Patent Publication Number: US-11652484-B1

Title: Application specific integrated circuit accelerators

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of and claims priority to U.S. patent application Ser. No. 16/827,409, filed Mar. 23, 2020, which is a continuation of and claims priority to U.S. patent application Ser. No. 16/042,839, filed Jul. 23, 2018, which claims the benefit of U.S. Provisional Application No. 62/535,652, filed Jul. 21, 2017, the contents of both of which are incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to application specific integrated circuit accelerators and methods for operating the same. 
     BACKGROUND 
     Neural networks are machine learning models that employ one or more layers of models to generate an output, e.g., a classification, for a received input. Some neural networks include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as input to the next layer in the network, i.e., the next hidden layer or the output layer of the network. Each layer of the network generates an output from a received input in accordance with current values of a respective set of parameters. 
     Some neural networks include one or more convolutional neural network layers. Each convolutional neural network layer has an associated set of kernels. Kernels can be represented as a matrix structure of weight inputs. Each convolutional layer can also process a set of activation inputs. The set of activation inputs can also be represented as a matrix structure. 
     Some existing systems perform computations for a given convolutional layer in software. For example, the software can apply each kernel for the layer to the set of activation inputs. That is, for each kernel, the software can overlay the kernel, which can be represented multi-dimensionally, over a first portion of activation inputs, which can be represented multi-dimensionally. The software can then compute a dot product from the overlapped elements. The dot product can correspond to a single activation input, e.g., an activation input element that has an upper-left position in the overlapped multi-dimensional space. For example, using a sliding window, the software then can shift the kernel to overlay a second portion of activation inputs and calculate another dot product corresponding to another activation input. The software can repeatedly perform this process until each activation input has a corresponding dot product. In some implementations, the dot products are input to an activation function, which generates activation values. The activation values can be combined, e.g., pooled, before being sent to a subsequent layer of the neural network. 
     SUMMARY 
     In general, in some aspects, the subject matter of the present disclosure encompasses an application specific integrated circuit (ASIC) chip including: a systolic array of cells; and multiple controllable bus lines configured to convey data among the systolic array of cells, in which the systolic array of cells is arranged in multiple tiles, each tile of the multiple tiles including 1) a corresponding subarray of cells of the systolic array of cells, 2) a corresponding subset of controllable bus lines of the multiple controllable bus lines, and 3) memory coupled to the subarray of cells. 
     In some implementations, the ASIC chip further includes: a communication interface; and a vector processing unit configured to receive outputs from the multiple tiles and to compute vector computation output values based on the outputs received from the multiple tiles, in which the multiple controllable bus lines are configured to convey data among the vector processing unit, the communication interface, and the multiple tiles. A first subset of the multiple tiles may be arranged in a first section on a first side of the vector processing unit, and a second subset of the multiple tiles may be arranged in a second section on a second side of the vector processing unit. The communication interface my be arranged adjacent to both a first border of the multiple tiles and to a second border of the multiple tiles. 
     In some implementations, the multiple tiles are arranged in a grid, a first group of controllable bus lines, from the multiple controllable bus lines, extends along a first direction of the grid, each bus line within the first group being spaced apart from an adjacent bus line within the first group along a second direction of the grid, and a second group of controllable bus lines, from the multiple controllable bus lines, extends along the second direction of the grid, each bus line within the second group being spaced apart from an adjacent bus line within the second group along the first direction of the grid. A first subset of controllable bus lines associated with a first tile in the multiple tiles may be hardwired to a second subset of controllable bus lines associated with a second tile in the multiple tiles, and in which the second tile is spaced apart from the first tile by at least one other tile in the multiple tiles. 
     In some implementations, each tile, of the multiple tiles, includes the same total number of cells. 
     In some implementations, each controllable bus line, of the multiple controllable bus lines, includes multiple multiplexers, each multiplexer, of the multiple multiplexers, being associated with a corresponding tile, and each controllable bus line, of the multiple controllable bus lines, includes multiple conveyer elements, each conveyer element, of the multiple conveyer element, being associated with a corresponding tile. 
     In some implementations, during operation the ASIC chip, at least one tile of the multiple tiles is configured to store control instructions, in which the control instructions are configured to control operation of the controllable bus lines. 
     In some implementations, a first tile in the multiple tiles is configured to receive an output from a subarray of cells associated with a second tile in the multiple tiles. 
     In general, in another aspect, the subject matter of the present disclosure encompasses methods of operating an application specific integrated circuit (ASIC) chip including multiple tiles and multiple controllable bus lines configured to convey data among the multiple tiles, in which the multiple tiles are arranged in a grid, each tile of the multiple tiles including a corresponding computational array of cells, corresponding memory, and a corresponding subset of controllable bus lines of the multiple controllable bus lines, the method including: loading, for a first tile of the multiple tiles, multiple weight inputs and activation inputs into the memory of the first tile via a first subset of the controllable bus lines associated with the first tile; and performing, for the first tile, a computation with the computational array of cells of the first tile, using the multiple weight inputs and the multiple activation inputs from the memory of the first tile, to provide an output. 
     Implementations of the methods can include one or more of the following features. For example, in some implementations, the methods further include transferring, from the first tile, the output to a second tile of the multiple tiles. The second tile may be positioned at least one tile away from the first tile along a first dimension of the grid. 
     In some implementations, the methods include transferring, from the first tile, the output to a vector processing unit; performing a non-linear computation on the received output in the vector processing unit to provide a vector computation output. The methods may include storing the vector computation outputs in a first subset of the multiple tiles. The methods may include transferring the vector computation outputs from the first subset of the multiple tiles to a communication interface coupled to the multiple tiles. 
     In some implementations, performing the computation includes adding an output of the computational array of cells to a second subset of the controllable bus lines associated with the first tile. 
     In some implementations, loading, for the first tile, the multiple weight inputs and activation inputs includes transferring the multiple weight inputs and activation inputs from a second tile of the multiple tiles. In some implementations, loading, for the first tile, the multiple weight inputs and activation inputs includes transferring the multiple weight inputs and activation inputs from a communication interface that is coupled to the multiple tiles via the multiple controllable bus lines. 
     In some implementations, the multiple controllable bus lines include multiple multiplexers, in which each tile is associated with a corresponding subset of multiplexers, and in which loading the multiple weight inputs and activation inputs to the first tile includes sending control signals to a first multiplexer associated with the first tile. The methods may further include storing the control instructions in a first memory associated with the first tile. 
