Patent Publication Number: US-2019180183-A1

Title: On-chip computational network

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to and incorporates by reference for all purposes the full disclosure of co-pending U.S. patent application Ser. No. ______, filed concurrently herewith, entitled “MULTI-MEMORY ON-CHIP COMPUTATIONAL NETWORK” (Attorney Docket No. 102028-1060931 (100800US)) and co-pending U.S. patent application Ser. No. ______ filed concurrently herewith, entitled “FAST CONTEXT SWITCHING FOR NEURAL NETWORKS” (Attorney Docket No. 102028-1066785 (101300US)). 
    
    
     BACKGROUND 
     Neural networks attempt to replicate, using computer technology, logical reasoning performed by the biological neural networks that constitute animal brains. Neural networks take inspiration from the mechanics of the operation of the human brain. In a neural network, neurons are represented by nodes and synapses are represented by weighted connections between the nodes. The weights can reflect different responses to input. A neural network can be arranged in layers, where input data to be analyzed is provided to an input layer, and the outputs of each layer provide the inputs to the next layer. The last layer can output a result. The weight values can be determined through training, during which input data with a known result is provided to the neural network. 
     Neural networks can be implemented using a Central Processing Unit (CPU) to perform the computations. CPUs, however, tend to be optimized for sequential rather than parallel computations, and thus can suffer from poor response times. Graphics Processing Units (GPUs) are optimized for parallel computations, but not necessarily for the result from one computation unit to be provided directly to another computation unit. Often, the result must first be written to a memory. GPUs, though having better response times than CPUs, may nevertheless lag in response times. 
     Special-purpose neural network processors include computation arrays optimized for parallel, chained computations. In a neural network processor, computation units can output a result directly into another computation unit, without needing to write the result to memory. When the result does need to be written to memory, for example to start a new cycle of computations through the array, the result can be stored in a memory that is local to the computation array. Neural network processors can thus perform better than both CPUs and GPUs on the same input data. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various examples will be described with reference to the drawings, in which: 
         FIG. 1  illustrates an example of visual model for a neural network; 
         FIG. 2A  illustrates an example of a model for a neural network that includes feed-forward weights and recurrent weights; 
         FIG. 2B  illustrates an example of a model for a neural network that includes different connection types; 
         FIG. 3A  illustrates an example of a model of a 2-dimensional convolution; 
         FIG. 3B  illustrates an example of a model for convolutional neural network; 
         FIG. 4  illustrates an example of the effect of storing the weight values for a neural network on-chip instead of in off-chip memory; 
         FIG. 5  illustrates an example of a neural network processing engine that can be used to execute a neural network; 
         FIGS. 6A-6B  illustrate an example of a neural processing engine that can be used to execute a neural network; 
         FIGS. 7A-7C  illustrate an example of a neural network processing engine that can be used to execute a neural network; 
         FIG. 8  illustrate an example of a neural network processor that has multiple neural network processing engines; 
         FIG. 9  illustrates an example of a neural network processor configured for the weights of a neural network to be stored in the memory subsystems of two neural network processing engines; 
         FIG. 10  illustrates an example of a neural network processor configured for the weights of a neural network to be stored in the memory subsystems of two neural network processing engines; 
         FIG. 11  illustrates another solution for storing all the weights for a neural network on-chip; 
         FIG. 12  illustrates an example of a process that can be executed by a neural network processor when the neural network processor is executing a neural network; 
         FIG. 13  illustrates an example of a process that can be executed by a neural network processor when the neural network processor is executing a neural network; 
         FIG. 14  illustrates an example of a process that can be executed by a computing system that includes a neural network processor; and 
         FIG. 15  illustrates a network in which the various examples discussed above can be used. 
     
    
    
     DETAILED DESCRIPTION 
     In the following description, various example implementations will be described. For purposes of explanation, specific configurations and details are set forth in order to provide a thorough understanding of the examples. However, it will also be apparent to one skilled in the art that the examples may be practiced without the specific details. Furthermore, well-known features may be omitted or simplified in order not to obscure the examples being described. 
     Artificial neural networks attempt to replicate, using computer technology, logical reasoning performed by the biological neural networks that constitute animal brains. Artificial neural networks (which will be referred to herein as neural networks) are part of the field of artificial intelligence (AI), an area of research and engineering seeking to build intelligent machines that can make decisions in the same way that humans do. Neural networks fall within a sub-field of artificial intelligence called machine learning. Machine learning is a field of study that investigates giving computers the ability to learn without being explicitly programmed. A program that implements a machine learning algorithm is able to learn to do tasks without the program needing to include code that accounts for every possibility, and code that describes all possible behaviors. 
     Neural networks take inspiration from the mechanics of the operation of the human brain, to the extent that these operations are understood. According to various models of the brain, the main computational element of the brain is the neuron. Neurons are connected together with a number of elements, with elements entering a neuron being referred to as dendrites and an element leaving a neuron being referred to as an axon. A neuron accepts signals via dendrites, performs a computation on the signals, and outputs a signal on an axon. The input and output signals are referred to as activations. The axon of one neuron can branch out and be connected to the dendrites of multiple neurons. The connection between a branch of an axon and a dendrite is called a synapse. 
     A synapse can scale the signal crossing the synapse. The scaling factor is referred to as a weight, and is thought of as the way a brain is able to learn: different weights result from different responses to input. Learning can change the weights, but the organization of the neurons and synapses need not change to obtain the learning. The static structure of the brain can thus be used as a model for a program, and the weights can reflect tasks that the program has learned to perform. 
     Neural networks operate on the notion that a neuron&#39;s computation involves a weighted sum of input values. These weighted sums correspond to the value scaling performed by the synapses and the combining of those values in the neuron. A functional operation is performed in the neuron on the combined inputs. In the brain model, the operation appears to be a non-linear function that causes the neuron to generate an output only when the inputs cross some threshold. Thus, by analogy, the nodes of a neural network can apply a non-linear function to the weighted sum of the values input into the nodes. 
       FIG. 1  illustrates an example of a visual model  100  for a neural network. In this example, the model  100  includes an input layer  104 , a middle layer that is often referred to as a hidden layer  106 , and an output layer  108 . Each layer includes some number of nodes  102 . In this example, the nodes  102  of the input layer  104  are connected to each node  102  of the hidden layer  106 . The connections, which would be referred to as synapses in the brain model, are referred to as weights  110 . Also in this example, each node  102  of the hidden layer  106  has a connection or weight  110  with each node  102  of the output layer. The input layer  104  can receive inputs and can propagate the inputs to the hidden layer  106 . A neural network implementation can include multiple hidden layers. Weighted sums computed by the hidden layer  106  (or multiple hidden layers) are propagated to the output layer  108 , which can present final outputs to a user. The outputs of the nodes  102  can be referred to as activations, in keeping with the brain model. 
     An example of a computation that can occur at each layer in the example model  100  is as follows: 
     
       
         
           
             
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     In the above equation, W ij  is a weight, x i  is an input activation, y j  is an output activation, f( ) is a non-linear function, and b is a bias term. Various non-linear functions can be used to achieve different purposes. 
     The model  100  can be referred to as a directed, weighted graph. In a directed graph, each connection to or from a node indicates a direction (e.g., into the node or away from the node). In a weighted graph, each connection can have a weight. Tools for developing neural networks can visualize the neural network as a directed, weighted graph, for ease of understanding and debuggability. In some cases, these tools can also be used to train the neural network and output trained weight values. Executing the neural network is then a matter of using the weights to conduct computations on input data. 
     A neural network that has more than three layers (e.g., more than one hidden layer) is sometimes referred to as a deep neural network. Deep neural networks can have, for example, five to more than a thousand layers. 
     Neural networks with many layers can be capable of learning high-level features with more complexity and abstraction than shallower networks. As an example, a neural network can be taught to recognize images. In this example, pixels of an image can be fed into the input layer of the neural network, and the outputs of the first layer can indicate the presences of low-level features in the image, such as lines and edges. At subsequent layers, these features can be combined to measure the likely presence of higher level features: the lines can be combined into shapes, which can be further combined into sets of shapes. Given all this information, the neural network can output a probability that the high-level features represent a particular object or scene. For example, the neural network can output whether an image contains a cat or does not contain a cat. 
     The learning phase of a neural network is referred to as training the neural network. During training, the neural network is taught to perform a task. In learning the task, values for the weights (and possibly also the bias) are determined. The underlying program for the neural network (e.g., the organization of nodes into layers, the connections between the nodes of each layer, and the computation executed by each node), does not need to change during training. Once trained, the neural network can perform the task by computing a result using the weight values that were determined during training. For example, the neural network can output the probability that an image contains a particular object, the probability that an audio sequence contains a particular word, a bounding box in an image around an object, or a proposed action that should be taken. Running the program for the neural network is referred to as inference. 
     There are multiple ways in which weights can be trained. One method is called supervised learning. In supervised learning, all training samples are labeled, so that inputting each training sample into a neural network produces a known result. Another method is called unsupervised learning, where the training samples are not labeled and training aims to find a structure in the data or clusters in the data. Semi-supervised learning falls between supervised and unsupervised learning. In semi-supervised learning, a subset of training data is labeled. The unlabeled data can be used to define cluster boundaries and the labeled data can be used to label the clusters. 
     Neural networks have been used for a variety of applications, including, for example, in the areas of image and video, speech and language, medicine, game play, and robotics. In image and video, neural networks have been used for image classification, object localization and detection, image segmentation, and action recognition. In speech and language, neural networks have been used for speech recognition, machine translation, natural language processing, and audio generation. In the medical field, neural networks have been used in genomics and medical imaging. In game play, neural networks have been used to play video and board games, including games with immense numbers of possible moves such as Go. In robotics, neural networks have been used for motion planning of a robot, visual navigation, control stabilization, and driving strategies for autonomous vehicles. 
     Different varieties of neural networks have been developed. Various examples of neural networks can be divided into two forms: feed-forward and recurrent.  FIG. 2A  illustrates an example of a model  210  for a neural network that includes feed-forward weights  212  between an input layer  204  and a hidden layer  206 , and recurrent weights  214  at the output layer  208 . In a feed-forward neural network, the computation is a sequence of operations on the outputs of a previous layer, with the final layer generating the outputs of the neural network. In the example illustrated in  FIG. 2A , feed-forward is illustrated by the hidden layer  206 , whose nodes  202  operate only the outputs of the nodes  202  in the input layer  204 . A feed-forward neural network has no memory and the output for a given input can be always the same, irrespective of any previous inputs given to the neural network. The Multi-Layer Perceptron (MLP) is one type of neural network that has only feed-forward weights. 
     In contrast, recurrent neural networks have an internal memory that can allow dependencies to affect the output. In a recurrent neural network, some intermediate operations can generate values that are stored internally and can be used as inputs to other operations, in conjunction with the processing of later input. In the example of  FIG. 2A , recurrence is illustrated by the output layer  208 , where the outputs of the nodes  202  of the output layer  208  are connected back to the inputs of the nodes  202  of the output layer  208 . These looped-back connections can be referred to as recurrent weights  214 . Long Short-Term Memory (LSTM) is a frequently used recurrent neural network variant. 
