Patent Publication Number: US-11645041-B2

Title: Processing core with data associative adaptive rounding

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/573,728 filed Sep. 17, 2019, which claims the benefit of U.S. Provisional Patent Application No. 62/738,286 filed Sep. 28, 2018, both of which are incorporated by reference herein in their entirety for all purposes. 
    
    
     BACKGROUND 
     The recent surge in the performance of machine intelligence systems is not due to the development of revolutionary new algorithms. Indeed, the core algorithms used in machine intelligence applications today stem from a body of work that is now over half a century old. Instead, it has been improvements in the hardware and software that implement machine intelligence algorithms in an efficient manner that has fueled the recent surge. Algorithms that were once too computationally intensive to implement in a useful manner with even the most sophisticated of computers can now be executed with specialized hardware on an individual user&#39;s smart phone. The improvements in hardware and software take various forms. For example, graphical processing units traditionally used to process the vectors used to render polygons for computer graphics have been repurposed in an efficient manner to manipulate the data elements used in machine intelligence processes. As another example, certain classes of hardware have been designed from the ground-up to implement machine intelligence algorithms by using specialized processing elements such as systolic arrays. Further advances have centered around using collections of transistors and memory elements to mimic, directly in hardware, the behavior of neurons in a traditional artificial neural network (ANN). There is no question that the field of machine intelligence has benefited greatly from these improvements. However, despite the intense interest directed to these approaches, machine intelligence systems still represent one of the most computationally and energy intensive computing applications of the modern age and present a field that is ripe for further advances. 
     The reason machine intelligence applications are so resource hungry is that the data structures being operated on are generally very large, and the number of discrete primitive computations that must be executed on each of the data structures are likewise immense. A traditional ANN takes in an input vector, conducts calculations using the input vector and a set of weight vectors, and produces an output vector. Each weight vector in the set of weight vectors is often referred to as a layer of the network, and the output of each layer serves as the input to the next layer. In a traditional network, the layers are fully connected, which requires every element of the input vector to be involved in a calculation with every element of the weight vector. Therefore, the number of calculations involved increases with a power law relationship to the size of each layer. Furthermore, this aspect of machine intelligence algorithms makes them difficult to parallelize because the calculations for each layer depend on the output of the prior layer. 
     The problems mentioned in the prior paragraph are further exacerbated by modern ANNs. Modern ANN approaches are often referred to in the industry and literature as “deep learning” approaches. This is often a reference to the substantial number of layers involved, or the complexity of the relationships between the outputs of one layer and the inputs of the other layers. For example, in a modern deep learning ANN, the outputs of a downstream layer could be fed back to a prior layer which thereby adds a recursive element to the overall computation. Both the increase in layers, and the additional complexity associated with recursive relationships between the layers, increase the computational resources needed to implement a modern ANN. 
       FIG.  1    illustrates a directed graph  100  for the computation of a modern machine intelligence system. The input to directed graph  100  is an input tensor X. The output of directed graph  100  is an output tensor Y. The input could be an encoding for a picture, such as an image of a cat  101 . In this example, execution of directed graph  100  involves the graph providing an encoding of a textual guess as to what the content of the encoded image contained. The graph output can be referred to as an inference generated by the directed graph because the machine intelligence system is effectively inferring what the picture shows from the encoding of the picture. As such, if directed graph  100  represented a properly trained machine intelligence system, execution of graph  100  with input tensor X would produce an output tensor Y which encoded the word “CAT” as illustrated. 
     The edges of directed graph  100  represent calculations that must be conducted to execute the graph. In this example, the graph is broken into two sections-a convolutional section  102  and a fully connected section  103 . The convolutional portion can be referred to as a convolutional neural network (CNN). The vertices in the directed graph of CNN  102  form a set of layers which includes layers  106 ,  107 , and  108 . The layers each include sets of tensors such as tensors  109 ,  110 , and  111 . The vertices in the directed graph of fully connected section  103  also form a set of layers which includes layers  112  and  113 . Each edge in directed graph  100  represents a calculation involving the origin vertex of the edge. In CNN  102 , the calculations are convolutions between the origin vertex and a filter. Each edge in CNN  102  is associated with a different filter F 11 , F n1 , F 12 , F n2  etc. As illustrated, filter F 12  and tensor  109  are subjected to a full convolution to generate one element of tensor  111 . Filter F 12  is “slid around” tensor  109  until a convolution operation has been conducted between the filter and the origin vertex. In other approaches, filter F 12  and a portion of tensor  109  are multiplied to generate one element of tensor  111  and the full convolution is used to generate multiple elements of tensor  111 . In fully connected section  103 , the calculations are multiplications between a set of weights and the values from the prior layer. In fully connected section  103 , each edge is associated with a unique weight value that will be used in the calculation. For example, edge  114  represents a multiplication between weight w n  and input value  115 . The value of element  116  is the sum of a set of identical operations involving all the elements of layer  112  and a set of weight values that uniquely correspond to the origin vertex of each edge that leads to element  116 . 
