Last years have been characterized by an upsurge of opaque automatic decision support systems, such as Deep Neural Networks (DNNs). Although they have great generalization and prediction skills, their functioning does not allow obtaining detailed explanations of their behaviour. As opaque machine learning models are increasingly being employed to make important predictions in critical environments, the danger is to create and use decisions that are not justifiable or legitimate. Therefore, there is a general agreement on the importance of endowing machine learning models with explainability. The reason is that EXplainable Artificial Intelligence (XAI) techniques can serve to verify and certify model outputs and enhance them with desirable notions such as trustworthiness, accountability, transparency and fairness. This tutorial is meant to be the go-to handbook for any audience with a computer science background aiming at getting intuitive insights of machine learning models, accompanied with straight, fast, and intuitive explanations out of the box. We believe that these methods provide a valuable contribution for applying XAI techniques in their particular day-to-day models, datasets and use-cases. Figure \ref{fig:Flowchart} acts as a flowchart/map for the reader and should help him to find the ideal method to use according to his type of data. The reader will find a description of the proposed method as well as an example of use and a Python notebook that he can easily modify as he pleases in order to apply it to his own case of application.

In this work we aim to mimic the human ability to acquire the intuition to estimate the performance of a design from visual inspection and experience alone. We study the ability of convolutional neural networks to predict static and dynamic properties of cantilever beams directly from their raw cross-section images. Using pixels as the only input, the resulting models learn to predict beam properties such as volume maximum deflection and eigenfrequencies with 4.54% and 1.43% Mean Average Percentage Error (MAPE) respectively, compared to the Finite Element Analysis (FEA) approach. Training these models doesn't require prior knowledge of theory or relevant geometric properties, but rather relies solely on simulated or empirical data, thereby making predictions based on "experience" as opposed to theoretical knowledge. Since this approach is over 1000 times faster than FEA, it can be adopted to create surrogate models that could speed up the preliminary optimization studies where numerous consecutive evaluations of similar geometries are required. We suggest that this modeling approach would aid in addressing challenging optimization problems involving complex structures and physical phenomena for which theoretical models are unavailable.

To understand how deep learning works, it is crucial to understand the training dynamics of neural networks. Several interesting hypotheses about these dynamics have been made based on empirically observed phenomena, but there exists a limited theoretical understanding of when and why such phenomena occur. In this paper, we consider the training dynamics of gradient flow on kernel least-squares objectives, which is a limiting dynamics of SGD trained neural networks. Using precise high-dimensional asymptotics, we characterize the dynamics of the fitted model in two "worlds": in the Oracle World the model is trained on the population distribution and in the Empirical World the model is trained on a sampled dataset. We show that under mild conditions on the kernel and $L^2$ target regression function the training dynamics undergo three stages characterized by the behaviors of the models in the two worlds. Our theoretical results also mathematically formalize some interesting deep learning phenomena. Specifically, in our setting we show that SGD progressively learns more complex functions and that there is a "deep bootstrap" phenomenon: during the second stage, the test error of both worlds remain close despite the empirical training error being much smaller. Finally, we give a concrete example comparing the dynamics of two different kernels which shows that faster training is not necessary for better generalization.

For artificial deep neural networks, we prove expression rates for analytic functions $f:\mathbb{R}^d\to\mathbb{R}$ in the norm of $L^2(\mathbb{R}^d,\gamma_d)$ where $d\in {\mathbb{N}}\cup\{ \infty \}$. Here $\gamma_d$ denotes the Gaussian product probability measure on $\mathbb{R}^d$. We consider in particular ReLU and ReLU${}^k$ activations for integer $k\geq 2$. For $d\in\mathbb{N}$, we show exponential convergence rates in $L^2(\mathbb{R}^d,\gamma_d)$. In case $d=\infty$, under suitable smoothness and sparsity assumptions on $f:\mathbb{R}^{\mathbb{N}}\to\mathbb{R}$, with $\gamma_\infty$ denoting an infinite (Gaussian) product measure on $\mathbb{R}^{\mathbb{N}}$, we prove dimension-independent expression rate bounds in the norm of $L^2(\mathbb{R}^{\mathbb{N}},\gamma_\infty)$. The rates only depend on quantified holomorphy of (an analytic continuation of) the map $f$ to a product of strips in $\mathbb{C}^d$. As an application, we prove expression rate bounds of deep ReLU-NNs for response surfaces of elliptic PDEs with log-Gaussian random field inputs.