       FIG. 2B  illustrates an example of a model  220  for a neural network that includes different connection types. In this example model  220 , the input layer  204  and the hidden layer  206  are fully connected  222  layers. In a fully connected layer, all output activations are composed of the weighted input activations (e.g., the outputs of all the nodes  202  in the input layer  204  are connect to all of the inputs of the hidden layer  206 ). Fully connected layers can require a significant amount of storage and computations. Multi-Layer Perceptron neural networks are one type of neural network that is fully connected. 
     In some applications, some connections between the activations can be removed, for example by setting the weights for these connections to zero, without affecting the accuracy of the output. The result is sparsely connected  224  layers, illustrated in  FIG. 2B  by the weighs between the hidden layer  206  and the output layer  208 . Pooling is another example of a method that can achieve sparsely connected  224  layers. In pooling, the outputs of a cluster of nodes can be combined, for example by finding a maximum value, minimum value, mean value, or median value. 
     The efficiency of operating a neural network can be further improved in several different ways. For example, the number of weights that contribute to an output can be limited by having the output be a function of only a fixed-sized window of inputs. Even further efficiency can be gained when the same set of weights are used in the calculation of every output. Repeated use of the same weight values is referred to as weight sharing, and can significantly reduce the storage requirements for weights. 
     Windowing and weight sharing in a neural network layer can be accomplished by structuring the computation executed at each node as a convolution.  FIG. 3A  illustrates an example of a model  310  of a 2-dimensional convolution as applied to image processing. In this example model, a filter plane  304  is a set of weights arranged in a matrix having a height R and a width S. The filter plane  304  can be applied—using, for example, an element-wise multiplication  312 —to an input image, whose data can be referred to as an input feature map  306 . The height R and width S of the filter plane  304  are both less than the height H and width W of the input feature map  306 , thus application of the filter plane  304  to the input feature map  306  results in a small neighborhood of input activations  316  being computed (e.g., weights beyond the neighborhood can be set to zero). The input activations  316  can be combined using, for example, a partial sum accumulation  314  to produce an output activation  318  in an output feature map  308 . The output feature map  308  represents a higher-level abstraction of the input feature map  306 , and has a height E and a width F. In this model  310 , the same set of weights can be shared for every output (e.g., the filter space is invariant). 
       FIG. 3B  illustrates an example of a model  320  for convolutional neural network, as applied to image processing. A convolutional neural network can include multiple convolution layers. In a convolutional neural network, each layer can generate a successively higher level abstraction of the input data (that is, of, an input feature map  326 ). A convolutional neural network can achieve very good performance by employing a deep hierarchy of layers. 
     As illustrated by the example of  FIG. 3B , each convolution layer in a convolutional neural network is composed of a high-dimensional convolution. In this model  320 , the input activations  336  of a layer are structured as a set of 2-dimensional input feature maps  326 , each of which is referred to as a channel, C. Each channel is convolved with a particular 2-dimensional filter from a stack of filters  324 , which has a filter for each channel. The stack of filters  324  can be referred to as a single 3-dimensional filter. The results of the convolution of each point are summed across all channels to produce output activations  338  that together form one channel, M, of output feature map  328 . Additional 3-dimensional filters, M, corresponding to the number of output channels, can be used on the same input to generate additional output channels. To improve reuse of filter weights, multiple input feature maps  326 , labeled  1  through N in the illustrated example, can be batch processed. 
     Convolutional neural networks can include between five and more than a thousand layers. In some examples, a small number, such as between one and three, of fully connected layers can be applied after the convolutional layers, for classification purposes. A fully connected layer can also apply filters to input feature maps, but the filters are the same size as the input feature maps. A fully connected layer thus does not have the weight sharing property of a convolutional layer. 
     Training of a neural network can occur online, that is, when the neural network is in operation and available to users. More often, however, training occurs offline and before the neural network is put into operation. Training sample sets can be quite large, and thus training can require hours or days. Offline training can potentially also produce more accurate results. 
     Once trained, a neural network includes the weights determined during the training and a set of instructions describing the computation to be executed at each layer or node of the network. In some examples, the number of weights can be on the order of 5 million to 100 million. In some examples, a weight value can be represented using a 32-bit number, in which case 5 million to 100 million weights can require about 20 megabytes (MB) to 400 MB to store. In some examples, the number of weights can be as few as 1.5 million. 
     Operation of a neural network (e.g., conducting inference), as illustrated by the models discussed above, involves fetching input data or input activations, executing multiply-and-accumulate operations in parallel for each node in a layer, and providing output activations. Optimum performance of a neural network, measured by response time, can be achieved when a hardware architecture is capable of highly parallelized computations. Central Processing Units (CPUs), which can also be referred to as general purposed processing units, can have multiple cores, (e.g., 2 to 64 or more cores) and can increase parallelism through use of multiple execution threads. CPU cores, however, tend to be optimized for sequential processing. For example, a computation engine (e.g., an arithmetic logic unit (ALU)) of a core obtains operands from memory and writes a result to memory, such that memory operations are required for sequential computations. In this example, each memory operation can require management by control logic of the CPU. For this and other reasons, CPUs thus tend to have slow response times when performing inference for a neural network. 
     In contrast to CPUs, Graphics Processing Units (GPUs) achieve parallelism by having thousands of small and efficient cores, configured specifically for conducting parallel computations. GPUs thus can achieve far better performance than a CPU when executing a neural network. Individual GPU computation engines, however, can still be primarily sequential in nature, such that memory operations are required for the outputs of one computation engine to be provided to the inputs of another. 
     When executing a neural network, the performance bottleneck that can be encountered by both CPUs and GPUs is in accessing memory. A multiply-and-accumulate operation can require three memory reads, one each to fetch a weight value, an input feature map activation, and a partial sum, and a memory write to store an updated partial sum. In the worst case, all memory transactions go to off-chip memory, that is, a memory that is located on a different die and in a different package from the processor. This memory, which can be referred to as processor memory or main memory, can be dedicated to the processor for temporary storage of data that is actively being operated on by the processor. Dynamic Random Access Memory (DRAM) or DRAM variants are frequently used for processor memory, due to having high capacity and low cost. Reading from and writing to processor memory, however, is many orders of magnitude slower than the operation of the computation engine. The speed of a neural network can thus be limited by off-chip memory latency. 
     Special-purpose neural network processors can achieve better performance than both CPUs and GPUs when executing a neural network. Neural network processors can employ a spatial architecture, in which computation engines form processing chains and can pass data directly from one computation engine to another. This can significantly reduce the number of memory transactions. In some examples, neural network processors can also include an on-chip buffer that can store values read from processor memory, and that can distribute values to multiple computation engines in the processor. The computation engines can further include a small, local register file (e.g., a small memory) for storing intermediate results. Having an on-chip memory hierarchy can improve the efficiency of the operation of a neural network by reducing memory latencies. 
     Neural network processors can nevertheless become memory bandwidth limited when the weight values for a neural network are stored off-chip. The speed at which a computation matrix of a neural network processor can execute computations can quickly exceed the rate at which weight values and activations can be read from memory. For example, a computation matrix can perform 10,000 multiply-and-accumulate operations per clock cycle, thus requiring 30,000 input values per cycle. The clock speed of processor memory busses can be in the range of, for example thousands of megahertz (MHz) while the clock speed for processors can be in the multiples of gigahertz (GHz). The computation rate of a neural network processor can thus quickly outpace the ability of processor memory to supply data. 
     Reuse of weight values is one way in which memory bandwidth limitations can be circumvented. Reuse is common in convolution neural networks, where a weight value can be reused, for example, 1300 times on average. As discussed further below, neural networks with frequent reuse of weight values can potentially avoid the memory bandwidth limitation, and can instead be limited by the computation speed of the processor. 
     In Long Short-Term Memory neural networks and Multi-Layer Perceptron neural networks, the reuse factor of weight values is much lower, such as, for example, two times on average. 
     One solution used to increase weight value reuse is batching. Batching involves inputting more than one set of input data into a neural network at a time. The sets of input data need not be related. With batching, when the neural network is provided with, for example, ten sets of input data, each weight can be reused twenty times (e.g., twice per set of input data) after having been read once from memory. 
     Mathematical models suggest, however, that a high reuse factor is needed for a neural network processor to achieve maximum possible performance. For example, some examples suggest that a reuse factor of about 1000 is needed. When batching, it may be possible to collect, for example, 50 to 60 sets of input data at a time, but collecting 500 sets of input data may lead to other problems. For example, users of a neural network expect immediate responses when requesting, for example, a machine translation or image identification. When a neural network processing system waits to have 500 requests before the system begins calculating results, response time can be negatively impacted. 
     In various implementations, a neural network processing system can reduce memory bandwidth limitations and can approach optimal efficiency by storing the weights for a neural network in on-chip memory. On-chip means that the memory is on the same die and/or in the same package (e.g., the physical enclosure for the die) as the computation matrix. Neural network processors can have on-chip memory for storing intermediate results. In various implementations, the memory subsystem of the processor can be designed such that the on-chip memory can store both intermediate results and weight values. The neural network processor may still be memory bound, but it may be possible to read the on-chip memory as much as, for example, ten or fifty times faster than off-chip memory. Reducing memory delays by this amount may enable operation of a neural network to approach the computation speed limit of the processor. 
     In some cases, particularly for small neural networks, it may be possible for all of the weight values for the neural network to be stored in on-chip memory. Using a single monolithic memory, however, may still lead to memory delays because the single memory may have only for example, one or two sets of read and write channels, such that only one or two values can be read at a time. In various implementations, instead of one large memory, a neural network processor can be equipped with multiple memory banks, which can each be individually accessible. By being independently accessible, it may be possible to read more than one memory bank at the same time. 
     In a neural network processing engine, the computation matrix can be implemented as an array of processing engines. The neural network processing engine can further include a set of memory banks local to the array of processing engines, where local can mean physically close to and/or directly accessible by the array of processing engines. As noted above, the local memory banks can be used by the neural network processing engine to store intermediate results. In some cases, particularly when the neural network is small, all of the weight values for the neural network can also be stored in the memory banks of the neural network processing engine. In these cases, it may be possible for the array of processing engines to sustain full utilization in every clock cycle. 
     In some examples, not all of the weight values for a neural network can fit in the memory banks of a neural network processing engine. For example, the memory banks may have sufficient space for half of the weight values, with any remaining space being needed for storing intermediate results computed during the course of processing a set of input data. The size of the intermediate results, however, can decrease over the course of computing a result. Additionally, once used, some weight values may no longer be needed. Thus, in some implementations, as a computation progresses and memory space becomes available, the neural network processing engine can load additional weights into the available space. In some cases, the weights can come from an off-chip memory. In some cases, the weights can come from on-chip memory, for example the memory banks of another neural network processing engine. 
