Existing equivariant neural networks for continuous groups require discretization or group representations. All these approaches require detailed knowledge of the group parametrization and cannot learn entirely new symmetries. We propose to work with the Lie algebra (infinitesimal generators) instead of the Lie group.Our model, the Lie algebra convolutional network (L-conv) can learn potential symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant architecture. We discuss how CNNs and Graph Convolutional Networks are related to and can be expressed as L-conv with appropriate groups. We also derive the MSE loss for a single L-conv layer and find a deep relation with Lagrangians used in physics, with some of the physics aiding in defining generalization and symmetries in the loss landscape. Conversely, L-conv could be used to propose more general equivariant ans\"atze for scientific machine learning.

The notion of word embedding plays a fundamental role in natural language processing (NLP). However, pre-training word embedding for very large-scale vocabulary is computationally challenging for most existing methods. In this work, we show that with merely a small fraction of contexts (Q-contexts)which are typical in the whole corpus (and their mutual information with words), one can construct high-quality word embedding with negligible errors. Mutual information between contexts and words can be encoded canonically as a sampling state, thus, Q-contexts can be fast constructed. Furthermore, we present an efficient and effective WEQ method, which is capable of extracting word embedding directly from these typical contexts. In practical scenarios, our algorithm runs 11$\sim$13 times faster than well-established methods. By comparing with well-known methods such as matrix factorization, word2vec, GloVeand fasttext, we demonstrate that our method achieves comparable performance on a variety of downstream NLP tasks, and in the meanwhile maintains run-time and resource advantages over all these baselines.

Algorithmic harmonization - the automated harmonization of a musical piece given its melodic line - is a challenging problem that has garnered much interest from both music theorists and computer scientists. One genre of particular interest is the four-part Baroque chorales of J.S. Bach. Methods for algorithmic chorale harmonization typically adopt a black-box, "data-driven" approach: they do not explicitly integrate principles from music theory but rely on a complex learning model trained with a large amount of chorale data. We propose instead a new harmonization model, called BacHMMachine, which employs a "theory-driven" framework guided by music composition principles, along with a "data-driven" model for learning compositional features within this framework. As its name suggests, BacHMMachine uses a novel Hidden Markov Model based on key and chord transitions, providing a probabilistic framework for learning key modulations and chordal progressions from a given melodic line. This allows for the generation of creative, yet musically coherent chorale harmonizations; integrating compositional principles allows for a much simpler model that results in vast decreases in computational burden and greater interpretability compared to state-of-the-art algorithmic harmonization methods, at no penalty to quality of harmonization or musicality. We demonstrate this improvement via comprehensive experiments and Turing tests comparing BacHMMachine to existing methods.

In recent years, graph neural networks (GNNs) have gained increasing popularity and have shown very promising results for data that are represented by graphs. The majority of GNN architectures are designed based on developing new convolutional and/or pooling layers that better extract the hidden and deeper representations of the graphs to be used for different prediction tasks. The inputs to these layers are mainly the three default descriptors of a graph, node features $(X)$, adjacency matrix $(A)$, and edge features $(W)$ (if available). To provide a more enriched input to the network, we propose a random walk data processing of the graphs based on three selected lengths. Namely, (regular) walks of length 1 and 2, and a fractional walk of length $\gamma \in (0,1)$, in order to capture the different local and global dynamics on the graphs. We also calculate the stationary distribution of each random walk, which is then used as a scaling factor for the initial node features ($X$). This way, for each graph, the network receives multiple adjacency matrices along with their individual weighting for the node features. We test our method on various molecular datasets by passing the processed node features to the network in order to perform several classification and regression tasks. Interestingly, our method, not using edge features which are heavily exploited in molecular graph learning, let a shallow network outperform well known deep GNNs.

