sparse scattering network.

TorchBeast is a platform for reinforcement learning (RL) research in PyTorch. It implements a version of the popular IMPALA algorithm for fast, asynchronous, parallel training of RL agents. Additionally, TorchBeast has simplicity as an explicit design goal: We provide both a pure-Python implementation ("MonoBeast") as well as a multi-machine high-performance version ("PolyBeast"). In the latter, parts of the implementation are written in C++, but all parts pertaining to machine learning are kept in simple Python using PyTorch, with the environments provided using the OpenAI Gym interface. This enables researchers to conduct scalable RL research using TorchBeast without any programming knowledge beyond Python and PyTorch. In this paper, we describe the TorchBeast design principles and implementation and demonstrate that it performs on-par with IMPALA on Atari. TorchBeast is released as an open-source package under the Apache 2.0 license and is available at \url{https://github.com/facebookresearch/torchbeast}.

I NFERRING DYNAMICAL SYSTEMS WITH LONG-RANGE DEPENDENCIES THROUGH LINE ATTRACTOR REGULARIZATIONDominik Schmidt 1*, Georgia Koppe 1*, Max Beutelspacher 1,2, Daniel Durstewitz 1,3 1 Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany 3 Faculty of Physics and Astronomy, Heidelberg University * These authors contributed equally contact: {dominik.schmidt,georgia.koppe,daniel.durstewitz} A BSTRACT V anilla RNN with ReLU activation have a simple structure that is amenable to systematic dynamical systems analysis and interpretation, but they suffer from the exploding vs. vanishing gradients problem. Recent attempts to retain this simplicity while alleviating the gradient problem are based on proper initialization schemes or orthogonality/unitary constraints on the RNN's recurrence matrix, which, however, comes with limitations to its expressive power with regards to dynamical systems phenomena like chaos or multi-stability. Here, we instead suggest a regularization scheme that pushes part of the RNN's latent subspace toward a line attractor configuration that enables long short-term memory and arbitrarily slow time scales. We show that our approach excels on a number of benchmarks like the sequential MNIST or multiplication problems, and enables reconstruction of dynamical systems which harbor widely different time scales. 1 I NTRODUCTION Theories of complex systems in biology and physics are often formulated in terms of sets of stochastic differential or difference equations, i.e. as stochastic dynamical systems (DS). A longstanding desire is to retrieve these generating dynamical equations directly from observed time series data (Kantz & Schreiber, 2004). However, vanilla RNN as often used in this context are well known for their problems in capturing long-term dependencies and slow time scales in the data (Hochreiter & Schmidhuber, 1997; Bengio et al., 1994).

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing models that are robust to worst-case perturbations around predefined points. Unfortunately, one of the main issues in adversarial training is that robustness w.r.t. gradient-based attackers is always achieved at the cost of prediction accuracy. In this paper, a new algorithm, called Wasserstein Projected Gradient Descent (WPGD), for adversarial training is proposed. WPGD provides a simple way to obtain cost-sensitive robustness, resulting in a finer control of the robustness-accuracy trade-off. Moreover, WPGD solves an optimal transport problem on the output space of the network and it can efficiently discover directions where robustness is required, allowing to control the directional trade-off between accuracy and robustness. The proposed WPGD is validated in this work on image recognition tasks with different benchmark datasets and architectures. Moreover, real world-like datasets are often unbalanced: this paper shows that when dealing with such type of datasets, the performance of adversarial training are mainly affected in term of standard accuracy.