     Execution of directed graph  100  involves many calculations. In the illustration, dots are used in the vertical directions to indicate the large degree of repetition involved in the directed graph. Furthermore, directed graph  100  represents a relatively simply ANN, as modern ANNs can include far more layers with far more complex interrelationships between the layers. Although not illustrated by directed graph  100 , the outputs of one layer can loop back to be the inputs of a prior layer to form what is often referred to as a recursive neural network (RNN). The high degree of flexibility afforded to a machine intelligence system by having numerous elements, along with an increase in the number of layers and complexity of their interrelationships, makes it unlikely that machine intelligence systems will decrease in complexity in the future. Therefore, the computational complexity of machine intelligence systems is likely to increase in the future rather than diminish. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    illustrates a directed graph of an artificial neural network in accordance with the related art. 
         FIG.  2    illustrates a directed graph of an artificial neural network generating two different inferences from two different inputs in accordance with the related art. 
         FIG.  3    is a block diagram of a processing core that is in accordance with specific embodiments of the present invention. 
         FIG.  4    is a flow chart of a method for executing a directed graph using a processing core that is in accordance with specific embodiments of the present invention. 
         FIG.  5    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between directed graph data and a threshold. 
         FIG.  6    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a threshold. 
         FIG.  7    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a value used to calculate a threshold using that same directed graph data. 
         FIG.  8    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a threshold. 
         FIG.  9    is a block diagram of a processing core connected to an external controller and a cache memory that is in accordance with specific embodiments of the present invention. 
         FIG.  10    is a block diagram of a processing core with an integrated compression and decompression system in the main data path that is in accordance with specific embodiments of the present invention. 
         FIG.  11    is a block diagram of a processing core with an integrated metadata generator in the main data path that is in accordance with specific embodiments of the present invention. 
     
    
    
     SUMMARY 
     Processing cores with data associative adaptive rounding and associated methods are disclosed herein. Certain processing cores disclosed herein can be beneficially applied towards the execution of directed graphs. Certain processing cores disclosed herein can be beneficially applied toward the execution of an artificial neural network (ANN) in which an inference is generated in response to an input to the ANN. In specific embodiments, the use of data associative rounding increases the computational efficiency and decreases the power consumption associated with generating an inference from an ANN using a processing core with all else held equal. The use of data associative rounding can allow the generated inference to maintain fidelity to an inference generated without rounding while at the same time decreasing the power and computational resource consumption of the processing core. 
     Certain processing cores disclosed herein are particularly amenable to use with sparse directed graphs which need to be accurately executed. An example of a sparse directed graph is one used to instantiate an ANN in which most of the computations involve zero or near-zero data values that will not have an appreciable impact on an inference generated from the ANN. However, rounding all the near-zero values in such an ANN will not result in an accurate execution because certain near-zero data values may have a dispositive impact on the inference generated by the ANN. Accordingly, it is generally insufficient to apply a blanket rule in which all near-zero data values are forced to zero to alleviate the computational complexity of generating an inference from an ANN as that approach will lead to the generation of approximated values that do not maintain enough fidelity to the appropriate inference. Instead, rounding can be applied in a pattern that is associated to the underlying data of the directed graph, such that computational resources and power resources are consumed to a minimal degree while the accuracy of the generated inferences is preserved. 
       FIG.  2    illustrates a single directed graph  200  generating separate inferences  210  and  220  from two different respective inputs  201  and  202 . As illustrated, directed graph  200  performs as desired in both instances and generates the inference “CAT” in response to a picture of a cat and the inference “DOG” in response to a picture of a dog. The directed graph is highlighted differently in the two instances. This highlighting is reflective of the fact that a single directed graph will have high levels of activation in different places based on the inputs provided. The highlighted paths through the directed graph illustrate the most important values computed during the execution of the graph. As illustrated, the output of the second layer includes a tensor  230  with important inference-dispositive activation in both executions and a tensor  231  with less important activation in both executions. Accordingly, a processing core that is configured to allow for the execution of directed graph  200  must take care to preserve the accuracy of the computations that generate the values of tensor  230  but may be able to let the accuracy of the computations that generated tensor  231  relax while still being able to generate the correct inference in both cases. As such, different levels of rounding can be associated with the directed graph data that is tensor  230  as compared to the directed graph data that is tensor  231 . 
     Certain processing cores disclosed herein apply data associative rounding by associating a threshold with directed graph data, and rounding a computation involving that directed graph data using the associated threshold. The processing core can associate the threshold and directed graph data in a myriad of ways as will be described via specific examples below in the detailed disclosure. As used herein, all the data used to instantiate, execute, and modify a directed graph can be referred to as “directed graph data.” In the specific case of ANNs, the directed graph data can include specific activations, weights, biases, or any intermediate results necessary for the drawing of an inference from or applying training to the network. As used herein, an association to directed graph data refers to the data structure in the directed graph as opposed to the actual values held by that data structure during any given execution of the directed graph. In specific processing cores disclosed herein, thresholds can be “associated” with directed graph data via the use of data stored in the processing core and/or in a cache memory that is randomly accessible to the processing core. The processing core can store a set of thresholds where each threshold in the set of thresholds is associated with a different unit of directed graph data. These thresholds can be programmatically set via an external controller. The processing core can also store a set of values used to calculate the thresholds internally to the operation of the processing core where each value in the set of values is associated with a different unit of directed graph data. These values can be programmatically set via an external controller. 
