Abstract: One embodiment of an accelerator includes a computing unit; a first memory bank for storing input activations and a second memory bank for storing parameters used in performing computations, the second memory bank configured to store a sufficient amount of the neural network parameters on the computing unit to allow for latency below a specified level with throughput above a specified level. 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 computations associated with at least one element of a data array, the one or more computations performed by the MAC operator.

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: Methods, systems, and apparatus, including an apparatus for transferring data using multiple buffers, including multiple memories and one or more processing units configured to determine buffer memory addresses for a sequence of data elements stored in a first data storage location that are being transferred to a second data storage location. For each group of one or more of the data elements in the sequence, a value of a buffer assignment element that can be switched between multiple values each corresponding to a different one of the memories is identified. A buffer memory address for the group of one or more data elements is determined based on the value of the buffer assignment element. The value of the buffer assignment element is switched prior to determining the buffer memory address for a subsequent group of one or more data elements of the sequence of data elements.

Abstract: Methods, systems, and apparatus, including an apparatus for transferring data using multiple buffers, including multiple memories and one or more processing units configured to determine buffer memory addresses for a sequence of data elements stored in a first data storage location that are being transferred to a second data storage location. For each group of one or more of the data elements in the sequence, a value of a buffer assignment element that can be switched between multiple values each corresponding to a different one of the memories is identified. A buffer memory address for the group of one or more data elements is determined based on the value of the buffer assignment element. The value of the buffer assignment element is switched prior to determining the buffer memory address for a subsequent group of one or more data elements of the sequence of data elements.

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 includes receiving a batch of neural network inputs to be processed using a neural network on a hardware circuit. The neural network has multiple layers arranged in a directed graph and each layer has a respective set of parameters. The method includes determining a partitioning of the neural network layers into a sequence of superlayers. Each superlayer is a partition of the directed graph that includes one or more layers. The method includes processing the batch of inputs using the hardware circuit, which includes, for each superlayer in the sequence: i) loading the respective set of parameters for the layers in the superlayer into memory of the hardware circuit, and ii) for each input in the batch, processing the input through each of the layers in the superlayer using the parameters in the memory of the hardware circuit to generate a superlayer output for the input.

Abstract: Methods, systems, and apparatus for accessing a N-dimensional tensor are described. In some implementations, a method includes, for each of one or more first iterations of a first nested loop, performing iterations of a second nested loop that is nested within the first nested loop until a first loop bound for the second nested loop is reached. A number of iterations of the second nested loop for the one or more first iterations of the first nested loop is limited by the first loop bound in response to the second nested loop having a total number of iterations that exceeds a value of a hardware property of the computing system. After a penultimate iteration of the first nested loop has completed, one or more iterations of the second nested loop are performed for a final iteration of the first nested loop until an alternative loop bound is reached.

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: 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 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 includes receiving a batch of neural network inputs to be processed using a neural network on a hardware circuit. The neural network has multiple layers arranged in a directed graph and each layer has a respective set of parameters. The method includes determining a partitioning of the neural network layers into a sequence of superlayers. Each superlayer is a partition of the directed graph that includes one or more layers. The method includes processing the batch of inputs using the hardware circuit, which includes, for each superlayer in the sequence: i) loading the respective set of parameters for the layers in the superlayer into memory of the hardware circuit, and ii) for each input in the batch, processing the input through each of the layers in the superlayer using the parameters in the memory of the hardware circuit to generate a superlayer output for the input.

Abstract: A computer-implemented method includes receiving, by a computing device, input activations and determining, by a controller of the computing device, whether each of the input activations has either a zero value or a non-zero value. The method further includes storing, in a memory bank of the computing device, at least one of the input activations. Storing the at least one input activation includes generating an index comprising one or more memory address locations that have input activation values that are non-zero values. The method still further includes providing, by the controller and from the memory bank, at least one input activation onto a data bus that is accessible by one or more units of a computational array. The activations are provided, at least in part, from a memory address location associated with the index.

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 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: Methods, systems, and apparatus, including an apparatus for processing an instruction for accessing a N-dimensional tensor, the apparatus including multiple tensor index elements and multiple dimension multiplier elements, where each of the dimension multiplier elements has a corresponding tensor index element. The apparatus includes one or more processors configured to obtain an instruction to access a particular element of a N-dimensional tensor, where the N-dimensional tensor has multiple elements arranged across each of the N dimensions, and where N is an integer that is equal to or greater than one; determine, using one or more tensor index elements of the multiple tensor index elements and one or more dimension multiplier elements of the multiple dimension multiplier elements, an address of the particular element; and output data indicating the determined address for accessing the particular element of the N-dimensional tensor.

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: Methods, systems, and apparatus, including a system for transforming sparse elements to a dense matrix. The system is configured to receive a request for an output matrix based on sparse elements including sparse elements associated with a first dense matrix and sparse elements associated with a second dense matrix; obtain the sparse elements associated with the first dense matrix fetched by a first group of sparse element access units; obtain the sparse elements associated with the second dense matrix fetched by a second group of sparse element access units; and transform the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix to generate the output dense matrix that includes the sparse elements associated with the first dense matrix and the sparse elements associated with the second dense matrix.