     In some implementations, a neural network processor can be constructed with multiple neural network processing engines, each having an independent array of processing engines and local memory banks. In these implementations, each neural network processing engine can execute a neural network, so that multiple neural networks can be run at the same time. In some implementations, the weight values for one neural network can be stored in the memory banks of two or more neural network processing engines, with one designated as being the engine for processing the neural network. When the designated neural network processing engine needs the weights that are stored with another neural network processing engine, the weights can be read from the memory banks of the other neural network processing and loaded into the memory banks of the designated neural network processing engine. The other neural network processing engine can use any remaining available space in its own memory banks for other operations. 
     In some implementations, instead of moving weights from one neural network processor to another, the computation can be moved. For example, an intermediate result (e.g., the output activations from a layer) and a state (e.g., the last layer that was computed) can be copied from one neural network processing engine to a second neural network processing engine, where the second neural network processing engine has in its memory banks the next set of weight values needed to continue the computation. The second neural network processing engine can resume the computation, and possibly hand the computation off to yet another neural network processing engine. 
     The transfer of an in-progress computation from one neural network processing engine to another can, in some implementations, include transferring between individual neural network processors. In these implementations, the individual neural network processors can be on different dies and/or in different packages. Also in this example, the neural network processor can communicate using a host bus or processor bus. As when the neural network processing engines are on the same die, copying an intermediate result and state can move the computation from one neural network processor to another. 
     In various implementations, copying weights from one neural network processing engine to another, moving an in-progress computation between neural network processing engines and/or between physical neural network processor chips can be used in various combinations, with the goal being to store as many of the weight values for a neural network on-chip as is possible. By having the weight values on chip, the computations may be limited only by the relatively short on-chip memory latency, instead of being limited by the relatively long off-chip memory latency. As a result, operation of a neural network can be made much more efficient. 
       FIG. 4  illustrates an example of the effect of storing the weight values for a neural network on-chip instead of in off-chip memory. The graph  400  illustrated in  FIG. 4  illustrates an application of what is referred to as the roofline model. A roofline model is a performance model that can be used to provide estimates of the performance of a computing system. The roofline model can capture inherent hardware limitations and potential benefits of optimizations. In the example of  FIG. 4 , the roofline model is being used to illustrate the performance of a neural network processor in terms of operations per weight read from memory. The vertical axis illustrates the number of tera-operations (teraops) that can be conducted per second. The horizontal axis illustrates a number of operations or calculations executed per weight value. The number of operations executed per weight value can increase either through inherent reuse of the weight (e.g., the structure of the neural network leads to weight reuse) or through batching, that is, inputting multiple data sets into the neural network at the same time or in a pipelined fashion. 
     In the example of  FIG. 4 , the solid line  410  plotted on the graph  400  illustrates an example of the performance of a neural network processing system that stores weight values in off-chip memory. In such a system, the weight values are stored in processor memory and a neural network processor reads the weight values over a host bus or processor bus. By storing weight values in a separate memory, the neural network processing system must incur a delay whenever a weight value is read from the memory. 
     In the steep part  402  of the solid line  410 , the number of teraops per second that can be conducted increases approximately linearly for the number of operations conducted per weight value. In the steep part  402  of the solid line  410 , in order for the number of teraops per second to be increased, the reuse of any given weight must be increased. Stated in the converse, in the steep part  402  of the solid line  410 , at a given reuse value, the number of teraops per second is constrained by the speed at which the weight value can be read from off-chip memory. The neural network processing system is thus said to be memory bound in the steep part  402  of the solid line  410 . 
     In the flat part  404  of the solid line  410 , the number of teraops per second has reached a maximum (about 124 teraops per second, in the illustrated example). In the flat part  404  of the solid line  410 , increasing the reuse of weight value does not increase the number of teraops per second because the system has reached the maximum computation speed of the hardware. In the flat part  404  of the solid line  410 , the system is said to be compute-bound. 
     The roofline model thus illustrates that maximum performance capable by the hardware can be achieved for a neural network processing system. But as illustrated in the graph  400 , for a system with the weights stored in a separate chip from the processor, a high amount of reuse (about 1600 in the illustrated example) of each weight value is needed. As discussed previously, convolution neural networks can have a high rate of weight reuse, but many other neural networks, such as multi-layer perceptrons and recurrent neural networks, have very low weight reuse. Batching input data sets for these types of neural networks can increase reuse, but batching  1100  input data sets (assuming an inherent reuse of two for each weight value) can have other detrimental effects, such as delayed response times for the users providing the input data. 
     The dashed line  420  in the example of  FIG. 4  illustrates the roofline model as applied to a neural network processing system where weight values are stored on-chip. In this case, weight values are stored in the memory of the neural network processor, prior to the system receiving input data and possibly at all times during the operation of the system. Having the weight values stored on chip means that the delay for reading weight values from memory is significantly reduced. As illustrated by the steep part  412  of the dashed line  420 , reuse of only about 100 (as provided by this example) can overcome the memory latency. The neural network processing system thus can operate in the flat part  414  of the dashed line  420  most of the time and for all neural network types. 
     In various implementations, a neural network processor can be architected to support storing of weight values on the processor.  FIG. 5  illustrates an example of a neural network processing engine  502  that can be used to execute a neural network. In various implementations, the example neural network processing engine  502  is an integrated circuit that can be included in a neural network processor. The neural network processor is an integrated circuit that can have other components, including the additional neural network processing engine  502 . In various implementations, the neural network processing engine  502  can include a memory subsystem  504  and a processing engine array  510 . When in operation (e.g., when computing a result for a set of input data  550 ), the processing engine array  510  can read weight  506  and state  508  values from the memory subsystem  504 . The processing engine array  510  can output computation results to a results buffer  512 . In some cases, the example neural network processing engine  502  can perform an activation function using an activation  516  block and/or pooling using a pooling  518  block on the computation results, before the results are written to the memory subsystem  504 . 
     Weights  506 , in this example, are the weight values for a neural network. In various implementations, the weights  506  are post-training weights, meaning that values for the weights  506  were previously determined. State  508 , in this example, can include input data  550  when a computation begins, as well as values that reflect an in-progress computation. State  508 , for example, can include partial sums determined by the processing engine array  510 , a current layer of the neural network that is being operated on, and/or instructions for the processing engine array  510 , where the instructions may be associated with a particular layer. The weights  506  and the state  508  can be read from the memory subsystem  504  for operating on by the processing engine array  510 . 
     In various implementations, the memory subsystem  504  can include multiple memory banks  514 . In these implementations, each memory bank  514  is independently accessible, meaning that the read of one memory bank is not dependent on the read of another memory bank. Similarly, writing to one memory bank does not affect or limit writing to a different memory bank. In some cases each memory bank can be read and written at the same time. Various techniques can be used to have independently accessible memory banks  514 . For example, each memory bank can have at least one read channel and may have at least one separate write channel (in some cases, the memory bank may have combined read and write channels). In these examples, the memory subsystem  504  can permit simultaneous access to the the read or write channels of multiple memory banks. As another example, the memory subsystem  504  can include arbitration logic such that arbitration between, for example, the outputs of multiple memory banks  514  can result in more than one memory bank&#39;s output being granted. In these and other examples, though globally managed by the memory subsystem  504 , each memory bank can be operated independently of any other. 
     Having the memory banks  514  be independently accessible can increase the efficiency of the neural processing engine  502 . For example, weights  506  and state  508  can be simultaneously read and provided to each row of the processing engine array  510 , so that the entire processing engine array  510  can be activated in one cycle. As another example, weights  506  and state  508  can be read at the same time that intermediate results are written to the memory subsystem  504 . In contrast, a single memory, while still able to provide weights  506  and state  508  to the processing engine array  510  faster than off-chip memory, may be able to service one read or write at a time. With a single memory, multiple clock cycles can be required, for example, to read weights for each row of the processing engine array  510  before the processing engine array  510  can be started. 
     In various implementations, the memory subsystem  504  can be configured to simultaneously service multiple clients, including the processing engine array  510 , the activation  516  block, the pooling  518  block, and any external clients that access the memory subsystem  504  over a chip interconnect  520 . In some implementations, being able to service multiple clients can mean that the memory subsystem  504  has at least as many memory banks as there are clients. In some cases, each row of the processing engine array  510  can count as a separate read client. In these cases, weights  506  and state  508  can be stored separately, and thus require two reads, or can be concatenated and stored together, thus requiring one read. In some cases, each column of the processing engine array  510  can output an intermediate value, such that each column can count as a separate write client. In some cases, output from the processing engine array  510  can be written into the memory banks  514  that can then subsequently provide input data for the processing engine array  510 . The memory banks  514  can be implemented, for example, using static random access memory (SRAM). 
     In various implementations, the memory subsystem  504  can include control logic. The control logic can, for example, keep track of the address spaces of each of the memory banks  514 , identify memory banks  514  to read from or write to, and/or move data between memory banks  514 , if needed. In some implementations, the memory subsystem  504  can include multiplexors for selecting which memory bank to output to a particular client and/or to receive input from a particular client. In these implementations, the control logic can generate select signals for the multiplexors, which can enable some or all of the memory banks  514  to service each client. In some implementations, memory banks  514  can be hardwired to particular clients. For example, a set of memory banks  514  can be hardwired to provide weights  506  and state  508  to the rows of the processing engine array  510 . In these examples, the control logic can move data between memory banks  514 , for example, to move intermediate results from the memory banks  514  to which the intermediate results are written, to the memory banks  514  from which the intermediate results will be read for the next round of computation. 
     The processing engine array  510  is the computation matrix of the neural processing engine  502 . The processing engine array  510  can, for example, execute parallel integration, convolution, correlation, and/or matrix multiplication, among other things. The processing engine array  510  includes multiple processing engines  511 , arranged in rows and columns, such that results output by one processing engine  511  can be input directly into another processing engine  511 . Processing engines  511  that are not on the outside edges of the processing engine array  510  thus can receive data to operate on from other processing engines  511 , rather than from the memory subsystem  504 . 
     In various examples, the processing engine array  510  uses systolic execution, in which data arrives at each processing engine  511  from different directions at regular intervals. In some examples, input data can flow into the processing engine array  510  from the left and weight values can be loaded at the top. In some examples weights and input data can flow from the left and partial sums can flow from top to bottom. In these and other examples, a multiply-and-accumulate operation moves through the processing engine array  510  as a diagonal wave front, with data moving to the right and down across the array. Control signals can be input at the left at the same time as weights  506 , and can flow across and down along with the computation. 
     In various implementations, the number of columns in the processing engine array  510  determines the computational capacity of the processing engine array  510 , and the number of rows determines the required memory bandwidth for achieving maximum utilization of the processing engine array  510 . The processing engine array  510  can have, for example, 64 columns and 256 rows, or some other number of columns and rows. 