     In the specific case of a processing core executing a directed graph to generate an inference from an ANN, the processing core can be configured such that the weights and/or filters of the ANN are stored within the registers on the processing core and/or be available to a cache memory of the processing core via random memory access. In keeping with the same example, the processing core can be configured to store the data necessary to support the associations and apply thresholds when necessary in the registers on the processing core and/or in that same cache memory. In specific embodiments, the thresholds and associations can be programmatically provided to the internal memory locations or the cache memory via an external controller. 
     In specific embodiments of the invention, a processing core is provided. The processing core comprises a processing cluster configured to generate a value for a unit of directed graph data using input directed graph data. The processing core also includes a core controller configured to load a threshold value into a threshold register when the value for the unit of directed graph data is loaded into a data register. The processing core also includes a comparator coupled to the threshold register and the data register and configured to generate a comparator output based on: (i) the threshold value in the threshold register; and (ii) the value for the unit of directed graph data in the data register. The processing core also includes a rounding circuit: (i) configured to receive the value for the unit of directed graph data from the processing cluster; and (ii) configured to conditionally round the value for the unit of directed graph data based on the comparator output from the comparator. 
     In specific embodiments of the invention, a method is provided. The method comprises associating, in a processing core, a threshold with a unit of directed graph data. The directed graph data being from a directed graph. The method also comprises executing, using the processing core, the directed graph. The method also comprises generating, while executing the directed graph and using a processing cluster in the processing core, a value for the unit of directed graph data. The method also comprises generating a comparison of the value of the unit of directed graph data and the threshold. The method also comprises conditionally rounding, based on the comparison and using a rounding circuit in the processing core, the value of the unit of directed graph data. 
     In specific embodiments of the invention, a processing core is provided. The processing core comprises a means for associating a threshold value and a unit of directed graph data according to an association, a means for generating a value for the unit of directed graph data using input directed graph data, a means for generating a comparison of the threshold value and the value for the unit of directed graph data using the association, and a means for conditionally rounding the value for the unit of directed graph data based on the comparison. 
     DETAILED DESCRIPTION 
     Specific methods and systems associated with a processing core with data associative adaptive rounding in accordance with the summary above are provided in this section. The methods and systems disclosed in this section are nonlimiting embodiments of the invention, are provided for explanatory purposes only, and should not be used to constrict the full scope of the invention. 
     Processing core  300  in  FIG.  3    can be used to describe the operation of specific embodiments of the invention. The processing core includes a core controller  301 , a control connection  302 , and at least two memory connections  303  and  304 . The memory can be an external cache memory such that the memory connections are cache memory connections. The controller can be an external controller such that the control connection is an external controller connection. The core controller  301  can receive instructions via the control connection  302 . The instructions can include input data and the identification of a kernel. For example, during the execution of an ANN in response to a set of input data “input_1” and having a first layer of weights “weight_layer_1,” the control connection could receive an instruction in the form of: {conv, input_1, weights_layer_1}. Input data that is supplied to the input of a directed graph can be referred to herein as input directed graph data, where the set of input data “input_1” is a set of input directed graph data including multiple entries of directed graph data with particular values. The kernel for a convolution operation “conv” can then be accessed from an external memory by the core controller and used to form the instruction thread  305  for the processing core. Here “conv” refers to a convolution between input_1 and weights_layer_1 and serves as the kernel identifier for the kernel that will execute the convolution operation. The instruction can include the address of input_1 and weights_layer_1 in a memory or it can include the values themselves. The instructions could thereby involve a convolution between the input data to an ANN and the first layer of data that comprises the network. The thread  305  can then be used to administrate the main data path  306  of the processing core to execute that convolution. In this example, the thread  305  will result in the value output_layer_1 being generated by the main data path  306  and stored in a cache memory. 
     The main data path  306  of the processing core can involve fetching data from a memory connection  303 , loading it into the source memory  307  of a processing cluster  308 , conducting the processing, and storing the output in a destination memory. The source memory  307  and destination memory  309  can be registers that are integrated with the processing cluster. The memory from which the input data is retrieved and the output data is stored could be the same memory and could be an external cache memory that is amenable to random access. The processing cluster  308  can comprise the main computational units of the processing core. Examples of such computational units include arithmetic logic units (ALUs) and other logic blocks. As used herein, the term “ALU” is meant to refer to circuit blocks that operate on fixed point data elements as well as floating point units (FPUs) that operated on floating point data elements. In keeping with the example in the prior paragraph, the values for input_1 and weights_layer_1 could be retrieved from memory and the component values of those vectors could be provided to the processing cluster  308  in accordance with the instruction thread  305 . The connection between the core controller  301  and the circuit blocks of the main data path  306  can involve the provisioning of configuration data to the configuration registers of each block, the provisioning of instructions for computations, and the routing of metadata from and to the core controller  301  as will be described below. The output of the convolution of the input_1 and weight_layer_1 which we can refer to as output_layer_1 can then be stored in memory. 
