Abstract: Implementations provide an efficient system for calculating inner products between high-dimensionality vectors. An example method includes clustering database items represented as vectors, selecting a cluster center for each cluster, and storing the cluster center as an entry in a first layer codebook. The method also includes, for each database item, calculating a residual based on the cluster center for the cluster the database item is assigned to and projecting the residual into subspaces. The method also includes determining, for each of the subspaces, an entry in a second layer codebook for the subspace, and storing the entry in the first layer codebook and the respective entry in the second layer codebook for each of the subspaces as a quantized vector for the database item. The entry can be used to categorize an item represented by a query vector or to provide database items responsive to a query vector.

Abstract: The present disclosure provides systems and methods that include or otherwise leverage use of a multiscale quantization model that is configured to provide a quantized dataset. In particular, the multiscale quantization model can receive and perform vector quantization of a first dataset. The multiscale quantization model can generate a residual dataset based at least in part on a result of the vector quantization. The multiscale quantization model can apply a rotation matrix to the residual dataset to generate a rotated residual dataset that includes a plurality of rotated residuals. The multiscale quantization model can perform reparameterization of each rotated residual in the rotated residual dataset into a direction component and a scale component. The multiscale quantization model can perform product quantization of the direction components of the plurality of rotated residuals, and perform scalar quantization of the scale components of the plurality of rotated residuals.

Abstract: A systems and method for providing various improvements in the computing time and accuracy for finding items using a hybrid vector space inner-product search are described.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently performing linear projections. In one aspect, a method includes actions for obtaining a plurality of content items from one or more content sources. Additional actions include, extracting a plurality of features from each of the plurality of content items, generating a feature vector for each of the extracted features in order to create a search space, generating a series of element matrices based upon the generated feature vectors, transforming the series of element matrices into a structured matrix such that the transformation preserves one or more relationships associated with each element matrix of the series of element matrices, receiving a search object, searching the enhanced search space based on the received search object, provided one or more links to a content item that are responsive to the search object.

Abstract: The present disclosure provides systems and methods that perform stochastic generative hashing. According to one example aspect, a machine-learned hashing model that generates a binary hash for an input can be trained in conjunction with a machine-learned generative model that reconstructs the input from the binary hash. The present disclosure provides a novel generative approach to learn hash functions through Minimum Description Length principle such that the learned hash codes maximally compress the dataset. According to another example aspect, the present disclosure provides an efficient learning algorithm based on the stochastic distributional gradient, which avoids the notorious difficulty caused by binary output constraints, to jointly optimize the parameters of the hashing model and the associated generative model.

Abstract: Implementations provide an improved system for efficiently calculating inner products between a query item and a database of items. An example method includes generating a plurality of subspaces from search items in a database, the search items being represented as vectors of elements, a subspace being a block of elements from each search item that occur at the same vector position, generating a codebook for each subspace within soft constraints that are based on example queries, assigning each subspace of each search item an entry in the codebook for the subspace, the assignments for all subspaces of a search item representing a quantized search item, and storing the codebooks and the quantized search items. Generating a codebook for a particular subspace can include clustering the search item subspaces that correspond to the particular subspace, finding a cluster center for each cluster, and storing the cluster center as the codebook entry.

Abstract: Implementations provide an efficient system for calculating inner products between high-dimensionality vectors. An example method includes clustering database items represented as vectors, selecting a cluster center for each cluster, and storing the cluster center as an entry in a first layer codebook. The method also includes, for each database item, calculating a residual based on the cluster center for the cluster the database item is assigned to and projecting the residual into subspaces. The method also includes determining, for each of the subspaces, an entry in a second layer codebook for the subspace, and storing the entry in the first layer codebook and the respective entry in the second layer codebook for each of the subspaces as a quantized vector for the database item. The entry can be used to categorize an item represented by a query vector or to provide database items responsive to a query vector.

Abstract: A cryptographic decision-making of set membership is a method or system which make a secure decision-making for positive membership e?S or negative membership e?S in an unforgeable and non-repudiation way for any element e and a set S. The proposed method of the present invention comprises: acquire a set U={e1, . . . , en} and map each element ei in U into a random point vi in a cryptography space; acquire a set S={e?1, . . . , e?m}?U, determine a random point v?i corresponding to each element e?i in the set S, and construct a function ƒS(x) according to all random points v?i; introduce a random secret ? to generate ƒS(?) by using the function ƒS(x), and produce a public parameter mpk according to the random secret ?; and generate the cryptographic representation of set S by using the function ƒS(?) and the public parameter mpk.

Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for efficiently performing linear projections. In one aspect, a method includes actions for obtaining a plurality of content items from one or more content sources. Additional actions include, extracting a plurality of features from each of the plurality of content items, generating a feature vector for each of the extracted features in order to create a search space, generating a series of element matrices based upon the generated feature vectors, transforming the series of element matrices into a structured matrix such that the transformation preserves one or more relationships associated with each element matrix of the series of element matrices, receiving a search object, searching the enhanced search space based on the received search object, provided one or more links to a content item that are responsive to the search object.