The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI). In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field. In particular, we elucidate how the TVO naturally connects the three key variational schemes, namely the importance-weighted VI, Renyi-VI, and MCMC-VI, which subsumes most VI objectives employed in practice. To explain the performance gap between theory and practice, we reveal how the pathological geometry of thermodynamic curves negatively affects TVO. By generalizing the integration path from the geometric mean to the weighted Holder mean, we extend the theory of TVO and identify new opportunities for improving VI. This motivates our new VI objectives, named the Holder bounds, which flatten the thermodynamic curves and promise to achieve a one-step approximation of the exact marginal log-likelihood. A comprehensive discussion on the choices of numerical estimators is provided. We present strong empirical evidence on both synthetic and real-world datasets to support our claims.

In this paper, we detailedly describe our solution for the IEEE BigData Cup 2021: RL-based RecSys (Track 1: Item Combination Prediction). We first conduct an exploratory data analysis on the dataset and then utilize the findings to design our framework. Specifically, we use a two-headed transformer-based network to predict user feedback and unlocked sessions, along with the proposed session-aware reweighted loss, multi-tasking with click behavior prediction, and randomness-in-session augmentation. In the final private leaderboard on Kaggle, our method ranked 2nd with a categorization accuracy of 0.39224.

We evaluate the robustness of a Neural Architecture Search (NAS) algorithm known as Efficient NAS (ENAS) against data agnostic poisoning attacks on the original search space with carefully designed ineffective operations. We empirically demonstrate how our one shot search space poisoning approach exploits design flaws in the ENAS controller to degrade predictive performance on classification tasks. With just two poisoning operations injected into the search space, we inflate prediction error rates for child networks upto 90% on the CIFAR-10 dataset.

Teaching plays a fundamental role in human learning. Typically, a human teaching strategy would involve assessing a student's knowledge progress for tailoring the teaching materials in a way that enhances the learning progress. A human teacher would achieve this by tracing a student's knowledge over important learning concepts in a task. Albeit, such teaching strategy is not well exploited yet in machine learning as current machine teaching methods tend to directly assess the progress on individual training samples without paying attention to the underlying learning concepts in a learning task. In this paper, we propose a novel method, called Knowledge Augmented Data Teaching (KADT), which can optimize a data teaching strategy for a student model by tracing its knowledge progress over multiple learning concepts in a learning task. Specifically, the KADT method incorporates a knowledge tracing model to dynamically capture the knowledge progress of a student model in terms of latent learning concepts. Then we develop an attention pooling mechanism to distill knowledge representations of a student model with respect to class labels, which enables to develop a data teaching strategy on critical training samples. We have evaluated the performance of the KADT method on four different machine learning tasks including knowledge tracing, sentiment analysis, movie recommendation, and image classification. The results comparing to the state-of-the-art methods empirically validate that KADT consistently outperforms others on all tasks.

In this paper we investigate a variety of deep learning strategies for solving inverse problems. We classify existing deep learning solutions for inverse problems into three categories of Direct Mapping, Data Consistency Optimizer, and Deep Regularizer. We choose a sample of each inverse problem type, so as to compare the robustness of the three categories, and report a statistical analysis of their differences. We perform extensive experiments on the classic problem of linear regression and three well-known inverse problems in computer vision, namely image denoising, 3D human face inverse rendering, and object tracking, selected as representative prototypes for each class of inverse problems. The overall results and the statistical analyses show that the solution categories have a robustness behaviour dependent on the type of inverse problem domain, and specifically dependent on whether or not the problem includes measurement outliers. Based on our experimental results, we conclude by proposing the most robust solution category for each inverse problem class.

The idea of using quantum computers for machine learning has recently received attention both in academia and industry [1-13]. While proof of principle study have shown that some problems of mathematical interest quantum computers are useful [13], quantum advantage in machine learning algorithms for practical applications is still unclear [14]. On classical architectures, a first-principle theory of machine learning, especially the so-called deep learning that uses a large number of layers, is still in development. Early developments of the statistical learning theory provide rigorous guarantees on the learning capability in generic learning algorithms, but theoretical bounds obtained from information theory are sometimes weak in practical settings. The theory of neural tangent kernel (NTK) has been deemed an important tool to understand deep neural networks [15-21]. In the large-width limit, a generic neural network becomes nearly Gaussian when averaging over the initial weights and biases, and the learning capabilities become predictable. The NTK theory allows to derive analytical understanding of the neural networks dynamics, improving on statistical learning theory and shedding light on the underlying principle of deep learning [22-26]. In the quantum machine learning community, a similar first principle theory would help in understanding the training dynamics and selecting appropri-junyuliu@uchicago.edu