     An example of a processing engine  511  is illustrated in  FIG. 5 . As illustrated by this example, a processing engine  511  can include a multiplier-accumulator circuit. Inputs from the left can include, for example, input data i and a weight value w, where the input data is a value taken from a set of input data and the weight value is from a set of weight values that connect one layer of the neural network to the next. A set of input data can be, for example, an image being submitted for identification or object recognition, an audio clip being provided for speech recognition, a string of text for natural language processing or machine translation, or the current state of a game requiring analysis to determine a next move, among other things. In some examples, the input data and the weight value are output to the right, for input to the next processing engine  511 . 
     In the illustrated example, an input from above can include a partial sum, p_in, provided either from another processing engine  511  or from a previous round of computation by the processing engine array  510 . When starting a computation for a new set of input data, the top row of the processing engine array  510  can receive a fixed value for p_in, such as zero. As illustrated by this example, i and w are multiplied together and the result is summed with p_in to produce a new partial sum, p_out, which can be input into another processing engine  511 . Various other implementations of the processing engine  511  are possible. 
     Outputs from the last row in the processing engine array  510  can be temporarily stored in the results buffer  512 . The results can be intermediate results, which can be written to the memory banks  514  to be provided to the processing engine array  510  for additional computation. Alternatively, the results can be final results, which, once written to the memory banks  514  can be read from the memory subsystem  504  over the chip interconnect  520 , to be output by the system. 
     In some implementations, the neural processing engine  502  includes an activation  516  block. In these implementations, the activation  516  block can combine the results from the processing engine array  510  into one or more output activations. For example, for a convolution neural network, convolutions from multiple channels can be summed to produce an output activation for a single channel. In other examples, accumulating results from one or more columns in the processing engine array  510  may be needed to produce an output activation for a single node in the neural network. In some implementations, activation  516  block can be bypassed. 
     In some implementations, the neural processing engine  502  can include a pooling  518  block. Pooling is the combining of outputs of a cluster of nodes from a layer of a neural network. The combined output can be provided to the next layer. Combining can include for example, computing a maximum value, a minimum value, an average value, a median value, or some other value determined from the outputs of the cluster of nodes. In various implementations, the pooling  518  can be selectively activated, as needed for any particular neural network. 
     Input data  550  can arrive over the chip interconnect  520 . The chip interconnect  520  can connect the neural processing engine  502  to other components of a neural network processor, such as a Direct Memory Access (DMA) engine that can obtain input data  550  from an Input/Output (I/O) device, a storage drive, or a network interface. The input data  550  can be, for example one-dimensional data, such as a character string or numerical sequence, or two-dimensional data, such as an array of pixel values for an image or frequency and amplitude values over time for an audio signal. In some examples, the input data  550  can be three-dimensional, as may be the case with, for example, the situational information used by a self-driving car. In some implementations, the memory subsystem  604  can include a separate buffer for the input data  550 . In some implementations, the input data  550  can be stored in the memory banks  514  along with the weights  506 . 
     In various implementations, the weights  506  stored in the memory subsystem  504  can have been determined by training the neural network to perform one or more tasks. The input data  550  can include an instruction indicating the task to perform (e.g., image processing, speech recognition, machine translation, etc.). In various implementations, the neural processing engine  502  is configured for conducting inference (e.g., performing a task), rather than for training of the neural network. In some implementations, the neural processing engine  502  can be used for training, though perhaps with assistance from software to update the stored weights  506 . 
     In various implementations, the memory subsystem  504  can include enough memory to store both intermediate results and all of the weight values for a neural network. The memory subsystem  504  should have, at a minimum, enough memory in the memory subsystem  504  to store intermediate results, but in many cases the memory subsystem  504  can include many more memory banks  514  than are needed to store just intermediate results. This additional space can be used to store all of the weight values for a neural network. For example, a neural network may have 1.5 million weights, which, when each is represented by 32 bits, can require about 6 MB of memory. Intermediate results can require, for example, 10 MB of storage space, at most. On-chip memory of 20 MB is a reasonable size, and, in the preceding example, can readily accommodate the weight values, intermediate results, and any other data that the neural processing engine  502  can need during operation. 
     In some cases, not all of the weights for a neural network can fit in the memory of a neural processing engine. In these cases, some of the weights can be stored in the neural processing engine&#39;s memory, and the remaining weights can be loaded during the course of a computation.  FIGS. 6A-6B  illustrate an example of a neural processing engine  602  that can be used to execute a neural network. In various implementations, the neural network processing engine  602  can include a memory subsystem  604  and a processing engine array  610 . When in operation (e.g., when computing a result for a set of input data  650 ), the processing engine array  610  can read weight  606  and state  608  values from the memory subsystem  604 , where the state  608  values can initially include the input data  650 . Though not illustrated here, the processing engine array  610  can include an array of processing engines, each of which can execute, for example, a multiply-and-accumulate operation. The processing engine array  610  can output computation results to a results buffer  612 . In some cases, the example neural network processing engine  602  can perform an activation function using an activation  616  block and/or pooling using a pooling  618  block on the computation results, before the results are written to the memory subsystem  604 . 
     In operation, the neural network processing engine  602  reads weights  606  and state  608  from memory banks  614  in the memory subsystem  604 , and inputs the weights  606  and state  608  into the processing engine array  610 . The processing engine array  610  can output intermediate results to the results buffer  612 , from which the intermediate results can be written to the memory subsystem  604 . The activation  616  block can be selectively enabled when multiple intermediate results are to be combined into one output activation. The pooling  618  block can also be selectively activated, when the outputs of a cluster of nodes is to be combined into one output. Additional cycles of reading weights  606  and state  608  and computing results can occur, until the last layer in the neural network is reached and the processing engine array  610  outputs a final result. 
     In various implementations, a set of memory banks  614  can initially be reserved for storing intermediate results (e.g., state  608  values). For example, as illustrated in  FIG. 6A , half of the memory banks  614  can be reserved for storing immediate results. In this example, weights  606  can be stored in the remaining memory banks  614 . The weights  606  can be stored prior to the neural network processing engine  602  receiving any input data  650 , so that the weights  606  are ready as soon as input data  650  is received. In other examples, the memory banks  614  can be divided between storage for state  608  and storage for weights  606  in different proportions. In some implementations, individual memory banks  614  can be divided between storage for state  608  and storage for weights  606 . 
     In the example of  FIG. 6A , the weights  606  stored in the memory banks  614  are less than all of the weights for the neural network. The remaining weights are stored in additional memory, located outside of the neural network processing engine  602 . The additional memory  630  can be on-chip, such as, for example, in an on-chip cache. Alternatively or additionally, the additional memory  630  can be off-chip, such as, for example, in processor memory. As discussed above, weights  606  correspond to the layers of a neural network. In various implementations, the weights  606  can be divided according to layers, such that weights  606  for the first n layers are stored in the memory subsystem  604  before input data  650  is received, and the weights  606  for the remaining m layers are stored in the additional memory  630 . 
     Once the neural network processing engine  602  starts processing input data  650 , the amount of memory needed to store state  608  values can decrease. Additionally, for some neural networks, some weights  606 , once used, may not be needed anymore. For example, as discussed above, as discussed above, feed forward weights may be used only once, to compute the input values for a layer. Because some weights, once used, may not be needed again, over the course of processing a set of input data  650 , the memory used to store those weights can be repurposed. 
     Space in the memory banks  614  formerly used to store state  608  values and weight  606  that are no longer needed can be repurposed to store additional weight  606  values. As illustrated by  FIG. 6B , as a computation progresses, more of the memory banks  614  can be designated for storing weights  606 . 
     For example, on every clock cycle, a set of weights  606  can be read out of various memory banks  614  and intermediate results can be stored as state  608  values. The memory subsystem  604 , using control logic, can keep track of the memory used by the weights  606  that have not yet been used and the amount of space currently occupied by the state  608  values. Alternatively or additionally, software can manage the allocation of space in the memory subsystem  604 . As less memory space is needed to store the state  608 , the memory subsystem  604  (or software) can determine to assign more of the memory space to storing weights  606 . Additionally, at various times, the memory subsystem  604  can send requests over the chip interconnect  620  for more weights to be read from the additional memory  630 . Over the course of processing one set of input data, the neural network processing engine  602  can gradually move all of the weights  606  for the neural network into the memory banks  614 . 
     In some implementations, as processing of a set of input data nears completion, the number of weights  606  that are still needed can become smaller and smaller. As the number of remaining weights  606  decreases, the assignment of memory to weights  606  or state  608  can be reversed, so that gradually more of the memory is set aside for storing state  608 . By the end of the computation, the memory can again be divided as illustrated in  FIG. 6A . 
     As noted above, in some implementations, weights  606 , once used, can be deleted from the memory subsystem  604 , in that the memory occupied by these weights  606  can be given over to storing weights  606  that are still needed. In these implementations, as processing of a set of input data winds down, the weights  606  from initial layers can be reloaded into the memory subsystem  604 . Once processing of the input data is done, the neural network processing engine  602  can thus be ready to process the next input data. 
     When weights  606  that are not currently present in the memory subsystem  604  are in processor memory, reading the weights  606  from processor memory can cause the processing engine array  610  to stall while waiting for the weights  606  to be loaded. In various implementations, one technique for avoiding stalls caused by reading from processor memory is to queue read transactions to the processor memory well in advance of the weights  606  being needed. Another technique is to pre-fetch the weights  606  into an on-chip cache. Another technique is to use the memory of another neural network processing engine, as discussed further below. In various implementations, these and other techniques can be combined to suit the requirements of a given system. 
     In various implementations, space that becomes available, over the course of a computation, in the memory subsystem of a neural network processing engine can be used to store the weights of another neural network. This second neural network may have been trained to perform a different task than the neural network originally loaded into the neural network processing engine. By switching the weights stored in the neural network processing engine from the weights of the first neural network to the weights of a second neural network, the neural network processing engine can sequentially execute different tasks. 
     Configuring a neural network processing engine to switch between different neural networks and to sequentially perform different tasks can be useful in certain situations. For example, the inputs from a single user can require multiple operations, such as, for example, natural language understanding following by machine translation. While a neural network can be capable of performing a complex task, such as natural language understanding, one neural network may not be capable of both natural language understanding and also machine translation. Thus, frequently one neural network can be used to perform natural language understanding while another neural network can be used to perform machine translation. 
     To optimize the speed at which a neural network processor produces results for different (possibly unrelated) tasks, the neural network processor can be configured to perform a fast context switch. A context, as applied to a neural network processing system, describes one neural network, including the weights for the neural network and the computations executed to perform a task for which the neural network was trained. A context switch can involve reprogramming a neural network processing engine to execute a second neural network after having been configured to execute a first neural network. Reprogramming the neural network processing engine can include loading the weights for the second neural network into the memory of the neural network processing engine. 
