Machine learning (ML) is becoming an increasingly important part of the computing landscape. Machine learning is a branch of artificial intelligence (AI), and ML helps enable a software system to learn to recognize patterns from data without being directly programmed to do so. Neural networks (NN) are a type of ML which utilize a set of linked and layered functions (e.g., nodes, neurons, etc.) which are weighted to evaluate input data. In some NNs, sometimes referred to as convolution NNs (CNNs), convolution operations are performed in NN layers based on inputs received and weights rather than matrix multiplication used in traditional NN. Layers in CNNs may perform many types of functions, including, but not limited to, convolution, deconvolutional, pooling, up-sample, etc. CNNs are often used in a wide array of applications typically for recognition and classification, such as image recognition and classification, prediction and recommendation systems, speech and language recognition and translation, etc.
As ML becomes increasingly useful, there is a desire to execute complex ML techniques, such as NNs and CNNs, efficiently in devices with relatively limited compute and memory resources, such as embedded, or other low-power devices. To help efficiently run a given ML model, the ML model may be analyzed and optimized to tailor how the ML model is run to a target hardware resources to be used.
This disclosure relates to techniques for executing ML models, including receiving an indication to run an ML model on a processing core; determining a resource allocation for running the ML model on the processing core; determining that a layer of the ML model will use a first amount of the resource, wherein the first amount is more than an amount of the resource allocated; determining that an adaptation may be applied to executing the layer of the ML model; executing the layer of the ML model using the adaptation, wherein executing the layer using the adaptation reduces the first amount of the resource used by the layer as compared to running the layer without using the adaptation; and outputting a result of the ML model based on the executed layer.
Another aspect of the present disclosure relates to a non-transitory program storage device comprising instructions stored thereon to cause one or more processors to: receive an ML model, the ML model having one or more layers; simulate executing a layer of the ML model on a target hardware without an adaptation applied to determine a first adaptation criterion; simulate executing the layer of the ML model on the target hardware with the adaptation applied to determine a second adaptation criterion, wherein the adaptation reduces an amount of a resource used by the layer; determine that the adaptation may be applied to the layer based on a comparison of the first adaptation criterion and the second adaptation criterion and an adaptation threshold; and output an indication that the adaptation may be applied to the layer.
Another aspect of the present disclosure relates to an electronic device, comprising: a memory; and one or more processors operatively coupled to the memory, wherein the one or more processors are configured to execute instructions causing the one or more processors to: receive an indication to run an ML model on a processing core; determine a resource allocation for running the ML model on the processing core; determine that a layer of the ML model will use a first amount of the resource, wherein the first amount is more than an amount of the resource allocated; determine that an adaptation may be applied to executing the layer of the ML model; execute the layer of the ML model using the adaptation, wherein executing the layer using the adaptation reduces the first amount of the resource used by the layer as compared to running the layer without using the adaptation; and output a result of the ML model based on the executed layer.
For a detailed description of various examples, reference will now be made to the accompanying drawings in which:
As ML has becoming more common and powerful, hardware configured to execute ML models has been introduced. As used herein, an ML model may refer to an implementation of one or more ML algorithms which model a behavior, such as object recognition, behavior of a circuit, behavior of a neuron, etc. In cases where a target hardware for executing ML models is known, the ML models may be optimized for the target hardware configurations to help enhance performance. For example, ML models for object recognition, low-light enhancement, and facial recognition may be optimized to execute on a particular a mobile device, such as a smartphone configured with a certain ML processor. As another example, ML models for object recognition, movement prediction, and behavioral prediction may be optimized to execute on specific hardware found in certain partially or fully self-driving automobiles.
