Abstract: Methods, systems, and apparatus including a special purpose hardware chip for training neural networks are described. The special-purpose hardware chip may include a scalar processor configured to control computational operation of the special-purpose hardware chip. The chip may also include a vector processor configured to have a 2-dimensional array of vector processing units which all execute the same instruction in a single instruction, multiple-data manner and communicate with each other through load and store instructions of the vector processor. The chip may additionally include a matrix multiply unit that is coupled to the vector processor configured to multiply at least one two-dimensional matrix with a second one-dimensional vector or two-dimensional matrix in order to obtain a multiplication result.

Abstract: A circuit for performing neural network computations for a neural network is described. The circuit includes plurality of neural network layers each including a crossbar arrays. The plurality of crossbar arrays are formed in a common substrate in a stacked configuration. Each crossbar array includes a set of crosspoint devices. A respective electrical property of each of the crosspoint devices is adjustable to represent a weight value that is stored for each respective crosspoint device. A processing unit is configured to adjust the respective electrical properties of each of the crosspoint devices by pre-loading each of the crosspoint devices with a tuning signal. A value of the turning signal for each crosspoint device is a function of the weight value represented by each respective crosspoint device.

Abstract: Methods, systems, and apparatus, including an apparatus for accessing data. In some implementations, an apparatus includes address offset value elements that are each configured to store an address offset value. For each address offset value element, the apparatus can include address computation elements that each store a value used to determine the address offset value. One or more processors are configured to receive a program for performing computations using tensor elements of a tensor. The processor(s) can identify, in the program, a prologue or epilogue loop having a corresponding data array for storing values of the prologue or epilogue loop and populate, for a first address offset value element that corresponds to the prologue or epilogue loop, the address computation elements for the first address offset value element with respective values based at least on a number of iterations of the prologue or epilogue loop.

Abstract: A vector reduction circuit configured to reduce an input vector of elements comprises a plurality of cells, wherein each of the plurality of cells other than a designated first cell that receives a designated first element of the input vector is configured to receive a particular element of the input vector, receive, from another of the one or more cells, a temporary reduction element, perform a reduction operation using the particular element and the temporary reduction element, and provide, as a new temporary reduction element, a result of performing the reduction operation using the particular element and the temporary reduction element. The vector reduction circuit also comprises an output circuit configured to provide, for output as a reduction of the input vector, a new temporary reduction element corresponding to a result of performing the reduction operation using a last element of the input vector.

Abstract: A vector reduction circuit configured to reduce an input vector of elements comprises a plurality of cells, wherein each of the plurality of cells other than a designated first cell that receives a designated first element of the input vector is configured to receive a particular element of the input vector, receive, from another of the one or more cells, a temporary reduction element, perform a reduction operation using the particular element and the temporary reduction element, and provide, as a new temporary reduction element, a result of performing the reduction operation using the particular element and the temporary reduction element. The vector reduction circuit also comprises an output circuit configured to provide, for output as a reduction of the input vector, a new temporary reduction element corresponding to a result of performing the reduction operation using a last element of the input vector.

Abstract: A circuit comprises an input register configured to receive an input vector of elements, a control register configured to receive a control vector of elements, wherein each element of the control vector corresponds to a respective element of the input vector, and wherein each element specifies a permutation of a corresponding element of the input vector, and a permute execution circuit configured to generate an output vector of elements corresponding to a permutation of the input vector. Generating each element of the output vector comprises accessing, at the input register, a particular element of the input vector, accessing, at the control register, a particular element of the control vector corresponding to the particular element of the input vector, and outputting the particular element of the input vector as an element at a particular position of the output vector that is selected based on the particular element of the control vector.

Abstract: A computer-implemented method that includes receiving, by a processing unit, an instruction that specifies data values for performing a tensor computation. In response to receiving the instruction, the method may include, performing, by the processing unit, the tensor computation by executing a loop nest comprising a plurality of loops, wherein a structure of the loop nest is defined based on one or more of the data values of the instruction. The tensor computation can be at least a portion of a computation of a neural network layer. The data values specified by the instruction may comprise a value that specifies a type of the neural network layer, and the structure of the loop nest can be defined at least in part by the type of the neural network layer.

Abstract: A computer-implemented method that includes receiving, by a processing unit, an instruction that specifies data values for performing a tensor computation. In response to receiving the instruction, the method may include, performing, by the processing unit, the tensor computation by executing a loop nest comprising a plurality of loops, wherein a structure of the loop nest is defined based on one or more of the data values of the instruction. The tensor computation can be at least a portion of a computation of a neural network layer. The data values specified by the instruction may comprise a value that specifies a type of the neural network layer, and the structure of the loop nest can be defined at least in part by the type of the neural network layer.

