An apparatus and method for performing a transform on complex data. For example, one embodiment of a processor comprises: multiplier circuitry to multiply packed real N-bit data elements in the first source register with packed real M-bit data elements in the second source register and to multiply packed imaginary N-bit data elements in the first source register with packed imaginary M-bit data elements in the second source register to generate at least four real products, adder circuitry to subtract a first selected real product from a second selected real product to generate a first temporary result and to subtract a third selected real product from a fourth selected real product to generate a second temporary result, the adder circuitry to add the first temporary result to a first packed N-bit data element from the third source register to generate a first pre-scaled result, to subtract the first temporary result from the first packed N-bit data element to generate a second pre-scaled result, to add the second temporary result to a second packed N-bit data element from the third source register to generate a third pre-scaled result, and to subtract the second temporary result from the second packed N-bit data element to generate a fourth pre-scaled result; scaling circuitry to scale the first, second, third and fourth pre-scaled results to a specified bit width to generate first, second, third, and fourth final results; and a destination register to store the first, second, third, and fourth final results in specified data element positions.

Introduced here is a technique to detect and/or correct errors in computation. The ability to correct errors in computation can increase the speed of the processor, reduce the power consumption of the processor, and reduce the distance between the transistors within the processor because the errors thus generated can be detected and corrected. In one embodiment, an error correcting module, running either in software or in hardware, can detect an error in matrix multiplication, by calculating an expected sum of all elements in the resulting matrix, and an actual sum of all elements in the resulting matrix. When there is a difference between the expected sum and the resulting sum, the error correcting module detects an error. In another embodiment, in addition to detecting the error, the error correcting module can determine the location and the magnitude of the error, thus correcting the erroneous computation.

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for a hardware circuit configured as a signed multiword multiplier. The circuit includes a processing circuit that receives inputs that each have a respective bit-width. The processing circuit can represent at least one input as a signed multiword input based on the first input having a bit-width that exceeds a fixed bit-width of the hardware circuit. The circuit includes signed multipliers that are each configured to multiply signed inputs. Each signed multiplier includes multiplication circuitry configured to: receive the signed multiword input; receive a signed second input; and generate a signed output in response to multiplying the signed multiword input with the signed second input.

A function estimation hardware logic unit may be implemented as part of an execution pipeline in a processor. The function estimation hardware logic unit is arranged to calculate, in hardware logic, an improved estimate of a function of an input value, d, where the function is given by $1\text{/}\sqrt[i]{d}.$
The hardware logic comprises a plurality of multipliers and adders arranged to implement a m.sup.th-order polynomial with coefficients that are rational numbers, where m is not equal to two and in various examples m is not equal to a power of two. In various examples i=1, i=2 or i=3. In various examples m=3.

An information processing device includes: a memory; and a processor coupled to the memory and configured to calculate, for a plurality of bits corresponding to a plurality of spins included in an Ising model obtained by converting a problem to be calculated, in a case where the plurality of bits is divided into a plurality of groups, on the basis of a first local field value for a first bit having a value of 1 and a second local field value for a second bit having a value of 0 among a plurality of bits included in each of the plurality of groups, a first energy change of the Ising model due to a change of the value of the first bit from 1 to 0 and a change of the value of the second bit from 0 to 1.

According to one embodiment, an arithmetic device includes an arithmetic element part, and a controller. The arithmetic element part includes first and second elements. The first element includes a first conductive member and a first stacked body. The first conductive member includes first to third portions. The first stacked body includes a first magnetic layer, and a first counter magnetic layer. The second element includes a second conductive member and a second stacked body. The second conductive member includes fourth and fifth portions, and a sixth portion between the fourth and fifth portions. The second stacked body includes a second magnetic layer, and a second counter magnetic layer. The controller is configured to perform an XNOR operation of first and second inputs. The first input corresponds to electrical resistances of the stacked bodies. The second input corresponds to potentials of the magnetic layers.

According to one embodiment, an arithmetic device includes an arithmetic element part, and a controller. The arithmetic element part includes first and second elements. The first element includes a first conductive member and a first stacked body. The first conductive member includes first to third portions. The first stacked body includes a first magnetic layer, and a first counter magnetic layer. The second element includes a second conductive member and a second stacked body. The second conductive member includes fourth and fifth portions, and a sixth portion between the fourth and fifth portions. The second stacked body includes a second magnetic layer, and a second counter magnetic layer. The controller is configured to perform an XNOR operation of first and second inputs. The first input corresponds to electrical resistances of the stacked bodies. The second input corresponds to potentials of the magnetic layers.

In one embodiment, a computer-implemented method includes receiving digital field data from an agricultural field representing one or more parameters of the field, soil, or crops in the field; retrieving historical data for the same field from one or more field databases; training and/or applying machine learning models to the field data and the historical data to derive representations of causality of one or more agronomic processes pertaining to the field; receiving user input specifying an anomaly to address via treatment, application or experiment; automatically adjusting the treatment, application or experiment to create a modified treatment, application or experiment that is most likely to generate result data that is usable to train machine learning models in an optimal manner.

Embodiments of the present disclosure include systems and methods for providing hierarchical and shared exponent floating point data types. First and second shared exponent values are determined based on exponent values of a plurality of floating point values. A third shared exponent value is determined based the first shared exponent value and the second shared exponent value. First and second difference values are determined based on the first shared exponent value, the second shared exponent value, and the third shared exponent value. Sign values and mantissa values are determined for the plurality of floating point values. The sign value and the mantissa value for each floating point value in the plurality of floating point values, the third shared exponent value, the first difference value, and the second difference value are stored in a data structure for a shared exponent floating point data type.

A method of adaptive neural image compression with a hyperprior model by meta-learning is performed by at least one processor and includes generating a statistic feature, based on an input image and a hyperparameter, and generating a first shared feature and an estimated adaptive encoding parameter, encoding the input image to obtain a signal encoded image, based on the generated first shared feature and the generated estimated adaptive encoding parameter, generating a second shared feature and an estimated adaptive hyper encoding parameter, generating a hyper feature, based on the signal encoded image, the generated second shared feature, and the generated estimated adaptive hyper encoding parameter, and compressing the obtained signal encoded image, the generated statistic feature, and the generated hyper feature.