Example ML Model
In this example, first layer 106 represents a function based on a set of weights that are applied to the input parameters (e.g., input parameters 102 and 104) to generate output from first layer 106 that is input to the second layer 108. Different weights may be applied for the input received from each node of the previous layer by the subsequent layer. For example, for a node of the second layer 108, the node applies weights to input received from nodes of the first layer 106 and the node may apply a different weight to input received from each node of the first layer 106. Nodes compute one or more functions based on the inputs received and corresponding weights and outputs a number. In some cases, inputs and output to an ML model layer may be referred to as input or output features of the ML model layer. For example, the node may use a linear combination function which multiplies an input values from a node of the previous layer with a corresponding weight and sums across the results of the multiplication, coupled with a non-linear activation function which acts as a floor for the resulting number for output. It may be understood that any known weighted function may be applied by the node within the scope of this disclosure. This output number may be input to subsequent layers, or if the layer is a final layer, such as third layer 110 in this example, the number may be output as a result (e.g., output parameters or ML model outputs 112).
In some cases, the functions applied by nodes of a layer may differ as between layers. In some cases, each layer may have different resource requirements. For example, when the functions of multiple nodes are performed by a processor, the different functions may have different loads on the processor. Additionally, some functions may have different input or output parameters and thus consume more, or less, memory space and bandwidth. These differing processor and memory loads may also influence an amount of energy to power the processor and memory, as well as an amount of heat generated.
After an ML model, such as NN ML model 100, is defined with respect to nodes, layers, etc., the ML model may be trained. In some cases, the ML model 100 may be trained using a labelled data set corresponding to data to be input to ML model 100. For example, an object recognizer may be trained on images of objects. These images may include metadata labelling the object(s) in the image. The ML model 100 may be initiated with initial weights and the images input to the ML model 100 to generate predictions. The weights of the nodes may be adjusted based on how accurate the prediction is as compared to the labels. The weights applied by a node may be adjusted during training based on a loss function, which is a function that describes how accurately the predictions of the NN are as compared to the expected results; an optimization algorithm, which helps determine weight settings adjustments based on the loss function; and/or a backpropagation of error algorithm, which applies the weight adjustments back through the layers of the NN. Any optimization algorithm (e.g., gradient descent, mini-batch gradient descent, stochastic gradient descent, adaptive optimizers, momentum, etc.), loss function (e.g., mean-squared error, cross-entropy, maximum likelihood, etc.), and backpropagation of error algorithm (e.g., static or recurrent backpropagation) may be used within the scope of this disclosure.
In some cases, training the ML model 100 is performed during development of the ML model 100 and may be performed by a system or device separate from the system or device that runs the trained ML model.
Example Hardware for Executing ML Models
The CPU cores 202 may be coupled to a crossbar (e.g., interconnect) 206, which interconnects and routes data between various components of the device. In some cases, the crossbar 206 may be a memory controller or any other circuit that can provide an interconnect between peripherals. Peripherals may include master peripherals (e.g., components that access memory, such as various processors, processor packages, direct memory access (DMA)/input output components, etc.) and slave peripherals (e.g., memory components, such as double data rate (DDR) random access memory, other types of random access memory, DMA/input output components, etc.). In some cases, the processing cores, such as CPU cores 202, ML accelerator 208, and other processing cores 210 and crossbar 206 may be integrated on a single chip, such as a SoC 222 with a separate external memory. In this example, the crossbar 206 couples the CPU cores 202 with other peripherals, such as an ML accelerator 208 and other processing cores 210, such as a graphics processing unit, radio basebands, coprocessors, microcontrollers, etc., and external memory 214, such as DDR memory, dynamic random access memory (DRAM), flash memory, etc., which may be on a separate chip from the SoC. The crossbar 206 may include or provide access to one or more internal memories that may include any type of memory, such as static random access memory (SRAM), flash memory, etc. The ML accelerator 208 may include one or more ML cores 216. The ML cores 216 may be processor cores configured to accelerate machine learning models and the ML cores 216 may include one or more internal caches (not shown).