Abstract: A computing unit is disclosed, comprising a first memory bank for storing input activations and a second memory bank for storing parameters used in performing computations. The computing unit includes at least one cell comprising at least one multiply accumulate (“MAC”) operator that receives parameters from the second memory bank and performs computations. The computing unit further includes a first traversal unit that provides a control signal to the first memory bank to cause an input activation to be provided to a data bus accessible by the MAC operator. The computing unit performs one or more computations associated with at least one element of a data array, the one or more computations being performed by the MAC operator and comprising, in part, a multiply operation of the input activation received from the data bus and a parameter received from the second memory bank.

Abstract: A computer-implemented method that includes receiving, by a processing unit, an instruction that specifies data values for performing a tensor computation. In response to receiving the instruction, the method may include, performing, by the processing unit, the tensor computation by executing a loop nest comprising a plurality of loops, wherein a structure of the loop nest is defined based on one or more of the data values of the instruction. The tensor computation can be at least a portion of a computation of a neural network layer. The data values specified by the instruction may comprise a value that specifies a type of the neural network layer, and the structure of the loop nest can be defined at least in part by the type of the neural network layer.

Abstract: A circuit comprises an input register configured to receive an input vector of elements, a control register configured to receive a control vector of elements, wherein each element of the control vector corresponds to a respective element of the input vector, and wherein each element specifies a permutation of a corresponding element of the input vector, and a permute execution circuit configured to generate an output vector of elements corresponding to a permutation of the input vector. Generating each element of the output vector comprises accessing, at the input register, a particular element of the input vector, accessing, at the control register, a particular element of the control vector corresponding to the particular element of the input vector, and outputting the particular element of the input vector as an element at a particular position of the output vector that is selected based on the particular element of the control vector.

Abstract: Methods, systems, and apparatus, including an apparatus for accessing a N-dimensional tensor, the apparatus including, for each dimension of the N-dimensional tensor, a partial address offset value element that stores a partial address offset value for the dimension based at least on an initial value for the dimension, a step value for the dimension, and a number of iterations of a loop for the dimension. The apparatus includes a hardware adder and a processor. The processor obtains an instruction to access a particular element of the N-dimensional tensor. The N-dimensional tensor has multiple elements arranged across each of the N dimensions, where N is an integer that is equal to or greater than one. The processor determines, using the partial address offset value elements and the hardware adder, an address of the particular element and outputs data indicating the determined address for accessing the particular element of the N-dimensional tensor.

Abstract: A three dimensional neural network accelerator that includes a first neural network accelerator tile that includes a first transmission coil, and a second neural network accelerator tile that includes a second transmission coil, wherein the first neural network accelerator tile is adjacent to and aligned vertically with the second neural network accelerator tile, and wherein the first transmission coil is configured to wirelessly communicate with the second transmission coil via inductive coupling.

Abstract: A computer-implemented method that includes receiving, by a processing unit, an instruction that specifies data values for performing a tensor computation. In response to receiving the instruction, the method may include, performing, by the processing unit, the tensor computation by executing a loop nest comprising a plurality of loops, wherein a structure of the loop nest is defined based on one or more of the data values of the instruction. The tensor computation can be at least a portion of a computation of a neural network layer. The data values specified by the instruction may comprise a value that specifies a type of the neural network layer, and the structure of the loop nest can be defined at least in part by the type of the neural network layer.

Abstract: A computer-implemented method that includes receiving, by a processing unit, an instruction that specifies data values for performing a tensor computation. In response to receiving the instruction, the method may include, performing, by the processing unit, the tensor computation by executing a loop nest comprising a plurality of loops, wherein a structure of the loop nest is defined based on one or more of the data values of the instruction. The tensor computation can be at least a portion of a computation of a neural network layer. The data values specified by the instruction may comprise a value that specifies a type of the neural network layer, and the structure of the loop nest can be defined at least in part by the type of the neural network layer.

Abstract: A computing unit is disclosed, comprising a first memory bank for storing input activations and a second memory bank for storing parameters used in performing computations. The computing unit includes at least one cell comprising at least one multiply accumulate (“MAC”) operator that receives parameters from the second memory bank and performs computations. The computing unit further includes a first traversal unit that provides a control signal to the first memory bank to cause an input activation to be provided to a data bus accessible by the MAC operator. The computing unit performs one or more computations associated with at least one element of a data array, the one or more computations being performed by the MAC operator and comprising, in part, a multiply operation of the input activation received from the data bus and a parameter received from the second memory bank.