     In some implementations, each controllable bus line includes multiple conveyer elements, and in which transferring data over each controllable bus line comprises shifting, at each clock cycle, data from a first conveyer element of the controllable bus line to a second adjacent conveyer element of the controllable bus line 
     Various implementations include one or more of the following advantages. For example, in some implementations, the tiles within the ASIC include local memory allowing an increase in bandwidth. In some implementations, one or more tiles of the ASIC can be configured as dedicated control tiles for handling writing and reading activation in other tiles within the ASIC. Providing dedicated control tiles may also increase the bandwidth available in memory of other tiles within the ASIC. In some implementations, the tiles of the ASIC can be configured such that data skips at least one tile when transferring data between tiles. Skipping at least one tile can reduce an overall data path length, and thus reduce latency associated with operations performed by the ASIC. 
     The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic that illustrates an example of special purpose logic circuitry. 
         FIG.  2    is a schematic that illustrates an example of a tile for use in the ASIC chip of  FIG.  1   . 
         FIGS.  3 A,  4 A,  5 A,  6 A,  7 ,  8 A and  9 A  are schematics that illustrate an overview of a data flow through an ASIC at different times in an exemplary process implemented by the ASIC. 
         FIGS.  3 B,  4 B,  5 B,  6 B,  8 B and  9 B  are schematics that illustrate detail of data flow within a single tile of an ASIC at the times associated with  FIGS.  3 A,  4 A,  5 A,  6 A,  8 A and  9 A , respectively. 
     
    
    
     DETAILED DESCRIPTION 
     An application-specific integrated circuit (ASIC) is an integrated circuit (IC) that is customized for a particular use. For example, an ASIC may be designed to perform operations of machine learning models including, e.g., recognizing objects in images as part of deep neural networks, machine translation, speech recognition, or other machine learning algorithms. When used as an accelerator for a neural network, for instance, an ASIC can receive inputs to the neural network and compute a neural network inference for the inputs. Data inputs to a neural network layer, e.g., either the input to the neural network or the outputs of another layer of the neural network, can be referred to as activation inputs. The inferences can be computed in accordance with respective sets of weight inputs associated with the layers of the neural network. For example, some or all of the layers may receive a set of activation inputs and process the activation inputs in accordance with the set of weight inputs for the layer to generate outputs. 
       FIG.  1    is a schematic that illustrates an example of special purpose logic circuitry, in particular, an ASIC  100 . The ASIC  100  includes multiple tiles  102 , in which one or more of the tiles  102  includes special purpose circuitry configured to perform operations, such as e.g., multiplication and addition operations. In particular, each tile  102  can include a computational array of cells, in which each cell is configured to perform mathematical operations (see, e.g., the exemplary tile  200  shown in  FIG.  2   , and described herein). In some implementations, the tiles  102  are arranged in a grid pattern, with tiles  102  arranged along a first dimension  101  (e.g., rows) and along a second dimension  103  (e.g., columns). For instance, in the example shown in  FIG.  1   , the tiles  102  are divided into four different sections ( 110   a ,  110   b ,  110   c ,  110   d ), each section containing 288 tiles arranged in a grid of 18 tiles down by 16 tiles across. In some implementations, the ASIC  100  shown in  FIG.  1    may be understood as including a single systolic array of cells subdivided/arranged into separate tiles, in which each tile includes a subset/sub-array of cells, local memory and bus lines (see, e.g.,  FIG.  2   ). 
     The ASIC  100  also includes a vector processing unit  104 . The vector processing unit  104  includes circuitry configured to receive outputs from the tiles  102  and compute vector computation output values based on the outputs received from the tiles  102 . For example, in some implementations, the vector processing unit  104  includes circuitry (e.g., multiply circuitry, adder circuitry, shifters, and/or memory) configured to perform accumulation operations on the outputs received from the tiles  102 . Alternatively, or in addition, the vector processing unit  104  includes circuitry configured to apply a non-linear function to the outputs of the tiles  102 . Alternatively, or in addition, the vector processing unit  104  generates normalized values, pooled values, or both. The vector computation outputs of the vector processing units can be stored in one or more tiles. For example, the vector computation outputs can be stored in memory uniquely associated with a tile  102 . Alternatively, or in addition, the vector computation outputs of the vector processing unit  104  can be transferred to a circuit external to the ASIC  100 , e.g., as an output of a computation. In some implementations, the vector processing unit  104  is segmented, such that each segment includes circuitry configured to receive outputs from a corresponding collection of tiles  102  and computes vector computation outputs based on the received outputs. For instance, in the example shown in  FIG.  1   , the vector processing unit  104  includes two rows spanning along the first dimension  101 , each of the rows including 32 segments  106  arranged in 32 columns. Each segment  106  includes circuitry (e.g., multiply circuitry, adder circuitry, shifters, and/or memory) configured to perform a vector computation, as explained herein, based on outputs (e.g., an accumulated sum) from a corresponding column of tiles  102 . The vector processing unit  104  can be positioned in the middle of the grid of tiles  102  as shown in  FIG.  1   . Other positional arrangements of the vector processing unit  104  are also possible. 
     The ASIC  100  also includes a communication interface  108  (e.g., interfaces  108   a ,  108   b ). The communication interface  108  includes one or more sets of serializer/deserializer (SerDes) interfaces and a general purpose input/output (GPIO) interface. The SerDes interface is configured to receive instructions (e.g., instructions for operating controllable bus lines described below) and/or input data for the ASIC  100  and to output data from the ASIC  100  to an external circuit. For example, the SerDes interface can be configured to transmit instructions and/or input data at a rate of 32 Gbps, 56 Gbps, or any suitable data rate over the set of SerDes interfaces included within the communications interface  108 . The GPIO interface is configured to provide an interface for debugging and/or bootstrapping. For example, the ASIC  100  may run a boot program when it is turned on. If the program fails, an administrator may use the GPIO interface to debug the source of the failure. 
     The ASIC  100  further includes multiple controllable bus lines (see, e.g.,  FIG.  2   ) configured to convey data among the communications interface  108 , the vector processing unit  104 , and the multiple tiles  102 . Controllable bus lines include, e.g., wires that extend along both the first dimension  101  (e.g., rows) of the grid and the second dimension  103  (e.g., columns) of the grid. A first subset of the controllable bus lines extending along the first dimension  101  can be configured to transfer data in a first direction (e.g., to the right of  FIG.  1   ). A second subset of the controllable bus lines extending along the first dimension  101  can be configured to transfer data in a second direction (e.g., to the left of  FIG.  1   ). A first subset of the controllable bus lines extending along the second dimension  103  can be configured to transfer data in a third direction (e.g. to the top of  FIG.  1   ). A second subset of the controllable bus lines extending along the second dimension  103  can be configured to transfer data in a fourth direction (e.g., to the bottom of  FIG.  1   ). 