In operation, such as when executing one or more ML models, the ML cores 216 may store and access data for executing the one or more ML models in a scratch memory to help improve performance, as compared to storing and accessing the data in the external memory 214. In some cases, an amount of data needed by the ML model varies based on the ML models. For example, the amount of data may vary based on the inputs and outputs of layers of the ML model, operations performed in the layers, number of nodes in the layers, etc. In some cases, an amount of scratch memory may be allocated for use by each executing ML model. In this example, the ML accelerator 208 may include N ML cores 216 executing N ML models with a corresponding N static memory allocations 218. The size of the memory allocations 218 may be fixed based on the ML model. The static memory allocations 218 may be made from the one or more internal memories included in or accessible via the crossbar 206.
To help facilitate the ML cores 216 and executing ML models access the memory allocations 218, the crossbar may include N DMA engines 220. In some cases, each DMA engine may be associated with a particular ML core 216. The DMA engines 220 may be used by applications, such as ML models, to perform memory operations and/or to offload memory management tasks from a processor. Of note, for simplicity, each ML core 216 is described as executing a single ML model, but it should be understood that any number of ML models may execute on any ML core 216, and these ML models may access a corresponding number of static memory allocations 218. In some cases, the DMA engines 220 along with sufficient scratch memory for the static memory allocations 218 may be integrated on the ML cores 216.
When initializing an ML model, such as ML model 306A, for execution, memory, such as a portion of the shared memory, may be allocated 304A for the ML model 306A prior to ML model 306A execution. The runtime code and parameters for the ML model may be stored in the static allocated memory 304 for use during ML model execution. As shown each executing ML model, such as 306A, 306B, . . . 306n may be associated with a static allocated memory space, such as 304A, 304B, . . . 304n, in the shared memory. A total size of the shared memory may then be based on a sum of the size of the static allocated memory spaces for the ML models to be run. In some cases, the size of the static allocated memory space for an ML model may be based on information obtained during the ML model compilation for the target hardware. In other cases, the size of the static allocated memory space for each ML model may be fixed.
In some cases, each layer of an ML model may be associated with different memory usage. For example, each layer may include a different number of nodes utilizing a different set of input parameters and different weights being applied for nodes of the layer, which influence the memory usage of the layer. In some cases, certain layers of an ML model, when executed, may use more memory than the memory available in the static memory. That is, an ML layer memory usage may exceed the size of the static allocated memory space (e.g., a static resource) for the ML model. In such cases, the ML model may be able to access dynamic resources of a target hardware. In the case of memory usage, the target hardware may be configured with dynamic memory (e.g., a common memory pool) that may be allocated to specific cores for use when executing ML model layers which use more memory than what is available in the static allocated memory space for the ML model.
Generally, the target hardware has a limited amount of resources that may be allocated among executing software, such as the multiple ML models. For example, the target hardware may have a certain amount of internal memory available, a certain amount of memory throughput and bandwidth available, and a certain amount of power that the target hardware can draw. In accordance with aspects of the present disclosure, an ML model executing on target hardware may be allocated a set of static resources for execution. In some cases, the static resources may include a certain amount of memory (e.g., the static allocated memory), a certain amount of memory throughput, a certain amount of memory bandwidth, and a certain amount of power/current for the core executing the ML model. If execution of the ML model requires additional resources, dynamic resources from a set of common (e.g., shared between multiple ML models and cores) on-demand resources may be allocated for the ML model as needed. In some cases, the dynamic resources may also include an amount of memory (e.g., dynamic memory), a certain amount of memory throughput, a certain amount of memory bandwidth, and a certain amount of power/current.
In some cases, when resources are dynamically allocated, the multiple ML models may attempt to access one or more dynamic resources.
In some cases, to help avoid stalling execution of an ML model, execution of the ML model may be adapted based on an adaptation policy.
