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Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain.The basic observation is that if we take a random walk on the data, walking to a nearby data-point is more likely than walking to another that is far away.
Embedding vectors created using the Word2vec algorithm have some advantages compared to earlier algorithms [1] such as those using n-grams and latent semantic analysis. GloVe was developed by a team at Stanford specifically as a competitor, and the original paper noted multiple improvements of GloVe over word2vec. [9]
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
In Multi-Token Prediction, a single forward pass creates a final embedding vector, which then is un-embedded into a token probability. However, that vector can then be further processed by another Transformer block to predict the next token, and so on for arbitrarily many steps into the future.
A modality-embedding vector sequence, which indicates to the backbone about additional conditions for denoising. For example, in text-to-image generation, the text is divided into a sequence of tokens, then encoded by a text encoder, such as a CLIP encoder , before feeding into the backbone.
Maximum Variance Unfolding, Isomap and Locally Linear Embedding share a common intuition relying on the notion that if a manifold is properly unfolded, then variance over the points is maximized. Its initial step, like Isomap and Locally Linear Embedding, is finding the k-nearest neighbors of every point. It then seeks to solve the problem of ...
In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]
If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model.