     Each controllable bus line includes multiple conveyer elements, such as flip-flops, that are used to convey data along the lines in accordance with a clock signal. Transferring data over a controllable bus line can include shifting, at each clock cycle, data from a first conveyer element of the controllable bus line to a second adjacent conveyer element of the controllable bus line. In some implementations, data is conveyed over the controllable bus lines upon the rising or falling edge of a clock cycle. For example, data present, at a first clock cycle, on a first conveyer element (e.g., a flip-flop) of a controllable bus line can be transferred to a second conveyer element (e.g., a flip-flop) of the controllable bus line at a second clock cycle. In some implementations, the conveyer elements can be periodically spaced apart at a fixed distance from one another. For example, in some cases, each controllable bus line includes multiple conveyer elements, with each conveyer element positioned within or proximate to a corresponding tile  102 . 
     Each controllable bus line also includes multiple multiplexers and/or demultiplexers. A multiplexer/demultiplexer of a controllable bus line is configured to transfer data between the bus line and a component of the ASIC chip  100 . For example, a multiplexer/demultiplexer of a controllable bus line can be configured to transfer data to and/or from a tile  102 , to and/or from the vector processing unit  104 , or to and/or from the communication interface  108 . Transferring data among tiles  102 , the vector processing unit  104 , and the communication interface can include sending control signals to the multiplexers based on the desired data transfer to take place. The control signals can be stored in registers coupled directly to the multiplexer and/or demultiplexers. The value of the control signal then may determine, e.g., what data is transferred from a source (e.g., memory within a tile  102  or a vector processing unit  104 ) to a controllable bus line or, alternatively, what data is transferred from the controllable bus line to a sink (e.g., memory within a tile  102  or a vector processing unit  104 ). Further details on controllable bus lines are described herein with respect to  FIG.  4   . 
     The controllable bus lines are configured to be controlled on a local level, such that each tile, vector processing unit, and/or communication interface includes its own set of control elements for manipulating the controllable bus lines passing through that tile, vector processing unit, and/or communication interface. For example, each tile, 1D vector processing unit, and communication interface may include a corresponding set of conveyer elements, multiplexers and/or demultiplexers for controlling data transfer to and from that tile, 1D vector processing unit, and communication interface. 
     To minimize latency associated with operations of the ASIC chip  100 , the tiles  102  and vector processing unit  104  can be positioned to reduce the distance data travels among the various components. In a particular implementation, both the tiles  102  and communication interface  108  can be segregated into multiple sections, with both the tile sections and the communication interface sections being arranged such that the maximum distance data travels between a tile and a communication interface is reduced. For instance, in some implementations, a first group of tiles  102  can be arranged in a first section on a first side of the communications interface  108 , and a second group of tiles  102  can be arranged in a second section on a second side of the communication interface. 
     As a result, the distance from a communication interface to the furthest tile may be cut in half compared to a configuration in which all of the tiles  102  are arranged in a single section on one side of the communication interface. 
     Alternatively, the tiles may be arranged in a different number of sections, such as four sections. For instance, in the example shown in  FIG.  1   , the multiple tiles  102  of ASIC  100  are arranged in multiple sections  110  ( 110   a ,  110   b ,  110   c ,  110   d ). Each section  110  includes a similar number of tiles  102  arranged in a grid pattern (e.g., each section  110  can include 256 tiles arranged in 16 rows and 16 columns). The communication interface  108  also is divided into multiple sections: a first communication interface  108   a  and a second communication interface  108   b  arranged on either side of the sections  110  of tiles  102 . The first communication interface  108   a  can be coupled, through controllable bus lines, to the two tile sections  110   a ,  110   c  on the left side of the ASIC chip  100 . The second communication interface  108   b  can be coupled, through controllable bus lines, to the two tile sections  110   b ,  110   d  on the right side of the ASIC chip  100 . As a result, the maximum distance data travels (and thus the latency associated with the data propagation) to and/or from a communication interface  108  can be halved compared to an arrangement in which only a single communication interface is available. Other coupling arrangements of the tiles  102  and communication interfaces  108  are also possible to reduce data latency. The coupling arrangement of the tiles  102  and communication interface  108  can be programmed by providing control signals to the conveyer elements and multiplexers of the controllable bus lines. 
     In some implementations, one or more tiles  102  are configured to initiate reading and writing operations with respect to controllable bus lines and/or other tiles within the ASIC  100  (referred to herein as “control tiles”). The remaining tiles within the ASIC  100  can be configured to perform computations based on the input data (e.g., to compute layer inferences). In some implementations, the control tiles include the same components and configuration as the other tiles within the ASIC  100 . The control tiles can be added as an extra tile or tiles, an extra row or rows, or an extra column or columns of the ASIC  100 . For example, for a symmetric grid of tiles  102 , in which each tile  102  is configured to perform a computation on input data, one or more additional rows of control tiles can be included to handle reading and writing operations for the tiles  102  performing computations on the input data. For instance, each section  110  includes 18 rows of tiles, where the last two rows of tiles may include control tiles. Providing separate control tiles increases, in some implementations, the amount of memory available in the other tiles used to perform the computations. Separate tiles dedicated to providing control as described herein are not necessary, however, and in some cases, no separate control tiles are provided. Rather, each tile may store in its local memory instructions for initiating reading and writing operations for that tile. 
     Furthermore, while each section  110  shown in  FIG.  1    includes tiles arranged in 18 rows by 16 columns, the number of tiles  102  and their arrangement in a section can be different. For example, in some cases, the sections  110  may include an equal number of rows and columns. 
     Furthermore, although shown in  FIG.  1    as divided into four sections, the tiles  102  can be divided into other different groupings. For example, in some implementations, the tiles  102  are grouped into two different sections, such as a first section above the vector processing unit  104  (e.g., nearer the top of the page shown in  FIG.  1   ) and a second section below the vector processing unit  104  (e.g., nearer to the bottom of the page shown in  FIG.  1   ). In such an arrangement, each section may contain, e.g., 576 tiles arranged in a grid of 18 tiles down (along direction  103 ) by 32 tiles across (along direction  101 ). Sections may contain other total numbers of tiles and may be arranged in different sized arrays. In some cases, the divisions between sections are delineated by hardware features of the ASIC  100 . For example, as shown in  FIG.  1   , sections  110   a ,  110   b  may be separated from sections  110   c ,  110   d  by the vector processing unit  104 . 
     Latency also may be reduced by centrally locating the vector processing unit  104  relative to the tile sections  110 . In some implementations, a first half of the tiles  102  are arranged on a first side of the vector processing unit  104 , and a second half of the tiles  102  are arranged on a second side of the vector processing unit  104 . 