In some cases, a layer, such as a first layer 507 of ML model N 504N, may use more memory than available in the static memory 506N. In such cases, the first layer 507 may execute using dynamic resources (e.g., dynamic memory). Similarly, a second layer 508 of the ML model 2502B may also execute using dynamic resources. A third layer 510 of ML model 1504A may also use more memory than available in the static memory 506A and may attempt to access dynamic resources. In this case, as dynamic resources have been allocated to the first layer 507 and the second layer 508, there may be insufficient dynamic resources to allocate to the third layer 510. In such cases, the third layer 510 may execute under an adaptation policy that alters (e.g., adapts) the execution of the third layer 510. In some cases, not every layer of an ML model may be capable of executing under the adaptation policy. For example, a fourth layer 512 of ML model 1504A may not be capable of executing under the adaptation policy and may be allocated dynamic resources. A fifth layer 514 of ML model 2504B may instead be executing under the adaptation policy.
If the amount of the resource under the adaptation policy is less than the amount of the static and dynamic resource available for allocation to the layer, execution proceeds to block 406 as described above in conjunction with
In some cases, the adaptation policy may include various possible alterations to the execution of an ML model layer. These alterations may be used to help reduce the amount of resources of the target hardware used by layers of the ML model. For example, an amount of power/current used by a layer may be adapted by reducing the speed at which the layer is executed on the core and/or executing the layer on a more power-efficient core. Where executing a particular layer on a first core may cause the first core to use more than a certain amount of power (either from executing the particular layer, or in combination with another executing ML model), execution of the particular layer may be adapted by reducing the speed at which the layer is processed by the core, for example, by adjusting the clock of the core or by inserting waits between instructions associated with the layer. In some cases, when executing a particular layer on a first core may cause the first core to use more than a certain amount of power, the particular layer may be executed on a second core. The second core may be a more power-efficient core and/or may be a different type of processing core. For example, the layer may be executed on a digital signal processor (DSP) core rather than an ML core. In some cases, a second, more power-efficient core may be associated with a reduced performance as compared to the first core. Executing the layer using an adaptation policy which adapts the amount of power/current used by the layer helps avoid having to stall the execution of the layer, for example, to reduce power usage to stay within a power and/or thermal budget. Adapting the amount of power/current may result in reduced performance for the layer and the overall ML model but avoids stalling, and thus stopping, execution of the layer entirely for a period of time.
As another example, an amount of memory, an amount of memory throughput, and an amount of memory bandwidth used by a layer may be adapted by adjusting weight and/or input/output feature precision and/or by directly executing the ML model layer in external memory.
A layer of an ML model may receive a set of input features which may be input into nodes of the layer. The nodes of the layer may then determine a function based on one or more features input into the node along with one or more weights input into the node. The determined results of the function for the node may be output as a part of an output feature of the layer. In some cases, the weights and features may be associated with a particular bit precision. For example, the weights for the layer may be in the form of a 16-bit float representing a number between 0 and 1. The number of bits representing the weights and features is associated with a level of precision that is able to be represented. For example, 8-bits can represent up to 256 different values, while 16-bits can represent up to 65,536 different values. However, for certain layers, a difference between the number of values that can be represented by the bits representing the weights and features may not be representative of a difference in the quality of the output of the layer. That is, there may be a negligible difference in the quality of the output of certain layers (and ML model as a whole) if the bit value, and hence precision, of the bits representing the weights for the layer are reduced. For example, layers with relatively large weight values often can be quantized into lower bit values as there is often a larger difference between weight values of the layer.
In some cases, after training of an ML model, weights may be associated with the layers of the ML model. These weights may be considered the high-precision weights 708. The bit precision of weights associated with a layer may be reduced, for example, by quantizing (e.g., bucketing) bit values associated with the higher number of bits into equally spaced value buckets based on the values available in the lower bit rate. Layers in where the bit precision of the weights can be reduced with a negligible difference in quality may be identified during a compilation/preparation process of the ML model for the target hardware. The lower-precision weights 710 for a layer may be generated from the high-precision weights 708 as a part of the compilation/preparation process for those identified layers. For example, weights for the layer may then be quantized from the set of high-precision weights 708 into weights for a set of lower-precisions weights 710. In some cases, each identified layer of the ML model on which lower-precision weights 710 have a negligible impact on may have lower-precision weights generated for that layer. These lower-precision weights 710 may be stored in the external memory 706. When an adaptation policy is used for a layer, these lower-precision weights 710 may be loaded from the external memory 706 to the internal memory 704 for use in the ML model. The adaptation policy using lower-precision weights 710 may help reduce an amount of internal memory 704, reduce an amount of memory throughput of the internal memory 704, as well as reduce an amount of bandwidth as between the external memory 704 and the SoC 702 used to process the layer of the ML model.
