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For many years, sequence modelling and generation was done by using plain recurrent neural networks (RNNs). A well-cited early example was the Elman network (1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the vanishing-gradient problem leaves the model's state at the end of a long sentence without precise, extractable ...
Mamba [a] is a deep learning architecture focused on sequence modeling. It was developed by researchers from Carnegie Mellon University and Princeton University to address some limitations of transformer models, especially in processing long sequences. It is based on the Structured State Space sequence (S4) model. [2] [3] [4]
One of the core concepts in topological deep learning is the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Next, we introduce the most common ...
Major advances in this field can result from advances in learning algorithms (such as deep learning), computer hardware, and, less-intuitively, the availability of high-quality training datasets. [1] High-quality labeled training datasets for supervised and semi-supervised machine learning algorithms are usually difficult and expensive to ...
Real data is always finite, and so its study requires us to take stochasticity into account. Statistical analysis gives us the ability to separate true features of the data from artifacts introduced by random noise. Persistent homology has no inherent mechanism to distinguish between low-probability features and high-probability features.
With the rise of deep learning, a new family of methods, called deep generative models (DGMs), [8] [9] is formed through the combination of generative models and deep neural networks. An increase in the scale of the neural networks is typically accompanied by an increase in the scale of the training data, both of which are required for good ...
The dimensional model is a specialized adaptation of the relational model used to represent data in data warehouses in a way that data can be easily summarized using online analytical processing, or OLAP queries. In the dimensional model, a database schema consists of a single large table of facts that are described using dimensions and measures.
A flow-based generative model is a generative model used in machine learning that explicitly models a probability distribution by leveraging normalizing flow, [1] [2] [3] which is a statistical method using the change-of-variable law of probabilities to transform a simple distribution into a complex one.