     Processing core  300  includes a rounding block  310  that is downstream from the processing cluster  308  on the main data path  306 . The rounding block  310  can be configured to round specific values from the destination memory  309 . The rounding can be conducted according to a data associative rounding scheme. The values can be round down to zero. The values could alternatively be rounded to the nearest whole number, to one, to negative one, or to any other value or set of values that will simplify further downstream computations while maintaining the fidelity of the data path to an acceptable degree. In the context of a directed graph that instantiates an ANN, maintaining fidelity to an “acceptable degree” involves assuring that the same inference is generated by the ANN as would have been with data associative rounding disabled. In a specific embodiment of the invention, a subset of values generated during the execution of one layer of a directed graph will be rounded to zero to simplify further computations involved in the execution of subsequent layers of the directed graph. 
     In specific embodiments of the invention, a rounding block, such as rounding block  310 , can include a rounding circuit. The rounding circuit can include a comparator and round values based on a comparison produced by the comparator. The comparison can be a Boolean value and the value can be rounded to zero if the Boolean is true. The rounding block can apply a threshold and a value to the comparator to generate the comparison. The rounding block can round the value provided to the comparator based on the comparison. In specific embodiments of the invention, the specific threshold utilized by the rounding block can be associated with the data that is being evaluated. In keeping with the example above of a processing core executing a thread for the instruction {conv, input_1, weights_layer_1} the threshold could be associated with either the input_1 data structure or the weights_layer_1 data structure and could be applied to the rounding block to determine if the values in output_layer_1 should be rounded prior to storing output_layer_1 in memory. The association managed by the processing core could be with the data structure itself and not the values within the data structure. In other words, the same associated threshold could be applied to the rounding block whenever input data was provided to a given directed graph instantiated by the processing core, as opposed to whenever specific values were provided to the processing core. 
     In specific embodiments of the invention, the association between directed graph data and thresholds can take on numerous forms. The association can be between different units of directed graph data. For example, a single threshold can be associated with a data structure that holds a single data value, a data structure comprising a set of related data values within a vector or other tensor, a single plane of a multidimensional data structure, an entire tensor, a data tile used to hold one or more elements of directed graph data, an entire layer of a directed graph, or an entire graph. The association can also be between different types of directed graph data. For example, a single threshold can be associated with input data to the graph, an edge or node of the directed graph, or the output of the directed graph. In the example of a directed graph used to instantiate an ANN, the association can be with accumulation values, weight values, filter values, bias values, output values, input values, or any other data structure used or produced during the generation of an inference from the network. As will be apparent from examples below, the association between a threshold and a data structure can be an association with an operand to a computation while the rounding using the threshold is conducted on the output of that computation, or it can be an association between the output of the computation directly. In other words, an association can cause the processing core to apply a given threshold to round the output of any computation using a data structure or to any computation which produces the values for the data structure during an inference. 
     In specific embodiments of the invention, the thresholds can be provided to the processing core in various ways. For example, the thresholds could be provided programmatically to the processing core via an external controller. Once set, the threshold can be referred to as a programmatically selected threshold. The external controller and processing core could be configured to allow for the designation of associations between data structures and thresholds at the level of human readable source code to be compiled and implemented in the processing core as programmatically selected associations. Likewise, they could be configured to allow for the value of the thresholds, or equations used to derive those values, to be specified at the level of human readable source code to be compiled and implemented in the processing core as programmatically selected thresholds. The external controller could be a RISC controller able to receive PC commands that specify the associations and thresholds. The external controller could also provide the association in the form of an identification of the data to which the threshold should be associated. Alternatively, the external controller could store the threshold at a location in memory that the processing core had assigned to be related to a given unit of directed graph data such that the association was an inherent feature of the processor and the association was set by the external controller when loading a data value into that particular address. The thresholds could be stored in the memory of the core controller on-board the processing core, such as core controller  301 , or in an external cache memory available to the processing core. The external cache memory could be a random-access memory. The thresholds can also be stored in a metadata header along with the data structures to which they are associated. The processing core can thereby be configured to obtain the threshold as part of the ordinary course of obtaining values from the data structure with slight additional modifications to account for accessing threshold values from the header of the structure. For example, a data structure associated with input_data_1 could include a header, and a threshold to be applied to any computation in which input_data_1 was used could be stored in that header. As such, whenever input_data_1 was recalled from memory, the required threshold would also be retrieved as it was located in the packet header used to identify and recall the required values from memory. 
     The thresholds can take on various forms. The thresholds could be fixed numbers that are programmatically configured via an external controller. For example, an external controller could set a threshold of “100” and any value below “100” associated with the threshold could be rounded. The thresholds could also be adaptively derived based on the data values in the directed graph data structures. In these cases, the equations used to derive the threshold values could be programmatically configured via an external controller. For example, an external controller could set a value of “60” and the processing core would internally derive a threshold according to a series of equations based on a design which set the threshold to 60% of the maximum value of a set of data values. Alternatively, or in combination, the entirety, or a portion, of these equations could be configured in hardware on the rounding block. For example, a set of values provided from the destination memory of the core computation block could be evaluated by a series of logic gates to produce an average value of the set of values to be used as the threshold or be used to calculate the threshold. The rounding block could include different series of logic gates that could be programmatically applied to different data structures according to the associations. 