Features of an ML model may refer to inputs and outputs of a layer of the ML model. For example, a set of input features, which may represent aspects of a part of an image for a recognizer type ML model, may be input into a first layer of the ML model. This first layer may then output a set of output features. This set of output features then may be input as a set of input features to a second layer of the ML model. In some cases, a bit precision of the input features or output features may also be reduced. Layers in where the bit precision of the input features or output features can be reduced with a negligible difference in quality may be identified during a compilation/preparation process of the ML model for the target hardware.
As shown in diagram 750 of
In a second example, the layer of the ML model may execute on SoC 752 using lower-precision features 760 loaded into the internal memory 756 from external memory 758. For example, a previous layer of the ML model may have output lower-precision features 760. Where the adaptation policy is used for the current layer, the lower-precision features 760 may be loaded from the external memory 758 to the internal memory 756 for use by the current layer. The adaptation policy using lower-precision features 760 may help reduce an amount of internal memory 756, reduce an amount of memory throughput of the internal memory 756, as well as reduce an amount of bandwidth as between the external memory 758 and the SoC 752 used to process the layer of the ML model.
In some cases, under an adaptation policy, an ML model layer may execute using data directly from external memory.
ML Model Compilation
Once an ML model 902 is trained, the ML model 902 may be compiled and/or prepared for a target hardware by an ML model complier 904A, 904B, . . . 904n (collectively). It may be understood that the compilation process may include multiple processes, steps, operations, etc., which may be performed separately, and/or in an automated fashion. In this example, the target hardware 906 is shown as a simplified version of the device shown in
It may be understood that the compilation process may include multiple sub-processes. For example, in addition to translating the ML model 902 to runtime code, the compilation process may also include one or more sub-processes analyzing execution of the ML model 902 on the target hardware. In cases with multiple ML models 902 executing on multiple cores 910, the ML model compiler 904 may determine which core 910 an ML model 902 should run on. The ML model compiler 904 may also parameterize the ML model 902 being compiled. In some cases, the ML parameters may include information that may be dynamically loaded from memory for executing the ML model 902, such as weights, layer-ordering information, structure, memory needed to store data input/output between layers, etc.
As shown, trained ML models 902 may be compiled and/or translated for a target hardware by an ML model complier 904. In some cases, simulations may be performed after the ML model is trained and as a part of preparing the trained ML model 902 for execution on the target hardware 906. For example, as a part of the compilation and/or translation process, ML model execution on the target hardware 906 may be simulated. In some cases, the simulation of the ML model execution may be performed as a separate process from the compilation/translation process.
In some cases, the simulation may be repeated with a number of variations of certain constraints, such as with various amounts of available dynamic memory available to be allocated for the cores. In some cases, these simulations may help determine which layers of the ML model 902 may be adapted. Layers of the ML model 902 may be simulated executing on the target hardware with one or more adaptation applied. For example, layers of the ML model 902 may be simulated executing on the target hardware with high-precision weights as well as lower-precision weights to analyze an impact the lower-precision weights have on the overall quality of the ML model. Layers associated with a negligible impact on quality may be identified as layers on which a weight-precision adaptation policy may be applied. For example, output features of a simulated layer using lower-precision weights may be compared to output features of a simulated layer using high-precision weights. If the difference is below a certain threshold, then the layer may be identified as supporting the weight-precision adaptation policy. As another example, output features of the ML model using lower-precision weights for a layer may be compared to output features of the ML model using higher-precision weights for the layer. If the difference is below a certain threshold, then the layer may be identified as supporting the weight-precision adaptation policy. In some cases, each layer of the ML model 902 may be simulated with and without one or more adaptations applied. In other cases, a subset of the layers of the ML model 902 may be simulated with one or more adaptations applied. For example, the layers which use more of a resource than the static allocation of the resources may be simulated with one or more adaptations applied.