     A fast context switch can occur when the neural network processing engine is ready to execute the second neural network immediately upon completing a computation using the first neural network. Immediately can mean, for example, within one or a few clock cycles. In various implementations, as a computation for a first neural network progresses and memory space becomes available in the memory of a neural network processor, the weights for a second neural network can be stored in the available space. Once the first computation completes, some or all of the weights for the second neural network are present in the memory, and a computation using these weights can begin. 
       FIGS. 7A-7C  illustrate an example of a neural network processing engine  702  that can be used to execute a neural network. In various implementations, the neural network processing engine  702  can include a memory subsystem  704  and a processing engine array  710 . When in operation (e.g., when computing a result for a set of input data), the processing engine array  710  can read weight  706  and state  708  values from the memory subsystem  704 , where the state  708  values can initially include the input data. Though not illustrated here, the processing engine array  710  can include an array of processing engines, each of which can execute, for example, a multiply-and-accumulate operation. The processing engine array  710  can output computation results to a results buffer  712 . In some cases, the example neural network processing engine  702  can perform an activation function using an activation  716  block and/or pooling using a pooling  718  block on the computation results, before the results are written to the memory subsystem  704 . 
     In operation, the neural network processing engine  702  reads weights  706  and state  708  from memory banks  714  in the memory subsystem  704 , and inputs the weights  706  and state  708  into the processing engine array  710 . The processing engine array  710  can output intermediate results to the results buffer  712 , from which the intermediate results can be written to the memory subsystem  704 . The activation  716  block can be selectively enabled when multiple intermediate results are to be combined into one output activation. The pooling  718  block can also be selectively activated, when the outputs of a cluster of nodes is to be combined into one output. When neither activation  716  nor pooling  718  are enabled, results from the processing engine array  710  can be moved directly from the results buffer to the memory subsystem  704 . Additional cycles of reading weights  706  and state  708  and computing results can occur, until the last layer in the neural network is reached and the processing engine array  710  outputs a final result. In some cases, the final result can be operated on by the activation  716  and/or the pooling  718  blocks prior to being written to the memory subsystem  704 . 
     As illustrated in  FIG. 7A , in various implementations, a portion of the memory banks  714  can be used to store weight  706  values and a different portion can be used to store state  708  values. In these implementations, the weight  706  values for a neural network can be stored in the portion of the memory banks  714  set aside for the weights  706 , prior to the neural network processing engine  702  receiving any input data. In some cases, the weights  706  stored in the memory banks  714  can include all of the weights for the neural network. In some cases, the stored weights  706  can include fewer than all of the weights for the neural network, with the remaining weights being read from an additional memory  730  when a computation is in-progress (as discussed above). Also in these implementations, during the course of a computation, intermediate results (e.g., state  708  values) can be stored in the portion of the memory banks  714  reserved for storing state  708  values. The portion of the memory banks  714  used to store weights  706 , the portion used to store state  708 , and any unused portion generally do not overlap. 
     In the example of  FIG. 7A , the weights  706  stored in the memory subsystem  704  when first input data  750  is received are the weights  706  for a first neural network. The first neural network, including the weights  706 , the task (referred to in the following examples as the first task) the first neural network was trained to perform, and possibly also instructions for the processing engine array  710 , activation  716  block and/or pooling  718  block, can represent a first context for the neural network processing engine  702 . When the first input data  750  is received by the neural network processing engine  702  the first task will be performed on the first input data  750 . 
     As discussed above, as the computation for performing the first task progresses, space in the memory subsystem  704  may become available or may be considered unused. For example, the portion of the memory banks  714  used to store state  708  values can become smaller as the amount of memory needed to store intermediate results becomes less. In some examples, logic in the memory subsystem  704  can determine the amount of memory needed to store intermediate results. In some examples, software can determine the amount of memory needed to store intermediate results, and can, accordingly reduce the portion of memory banks  714  that is being used to store the state  708  values. As a further example, the portion of the memory banks  714  used to store the weights  706  for the first neural network can become smaller due to weight  706  values, having been used, being marked as no longer needed. In some examples, logic in the memory subsystem  704  can mark address locations of used weights as available. In some examples, software can keep track of the weight values that are still needed and weight values that have been used and are no longer needed. 
     In various implementations, as space in the memory subsystem  704  becomes unused or available, as illustrated in  FIG. 7B , weight  707  values for a second neural network can be stored in the available space. In the example illustrated in  FIG. 7B , several memory banks  714  formerly used to store weights  706  for the first neural network and several memory banks  714  formerly used to store state  708  values have been repurposed to store the weight  707  values for a second neural network. The second neural network may have been trained to perform a task, referred to hereafter as the second task, which may be different from the first task. The weights  707 , the second task, and possibly commands for the processing engine array  710 , activation  716  block, and/or pooling  718  block can be considered a second context for the neural network processing engine  702 . The weights  707  can be read, over a chip interconnect  720 , from an additional memory  730 , which can be an on-chip cache, a processor memory, and/or the memory of another neural network processing engine  702 . 
     In various implementations, storing of the weights  707  for the second neural network can occur during computation of a result for the first input data  750 . That is, as the computation of the result for the first input data  750  progresses and space becomes available in the memory banks  714 , the neural network processing engine  702  can start loading the now unused space with the weights  707  for the second neural network. Storing of the weights  707  for the second neural network can start concurrently with receipt by the neural network processing engine  702  of second input data  751 , on which the second task will be performed. In some cases, the second input data  751  is received while the neural network processing engine  702  is in the process of computing a result for the first input data  750 . In some cases, storing of the weights  707  for the second neural network can start before or after the second input data  751  is received. In some examples, receipt of the second input data  751  triggers loading of the weights  707  for the second neural network. In some examples, receipt of the second input data  751  triggers computation of a result for the second input data  751 . 
     In some cases, only memory banks  714  used to store the weights  706  for the first neural network are repurposed to store the weights  707  for the second neural network. In these cases, the portion of the memory banks  714  used to store the state  708  is always available to store intermediate results. 
     In some cases, repurposing the memory banks  714  can include moving data between the memory banks  714 . For example, as the portion of the memory banks  714  used to store state  708  becomes smaller, not-yet-used weights  706  can be moved into this portion. In this example, the portion of the memory banks  714  formerly occupied by the weights  706  for the first neural network can gradually become occupied by the weights  707  for the second neural network, so that once the context switch is complete the allocation of memory is the same as for the first neural network. 
     In various implementations, once the neural network processing engine  702  completes computation of a result for the first input data  750 , the neural network processing engine  702  can be ready to perform the computation for the second input data  751 . In the example illustrated in  FIG. 7C , the neural network processing engine  702  has completed the context switch from the first neural network to the second neural network. As illustrated in this example, the weights  707  for the second neural network have been loaded into the memory subsystem  704  and the neural network processing engine  702  is ready to start computing a result for the second input data  751 . 
     In various implementations, the neural network processing engine  702  can begin computing a result for the second input data  751  within one or two cycles of completing the computation for the first input data  750 . In some implementations, the neural network processing engine  702  can begin computing a result for the second input data  751  before the result for the first input data  750  is complete. For example, the final cycles of the computation for the first input data  750  may still be progressing through processing engine array  710  as state  708  and weights  707  for computing a result for the second input data  751  are being input into the processing engine array  710 . In this example, computations for the first input data  750  and the second input data  751  may be present in the processing engine array  710  at the same time. 
     In some cases, the weights  707  now stored in the memory subsystem  704  include all the weights for the second neural network. In some cases, the weights  707  are fewer than all of the weights for the second neural network, and any remaining weights can be read from the additional memory  730  as space becomes available in the memory banks  714 . 
     In some cases, in the example illustrated in  FIG. 7C , there may still be some data related to the first context in the memory subsystem  704 . For example, some weight  706  values for the first neural network, such as the last ones used, may still be in the memory banks  714 . In this example, once the computation for the second input data  751  begins, these weights  706  can be overwritten. As another example, a final result of the computation for the first input data  750  may still be in the memory banks  714 , waiting to be read out over the chip interconnect  720 . The final result can remain in the memory subsystem  704  while the computation for the second input data  751  is in progress, or can be read out before the computation for the second input data  751  begins. 
     Loading the weight  707  values for the second neural network while the neural network processing engine  702  is computing a result using the weight  706  values for the first neural network enables the neural network processing engine  702  to perform a fast context switch between the first neural network and the second neural network. A fast context switch can enable the neural network processing engine  702  to increase throughput and produce results faster. 
     Another technique for increasing throughput through a neural network processer is to equip the neural network processor with multiple neural network processing engines that can operate in parallel. The neural network processor can, for example, execute multiple, possibly different neural networks on different neural network processing engines, at the same time. As another example, the neural network processor can batch processes more sets of input data, thus increasing reuse of weight values. 
       FIG. 8  illustrates an example of a neural network processor  800  that has multiple neural network processing engines  802   a - 802   n . Each of the neural network processing engines  802   a - 802   n  can include a memory subsystem and processing engine array, and can execute the computation required for a neural network to perform a task for which the neural network was programmed. In the illustrated example, the neural network processor  800  includes n neural network processing engines  802   a - 802   n.    
     The example neural network processor  800  further includes DRAM controllers  842   a - 842   k  for communicating with processor memory, implemented in this example using DRAM  830 . In the illustrated example, the neural network processor  800  includes k DRAM controllers  842   a - 842   k , each of which may be able to communicate with an independent set of banks of DRAM. In other examples, other types of RAM technology can be used for the processor memory. The DRAM controllers  842   a - 842   k  can also be referred to as memory controllers. 
     The example neural network processor  800  further includes Peripheral Component Interconnect (PCI) controllers  844   a - 844   p  for communicating with PCI devices  832  in the system. In this example, PCI is the bus protocol being used to implement a processor bus. The processor bus can connect the neural network processor  800  to PCI devices  832  such as, for example, I/O devices, memory controllers, storage devices, and/or network interface cards, among other things. In this example, the neural network processor  800  includes p PCI controllers  844   a - 844   p , each of which may include a separate root complex and may communicate with a separate set of PCI devices  832 . In other examples, other standardized bus protocols, such as Ultra Path Interconnect (UPI) can be used for the host bus. In other examples, a proprietary bus protocol can be used. 
     The example neural network processor  800  further includes DMA engines  846   a - 846   d  that can move data between the neural network processing engines  802   a - 802   n , DRAM controllers  842   a - 842   k , and PCI controllers  844   a - 844   p . In the illustrated example, the neural network processor  800  includes d DMA engines  846   a - 846   d . In some implementations, the DMA engines  846   a - 846   d  can be assigned to specific tasks, such as moving data from the DRAM controllers  842   a -to the neural network processing engines  802   a - 802   n , or moving data between the PCI controllers  844   a - 844   p  and the neural network processing engines  802   a - 802   n . In some implementations, at least one DMA engine  846   a - 846   d  can be dedicated to each neural network processing engine  802   a - 802   n . In some implementations, the DMA engines  846   a - 846   d  can be treated as a pool instead of being dedicated to a function or component, such that whenever data needs to be moved, an available DMA engine  846   a - 846   d  is engaged. 