     For example, in the ASIC chip  100  shown in  FIG.  1   , the vector processing unit  104  includes two sections (e.g., two rows), each of which includes a number of segments  106  that matches the number of columns of tiles  102 . Each segment  106  can be positioned and configured to receive an output, such as an accumulated sum, from a corresponding column of tiles  102  within a section  110  of tiles. In the example shown in  FIG.  1   , the tile sections  110   a ,  110   b  positioned on a first side of the vector processing unit  104  (e.g., above the vector processing unit  104 ) can be coupled, through controllable bus lines, to the top row of segments  106 . The tile sections  110   c ,  110   d  positioned on a second side of the vector processing unit  104  (e.g., below the vector processing unit  104 ) can be coupled, through controllable bus lines, to the bottom row of segments  106 . Furthermore, each tile  102  within the first half above the processing unit  104  can be positioned at a same distance from the vector processing unit  104  as a respective tile  102  within the second half below the processing unit  104 , such that there is no difference in overall latency between the two halves. For instance, the tiles  102  in row i in the first section  110   a  (where the variable i corresponds to the row position) can be positioned at the same distance away from vector processing unit  104  as the tiles  102  in row m−1-i in a second section of tiles (e.g., the section  110   c ) (where m represents the total number of rows in each section, and assuming rows are incremented along the same direction in both sections). 
     Configuring the tile sections  110  in this manner can halve the distance data travels (and thus the latency associated with the data propagation) to and/or from the vector processing unit  104  compared to an arrangement in which the vector processing unit  104  is positioned at a far end (e.g., the bottom) of all the tiles  102 . For instance, the latency associated with receiving an accumulated sum through a column of tiles  102  from section  110   a  can be half the latency associated with receiving an accumulated sum through a column of tiles  102  from sections  110   a  and  110   c . The coupling arrangements of the tiles  102  and the vector processing unit  104  can be programmed by providing control signals to the conveyer elements and multiplexers of the controllable bus lines. 
     During operation of the ASIC chip  100 , activation inputs may be shifted between tiles. For example, activation inputs can be shifted along the first dimension  101 . In addition, outputs from computations performed by the tiles  102  (e.g., outputs of computations performed by computational array within the tile  102 ) can be shifted along the second dimension  103  between tiles. 
     In some implementations, the controllable bus lines can be physically hardwired, to cause data to skip tiles  102  to reduce latency associated with the operations of the ASIC chip  100 . For example, an output of a computation performed by a first tile  102  can be shifted along the second dimension  103  of the grid to a second tile  102  positioned at least one tile away from the first tile  102 , thus skipping the tile in between. In another example, an activation input from a first tile  102  can be shifted along the first dimension  101  of the grid to a second tile  102  positioned at least one tile away from the first tile  102 , thus skipping the tile in between. By skipping at least one tile when shifting the activation input or the output data, the overall data path length can be reduced, such that the data is transferred faster (e.g., there is no need to utilize a clock cycle to store data at the skipped tile), and latency is reduced. 
     In an example implementation, each tile  102  within each column of section  110   a  can be configured, through the controllable bus lines, to pass output data along the second dimension  103  toward the vector processing unit  104 . The tiles  102  within each column can be further configured to pass the data toward the vector processing unit  104  by skipping the next adjacent tile (e.g., through physical hardwiring of the controllable bus lines between tiles). That is, a tile  102  at a position (i, j)=(0, 0) in the first section  110   a  (where the variable i corresponds to the row position and the variable j corresponds to the column position) can be hardwired to pass output data to a tile  102  at a position (1,1)=(2, 0); similarly, the tile  102  at a position (i, j)=(2, 0) in the first section  110   a  can be hardwired to pass output data to a tile  102  at a position (i, j)=(4, 0), and so forth. The last tile that is not skipped (e.g., the tile  102  located at position (i, j)=(16, 0)) passes output data to the vector processing unit  104 . For a section  110  having 18 rows of tiles, such as the example shown in  FIG.  1   , the tile skipping ensure that all tiles within a section  110  are at most 9 “tile hops” away from the vector processing unit  104 , thus improving the ASIC chip  100  performance by reducing the data path length and resulting data latency by half. 
     In another example implementation, each tile  102  within each row of sections  110   a ,  110   c  and within each row of sections  110   b ,  110   d  can be configured, through the controllable bus lines, to pass activation inputs along the first dimension  101 . For example, some tiles within the sections  110   a ,  110   b ,  110   c ,  110   d  can be configured to pass activation inputs toward a center of the grid  100  or toward the communication interfaces  108 . The tiles  102  within each row can be further configured skip adjacent tiles, e.g., by hardwiring the controllable bus lines between tiles. For example, a tile  102  at a position (i, j)=(0, 0) in the first section  110   a  (where the variable i corresponds to the row position and the variable j corresponds to the column position) can be configured to pass activation inputs to a tile  102  at a position (i, j)=(0, 2); similarly, a tile  102  at a position (i, j)=(0, 2) in the first section  110   a  can be configured to pass activation inputs to a tile  102  at a position (i, j)=(0, 4), and so forth. In some cases, the last tile that is not skipped (e.g., the tile  102  located at position (i, j)=(0, 14)) does not pass the activation input on to another tile. 
     Similarly, tiles that are skipped may pass activation inputs in the opposite direction. For example, a tile  102  at a position (i, j)=(0, 15) in the first section  110   a  (where the variable i corresponds to the row position and the variable j corresponds to the column position) can be configured to activation inputs to a tile  102  at a position (i, j)=(0, 13); similarly, a tile  102  at a position (i, j)=(0, 13) in the first section  110   a  can be configured to pass activation inputs to a tile  102  at a position (i, j)=(0, 11), and so forth. In some cases, the last tile that is not skipped (e.g., the tile  102  located at position (i, j)=(0, 1)) does not pass the activation input on to another tile. By skipping tiles, it is possible, in some implementations, to improve the ASIC chip  100  performance by reducing the data path length and resulting data latency by half. 
     As explained herein, in some implementations, one or more of the tiles  102  are dedicated to storing control information. That is, the tiles  102  dedicated to storing control information do not take part in performing calculations on input data such as weight inputs and activation inputs. Control information can include, e.g., control data for configuring the controllable bus lines during operation of the ASIC chip  100  so that data can be moved around the ASIC chip  100 . The control data can be provided to the controllable bus lines in the form of control signals for controlling the conveyer elements and multiplexers of the controllable bus lines. The control data specifies whether particular conveyer elements of the controllable bus lines pass data to a next conveyer element of the controllable bus line so that data is transferred among the tiles according to a predetermined schedule. The control data additionally specifies whether data is transferred from or to a bus line. For example, the control data can include control signals that direct a multiplexer to transfer data from a bus line to memory and/or other circuitry within a tile. In another example, the control data can include control signals that direct a multiplexer to transfer data from the memory and/or circuitry within the tile to the bus line. In another example, the control data can include control signals that direct a multiplexer to transfer data between a bus line and the communications interface  108  and/or between the bus line and the vector processing unit  104 . Alternatively, as disclosed herein, dedicated control tiles are not used. Rather, in such cases, the local memory of each tile stores the control information for that particular tile. 