     In specific embodiments of the invention, thresholds can be adaptively derived to round values that are relatively insignificant with respect to the other values in the same unit of directed graph data. For example, the threshold could be derived as a programmatically defined fraction of the largest value in a set of data values in a given data structure (e.g., ¼ of the largest value in a vector of accumulation values produced during the execution of an ANN). These approaches can exhibit certain benefits when applied to the execution of ANNs in that the larger value in some data structures will dominate the effect of the smaller values in generating the inference. The equations used to derive a threshold can be more complex and can involve finding the maximum, mode, mean, median, or minimum in a given data structure. The equations can also involve determining a standard deviation of the data values, analyzing a histogram of the values, and conducting complex statistical analyses on the data values. The equations used to derive the threshold values and conduct these intermittent analyses can be programmatically defined, associated with a kernel accessible to the processing core, and/or implemented directly in hardware in the rounding block of the processing core. 
     In specific embodiments of the invention, thresholds can be adaptively derived to round values that are relatively insignificant with respect to the other values in a different unit of directed graph data. The relationship between these different units of directed graph data can also be programmatically defined as can the equation used to derive the threshold therefrom. For example, a threshold for the values in the outputs from layer two of a CNN can be set to ½ of the average filter values used to compute the outputs of layer two of the CNN. 
     In specific embodiments of the invention, the thresholds can be provided with reference to a particular aspect of a data value as opposed to its absolute logical value. Approaches in accordance with these embodiments exhibit certain benefits in terms of the efficiency of conducting the comparison between the threshold and the data value. For example, the threshold could be provided or derived with reference to the exponent value of a floating-point number in approaches in which the data values are stored as floating-point numbers. As such, the threshold could be a set number such as “8” and the comparison would involve a basic compare operation between the integer value “8” and the value stored in the exponent bits of the floating-point number. The benefit of this approach is that the entire data value does not need to be analyzed by the system and can indeed be entirely neglected. For example, the mantissa of a floating-point number does not need to be analyzed. At the same time, the exponent provides a good source of information concerning the relative impact that different data values may have on the execution of a directed graph such that in certain applications rounding by exponents can achieve the benefit of maintaining the fidelity of the execution of the directed graph while also minimizing the computational resource consumption of the execution. 
     The associations between data and thresholds can be applied during computation in various ways. For example, the core controller can store the thresholds in the instruction thread and apply the thresholds to a configuration register of the rounding block at the time the associated data values are being delivered from the destination memory of the processing cluster. In this sense, the association is applied via the timing of the main data path as orchestrated by the instruction thread. In these approaches, the threshold may be stored as a data value in the instruction thread and could be provided in unmodified form from the thread controller to a comparator in the rounding block when the data values to which it is being applied are delivered to an alternative input to the comparator. As another example, the threshold could be stored in memory for an entire data structure or subset thereof. The data structure could include a portion of directed graph data. The threshold value, or values, could then be pre-programmed by the core controller block before data is moved from the FPU cluster output and remain stable until data movement completed. The core controller could program one threshold for all the math results conducted, or it could be updated for each data structure or subset thereof. 
     In specific embodiments of the invention, rounding can be conducted at various points in a main data path. As illustrated in  FIG.  3   , rounding occurs in rounding block  310  immediately after the values are obtained from the computation cluster. Alternatively, a similar approach could be applied to round the values just prior to being provided to the main computation cluster, instead of just after as in  FIG.  3   . However, as described below, certain benefits accrue to approaches in which the values are rounded prior to storage as opposed to being stored in unrounded form and then rounded when they are recalled for use later. 
     The appropriate thresholds and associations can be selected to improve the efficiency of the processing core while maintaining the accuracy of an execution of the directed graph at an “acceptable level.” The appropriate thresholds and associations can be determined after a processing core is configured to execute a directed graph by feeding the directed graph with sets of input data that are tagged with the appropriate inference that should be generated by the directed graph. The training data can be used to modify the thresholds using a supervised machine learning approach. The thresholds and associations can be selected or solved for using any kind of iterative evaluation using known techniques for supervised learning. For example, the training data can be used to train a regression classifier which will be trained to determine a set of thresholds for the directed graph. In contrast to certain applications where obtaining large volumes of tagged input data is difficult, the processing core can generate its own training data by deactivating the rounding operation of the rounding block. The processing core can be placed in this state using a command provided by an external controller. The core can then either be fed a series of input data for which the “correct” outputs are derived from the execution of the directed graph. The inputs and derived outputs can then be combined to form a training data set. The obtained training data can then be used to set the thresholds and associations. Alternatively, the processing core can generate its training data in situ as the state of the processing core is continually switched between having rounding activated and deactivated while the processing core is being asked to execute new input data (i.e., tagged training data can be harvested while the processing core is operational and the rounding feature is turned off). 