Probabilistic time-series forecasting enables reliable decision making across many domains. Most forecasting problems have diverse sources of data containing multiple modalities and structures. Leveraging information as well as uncertainty from these data sources for well-calibrated and accurate forecasts is an important challenging problem. Most previous work on multi-modal learning and forecasting simply aggregate intermediate representations from each data view by simple methods of summation or concatenation and do not explicitly model uncertainty for each data-view. We propose a general probabilistic multi-view forecasting framework CAMul, that can learn representations and uncertainty from diverse data sources. It integrates the knowledge and uncertainty from each data view in a dynamic context-specific manner assigning more importance to useful views to model a well-calibrated forecast distribution. We use CAMul for multiple domains with varied sources and modalities and show that CAMul outperforms other state-of-art probabilistic forecasting models by over 25\% in accuracy and calibration.

Machine learning techniques allow a direct mapping of atomic positions and nuclear charges to the potential energy surface with almost ab-initio accuracy and the computational efficiency of empirical potentials. In this work we propose a machine learning method for constructing high-dimensional potential energy surfaces based on feed-forward neural networks. As input to the neural network we propose an extendable invariant local molecular descriptor constructed from geometric moments. Their formulation via pairwise distance vectors and tensor contractions allows a very efficient implementation on graphical processing units (GPUs). The atomic species is encoded in the molecular descriptor, which allows the restriction to one neural network for the training of all atomic species in the data set. We demonstrate that the accuracy of the developed approach in representing both chemical and configurational spaces is comparable to the one of several established machine learning models. Due to its high accuracy and efficiency, the proposed machine-learned potentials can be used for any further tasks, for example the optimization of molecular geometries, the calculation of rate constants or molecular dynamics.

Precise identification of mouse brain microscopy images is a crucial first step when anatomical structures in the mouse brain are to be registered to a reference atlas. Practitioners usually rely on manual comparison of images or tools that assume the presence of complete images. This work explores Siamese Networks as the method for finding corresponding 2D reference atlas plates for given partial 2D mouse brain images. Siamese networks are a class of convolutional neural networks (CNNs) that use weight-shared paths to obtain low dimensional embeddings of pairs of input images. The correspondence between the partial mouse brain image and reference atlas plate is determined based on the distance between low dimensional embeddings of brain slices and atlas plates that are obtained from Siamese networks using contrastive learning. Experiments showed that Siamese CNNs can precisely identify brain slices using the Allen mouse brain atlas when training and testing images come from the same source. They achieved TOP-1 and TOP-5 accuracy of 25% and 100%, respectively, taking only 7.2 seconds to identify 29 images.

Build a deep learning model that can detect Pneumonia from patients' chest X-Ray images. Below is the high-level approach on how I created the deep learning model. I first collected the data from Kaggle, which are chest X-Ray images of patients from China. Then, I moved onto creating the architecture of convolutional neural network (CNN) model, which is a type of deep learning model. Data, obtained from Kaggle, contains 5,856 chest X-Ray images of pediatric patients under age of 5 from a medical center in Guangzhou, China.

Marktechpost, LLC. is a California-based Artificial Intelligence Media Platform for the latest updates in machine learning, deep learning, and data science research. Marktechpost's key focus is on spreading AI Awareness across the globe. The Marktechpost AI Introductory Course is a basic Artificial Intelligence (AI) Intro Course comprised of four video lectures. This course will cover what AI is, how it works, and why AI is taking off now. Fabio is a data scientist from Italy.

Geoscape Australia, a government-owned geospatial data company, has announced it has partnered with an Israeli artificial intelligence start-up to use machine vision and deep learning technology to enhance its 3D digital maps of Australia. The CEO of Geoscape Australia said that the partnership will advance what is known about every address across the country. Applying the Israeli AI start-up's patented AI technology to the highest quality aerial imagery will significantly evolve the current digital model of Australia. The company says more accurate digital models of Australia's urban environment will enable the data-driven foundation of Digital Twin applications that better reflect the real world. The up-to-date data will also improve the assessment of risk for insurers, allow architects to visualise new developments in the context of their surroundings, help noise modellers better understand what will be impacted by noise, and power modelling of energy use patterns in commercial and residential buildings.