     A schematic illustrating an example of a tile  200  for use in the ASIC chip  100  is shown in  FIG.  2   . Each tile  200  includes local memory  202  and a computational array  204  coupled to the memory  202 . The local memory  202  includes physical memory positioned proximate to the computational array  204 . The computational array  204  includes multiple cells  206 . Each cell  206  of the computational array  204  includes circuitry configured to perform a computation (e.g., a multiply and accumulate operation) based on data inputs, such as activation inputs and weight inputs, to the cell  206 . Each cell can perform the computation (e.g., the multiply and accumulation operation) on a cycle of the clock signal. The computational array  204  can have more rows than columns, more columns than rows, or an equal number of columns and rows. For instance, in the example shown in  FIG.  2   , the computational array  204  includes 64 cells arranged in 8 rows and 8 columns. Other computational array sizes are also possible, such as computational arrays having 16 cells, 32 cells, 128 cells, or 256 cells, among others. Each tile can include the same number of cells and/or the same size computational array. The total number of operations that can be performed in parallel for the ASIC chip then depends on the total number of tiles having the same size computational array within the chip. For example, for the ASIC chip  100  shown in  FIG.  1   , which contains approximately 1150 tiles, this means that approximately 72,000 computations can be performed in parallel every cycle. Examples of clock speeds that may be used include, but are not limited to, 225 MHz, 500 MHz, 750 MHz, 1 GHz, 1.25 GHz, 1.5 GHz, 1.75 GHz, or 2 GHz. The computational arrays  204  of each individual tile is a subset of the larger systolic array of tiles, as illustrated in  FIG.  1   . 
     The memory  202  contained in the tile  200  can include, e.g., random-access memory (RAM), such as SRAM. Other memory can be used instead. Each memory  202  can be configured to store (1/n) th  of the total memory associated with n tiles  102  of the ASIC chip. The memory  202  can provided as a single chip or in multiple chips. For example, memory  202  shown in  FIG.  2    is provided as four single-port SRAMs, each of which is coupled to the computational array  204 . Alternatively, the memory  202  can be provided as two single-port SRAMs or eight single-port SRAMS, among other configurations. The joint capacity of the memory can be, but is not limited to, e.g., 16 kB, 32 kB, 64 kB, or 128 kB, after error correction coding. By providing the physical memory  202  locally to the computational arrays, the density of wiring for the ASIC  100  can be, in some implementations, vastly reduced. In an alternate configuration in which memory is centralized within the ASIC  100 , as opposed to provided locally as described herein, may require a wire for each bit of memory bandwidth. The total number of wires needed to cover each tile of the ASIC  100  would far exceed the available space within the ASIC  100 . In contrast, with dedicated memory provided for each tile, the total number of required to span the area of the ASIC  100  can be substantially reduced. 
     The tile  200  also includes controllable bus lines. The controllable bus lines may be categorized into multiple different groups. For example, the controllable bus lines can include a first group of general purpose controllable bus lines  210  configured to transfer data among tiles in each cardinal direction. That is, the first group of controllable bus lines  210  can include: bus lines  210   a  configured to transfer data toward a first direction along the first dimension  101  of the grid of tiles (referred to as “East” in  FIG.  2   ); bus lines  210   b  configured to transfer data toward a second direction along the first dimension  101  of the grid of tiles (referred to as “West” in  FIG.  2   ), in which the second direction is opposite to that of the first direction; bus lines  210   c  configured to transfer data toward a third direction along the second dimension  103  of the grid of tiles (referred to as “North” in  FIG.  2   ); and bus lines  210   d  configured to transfer data toward a fourth direction along the second dimension  103  of the grid of tiles (referred to as “South” in  FIG.  2   ), in which the fourth direction is opposite to the third direction. General purpose bus lines  210  can be configured to carry control data, activation input data, data from and/or to the communications interface, data from and/or to the vector processing unit, and data to be stored and/or used by the tile  200  (e.g., weight inputs). The tile  200  may include one or more control elements  221  (e.g., flip-flops and multiplexers) for controlling the controllable bus lines, and thus routing data to and/or from the tile  200  and/or from memory  202 . 
     The controllable bus lines also can include a second group of controllable bus lines, referred to herein as computational array partial sum bus lines  220 . The computational array partial sum bus lines  220  can be configured to carry data output from computations performed by the computational array  204 . For example, the bus lines  220  can be configured to carry partial sum data obtained from the rows in the computational array  204 , as shown in  FIG.  2   . In such case, the number of bus lines  220  would match the number of rows in the array  204 . For instance, for a 8×8 computational array, there would be 8 partial sum bus lines  220 , each of which is coupled to the output of a corresponding column in the computational array. The computational array output bus lines  220  can be further configured to couple to another tile within the ASIC chip, e.g., as inputs to a computational array of another tile within the ASIC chip. For example, the array partial sum bus lines  220  of tile  200  can be configured to receive inputs (e.g., partial sums  220   a ) of a computational array of a second tile that is located at least one tile away from the tile  200 . The outputs of computational array  204  then are added to the partial sum lines  220  to produce new partial sums  220   b , which may be output from the tile  200 . The partial sums  220   b  then may be passed to another tile or, alternatively, to the vector processing unit. For example, each bus line  220  may be coupled to a corresponding segment (such as segments  106  in  FIG.  1   ) of the vector processing unit. 
     As explained with respect to  FIG.  1   , the controllable bus lines can include circuitry such as conveyer elements (e.g., flip-flops) configured to allow data to be conveyed along the bus lines. In some implementations, each controllable bus line includes, for each tile, a corresponding conveyer element. As further explained with respect to  FIG.  1   , the controllable bus lines can include circuitry such as multiplexers configured to allow data to be transferred among the different tiles, the vector processing unit and the communications interface of the ASIC chip. The multiplexers can be located wherever there is a source or sink for data. For example, in some implementations, as shown in  FIG.  2   , control circuitry  221 , such as multiplexers, can be located at crossings of controllable bus line (e.g., at the crossing of general purpose bus lines  210   a  and  210   d , at the crossing of general purpose bus lines  210   a  and  210   c , at the crossing of general purpose bus lines  210   b  and  210   d , and/or at the crossing of general purpose bus lines  210   b  and  210   c ). The multiplexers at the bus line crossings can be configured to transfer data between the bus lines at the crossings. Accordingly, by proper operation of the multiplexers, it can be possible to change the direction in which data travels over the controllable bus lines. For example, data traveling along the first dimension  101  on general purpose bus lines  210   a  can be transferred to general purpose bus lines  210   d , such that the data instead travels along the second dimension  103 . In some implementations, multiplexers can be located adjacent to the memory  202  of the tile  200  so that data can be transferred to and/or from memory  202 . 