     In the example neural network processor  800 , the various components can communicate over a chip interconnect  820 . The chip interconnect  820  primarily includes wiring for routing data between the components of the neural network processor  800 . In some cases, the chip interconnect  820  can include a minimal amount of logic, such as multiplexors to control the direction of data, flip-flops for handling clock domain crossings, and timing logic. 
       FIG. 9  illustrates an example of neural network processor  900 , that has been configured for the weights  906  of a neural network to be stored in the memory subsystems of two neural network processing engines  902   a - 902   b . The neural network processor  900  can be similar to the neural network processor  800  illustrated in  FIG. 8 . As illustrated in  FIG. 9 , each neural network processing engine  902   a - 902   n  includes a memory subsystem  904   a - 904   n  and a processing engine array  910   a - 910   n . In various implementations, each of the memory subsystems  904   a - 904   n  can store the weights for a neural network, such that each of the neural network processing engines  902   a - 902   n  can independently execute a neural network. 
     In some cases, one of the neural network processing engines  902   a - 902   n , such as the second neural network processing engine  902   b , may not need all of the space in the memory subsystem  904   b  of the neural network processing engine  902   b . For example, the neural network processing engine  902   b  may need less than all of the space in the memory subsystem  904   b  to store the weights for a neural network. Alternatively, as another example, the neural network processing engine  902   b  may have been designated as obtaining weight values only or primarily from DRAM  930  (e.g., the neural network that the neural network processing engine  902   b  is executing has a high degree of weight reuse). 
     In various implementations, the available memory in the second neural network processing engine  902   b  can be used to store weights  906  for a neural network that is being executed by the first neural network processing engine  902   a . The weights  906  for the neural network may be, for example, too numerous to store entirely in the memory subsystem  904   a  of the first neural network processing engine  902   a . As noted previously, the weights  906  that do not fit in the first neural network processing engine  902   a  can be stored in DRAM  930 . Storing these weights in the available space of the second neural network processing engine  902   b  can be much more efficient, however, since copying weights  906  from one neural network processing engine  902   b  to another neural network processing engine  902   a  can be done much faster than reading the weights  906  from DRAM  930 . 
     As discussed above, the weights  906  can be copied from the second neural network processing engine  902   b  to the first neural network processing engine  902   a  as the first neural network processing engine  902   a  is processing a set of input data. In some cases, used-and-no-longer-needed weights  906  can be moved from the first neural network processing engine  902   a  to the second neural network processing engine  902   b  until the processing of the input data is complete. In various implementations, a DMA engine  946   a - 946   d  can copy or move data between the neural network processing engines  902   a - 902   n , so that the neural network processing engines  902   a - 902   n  need not take time away from executing computations for the neural networks. 
     Any space in the memory subsystem  904   b  of the second neural network processing engine  902   b  that is not used to store weights  906  for the first neural network processing engine  902   a  can be used by the neural network processing engine  902   b  to perform its own computations. 
     In some implementations, instead of moving weights between the neural network processing engines  1002   a - 1002   n , an in-progress computation can be moved instead.  FIG. 10  illustrates an example where of a neural network processor  1000  that has been configured for the weights  1006  of a neural network to be stored in the memory subsystems of two neural network processing engines  1002   a - 1002   b . The neural network processor  1000  can be similar to the neural network processor illustrated in  FIG. 8 . As in the example of  FIG. 9 , in the example of  FIG. 10 , the weights  1006  for a neural network are stored in the memory subsystems  1004   a - 1004   b  of two neural network processing engines  1002   a - 1002   b , possibly because the amount of memory needed to store all the weights  1006  on-chip is more than the amount of memory of any one neural network processing engine  1002   a - 1002   n.    
     As noted previously, the weights  1006  can be associated with specific layers of a neural network. Thus, weights  1006  for a first set of layers can be stored in the first neural network processing engine  1002   a  and the weights  1006  for the remaining layers can be stored in the neural network processing engine  1002   b.    
     In various implementations, when input data is received for the neural network associated with the weights  1006 , the input data can be provided to the first neural network processing engine  1002   a , since the first neural network processing engine  1002   a  has the weights for the initial layers of the neural network. The first neural network processing engine  1002   a  can proceed to process the input data, reading weights  1006  from the memory subsystem  1004   a , computing intermediate results with the processing engine array  1010   a , and writing the intermediate results back to the memory subsystem  1004   a.    
     Once the first neural network processing engine  1002   a  has executed computations for each layer for which the first neural network processing engine  1002   a  has weights, the first neural network processing engine  1002   a  can cause the in-progress computation to be moved to the second neural network processing engine  1002   b . Moving the in-progress computation can include moving state  1008  values. The state  1008  can include, for example, a set of intermediate results. In some examples, the state  1008  can further include identification of the last layer that was processed, control inputs for the processing engine array  1010   b , a state value for an activation function, and/or a state value for a pooling function, among other things. In various implementations, a DMA engine  1046   a - 1046   d  can be engaged to copy state  1008  values from the first neural network processing engine  1002   a  to the second neural network processing engine  1002   b.    
     In various implementations, once the state  1008  has been copied to the second neural network processing engine  1002   b , the neural network processing engine  1002   b  can receive a signal to resume the in-progress computation. The signal can take the form of, for example, an interrupt, a write to a register in the second neural network processing engine  1002   b , or an instruction sent over a control bus between the neural network processing engines  1002   a - 1002   n , among other examples. In some cases, the second neural network processing engine  1002   b  can automatically start computation. For example, intermediate results can be input in the same manner as input data, thus activating the same mechanism in the second neural network processing engine  1002   b  that would be activated for input data. 
     In various implementations, resuming an in-progress computation can include inputting weights  1006  from a middle layer into the processing engine array  1010   b , along with intermediate results from the first neural network processing engine  1002   a . In various implementations, the neural network processing engine  1002   b  does not require any special or different behavior for resuming an in-progress computation, either because the neural network processing engine  1002   b  can treat the in-progress computation as the start of a new computation, or because the neural network processing engine  1002   b  can pick up exactly where the first neural network processing engine  1002   a  left off. 
     In the examples of  FIGS. 9 and 10 , solutions are provided for when all of the weights for a neural network cannot be kept in the local memory of a processing engine array. Though some latency can be incurred in moving data between neural network processing engines, this latency will still be quite small compared to the latency incurred when reading weights from off-chip memory. 
       FIG. 11  illustrates another solution for storing all the weights for a neural network on-chip when all of the weights cannot be stored local to a single processing engine array.  FIG. 11  illustrates an example of a neural network processing system  1100  that includes two neural network processors  1101   a - 1101   b . In this example, each neural network processor  1101   a - 1101   b  is a separate chip, having separate dies and being enclosed in different packages. The neural network processors  1101   a - 1101   b  can communicate with each other and other components in the neural network processing system  1100  using a host bus or processor bus. The processor bus can be implemented using, for example, a PCI-based protocol. 
     In various implementations, each of the neural network processors  1101   a - 1101   b  include at least one, and possibly more, neural network processing engines  1102   a - 1102   b . As discussed above, each of the neural network processing engines  1102   a - 1102   b  can include a processing engine array  1010   a - 1010   b  and a memory subsystem  1104   a - 1104   b.    
     For communications between the neural network processing engines  1102   a - 1102   b  and other components in each neural network processor  1101   a - 1101   b , the neural network processors  1101   a - 1101   b  can include a chip interconnect  1020   a - 1020   b . The chip interconnect  1020   a - 1020   b  can include primarily wiring for routing signals between the components of the neural network processors  1101   a - 1101   b , and possibly also some timing logic. 
     Other components of the neural network processors  1101   a - 1101   b  can include a PCI controller  1144   a - 1144   b  for communicating with the processor bus. In various implementations, the neural network processors  1101   a - 1101   b  can include components not illustrated, such as DRAM and DMA controllers. 
     In the example of  FIG. 11 , the weights  1106  for a neural network can be divided in two, with the two parts being the same in size or different in size. The first set of weights  1106 , corresponding to the initial layers of the neural network can be loaded into the memory subsystem  1104   a  of the neural network processing engine  1102   a  in the first neural network processors  1101   a . The second set of weights  1106  can be loaded into the memory subsystem  1104   b  of the neural network processing engine  1102   b  in the second neural network processor  1101   b . In this configuration, when input data is received for the neural network, the input data can be provided to the neural network processing engines  1102   a  in the first neural network processor  1101   a . The neural network processing engines  1102   a  can proceed with computations for the input data. 
     Once the neural network processing engine  1102   a  has executed computations for each of the layers for which the neural network processing engine  1102   a  has weights  1106 , the neural network processing engine  1102   a  can cause the in-progress computation to be transferred to the neural network processing engine  1102   b  in the second neural network processor  1101   b . For example, the neural network processing engine  1102   a  can instruct a DMA engine to copy the state  1108  of the computation to PCI controller  1144   a , where the state  1108  can include intermediate results, among other things. In this example, the PCI controller  1144   a  can generate one or more writes to the second neural network processor  1101   b , where the writes include the state  1108  values. In some implementations, the first neural network processor  1101   a  can write directly into the memory subsystem  1104   b  of the neural network processing engine  1102   b . In some implementations, the state  1108  data is cached by the PCI controller  1144   b  in the second neural network processor  1101   b . In these implementations, a DMA engine, for example, can move the state  1108  data from the PCI controller  1144   b  to the neural network processing engine  1102   b.    
     Once the state  1108  has been loaded into the memory subsystem  1104   b  of the neural network processing engine  1102   b  in the second neural network processor  1101   b , the neural network processing engine  1102   b  can resume the in-progress computation. In some examples, the first neural network processor  1101   a  triggers the second neural network processing engine  1102   b  by generating an interrupt to the second neural network processor  1101   b  or by writing a value to a register in the second neural network processor  1101   b . Once the neural network processing engine  1102   b  has computed the final result, the second neural network processor  1101   b  can output the result. 
     In the example of  FIG. 11 , all of the weights  1106  for a neural network are stored local to a processing engine array  1010   a - 1010   b , so that the neural network processors  1101   a - 1101   b  can avoid having to read processor memory to obtain the weights  1106 . Some delay is incurred in transferring the state  1108  between the neural network processors  1101   a - 1101   b , but the delay may still be much less than the delay caused by multiple reads to processor memory. 
     In various implementations, the examples illustrated in  FIG. 10  and  FIG. 11  can be combined in various ways. For example, processing a set of input data can begin in one neural network processing engine, and can be transferred to a second neural network processing engine in the same neural network processor. The in-progress computation can then be transferred from the second neural network processing engine to a third, where the third neural network processing engine is in a different neural network processor. Various configurations are possible to enable all the weights for a neural network to be stored on-chip, and for reads from processor memory to be minimized or eliminated. 
