The present application relates to a device for selecting top values from a set of raw values, comprising: an output queue, a loop queue, a top value storage module and a control module. The control module is configured to, at a higher priority, merge the intermediate sequence stored in the loop queue with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence, until a predetermined number of storage areas in the top value storage module are traversed; wherein the control module is further configured to, when there is no intermediate sequence being stored in the loop queue, merge the output sequence with the at most N top values stored in a storage area of the top value storage module, and sort the merged values to generate a merged sequence; wherein the control module is further configured to provide a first subsequence in the merged sequence which is closer to a top most value of the merged sequence to the top value storage module to update the top value storage module, and provide a second subsequence in the merged sequence which is farther away from the top most value of the merged sequence to the loop queue to generate or update the intermediate sequence.

An apparatus of searching for a combination of values of state variables with which a value of an evaluation function of an Ising-type becomes a local minimum or maximum, the data processing apparatus including: a memory configured to store first local fields representative of first change amounts of the value of the evaluation function in a case where a value of each of the state variables changes, first coefficients indicative of strength of influence of each of the state variables on each of constraint terms representative of a constraint condition, and second local fields represented by a sum of a total sum of products of each of the first coefficients and each of the state variables and a second coefficient related to the constraint condition; and a processor configured to perform: reading any of the first coefficients related to a first state variable being any of the state variables.

An apparatus of searching for a combination of values of state variables with which a value of an evaluation function of an Ising-type becomes a local minimum or maximum, the data processing apparatus including: a memory configured to store first local fields representative of first change amounts of the value of the evaluation function in a case where a value of each of the state variables changes, first coefficients indicative of strength of influence of each of the state variables on each of constraint terms representative of a constraint condition, and second local fields represented by a sum of a total sum of products of each of the first coefficients and each of the state variables and a second coefficient related to the constraint condition; and a processor configured to perform: reading any of the first coefficients related to a first state variable being any of the state variables.

Some embodiments provide a program that determines a plurality of data objects. Each data object in the plurality of data objects includes a first attribute and a second attribute. The program further sorts values of the first attribute of the plurality of data objects. The program also sorts values of the second attribute of the plurality of data objects. The program further determines a first distance value based on the sorted values of the first attribute of the plurality of data objects. The program also determines a second distance value based on the sorted values of the second attribute of the plurality of data objects. The program further defines a plurality of clusters based on the sorted values of the first attribute of the plurality of data objects, the first distance value, the sorted values of the second attribute of the plurality of data objects, and the second distance value.

A method may include: a computer program populating a Hermitian matrix A with input data; calculating an upper bound a for a maximum eigenvalue for the Hermitian matrix A; initializing a time evolution value t=1/a; generating a first quantum computer program using the time evolution value t; communicating the first quantum computer program to a quantum computer; receiving a result including a binary value for each n-bit string and a probability for each binary value; converting each binary value into an integer; identifying a maximum absolute value of the integers; determining a value x for the maximum absolute value of all of the integers; updating the time evolution value t based on the value of x; generating a second quantum computer program using the updated time evolution value t; and communicating, by the classical computer program, the second quantum computer program to the quantum computer.

A method may include: a computer program populating a Hermitian matrix A with input data; calculating an upper bound a for a maximum eigenvalue for the Hermitian matrix A; initializing a time evolution value t=1/a; generating a first quantum computer program using the time evolution value t; communicating the first quantum computer program to a quantum computer; receiving a result including a binary value for each n-bit string and a probability for each binary value; converting each binary value into an integer; identifying a maximum absolute value of the integers; determining a value x for the maximum absolute value of all of the integers; updating the time evolution value t based on the value of x; generating a second quantum computer program using the updated time evolution value t; and communicating, by the classical computer program, the second quantum computer program to the quantum computer.

Devices and techniques are generally described for ranking of search results based on multiple objectives. A first ranking for a plurality of search results is determined using a first machine learning model optimized for a first objective for ranking search results. A second objective for ranking search results is determined. A constraint is determined for the at least one second objective. The first machine learning model is iteratively updated to generate an updated machine learning model by minimizing a cost of the first objective subject to the constraint, wherein violations of the constraint are penalized using a penalty term. A second ranking for the plurality of search results is determined using the updated machine learning model. The search results of the second ranking are reordered relative to the search results of the first ranking.

Devices and techniques are generally described for ranking of search results based on multiple objectives. A first ranking for a plurality of search results is determined using a first machine learning model optimized for a first objective for ranking search results. A second objective for ranking search results is determined. A constraint is determined for the at least one second objective. The first machine learning model is iteratively updated to generate an updated machine learning model by minimizing a cost of the first objective subject to the constraint, wherein violations of the constraint are penalized using a penalty term. A second ranking for the plurality of search results is determined using the updated machine learning model. The search results of the second ranking are reordered relative to the search results of the first ranking.

A method, system, and computer program product, including generating a contrastive explanation for a decision of a classifier trained on structured data, highlighting an important feature that justifies the decision, and determining a minimal set of new values for features that alter the decision.

A method, system, and computer program product, including generating a contrastive explanation for a decision of a classifier trained on structured data, highlighting an important feature that justifies the decision, and determining a minimal set of new values for features that alter the decision.