       FIGS.  3 A- 9 B  are schematics that illustrate an example process in which the ASIC  100  is used as a hardware accelerator for computing neural network inferences.  FIGS.  3 A,  4 A,  5 A,  6 A,  7 ,  8 A and  9 A  are schematics that illustrate an overview of data flow through the ASIC  100  at different times in the process.  FIGS.  3 B,  4 B,  5 B,  6 B,  8 B and  9 B  are schematics that illustrate data flow within a single tile (e.g., a control tile or other tile  102 ) of the ASIC  100  at the times associated with  FIGS.  3 A,  4 A,  5 A,  6 A,  8 A and  9 A , respectively. The ellipses in  FIGS.  3 A- 9 B  indicate the presence of repeating features that are not shown in the figures. A compass  300  is provided in each of  FIGS.  3 A- 9 B  to provide orientation for data flow. The labels “N,” “W,” “S” and “E” do not correspond to actual geographic directions, but instead are used to indicate different relative directions in which data can flow through the grid. Controllable bus lines conveying data in the directions indicated by the labels “N,” “W,” “S” and “E” are referred to herein as north-flowing bus lines, west-flowing bus lines, south-flowing bus lines, and east-flowing bus lines. 
     The arrangement of tiles  102  and vector processing unit  104  in  FIGS.  3 A- 9 A  is similar to the arrangement shown in  FIG.  1   . For example, half of the tiles  102  can be arranged on a first side of the vector processing unit  104  and the other half of tiles  102  can be arranged on a second opposite side of the vector processing unit  104 . The communication interfaces  108  are shown in  FIGS.  3 A- 9 A  as arranged on entirely on the right side of the tile grid, but can be positioned on either side of the tile grid as depicted in the schematic of  FIG.  1   . 
     In a first step, as shown in  FIG.  3 A , input values (e.g., activation inputs and/or weight inputs) for a first layer of a model (e.g., a neural network model) are loaded from the communication interfaces  108  onto one or more tiles  102  (e.g., all of the tiles  102 ) within the ASIC  100 . In some implementations, one or more the tiles  102  onto which the input values are loaded also can be dedicated to storing control information and/or output information from the vector processing unit  104 . Such tiles may be referred to herein as “control tiles.” Control tiles include tiles  102  of the ASIC  100  that are configured to provide programs, also referred to as control instructions (e.g., instructions to perform read and/or write operations with respect to the controllable bus lines) to other tiles  102 . The programs/control instructions may be received in a tile  102  (a control tile or any tile in the ASIC as described herein) from a circuit element external to the tile, such as the communication interface. The input values provided to the one or more control tiles can include, e.g., weight inputs and/or activation inputs for a neural network layer and is represented as dots  301  in  FIGS.  3 A- 3 B . In some implementations, the one or more control tiles are positioned directly adjacent to the vector processing unit  104 . By positioning the one or more control tiles directly adjacent to the vector processing unit  104 , the data path length required for output data to pass from the vector processing unit  104  to the one or more control tiles can be reduced (e.g., in cases where the one or more control tiles are configured to store output data from the vector processing unit  104 ). 
     The remaining tiles  102  within the ASIC  100  can be configured to perform computations based on input data (e.g., weight inputs and activation inputs) received from the control tiles, communication interface  108 , and/or vector processing unit  104 . In some implementations, such as shown in the examples of  FIGS.  3 A- 9 B , control tiles and the remaining tiles  102  of the ASIC  100  include the same components and configuration. 
     From the communications interfaces  108 , the input values follow a data path along the controllable bus lines (e.g., such as the general purpose controllable bus lines described herein) to the one or more control tiles. The data can be transferred between different bus lines through the use of multiplexers at locations where the different bus lines cross (e.g., see routing element  221  in  FIG.  2   ). For example, as shown in  FIG.  3 A , the input data flows along a data path that entails traveling on west-flowing general purpose controllable bus lines and then on south-flowing general purpose controllable bus lines. The input data can be transferred from the west-flowing bus lines to the south-flowing bus lines through the use of multiplexers at locations where the west-flowing bus lines and south-flowing bus lines cross. In some implementations, the weight inputs for a second inference can be loaded to the one or more control tiles while a previous first inference is being executed by the ASIC  100 . 
       FIG.  3 B  is a schematic that illustrates a detailed view of an example of a tile  102 , from the ASIC  100 . As shown in  FIG.  3 B , the tile  102  can include memory  302  on which the input values are stored. Memory  302  can include any suitable memory as described herein with respect to  FIG.  2   . The input values are obtained from one or more south-flowing general purpose controllable bus lines  310   d  that pass adjacent to or through the tile  102 . The data from the south-flowing controllable bus lines  310   d  can be transferred to the memory  302  through the use of a multiplexer. Other general purpose controllable bus lines ( 310   a ,  310   b ,  310   c ) are not used during this step. 
     Tile  102  also includes a computational array of cells  306  directly coupled to memory  302 . As explained herein, the computational array of cells  306  may be a subset of a larger systolic array of cells that makes up the tiles of the ASIC. The cells  306  are arranged in an array, with a single cell  306  shown in  FIG.  3 B  at a position (i, j)=(0, 0), where the parameter i represents a cell row position within the array and j represents a cell column position in the array. In the example shown in  FIG.  3 B , the computational array has 8 rows and 8 columns, though other sizes also are possible. Each cell  306  of the computational array can include circuitry configured to perform computations based on data received at the tile. For example, each cell  306  can include multiplier circuitry, adder circuitry, and one or more registers. The output of each cell  306  can be passed as a partial sum to an adjacent cell within the computational array or to a cell within a computational array of another tile in the ASIC  100 . The computational array of cells  306  is used in later steps. 
     The tile  102  also includes controllable bus lines  320  for providing data from previous tiles. For example, the controllable bus lines  320  can carry partial sum output data obtained from a computational array of a previous tile in the ASIC  100  and provide the partial sum output data as an input to the cells of the computational array within tile  102 . Controllable bus lines  320  are not used in this step. 
     The tile  102  also includes controllable bus lines  330  for providing activation input values as an input to the cells  306  of the computational array. For example, the activation input values can be provided to multiplier circuitry within the cell  306 . The activation input values can be obtained from the communications interface  108  or from cells within another tile in the ASIC  100 . The data from the controllable bus lines  330  can be transferred to the cells  306  through the use of a multiplexer. Controllable bus lines  330  are not used in the example step depicted in  FIGS.  3 A- 3 B . 