       FIG.  4    provides a flow chart  400  of a set of methods for executing a directed graph on a processing core. The flow chart beings with a step  401  of associating a threshold with a unit of directed graph data. The step is illustrated by a data link between the identification of a layer of weights of an ANN “layer_1_weight” and a fixed value of 0.8. As mentioned above, the value 0.8 can either be the threshold itself or can be a value used to derive a threshold later. The step can be conducted by a means for associating including an external controller, a cache memory, and a core controller on the processing core. 
     The flow chart continues with a step  402  of executing the directed graph. Step  402  can involve executing a single-instruction involved with the execution of the entire directed graph. As illustrated, the instruction can be for a single convolution operation between an input to the directed graph and a layer of weights in the directed graph. The flow chart continues with a step  403  in which a value is generated using a unit of directed graph data. Step  403  can essentially be a sub-step of step  402  such that it is conducted as part of the instruction execution. In this case, the two units of directed graph data are “input” and “layer_1_weight” and the operation involves the convolution of the values of that directed graph data to produce the values for “layer_1_output.” Step  403  can be conducted by a means for generating a value such as the main computational cluster of the processing core under control of the core controller using operands obtained from a cache memory. 
     The flow chart continues with a step  404  in which a comparison value is generated. This step can involve the delivery of the output of step  403  and a threshold to the inputs of a comparator to produce a comparison on the output of that comparator. In a processing core, this can involve the delivery of directed graph data to a data register  410  and the delivery of a threshold to a threshold register  411 . The data can be kept temporarily in these registers until it is time to execute the comparison using a comparator  412  with access to those registers. The timing can be conducted by a controller of the processing core, such as core controller  301 , to assure that the comparator output  413  provided at any given time relates to the data currently being held for a potential rounding operation by the rounding circuit of the processing core, such as the rounding circuit in rounding block  310 . As illustrated, the threshold was associated with the operands used in step  403  and the associated threshold value is delivered to the comparator to be used in a comparison with the output of the operation in step  403 . However, as mentioned previously, the threshold could have alternatively been associated with the output data structure for which step  403  generated a value. Regardless, the value for the unit of directed graph data generated in step  403  will be provided to a comparator at the same time the associated threshold is provided to the comparator. Step  404  can be executed by a means for generating a comparison such as a comparator and a set of control elements that coordinate the delivery of the required values thereto including the core controller of the processing core. In specific approaches, the unit of directed graph data provided to the comparator is a portion of the operand or output of step  403 . For example, the unit of directed graph data could be an exponent of a fixed-point data value which was used or generated in step  403 . 
     The flow chart contains an optional step  405  in which a threshold is calculated. The threshold could be calculated based on the data values used or generated in step  403  and a prestored value. Variations of this approach are described above. In addition, the illustrated value of 0.8 might not be a fixed value but instead may be an equation or algorithm that does not depend on the execution of step  403  as does step  405 . As mentioned previously, the threshold can be derived from the values in data structures that are not involved in the current or recent actions of the processing unit. As such, step  405  can independently feed into step  404  as opposed to linking thereto from step  403 . The threshold can be generated using a set of entries in a data structure. Step  405  can be executed by a means for generating a threshold value such as the series of logic gates that are coupled to the destination memory of a processing cluster of the processing core referenced above and/or an external controller and a cache memory. 
     The flow chart continues with a step  406  in which a value is conditionally rounded based on the comparison generated in step  404 . The rounding can be conducted by a rounding circuit block that is configured to provide a rounded value in place of an original value. The rounding circuit can be in the main data pipeline of the processing core as shown in  FIG.  3   . The means for rounding can include a rounding block, such as rounding block  310 , and retrieve a value from a hardware memory, modify a received value, or link a particular circuit node to either ground or power to execute a rounding operation, where an input to the block is the value from step  403  as an input and the comparison from step  404  as a control signal. 
       FIGS.  5 - 8    are functional block diagrams that provide examples of the specific methods enabled and disclosed in  FIG.  4   . Block diagram  500  illustrates an association  501  formed between a unit of input directed graph data “Z” and a threshold “TH.” The association and values for Z and TH can all be available ex ante to the flow illustrated by block diagram  500 . Association  501  can take on any of the forms disclosed herein and can be created using any of the approaches disclosed herein. A controller of a processing core can utilize association  501  to assure that the value for TH is made available in threshold register  502  at the same time the value for Z is made available in data register  503 . The two values can then be compared using a comparator  504  in rounding block  505 . The comparator output  510  of the comparator  504  can then be used to control the operation of a rounding circuit  506  in rounding block  505 . As a result, the product of a computation involving values X and Y, as produced using computation unit  507 , will be conditionally rounded based on the prestored association  501  and the value TH. The association  501  is therefore used so that the threshold is applied whenever the value for the associated data structure is computed. With reference back to  FIG.  3   , rounding block  505  can serve in place of rounding block  310 , computation unit  507  can serve as part of processing cluster  308 , and the input data registers  508  and  509  can be part of source memory  307 . 
