Predicting the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter space undergoes discrete finite steps along complex stochastic gradients derived from real-world datasets. We circumvent this obstacle through a unifying theoretical framework based on intrinsic symmetries embedded in a network's architecture that are present for any dataset. We show that any such symmetry imposes stringent geometric constraints on gradients and Hessians, leading to an associated conservation law in the continuous-time limit of stochastic gradient descent (SGD), akin to Noether's theorem in physics. We further show that finite learning rates used in practice can actually break these symmetry induced conservation laws. We apply tools from finite difference methods to derive modified gradient flow, a differential equation that better approximates the numerical trajectory taken by SGD at finite learning rates. We combine modified gradient flow with our framework of symmetries to derive exact integral expressions for the dynamics of certain parameter combinations. We empirically validate our analytic predictions for learning dynamics on VGG-16 trained on Tiny ImageNet. Overall, by exploiting symmetry, our work demonstrates that we can analytically describe the learning dynamics of various parameter combinations at finite learning rates and batch sizes for state of the art architectures trained on any dataset. Just like the fundamental laws of classical and quantum mechanics taught us how to control and optimize the physical world for engineering purposes, a better understanding of the laws governing neural network learning dynamics can have a profound impact on the optimization of artificial neural networks.

Accurate 3D object detection (3DOD) is crucial for safe navigation of complex environments by autonomous robots. Regressing accurate 3D bounding boxes in cluttered environments based on sparse LiDAR data is however a highly challenging problem. We address this task by exploring recent advances in conditional energy-based models (EBMs) for probabilistic regression. While methods employing EBMs for regression have demonstrated impressive performance on 2D object detection in images, these techniques are not directly applicable to 3D bounding boxes. In this work, we therefore design a differentiable pooling operator for 3D bounding boxes, serving as the core module of our EBM network. We further integrate this general approach into the state-of-the-art 3D object detector SA-SSD. On the KITTI dataset, our proposed approach consistently outperforms the SA-SSD baseline across all 3DOD metrics, demonstrating the potential of EBM-based regression for highly accurate 3DOD. Code is available at https://github.com/fregu856/ebms_3dod.

The COVID-19 pandemic has caused international social tension and unrest. Besides the crisis itself, there are growing signs of rising conflict potential of societies around the world. Indicators of global mood changes are hard to detect and direct questionnaires suffer from social desirability biases. However, so-called implicit methods can reveal humans intrinsic desires from e.g. social media texts. We present psychologically validated social unrest predictors and replicate scalable and automated predictions, setting a new state of the art on a recent German shared task dataset. We employ this model to investigate a change of language towards social unrest during the COVID-19 pandemic by comparing established psychological predictors on samples of tweets from spring 2019 with spring 2020. The results show a significant increase of the conflict indicating psychometrics. With this work, we demonstrate the applicability of automated NLP-based approaches to quantitative psychological research.

In this work, we propose a deep neural network method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. By properly choosing network architecture, our estimator achieves the optimal nonparametric convergence rate in empirical norm. Under certain circumstances such as trigonometric polynomial kernel and a sufficiently large sampling frequency, the convergence rate is even faster than root-$n$ rate. Through Monte Carlo simulation studies we examine the finite-sample performance of the proposed method. Finally, the proposed method is applied to analyze positron emission tomography images of patients with Alzheimer disease obtained from the Alzheimer Disease Neuroimaging Initiative database.

Machine learning models are commonly trained end-to-end and in a supervised setting, using paired (input, output) data. Classical examples include recent super-resolution methods that train on pairs of (low-resolution, high-resolution) images. However, these end-to-end approaches require re-training every time there is a distribution shift in the inputs (e.g., night images vs daylight) or relevant latent variables (e.g., camera blur or hand motion). In this work, we leverage state-of-the-art (SOTA) generative models (here StyleGAN2) for building powerful image priors, which enable application of Bayes' theorem for many downstream reconstruction tasks. Our method, called Bayesian Reconstruction through Generative Models (BRGM), uses a single pre-trained generator model to solve different image restoration tasks, i.e., super-resolution and in-painting, by combining it with different forward corruption models. We demonstrate BRGM on three large, yet diverse, datasets that enable us to build powerful priors: (i) 60,000 images from the Flick Faces High Quality dataset \cite{karras2019style} (ii) 240,000 chest X-rays from MIMIC III and (iii) a combined collection of 5 brain MRI datasets with 7,329 scans. Across all three datasets and without any dataset-specific hyperparameter tuning, our approach yields state-of-the-art performance on super-resolution, particularly at low-resolution levels, as well as inpainting, compared to state-of-the-art methods that are specific to each reconstruction task. We will make our code and pre-trained models available online.