     As explained herein, in some implementations, one or more tiles  102  are dedicated to storing control information and/or output information from the vector processing unit  104 . In some implementations, the computational arrays within the one or more control tiles may not be used to perform computations. Alternatively, the one or more control tiles can be configured to store control data in addition to performing computations on input data, such as received weight inputs and activation values. In some implementations, the weight inputs are loaded into the memory of each tile  102  where the weight inputs will be used, without first storing the weight inputs in a subset of one or more control tiles. 
     In a second step, as shown in  FIG.  4 A , weight inputs  301  are loaded into the individual cells  306  of the computational arrays within the tiles  102 . Loading the weight inputs  301  into the individual cells  306  can include transferring the data from the memory of one or more control tiles to the corresponding tiles  102  in which the weight inputs  301  belong. The weight inputs  301  can be conveyed along the general purpose controllable bus lines to the tiles  102  and transferred to the memory through multiplexers coupled to the bus lines and memory.  FIG.  4 B  is a detailed view of an example of a tile  102 . The weight inputs  301  can be stored in the memory  302  for the duration of the model execution, which may include computation of multiple inferences. As an alternative to loading the weight inputs  301  from the one or more control tiles, the weight inputs  301  may have been pre-loaded into the memory of tiles  102  directly from the communication interfaces  108 . To prepare a model for execution, the weight inputs  301 , for each tile  102 , can be loaded from the memory  302  of the tile  102  into each cell  306  of the computational array within that tile  102 . For example, the weight inputs  301  can be loaded into a register  400  (also referred to as a “back register”) within the cell  306 . The use of back registers allows a computation to be performed by the cell  306  on a current weight input while a next weight input is loaded into the back register. Although loading weight registers is shown for only one cell  306  in  FIG.  4 B , weight registers of other cells within the computational array also can be loaded during this step. 
     In a third step, as shown in  FIG.  5 A , activation values  500  are introduced into the tiles  102  and may be stored within memory  302  there. The activation values  500  can be transferred over multiple clock cycles. Computations then are performed by the computational arrays of each tile  102  with the received activation values  500  and the weight inputs  301  from the memory  302  in the tile  102 . For example, the computation can include multiplying an activation value by a weight input and then summing the result with the product of a different weight input and activation value. In some implementations, the activation values  500  are conveyed to and between tiles  102  on controllable bus lines  330 . Each of the controllable bus lines  330  can extend along a same direction. For example, as shown in  FIG.  5 B , the controllable bus lines  330  extend laterally along a grid dimension that is orthogonal to a grid dimension along which controllable bus lines  320  extend. Furthermore, as indicated by the arrows  501  in  FIG.  5 A , and the arrows  501  on controllable bus lines  330  in  FIG.  5 B , the activation input data  500  travels on the bus lines  330  in the same (e.g., east-flowing) direction. Alternatively, in some implementations, some of the activation input values  500  travel on some of the controllable bus lines  330  in a first direction (e.g., east-flowing direction) and some other activation input values  500  travel on some other controllable bus lines  330  in a second opposite direction (e.g., west-flowing direction). In some implementations, the activation input data  500  is conveyed along the controllable bus lines  330  such that at least one tile  102  is skipped. For instance, activation input data  500  may be provided to a first tile in a first row of tiles in the ASIC, and then conveyed from the first tile to a second tile in the first row in which the second tile is located at least one tile away from the first tile. 
     In some implementations, the number of controllable bus lines  330  that extend through each tile  102  is determined by the size of the computational array. For example, the number of controllable bus lines  330  that extend through each tile  102  may be equal to at least the number of rows of cells within the computational array. In the example shown in  FIG.  5 B , there are 8 controllable bus lines  330  that pass through tile  102  given that there are 8 rows of cells  306  within the computational array of tile  102 . In some implementations, each separate controllable bus line  330  transfers activation input values  500  to the cells  306  within a corresponding row of the computational array. For instance, for an 8×8 computational array of cells  306  within a tile  102 , a first controllable bus line  330  transfers activation input values  500  to the cells  306  within a first row of the array, a second controllable bus line  330  transfers activation input values  500  to the cells  306  within a second row of the array, etc., up to the last controllable bus line  330 , which transfers activation input values  500  to the cells  306  within the last row of the array. Additional controllable bus lines (e.g., partial sum bus lines) may pass through each tile to provide partial sums from another tile, to receive and combine results of computations within the tile to the provided partial sums, and to output the new partial sums to a new tile or to the vector processing unit. 
     In some implementations, the controllable bus lines  330  transfer the activation input values  500  to circuitry configured to perform a computation within the cell  306 . For example, as shown in  FIG.  5 B , the controllable bus lines  330  are configured to transfer activation input values  500  to multiplier circuit  502  within the cell  306 . The activation input values  500  can be transferred to the multiplier circuit  502  through the use of multiplexers on the controllable bus lines  330 . 
     In some implementations, once the activation input values  500  and weight input values  301  are determined to be in place (e.g., by inspecting control signals), the cells  306  of the computational array within the tile  102  perform a computation using the received activation input values  500  and the weight input values  301  from the memory  302  in the tile  102 . For example, as shown in  FIG.  5 B , the weight input values  301  that were previously stored in register  400  are transferred to register  504  (also referred to as a “front register”). Then, using the multiplier circuit  502 , the weight input values  301  are multiplied with the received activation input values  500 . 
     As explained herein, the activation input values  500  are conveyed on controllable bus lines  330 . In some implementations, the controllable bus lines  330  are general purpose controllable bus lines. In some implementations, the controllable bus lines  330  can be dedicated to providing activation inputs. For example, as shown in  FIG.  5 B , activation input values can be provided to a tile  102  (e.g., to the cells  306  of a computational array within the tile  102 ) by lines  330 , whereas other general purpose controllable bus lines  310   b  can be used to provide other data and/or instructions to the tile  102 . 
     In a fourth step, as shown in  FIG.  6 B , a result of a computation between the weight input values  301  and the activation input values  500 , within each cell  306 , is passed to circuitry  602  within the cell  306  to produce an output value  600 . In the example of  FIG.  6 B , the circuitry  602  includes a summation circuit. The summation circuit  602  within each cell  306  is configured to sum the product of the multiplier circuit  502  with another value obtained from either another tile  102  in the ASIC  100  or from another cell  306  within the computational array. The value obtained from another tile  102  or from another cell  306  can include, e.g., an accumulated value. Accordingly, the output value  600  of the summation circuit  602  is a new accumulated value. The summation circuit  602  then can send the new accumulated value  600  to another cell located in a bottom (e.g., in a south-flowing direction) adjacent cell of the computational array within the tile  102 . The new accumulated value  600  can be used as an operand for a summation in the bottom adjacent cell. For the last row of cells within the computational array, the new accumulated values  600  can be transferred to another tile  102  within the ASIC  100 , as shown in  FIG.  6 A . In another example, the new accumulated values  600  can be transferred to another tile  102  that is at least one tile away from the tile  102  in which the new accumulated values  600  were generated. Alternatively, as also shown in  FIG.  6 A , the new accumulated values  600  from the last row of cells within the computational array are transferred to the vector processing unit  104 . 