       FIG.  6    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a threshold. Block diagram  600  illustrates an association  601  formed between a unit of input directed graph data “X” and a threshold “TH.” The association and values for X and TH can all be available ex ante to the flow illustrated by block diagram  600 . Association  601  can take on any of the forms disclosed herein and can be created using any of the approaches disclosed herein. A controller of a processing core can utilize association  601  to assure that the value for TH is made available in threshold register  502  at the same time the value for Z is made available in data register  503 . The association  601  is therefore used differently than the association  501  in that the threshold is applied whenever the input directed graph data X is used as an input to a computation and is used to round the output of that computation. While differing in this regard,  FIGS.  5  and  6    are similar in that the threshold is not independently calculated (i.e., the optional step of calculating the threshold  405  in  FIG.  4    is not utilized in block diagrams  500  and  600 ). In contrast,  FIGS.  7  and  8    illustrate approaches in which step  405  is required to compute the threshold. 
       FIG.  7    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a value for calculating a threshold. Block diagram  700  illustrates an association  701  formed between a unit of input directed graph data “X” and a value “V.” Block diagram  700  includes an execution of step  405  in  FIG.  4    in that the threshold is not a prestored value. Instead, as illustrated, the value for data structure V is loaded into a register  703  and is used along with the value for data structure Z by computation block  702  to calculate a threshold value for data structure TH. The form of computation block  702  will depend upon the specific manner in which the threshold value is calculated. For example, the computation could involve a histogram of the values in data structure Z or a more basic calculation such as dividing the largest value in data structure Z in half, and the complexity of computation block  702  will be set to accommodate that calculation. The calculated value, as computed by computation block  702 , is then stored in threshold register  502 . The value for TH is then used to conditionally round the value of data structure Z using an approach similar to that of  FIGS.  5  and  6   . The association and values for X and V can all be available ex ante to the flow illustrated by block diagram  700 . Association  701  can take on any of the forms disclosed herein and can be created using any of the approaches disclosed herein. A controller of a processing core can utilize association  701  to assure that the calculated value for TH is made available in threshold register  502  at the same time the value for Z is made available in data register  503 . The association  701  is therefore used to assure that a customized rounding value based on the value of the output data Z is used to round the output data where the customized rounding is set by a value associated with input data X which is used to compute the value for data structure Z. In other embodiments of the invention, association  701  could instead have been between data structure Z and data structure V while the flow diagram would otherwise be the same as that illustrated in  FIG.  7   . 
       FIG.  8    is a functional block diagram for implementing specific methods disclosed in  FIG.  4    using an association between input directed graph data and a threshold. Block diagram  800  utilizes the same association  701  formed between a unit of input directed graph data “X” and a value “V” as in  FIG.  7   . Furthermore,  FIG.  8    can be modified in the same manner as  FIG.  7    such that the association could have been between data structure Z and data structure V while the flow diagram would otherwise be the same as that illustrated in  FIG.  8   . Block diagram  800  includes an execution of step  405  in  FIG.  4    in that the threshold is not a prestored value. Instead, as illustrated, the value for data structure V is loaded into a register  703  and is used along with the value for data structure X by a computation block  801  to calculate a threshold value for data structure TH. This is different than the approach in  FIG.  7    in that the input data to the computation is used to calculate the threshold as opposed to the output data. The form of computation block  801  will depend upon the specific manner in which the threshold value is calculated as in the example of computation block  702 . The calculated value is then stored in threshold register  502 . The value for TH is then used to conditionally round the value of data structure Z using an approach similar to that of  FIGS.  5  and  6   . The association and values for X and V can all be available ex ante to the flow illustrated by block diagram  700 . A controller of a processing core can utilize association  701  to assure that the calculated value for TH is made available in threshold register  502  at the same time the value for Z is made available in data register  503 . The association  701  is therefore used to assure that a customized rounding value based on the value of the unit of directed graph data X is used to round the output data. 
       FIG.  9    provides a block diagram of a processing core  300  that is connected to an external memory  900  and can receive control inputs from an external controller  901 . In this configuration, the processing core can receive command inputs by accessing a known location in memory  900  into which the external controller  901  loads commands. The external memory  900  can store directed graph data for execution by the processing core along with kernels for conducting that execution, the associations and thresholds disclosed herein, and other data required for the processing core&#39;s operation. In the illustrated case, external memory  900  is an L1 cache memory and external controller  901  is a reduced instruction set (RISC) controller. However, other kinds of memory and controllers could serve the same purpose as the illustrated components. An external controller such as external controller  901  can execute any of the method steps disclosed herein requiring an external controller. A memory such as memory  900  can be involved in any of the method steps disclosed herein requiring an external memory. A higher-level PC controller can have a connection to external controller  901  and an optional direct connection to core controller  301 . Memory  900  may be shared among multiple processing cores that cooperate to execute a directed graph in parallel. 