Analyzing data from the Large Hadron Collider (LHC) present a hyper challenge. A given collision event may result in hundreds of outgoing particles, each with many features (momentum, electric charge, etc.). This hyper variate phase space is then observed by complex multi-channel detectors that are essentially hyperspectral cameras. The LHC detectors have millions of readout channels and dimensionality reduction is essential for data analysis. One natural and nearly lossless reduction is the reconstruction of charged particle trajectories ('tracks'). The innermost layers of the detectors at the LHC are constructed to register the passage of charged particles without significantly altering the particle energy or direction. In the ATLAS and CMS detectors, this is achieved using silicon sensors that are finely segmented in one or two directions and are called strips and pixels, respectively. We will focus on pixels, although our methodology applies more generally. Typically, the first step in a tracking algorithm is the construction of seeds, which are sets of three or more hit pixel clusters that can be used to fit charged-particle trajectories (see e.g.

Neural Tangent Kernel (NTK) theory is widely used to study the dynamics of infinitely-wide deep neural networks (DNNs) under gradient descent. But do the results for infinitely-wide networks give us hints about the behaviour of real finite-width ones? In this paper we study empirically when NTK theory is valid in practice for fully-connected ReLu and sigmoid networks. We find out that whether a network is in the NTK regime depends on the hyperparameters of random initialization and network's depth. In particular, NTK theory does not explain behaviour of sufficiently deep networks initialized so that their gradients explode: the kernel is random at initialization and changes significantly during training, contrary to NTK theory. On the other hand, in case of vanishing gradients DNNs are in the NTK regime but become untrainable rapidly with depth. We also describe a framework to study generalization properties of DNNs by means of NTK theory and discuss its limits.

The expressiveness of deep neural network (DNN) is a perspective to understand the surprising performance of DNN. The number of linear regions, i.e. pieces that a piece-wise-linear function represented by a DNN, is generally used to measure the expressiveness. And the upper bound of regions number partitioned by a rectifier network, instead of the number itself, is a more practical measurement of expressiveness of a rectifier DNN. In this work, we propose a new and tighter upper bound of regions number. Inspired by the proof of this upper bound and the framework of matrix computation in Hinz & Van de Geer (2019), we propose a general computational approach to compute a tight upper bound of regions number for theoretically any network structures (e.g. DNN with all kind of skip connections and residual structures). Our experiments show our upper bound is tighter than existing ones, and explain why skip connections and residual structures can improve network performance.

Active learning (AL) could contribute to solving critical environmental problems through improved spatiotemporal predictions. Yet such predictions involve high-dimensional feature spaces with mixed data types and missing data, which existing methods have difficulties dealing with. Here, we propose a novel batch AL method that fills this gap. We encode and cluster features of candidate data points, and query the best data based on the distance of embedded features to their cluster centers. We introduce a new metric of informativeness that we call embedding entropy and a general class of neural networks that we call embedding networks for using it. Empirical tests on forecasting electricity demand show a simultaneous reduction in average prediction RMSE by up to 63-88% and data usage by up to 50-69% compared to passive learning (PL) benchmarks. Examples include the electricity consumption of buildings, required to operate sustainable power grids; the travel time between city zones, required for the smart charging of electric vehicles; and meteorological conditions, required for weather-based forecasting of wind and solar electricity generation. Sensing and labeling the ground truth data that is necessary for making these predictions in time and space usually comes at a high cost. This cost constrains the total number of sensors that we can place and use to query new data. A fundamental question that arises for many spatiotemporal prediction tasks is where and when to measure and query the data required to make the best possible predictions while staying within a maximum budget for sensors and data.

In drug discovery, molecule optimization is an important step in order to modify drug candidates into better ones in terms of desired drug properties. With the recent advance of Artificial Intelligence, this traditionally in vitro process has been increasingly facilitated by in silico approaches. We present an innovative in silico approach to computationally optimizing molecules and formulate the problem as to generate optimized molecular graphs via deep generative models. Our generative models follow the key idea of fragment-based drug design, and optimize molecules by modifying their small fragments. Our models learn how to identify the to-be-optimized fragments and how to modify such fragments by learning from the difference of molecules that have good and bad properties. In optimizing a new molecule, our models apply the learned signals to decode optimized fragments at the predicted location of the fragments. We also construct multiple such models into a pipeline such that each of the models in the pipeline is able to optimize one fragment, and thus the entire pipeline is able to modify multiple fragments of molecule if needed. We compare our models with other state-of-the-art methods on benchmark datasets and demonstrate that our methods significantly outperform others with more than 80% property improvement under moderate molecular similarity constraints, and more than 10% property improvement under high molecular similarity constraints.