     The accumulated values  600  that are transferred into a tile  102  or transferred out of a tile  102  can be conveyed along controllable bus lines  320 . Each of the controllable bus lines  320  extend along a same direction. For example, as shown in  FIG.  6 B , the controllable bus lines  320  extend vertically along a grid dimension that is orthogonal to a grid dimension along which controllable bus lines  330  extend. Furthermore, as indicated by the arrows  604  in  FIG.  6 A , and the arrows  604  in  FIG.  6 B , the accumulated values  600  travel on the controllable bus lines  320  in either a north-flowing or south-flowing direction depending on the location of the vector processing unit  104  relative to the tiles  102  from which the accumulated values  600  are generated. For example, for the tiles  102  located above the vector processing unit  104  in  FIG.  6 A , the accumulated values  600  travel on the controllable bus lines  320  in a south-flowing direction towards the vector processing unit  104 , whereas for the tiles  102  located below the vector processing unit  104 , the accumulated values  600  travel in a north-flowing direction towards the vector processing unit  104 . 
     In some implementations, the number of controllable bus lines  320  that provide accumulated values entering a tile  102  is determined by the size of the computational array. For example, the number of controllable bus lines  320  that provide accumulated values entering a tile  102  equals the number of columns of cells within the computational array. In the example shown in  FIG.  6 B , there are 8 controllable bus lines  320  entering tile  102  given that there are 8 columns of cells  306  within the computational array of tile  102 . In some implementations, each separate controllable bus line  320  that enters the tile  102  transfers an accumulated value  600  to a different corresponding cell  306  in the first row of cells of the computational array. As explained herein, the accumulated value  600  received in each cell then is used as an operand to produce a new accumulated value, which is passed to an adjacent cell within the array. 
     Similarly, in some implementations, the number of controllable bus lines  320  that provide accumulated values exiting a tile  102  also is determined by the size of the computational array. For example, the number of controllable bus lines  320  that provide accumulated values exiting a tile  102  equals the number of columns of cells within the computational array. For instance, each separate controllable bus line  320  transfers a new accumulated value  600  from a different corresponding cell  306  in a last row of cells of the computational array to either another tile  102  within the ASIC  100  or to the vector processing unit  104 . 
     In a fifth step as shown in  FIG.  7   , the data (e.g., the accumulated values) received by the vector processing unit  104  are processed by the vector processing unit  104  to provide processed values  700 . Processing of the data at the vector processing unit  104  can include applying a bias to the data received at the vector processing unit  104 , performing additional accumulation operations, and/or applying a non-linear function (e.g., a rectifier function or sigmoid function as known in neural network systems) to the received data. Other operations also can be applied by the vector processing unit  104 . The vector processing unit  104  can include circuitry arranged in multiple segments  106 , in which each segment  106  is configured to process data received from a corresponding column of tiles  102  and generate a corresponding processed value  700 . 
     In a sixth step, as shown in  FIG.  8 A , the processed values  700  from the vector processing unit  104  are transferred to and stored in one or more tiles of the ASIC  100 , e.g., a subset of the tiles of the ASIC  100 . For example, the processed values  700  can be sent to the control tiles  103 , which are located directly adjacent to the vector processing unit  104 . Alternatively, or in addition, the processed values  700  can be sent to one or more of the other tiles  102  within the ASIC  100 . The processed values  700  can be transferred to one or more tiles over a general purpose controllable bus line, such as controllable bus lines  310   c . Upon reaching a tile (e.g., a control tile or other tile  102 ), the processed values  700  can be stored in the memory  202  of the tile. For example, the processed values  700  can be transferred to the memory  702  using a multiplexer associated with the controllable bus line  310   c . The step of storing the processed values  700  can occur after the inferences of each model layer are obtained. In some implementations, the processed values  700  can be provided as input values to a next layer of the model. 
     In a seventh step, as shown in  FIGS.  9 A and  9 B , the processed values  700  can be exported off the ASIC  100 . For example, the processed values  700  can be transferred from the memory  202  of the one or more control tiles to the communications interface  108 . The processed values  700  can be conveyed to the communications interface  108  on controllable bus lines (e.g., controllable bus lines  310   c  and/or  310   d ). The processed values  700  can be transferred to the controllable bus lines through multiplexers associated with the bus lines. 
     The processed values  700  may be exported off the ASIC  100 , e.g., if the inferences for a final layer of a model have been obtained or if the model has been partitioned among multiple ASICs and the inferences for the final layer associated with ASIC  100  have been obtained. The processed values  700  can be received and exported by the SerDes interfaces of the communications interface  108  to another destination including, but not limited to, e.g., another ASIC  100  or a field-programmable gate array chip. 
     The example process described with respect to  FIGS.  3 A- 9 B  may require that the activation values and weight inputs being fully propagated throughout the computational arrays of each tile before the cell computations are performed, or the cells may perform computations before all values are fully propagated. Furthermore, although the ASIC  100  has been described with weight inputs being sent to columns of a computational array and activation inputs being sent to rows of the computational array, in some implementations, the weight inputs are sent to rows of the array and the activation inputs are sent to columns of the array. 
     Furthermore, although the computational arrays have been described herein as using individual summation circuits within each cell, groups of cells within the computational array (e.g., all the cells within a column) may be coupled directly to a single summation circuit, which sums the received outputs from the cells in the group, thus reducing the number of summation circuits required to store the outputs. 
     Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non transitory program carrier for execution by, or to control the operation of, data processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. 
     The term “data processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC. The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. 
     A computer program (which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code) can be written in any form of programming language, including compiled or interpreted languages, or functionally-pure or declarative or procedural languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA, an ASIC, or a GPGPU (general purpose graphics processing unit). 
     Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few. 
     Computer readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     To send for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can send input to the computer. Other kinds of devices can be used to send for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user&#39;s client device in response to requests received from the web browser. 
     Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), e.g., the Internet. 
     The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. 
     Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, although bus lines are described as “controllable,” not all bus lines need to have the same level of control. For instance, there can be varying degrees of controllability, where some bus lines can be controlled only where some bus lines are restricted in terms of the number of tiles from which they can source data or to which they can send data. In an another example, some bus lines may be dedicated to providing data along a single direction, such as north, east, west, or south as described herein. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.