Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context [1]. Crucially, these models allow for the direct estimation of the free energy at a given point in parameter space. This is in contrast to existing methods based on Markov chains which generically require integration through parameter space. In this contribution, we will review this novel machine-learning-based estimation method. We will in detail discuss the issue of mode collapse and outline mitigation techniques which are particularly suited for applications at finite temperature.

Explaining Bayesian Neural Networks

To make advanced learning machines such as Deep Neural Networks (DNNs) more transparent in decision making, explainable AI (XAI) aims to provide interpretations of DNNs' predictions. These interpretations are usually given in the form of heatmaps, each one illustrating relevant patterns regarding the prediction for a given instance. Bayesian approaches such as Bayesian Neural Networks (BNNs) so far have a limited form of transparency (model transparency) already built-in through their prior weight distribution, but notably, they lack explanations of their predictions for given instances. In this work, we bring together these two perspectives of transparency into a holistic explanation framework for explaining BNNs. Within the Bayesian framework, the network weights follow a probability distribution. Hence, the standard (deterministic) prediction strategy of DNNs extends in BNNs to a predictive distribution, and thus the standard explanation extends to an explanation distribution. Exploiting this view, we uncover that BNNs implicitly employ multiple heterogeneous prediction strategies. While some of these are inherited from standard DNNs, others are revealed to us by considering the inherent uncertainty in BNNs. Our quantitative and qualitative experiments on toy/benchmark data and real-world data from pathology show that the proposed approach of explaining BNNs can lead to more effective and insightful explanations.

NoiseGrad: enhancing explanations by introducing stochasticity to model weights

Attribution methods remain a practical instrument that is used in real-world applications to explain the decision-making process of complex learning machines. It has been shown that a simple method called SmoothGrad can effectively reduce the visual diffusion of gradient-based attribution methods and has established itself among both researchers and practitioners. What remains unexplored in research, however, is how explanations can be improved by introducing stochasticity to the model weights. In the light of this, we introduce - NoiseGrad - a stochastic, method-agnostic explanation-enhancing method that adds noise to the weights instead of the input data. We investigate our proposed method through various experiments including different datasets, explanation methods and network architectures and conclude that NoiseGrad (and its extension NoiseGrad++) with multiplicative Gaussian noise offers a clear advantage compared to SmoothGrad on several evaluation criteria. We connect our proposed method to Bayesian Learning and provide the user with a heuristic for choosing hyperparameters.

Optimal Sampling Density for Nonparametric Regression

We propose a novel active learning strategy for regression, which is model-agnostic, robust against model mismatch, and interpretable. Assuming that a small number of initial samples are available, we derive the optimal training density that minimizes the generalization error of local polynomial smoothing (LPS) with its kernel bandwidth tuned locally: We adopt the mean integrated squared error (MISE) as a generalization criterion, and use the asymptotic behavior of the MISE as well as thelocally optimal bandwidths (LOB) -- the bandwidth function that minimizes MISE in the asymptotic limit. The asymptotic expression of our objective then reveals the dependence of the MISE on the training density, enabling analytic minimization. As a result, we obtain the optimal training density in a closed-form. The almost model-free nature of our approach should encode raw properties of the target problem, and thus provide a robust and model-agnostic active learning strategy. Furthermore, the obtained training density factorizes the influence of local function complexity, noise leveland test density in a transparent and interpretable way. We validate our theory in numerical simulations, and show that the proposed active learning method outperforms the existing state-of-the-art model-agnostic approaches.

Langevin Cooling for Domain Translation

Domain translation is the task of finding correspondence between two domains. Several Deep Neural Network (DNN) models, e.g., CycleGAN and cross-lingual language models, have shown remarkable successes on this task under the unsupervised setting---the mappings between the domains are learned from two independent sets of training data in both domains (without paired samples). However, those methods typically do not perform well on a significant proportion of test samples. In this paper, we hypothesize that many of such unsuccessful samples lie at the fringe---relatively low-density areas---of data distribution, where the DNN was not trained very well, and propose to perform Langevin dynamics to bring such fringe samples towards high density areas. We demonstrate qualitatively and quantitatively that our strategy, called Langevin Cooling (L-Cool), enhances state-of-the-art methods in image translation and language translation tasks.

On Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models

In this work, we demonstrate that applying deep generative machine learning models for lattice field theory is a promising route for solving problems where Markov Chain Monte Carlo (MCMC) methods are problematic. More specifically, we show that generative models can be used to estimate the absolute value of the free energy, which is in contrast to existing MCMC-based methods which are limited to only estimate free energy differences. We demonstrate the effectiveness of the proposed method for two-dimensional $\phi^4$ theory and compare it to MCMC-based methods in detailed numerical experiments.

How Much Can I Trust You? -- Quantifying Uncertainties in Explaining Neural Networks

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in e.g. safety-critical areas. So far, however, no methods for quantifying uncertainties of explanations have been conceived, which is problematic in domains where a high confidence in explanations is a prerequisite. We therefore contribute by proposing a new framework that allows to convert any arbitrary explanation method for neural networks into an explanation method for Bayesian neural networks, with an in-built modeling of uncertainties. Within the Bayesian framework a network's weights follow a distribution that extends standard single explanation scores and heatmaps to distributions thereof, in this manner translating the intrinsic network model uncertainties into a quantification of explanation uncertainties. This allows us for the first time to carve out uncertainties associated with a model explanation and subsequently gauge the appropriate level of explanation confidence for a user (using percentiles). We demonstrate the effectiveness and usefulness of our approach extensively in various experiments, both qualitatively and quantitatively.

XAI for Graphs: Explaining Graph Neural Network Predictions by Identifying Relevant Walks

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI (XAI) approaches are not applicable. To a large extent, GNNs have remained black-boxes for the user so far. In this paper, we contribute by proposing a new XAI approach for GNNs. Our approach is derived from high-order Taylor expansions and is able to generate a decomposition of the GNN prediction as a collection of relevant walks on the input graph. We find that these high-order Taylor expansions can be equivalently (and more simply) computed using multiple backpropagation passes from the top layer of the GNN to the first layer. The explanation can then be further robustified and generalized by using layer-wise-relevance propagation (LRP) in place of the standard equations for gradient propagation. Our novel method which we denote as 'GNN-LRP' is tested on scale-free graphs, sentence parsing trees, molecular graphs, and pixel lattices representing images. In each case, it performs stably and accurately, and delivers interesting and novel application insights.