       FIG.  9    also illustrates flow diagram step  902  which can be a precursor step to step  401  in  FIG.  4   . Flow diagram step  902  involves an iterative machine learning technique for training the thresholds and associations required for the processing core  300  to optimize the execution of a directed graph. The training can be conducted via the PC controller mentioned above in combination with controller  901  and memory  900 . The training can involve the provisioning of test inputs to the controller  901 , and the ultimate programming of threshold values and associations to be stored in memory  900  and the configuration registers and other memory locations on processing core  300 . 
       FIG.  10    illustrates a processing core  1000  which includes decompression  1002  and compression  1001  blocks in the main data path. The decompression and compression blocks can limit the amount of processing and memory bandwidth resources that are consumed through the execution of a directed graph. The decompression and compression blocks can include compression circuits and decompression circuits for compressing binary data or execute compression at the scale of directed graph data values. In the case of a sparse directed graph, reducing the size of the data structures that need to be moved through the system can provide significant gains with relatively low overhead costs in terms of the execution of the compression and decompression. In particular, the compression block  1001  can utilize a run length style of encoding which changes long strings of the same value into a symbol representing the value and a symbol representing the length of the run (i.e., “00000000” can be compressed to “80” meaning 8 consecutive zeroes). Such an operation can be referred to as a run length compression. The values selected for the tracked runs in the run length encoding can beneficially be set to the values towards which the rounding circuit rounds the values. For example, if the compression system used a “0” run length encoding, then the rounding circuit would be configured to round near-zero values to 0 and favor rounding values for directed graph data structure that did not appear to have a dispositive effect on the execution of the directed graph to zero as well. The compression block  1001  can also be configured to encode run lengths of multiple values where the multiple values are selected based on which values the rounding block rounds to. 
     The flow chart also includes a flow chart step  1003  which can be executed following step  406  from  FIG.  4   . The benefit of executing the step in this order has been described immediately above in that the rounding will increase the run length and enhance the efficiency of the compression. Step  1003  can be conducted by a means for compressing such as the compression block  1001  in  FIG.  10   . The compression block  1001  can include nonsparse value counters, reset circuits that reset the counters upon detecting a sparse value, and registers for storing the output of the counters when they are reset. The circuit elements could be configured to count a maximum number of consecutive non-sparse values to measure deltas of a given size. For example, the registers could be configured to store, the counters could be configured to count, and the reset circuits could be configured to automatically reset upon detecting, X-bits worth of sparse values. Specifically, the deltas could be less than X to the power of two sparse values. 
       FIG.  11    illustrates a processing core  1100  which includes a metadata generation block  1101  in the main data path  306 . The metadata generation block  1101  can evaluate the output of the main computational cluster and generate metadata that is reflective of the values in that output. The metadata generation block  1101  can be a metadata generator circuit which evaluates the output of the rounding block using sequential logic and stored values for comparison. The metadata generator circuit can include configuration registers for receiving commands or other configuration information from the processing core controller. The metadata can then be associated with the data structure that will store that output using the core controller and/or a header of the data structure in which the output is stored. In particular, the metadata generation block  1101  can generate data that is used by the rounding block, or other circuitry, to derive the appropriate threshold for a unit of directed graph data. For example, as mentioned previously, the threshold may be generated based on a histogram or standard deviation of the values in the data structure, and such information can be produced by the metadata generation block  1101 . Alternatively, or in combination, the metadata generation block can generate data indicative of how sparse the output data from the computational cluster is. For example, metadata generation block  1101  can generate a zero flag to be associated with the data structure if all of the values in the data structure are zero. This flag can then be used at a later time to suppress computation using the data structure in which the fact that all of the values are zero is dispositive. As such, connecting metadata generation block  1101  to the output of the rounding block in the main data path produces significant benefits because it will generate more zero flags and further increase the efficiency of the execution of a directed graph using the processing core. 
     The flow chart also includes a flow chart step  1102  which can be executed following step  406  from  FIG.  4   . The benefit of executing the step in this order has been described immediately above in that the rounding may increase the number of zero flags or other metadata based on sparsity or repetition that is then used to increase the efficiency of computation using the associated data structure. Step  1102  can be conducted by a means for generating a zero flag such as metadata generator block  1101  in  FIG.  11   . The metadata generator block  1101  could include comparators, logic gates, and output registers. The comparators could evaluate a set of values from the rounding block against a fixed value such as zero. The logic gates could then generate a zero flag if a set of evaluated values from the rounding block were zero. The output registers could then hold the zero flag, potentially along with multiple other zero flags, such that the zero flags can ultimately be read and associated with the data that was evaluated by the comparators. 
     While the specification has been described in detail with respect to specific embodiments of the invention, it will be appreciated that those skilled in the art, upon attaining an understanding of the foregoing, may readily conceive of alterations to, variations of, and equivalents to these embodiments. Although examples in the disclosure where generally directed to processing core executing a convolution instruction, the same approaches could be utilized to simplify the execution of any composite calculation or composite logic operation including sum-of-products calculations. These and other modifications and variations to the present invention may be practiced by those skilled in the art, without departing from the scope of the present invention, which is more particularly set forth in the appended claims.