       FIG. 12  illustrates an example of a process  1200  that can be executed by a neural network processor when the neural network processor is executing a neural network. 
     At step  1202  the process  1200  includes storing a set of weight values in a plurality of memory banks of a neural network processing circuit, wherein the neural network processing circuit includes an array of processing engines on a same die as the plurality of memory banks, and wherein the set of weight values are stored prior to receiving input data. In various implementations, the neural network processing circuit is part of a neural network processor. In some examples, the set weight values include all weight values for the neural network. 
     At step  1204 , the process  1200  includes receiving input data. In various examples, the input data can be an image, an audio signal, a string of text, a sequence of numbers, or some other input. 
     At step  1206 , the process  1200  includes using the set of weight values to perform a task defined for the neural network. The task can include, for example, image identification, speech recognition, natural language processing, game play, etc. The weight values can have been previously determined through training, in which, for example, input data whose output result is known was input into the neural network. 
     Step  1206  can include further steps for performing the task. At step  1208 , performing the task includes reading weight values from the plurality of memory banks. In some examples, reading the weight values includes simultaneously reading a first weight value from a first memory bank from the plurality of memory banks and reading a second weight value from a second memory bank from the plurality of memory banks. 
     At step  1210 , performing the task can further include inputting the weight values and the input data into the array of processing engines. In some examples, the array of processing engines is a systolic array. In some examples, step  1210  can further include determining, using the array of processing engines, an intermediate result, and storing the intermediate result in a memory bank from the plurality of memory banks. In some examples, the intermediate result can be written at the same time that additional weight values are read. 
     At step  1212 , performing the task can further include computing a result using the array of processing engines, wherein the result corresponds to an outcome of performing the task. 
     In some implementations, the set of weight values stored in step  1202  include a first portion of all weight values for the neural network. In these implementations, the process  1200  can further include determining that the plurality of memory banks has available space. The available space may be from intermediate results requiring less memory space and/or from weight values that are no longer needed. The process  1200  can further include reading a second portion of all weight values for the neural network, wherein the second portion is read from an additional memory. In some examples, the additional memory can be associated with a second array of processing engines on the same die. In some examples, the additional memory can be off-chip. The process  1200  can further include writing the second portion to the available space. The second portion of weights can then be used to continue performing the task. 
       FIG. 13  illustrates an example of a process  1300  that can be executed by a neural network processor when the neural network processor is executing a neural network. 
     At step  1302 , the process  1300  includes storing a first set of weight values in a first set of memory banks of a neural network processing system. 
     At step  1304 , the process  1300  includes storing a second set of weight values in a second set of memory banks of the neural network processing system, wherein the first set of weight values and the second set of weight values comprise all weight values of a neural network, and wherein the first set of weight values and the second set of weight values are stored prior to input data being received by the neural network processing system. 
     At step  1306 , the process  1300  includes receiving input data. In various examples, the input data can be an image, an audio signal, a string of text, a sequence of numbers, or some other input. 
     At step  1308 , the process  1300  includes performing a task defined for the neural network. In various examples, the task correlates to a type of the input data (e.g. image recognition for an input image, speech recognition for an audio signal, etc.). 
     Step  1308  can include further steps for performing the task. At step  1310 , performing the task includes computing, using a first array of processing engines, an intermediate result, wherein the first array of processing engines is on a same first die as the first set of memory banks, and wherein the first array of processing engines uses the first set of weight values and the input data to compute the intermediate result. Computing the intermediate result can include simultaneously reading two or more weight values from the first set of memory banks. In some examples, the intermediate result reflects the outputs of one or more initial layers of the neural network. 
     At step  1312 , performing the task further includes copying the intermediate result and a state from the first set of memory banks to the second set of memory banks, wherein the state describes a stage of the task completed by the first array of processing engines. In some examples, when the intermediate result and the state are ready to be copied, the first array of processing has completed operations on the input data, and can begin operating on new input data. 
     At step  1314 , performing the task further includes computing, using a second array of processing engines, a final result, wherein the second array of processing engines is on a same second die as the second set of memory banks, wherein the second array of processing engines uses the second set of weight values, the intermediate result, and the state to compute the final result, and wherein the final result corresponds to an outcome of performing the task. Computing the final result can include simultaneously reading two or more weight values from the second set of memory banks. In some examples, the final result reflects the outputs of one or more final layers of the neural network. 
     In some examples, the first die, containing the first set of memory banks and the first array of processing engines, and the second die, containing the second set of memory banks and the second array of processing engines, are portions of a same die. The die can be for a neural network processor, where the neural network processer includes more than one neural network processing engine (e.g., where a neural network processing engine includes a set of memory banks and an array of processing engines). In some examples, the neural network processor can include an internal communication fabric, over which the intermediate result and state can be copied. 
     In some examples, the first die and the second die are each part of a different neural network processor, and thus reside in different packages. In these examples, a host bus can enable the two neural network processors to intercommunicate, including to copy the intermediate result and state from one to the other. 
     As noted in step  1304 , the first set of weight values and the second set of weight values can be all of the weight values for a neural network. This can mean that no weight values are read from a processor memory. The processor memory is in a different package than either the first die or the second die, and thus may have a significant read delay. 
       FIG. 14  illustrates an example of a process  1400  that can be executed by a computing system that includes a neural network processor. 
     At step  1402 , the process  1400  includes storing a first set of weight values for a first neural network, wherein the first neural network is configured to perform a first task, and wherein the first set of weight values are stored in a first portion of a memory in the neural network processor. The first set of weight values and the first task can be considered a first context. 
     At step  1404 , the process  1400  includes receiving first input data associated with the first task, wherein the first input data is received after storing of the first set of weight values. The first task is to be performed using the first input data as input. In various implementations, the first set of weight values are stored in the memory in advance of any input data being received. 
     At step  1406 , the process  1400  includes computing, using the neural network processor, a first result, wherein computing the first result includes using the first set of weight values and the first input data, wherein the first result corresponds to an outcome of performing the first task, and wherein, during computation of the first result, an intermediate result is stored in a second portion of the memory. The first portion and the second portion of the memory generally do not overlap. 
     At step  1408 , the process  1400  includes identifying, during computation of the first result, a third portion of the memory, wherein the third portion includes unused space in the memory. The unused space can include space formerly, but no longer, part of the first portion (e.g., the portion used to store the first set of weight values) and/or space formerly and no longer part of the second portion (e.g., the portion used to store the intermediate result). The third portion generally does not overlap with the first portion or the second portion. 
     At step  1410 , the process  1400  includes storing a second set of weight values in the third portion, wherein the second set of weight values are for a second neural network, wherein the second neural network is configured to perform a second task. In some cases, the second task is different from the first task. The second set of weight values can be stored before computation of the first result completes. 
     At step  1412 , the process  1400  includes receiving second input data associated with the second task. The second task is to be performed using the second input data as an input. 
     At step  1414 , the process  1400  includes computing, using the neural network processor, a second result, wherein computing the second result includes using the second set of weight of weight values and the second input data, wherein computation of the second result occurs upon completion of computation of the first result, and wherein the second result corresponds to an outcome of performing the second task. 
     In some implementations, the process  1400  can further include reducing a size of the first portion of the memory, wherein reduction in the size corresponds to weight values from the first set of weight values that are not needed to complete computation of the first result. The weight values that are not needed can include weight values that have already been used. Reducing the size of the first portion can include designating parts of the first portion as unused, and treating the unused parts as no longer part of the first portion. 
     In some implementations, the process  1400  can further include reducing a size of the second portion of the memory, wherein the size corresponds to an amount of memory needed to store the intermediate result. The amount of memory can decrease over the course of computing the first result. Reducing the size of the second portion can include designating parts of the second portion as no longer part of the second portion. 
     In some implementations, the first set of weight values includes fewer than all of the weight values for the first neural network. In these implementations, the process  1400  can further include reading an additional set of weight values for the first neural network from a second memory of the computing system. The second memory can be off-chip processor memory, an on-chip cache, and/or the memory of a second neural network processor. The process  1400  can further include storing the additional set of weight values in first portion of the memory, wherein the additional set of weight values are stored prior to storing the second set of weight values. 
       FIG. 15  illustrates a network  1500  in which the various examples discussed above can be used. The example network  1500  of  FIG. 15  includes various different types of network devices, such as nodes comprising the network device, switches and routers. In certain examples, the network  1500  may be based on a switched architecture with point-to-point links. As illustrated in  FIG. 15 , the network  1500  includes a plurality of switches  1104   a - 1104   d , which may be arranged in a network. In some cases, the switches are arranged in a multi-layered network, such as a Clos network. A network device that filters and forwards packets between local area network (LAN) segments may be referred to as a switch. Switches generally operate at the data link layer (layer 2) and sometimes the network layer (layer 3) of the Open System Interconnect (OSI) Reference Model and may support several packet protocols. Switches  1104   a - 1104   d  may be connected to a plurality of nodes  1102   a - 1102   h  and provide multiple paths between any two nodes. 
     The network  1500  may also include one or more network devices for connection with other networks  1508 , such as other subnets, LANs, wide area networks (WANs), or the Internet, and may be referred to as routers  1506 . Routers use headers and forwarding tables to determine the best path for forwarding the packets, and use protocols such as internet control message protocol (ICMP) to communicate with each other and configure the best route between any two devices. 
     In some examples, network(s)  1500  may include any one or a combination of many different types of networks, such as cable networks, the Internet, wireless networks, cellular networks and other private and/or public networks. Interconnected switches  1104   a - 1104   d  and router  1506 , if present, may be referred to as a switch fabric, a fabric, a network fabric, or simply a network. In the context of a computer network, terms “fabric” and “network” may be used interchangeably herein. 
     Nodes  1102   a - 1102   h  may be any combination of host systems, processor nodes, storage subsystems, and I/O chassis that represent user devices, service provider computers or third party computers. 
     User devices may include computing devices to access an application  1532  (e.g., a web browser or mobile device application). In some aspects, the application  1532  may be hosted, managed, and/or provided by a computing resources service or service provider. The application  1532  may allow the user(s) to interact with the service provider computer(s) to, for example, access web content (e.g., web pages, music, video, etc.). The user device(s) may be a computing device such as for example a mobile phone, a smart phone, a personal digital assistant (PDA), a laptop computer, a netbook computer, a desktop computer, a thin-client device, a tablet computer, an electronic book (e-book) reader, a gaming console, etc. In some examples, the user device(s) may be in communication with the service provider computer(s) via the other network(s)  1508 . Additionally, the user device(s) may be part of the distributed system managed by, controlled by, or otherwise part of the service provider computer(s) (e.g., a console device integrated with the service provider computers). 
