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: Methods, systems, and apparatus, including an apparatus for determining pixel coordinates for image transformation and memory addresses for storing the transformed image data. In some implementations, a system includes a processing unit configured to perform machine learning computations for images using a machine learning model and pixel values for the images, a storage medium configured to store the pixel values for the images, and a memory address computation unit that includes one or more hardware processors. The processor(s) are configured to receive image data for an image and determine that the dimensions of the image do not match the dimensions of the machine learning model. In response, the processor(s) determine pixel coordinates for a transformed version of the input image and, for each of the pixel coordinates, memory address(es), in the storage medium, for storing pixel value(s) that will be used to generate an input to the machine learning model.

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, including computer-readable media, are described for a hardware circuit configured to implement a neural network. The circuit includes multiple super tiles. Each super tile includes a unified memory for storing inputs to a neural network layer and weights for the layer. Each super tile includes multiple compute tiles. Each compute tile executes a compute thread that is used to perform the computations to generate an output for the neural network layer. Each super tile includes arbitration logic coupled to the unified memory and each compute tile. The arbitration logic is configured to: pass inputs stored in the unified memory to the compute tiles; pass weights stored in the unified memory to the compute tiles; and pass, to the unified memory, the output generated for the layer based on computations performed at the compute tiles using the inputs and the weights for the 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: 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: 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: Apparatus and methods for processing neural network models are provided. The apparatus can comprise a plurality of identical artificial intelligence processing dies. Each artificial intelligence processing die among the plurality of identical artificial intelligence processing dies can include at least one inter-die input block and at least one inter-die output block. Each artificial intelligence processing die among the plurality of identical artificial intelligence processing dies is communicatively coupled to another artificial intelligence processing die among the plurality of identical artificial intelligence processing dies by way of one or more communication paths from the at least one inter-die output block of the artificial intelligence processing die to the at least one inter-die input block of the artificial intelligence processing die.

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: Apparatus and methods for processing neural network models are provided. The apparatus can comprise a plurality of identical artificial intelligence processing dies. Each artificial intelligence processing die among the plurality of identical artificial intelligence processing dies can include at least one inter-die input block and at least one inter-die output block. Each artificial intelligence processing die among the plurality of identical artificial intelligence processing dies is communicatively coupled to another artificial intelligence processing die among the plurality of identical artificial intelligence processing dies by way of one or more communication paths from the at least one inter-die output block of the artificial intelligence processing die to the at least one inter-die input block of the artificial intelligence processing die.

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.

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 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 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: 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.

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 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 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 determining pixel coordinates for image transformation and memory addresses for storing the transformed image data. In some implementations, a system includes a processing unit configured to perform machine learning computations for images using a machine learning model and pixel values for the images, a storage medium configured to store the pixel values for the images, and a memory address computation unit that includes one or more hardware processors. The processor(s) are configured to receive image data for an image and determine that the dimensions of the image do not match the dimensions of the machine learning model. In response, the processor(s) determine pixel coordinates for a transformed version of the input image and, for each of the pixel coordinates, memory address(es), in the storage medium, for storing pixel value(s) that will be used to generate an input to the machine learning model.