     The node(s)  1102   a - 1102   h  of  FIG. 15  may also represent one or more service provider computers. One or more service provider computers may provide a native application that is configured to run on the user devices, which user(s) may interact with. The service provider computer(s) may, in some examples, provide computing resources such as, but not limited to, client entities, low latency data storage, durable data storage, data access, management, virtualization, cloud-based software solutions, electronic content performance management, and so on. The service provider computer(s) may also be operable to provide web hosting, databasing, computer application development and/or implementation platforms, combinations of the foregoing or the like to the user(s). In some embodiments, the service provider computer(s) may be provided as one or more virtual machines implemented in a hosted computing environment. The hosted computing environment may include one or more rapidly provisioned and released computing resources. These computing resources may include computing, networking and/or storage devices. A hosted computing environment may also be referred to as a cloud computing environment. The service provider computer(s) may include one or more servers, perhaps arranged in a cluster, as a server farm, or as individual servers not associated with one another and may host the application  1532  and/or cloud-based software services. These servers may be configured as part of an integrated, distributed computing environment. In some aspects, the service provider computer(s) may, additionally or alternatively, include computing devices such as for example a mobile phone, a smart phone, a personal digital assistant (PDA), a laptop computer, a desktop computer, a netbook computer, a server computer, a thin-client device, a tablet computer, a gaming console, etc. In some instances, the service provider computer(s), may communicate with one or more third party computers. 
     In one example configuration, the node(s)  1102   a - 1102   h  may include at least one memory  1518  and one or more processing units (or processor(s)  1520 ). The processor(s)  1520  may be implemented in hardware, computer-executable instructions, firmware, or combinations thereof. Computer-executable instruction or firmware implementations of the processor(s)  1520  may include computer-executable or machine-executable instructions written in any suitable programming language to perform the various functions described. 
     In some instances, the hardware processor(s)  1520  may be a single core processor or a multi-core processor. A multi-core processor may include multiple processing units within the same processor. In some embodiments, the multi-core processors may share certain resources, such as buses and second or third level caches. In some instances, each core in a single or multi-core processor may also include multiple executing logical processors (or executing threads). In such a core (e.g., those with multiple logical processors), several stages of the execution pipeline and also lower level caches may also be shared. 
     The memory  1518  may store program instructions that are loadable and executable on the processor(s)  1520 , as well as data generated during the execution of these programs. Depending on the configuration and type of the node(s)  1102   a - 1102   h , the memory  1518  may be volatile (such as RAM) and/or non-volatile (such as ROM, flash memory, etc.). The memory  1518  may include an operating system  1528 , one or more data stores  1530 , one or more application programs  1532 , one or more drivers  1534 , and/or services for implementing the features disclosed herein. 
     The operating system  1528  may support nodes  1102   a - 1102   h  basic functions, such as scheduling tasks, executing applications, and/or controller peripheral devices. In some implementations, a service provider computer may host one or more virtual machines. In these implementations, each virtual machine may be configured to execute its own operating system. Examples of operating systems include Unix, Linux, Windows, Mac OS, iOS, Android, and the like. The operating system  1528  may also be a proprietary operating system. 
     The data stores  1530  may include permanent or transitory data used and/or operated on by the operating system  1528 , application programs  1532 , or drivers  1534 . Examples of such data include web pages, video data, audio data, images, user data, and so on. The information in the data stores  1530  may, in some implementations, be provided over the network(s)  1508  to the nodes  1102   a - 1102   h . In some cases, the data stores  1530  may additionally or alternatively include stored application programs and/or drivers. Alternatively or additionally, the data stores  1530  may store standard and/or proprietary software libraries, and/or standard and/or proprietary application user interface (API) libraries. Information stored in the data stores  1530  may be machine-readable object code, source code, interpreted code, or intermediate code. 
     The drivers  1534  include programs that may provide communication between components in a node. For example, some drivers  1534  may provide communication between the operating system  1528  and additional storage  1522 , network device  1524 , and/or I/O device  1526 . Alternatively or additionally, some drivers  1534  may provide communication between application programs  1532  and the operating system  1528 , and/or application programs  1532  and peripheral devices accessible to the service provider computer. In many cases, the drivers  1534  may include drivers that provide well-understood functionality (e.g., printer drivers, display drivers, hard disk drivers, Solid State Device drivers). In other cases, the drivers  1534  may provide proprietary or specialized functionality. 
     The service provider computer(s) or servers may also include additional storage  1522 , which may include removable storage and/or non-removable storage. The additional storage  1522  may include magnetic storage, optical disks, solid state disks, flash memory, and/or tape storage. The additional storage  1522  may be housed in the same chassis as the node(s)  1102   a - 1102   h  or may be in an external enclosure. The memory  1518  and/or additional storage  1522  and their associated computer-readable media may provide non-volatile storage of computer-readable instructions, data structures, program modules, and other data for the computing devices. In some implementations, the memory  1518  may include multiple different types of memory, such as SRAM, DRAM, or ROM. 
     The memory  1518  and the additional storage  1522 , both removable and non-removable, are examples of computer-readable storage media. For example, computer-readable storage media may include volatile or non-volatile, removable or non-removable media implemented in a method or technology for storage of information, the information including, for example, computer-readable instructions, data structures, program modules, or other data. The memory  1518  and the additional storage  1522  are examples of computer storage media. Additional types of computer storage media that may be present in the node(s)  1102   a - 1102   h  may include, but are not limited to, PRAM, SRAM, DRAM, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, solid state drives, or some other medium which can be used to store the desired information and which can be accessed by the node(s)  1102   a - 1102   h . Computer-readable media also includes combinations of any of the above media types, including multiple units of one media type. 
     Alternatively or additionally, computer-readable communication media may include computer-readable instructions, program modules or other data transmitted within a data signal, such as a carrier wave or other transmission. However, as used herein, computer-readable storage media does not include computer-readable communication media. 
     The node(s)  1102   a - 1102   h  may also include I/O device(s)  1526 , such as a keyboard, a mouse, a pen, a voice input device, a touch input device, a display, speakers, a printer, and the like. The node(s)  1102   a - 1102   h  may also include one or more communication channels  1536 . A communication channel  1536  may provide a medium over which the various components of the node(s)  1102   a - 1102   h  can communicate. The communication channel or channels  1536  may take the form of a bus, a ring, a switching fabric, or a network. 
     The node(s)  1102   a - 1102   h  may also contain network device(s)  1524  that allow the node(s)  1102   a - 1102   h  to communicate with a stored database, another computing device or server, user terminals and/or other devices on the network(s)  1500 . 
     In some implementations, the network device  1524  is a peripheral device, such as a PCI-based device. In these implementations, the network device  1524  includes a PCI interface for communicating with a host device. The term “PCI” or “PCI-based” may be used to describe any protocol in the PCI family of bus protocols, including the original PCI standard, PCI-X, Accelerated Graphics Port (AGP), and PCI-Express (PCIe) or any other improvement or derived protocols that are based on the PCI protocols discussed herein. The PCI-based protocols are standard bus protocols for connecting devices, such as a local peripheral device to a host device. A standard bus protocol is a data transfer protocol for which a specification has been defined and adopted by various manufacturers. Manufacturers ensure that compliant devices are compatible with computing systems implementing the bus protocol, and vice versa. As used herein, PCI-based devices also include devices that communicate using Non-Volatile Memory Express (NVMe). NVMe is a device interface specification for accessing non-volatile storage media attached to a computing system using PCIe. For example, a bus interface module may implement NVMe, and the network device  1524  may be connected to a computing system using a PCIe interface. 
     A PCI-based device may include one or more functions. A “function” describes operations that may be provided by the network device  1524 . Examples of functions include mass storage controllers, network controllers, display controllers, memory controllers, serial bus controllers, wireless controllers, and encryption and decryption controllers, among others. In some cases, a PCI-based device may include more than one function. For example, a PCI-based device may provide a mass storage controller and a network adapter. As another example, a PCI-based device may provide two storage controllers, to control two different storage resources. In some implementations, a PCI-based device may have up to eight functions. 
     In some implementations, the network device  1524  may include single-root I/O virtualization (SR-IOV). SR-IOV is an extended capability that may be included in a PCI-based device. SR-IOV allows a physical resource (e.g., a single network interface controller) to appear as multiple resources (e.g., sixty-four network interface controllers). Thus, a PCI-based device providing a certain functionality (e.g., a network interface controller) may appear to a device making use of the PCI-based device to be multiple devices providing the same functionality. The functions of an SR-IOV-capable storage adapter device may be classified as physical functions (PFs) or virtual functions (VFs). Physical functions are fully featured functions of the device that can be discovered, managed, and manipulated. Physical functions have configuration resources that can be used to configure or control the storage adapter device. Physical functions include the same configuration address space and memory address space that a non-virtualized device would have. A physical function may have a number of virtual functions associated with it. Virtual functions are similar to physical functions, but are light-weight functions that may generally lack configuration resources, and are generally controlled by the configuration of their underlying physical functions. Each of the physical functions and/or virtual functions may be assigned to a respective thread of execution (such as for example, a virtual machine) running on a host device. 
     As part of a suite of capabilities, in various examples, one or more of the nodes  1102   a - 1102   h  can include a neural network processing engine and/or a neural network processor, various examples of which are discussed above. In these examples, the nodes  1102   a - 1102   h  equipped so equipped can be optimized for machine learning and neural network processing tasks. 
     The modules described herein may be software modules, hardware modules or a suitable combination thereof. If the modules are software modules, the modules can be embodied on a non-transitory computer readable medium and processed by a processor in any of the computer systems described herein. It should be noted that the described processes and architectures can be performed either in real-time or in an asynchronous mode prior to any user interaction. The modules may be configured in the manner suggested in  FIG. 15 , and/or functions described herein can be provided by one or more modules that exist as separate modules and/or module functions described herein can be spread over multiple modules. 
     The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the disclosure as set forth in the claims. 
     Other variations are within the spirit of the present disclosure. Thus, while the disclosed techniques are susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the disclosure to the specific form or forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the disclosure, as defined in the appended claims. 
     The use of the terms “a” and “an” and “the” and similar referents in the context of describing the disclosed embodiments (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. The term “connected” is to be construed as partly or wholly contained within, attached to, or joined together, even if there is something intervening. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate embodiments of the disclosure and does not pose a limitation on the scope of the disclosure unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the disclosure. 
     Disjunctive language such as the phrase “at least one of X, Y, or Z,” unless specifically stated otherwise, is intended to be understood within the context as used in general to present that an item, term, etc., may be either X, Y, or Z, or any combination thereof (e.g., X, Y, and/or Z). Thus, such disjunctive language is not generally intended to, and should not, imply that certain embodiments require at least one of X, at least one of Y, or at least one of Z to each be present. 
     Various embodiments of this disclosure are described herein, including the best mode known to the inventors for carrying out the disclosure. Variations of those embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate and the inventors intend for the disclosure to be practiced otherwise than as specifically described herein. Accordingly, this disclosure includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the disclosure unless otherwise indicated herein or otherwise clearly contradicted by context.