Similarly, the layers of the ML model 902 may be simulated executing on the target hardware with high-precision features as well as lower-precision features to help determine which layers of the ML model 902 may be adapted. For example, layers of the ML model 902 may be simulated executing on the target hardware with high-precision features as well as lower-precision features to analyze an impact the lower-precision features have on the overall quality of the ML model. Layers associated with a negligible impact on quality may be identified as layers on which a feature-precision adaptation policy may be applied. For example, output features of the ML model using lower-precision features for a layer may be compared to output features of the ML model using higher-precision features for the layer. If the difference is below a certain threshold, then the layer may be identified as supporting the feature-precision adaptation policy.
Similarly, the layers of the ML model 902 may be simulated for adaptation policies where the amount of power/current used by a layer may be adapted by reducing a speed at which the layer is executed on the core, executing the layer on a more power-efficient core, and/or executing the ML model layer using data from external memory. For example, layers of the ML model 902 may be simulated with and without one or more of the adaptations active to determine an impact the adaptation has on ML model execution speed, frames per second, latency, power usage, etc. These impacts may be compared to thresholds to determine whether to identify the layer as one on which a corresponding adaptation may be applied.
After the layers on which an adaptation may be applied are identified, an indication of these layers and what adaptation may be applied may be stored as a part of the runtime code and parameters 916 associated with the ML model. In some cases, portions of the runtime code and parameters 916 may be loaded into a common context 920 in the shared memory 912.
After compilation of the ML model 902 to runtime code 916 for the target hardware 906, the parameters of the ML model 902 may be stored, for example, in the external memory 914. When an ML model 902 is executed, portions of the runtime code and parameters 916 may be loaded, for example, into a static memory allocation 918 in shared memory 912 or other memory. In some cases, a particular ML model 902 may be executed by a particular ML core 910 of the ML cores 910. Multiple ML models may be executed concurrently across the multiple ML cores. In some cases, certain ML models may be designated to execute on certain cores of the target hardware.
In some cases, resources used by the layers of the ML models may also be determined as a part of the compilation process. As a part of simulations of the ML model executing on the target hardware, resource use of the target hardware may be monitored on a per-layer basis for the ML models. This layer resource usage information may be stored, for example, in the runtime code and parameters 916 and loaded as a part of the common context 920 upon ML model execution. In some cases, the layer resource usage information may be relative to the static resources. For example, the layer resource usage information may indicate cases in which a respective layer uses more of a resource than a static allocation of the resource to a core.
In some cases, the additional resource usage information may be stored as a part of the context information. In some cases, the additional resource information may be used to generate one or more adaptation policies. For example, the additional resource information generated with different (and/or different combinations) adaptations applied may be combined with information related to the impact the adaptation has on ML model, such as execution speed, frames per second, latency, power usage, etc. to determine one or more adaptation policies. As a more detailed example, if a layer under a first adaptation, such as weight/feature precision adaptation, uses more of the resource than a second adaptation, such as an adaptation where the layer is executed from external memory, but executes at a higher speed under the first adaptation, the first adaptation may be used as a part of a first adaptation policy and the second adaptation may be used as part of a second adaptation policy. These adaptation policies may be determined as a part of the compilation process and during execution of the ML model, either the first or the second adaptation policies may be applied based on the resources available during execution. For example, where more of the resource is available for dynamic allocation, then the first adaptation policy may be applied to help maintain execution speed with the adaptation policy applied. Where less of the resource is available for dynamic allocation, then the second adaptation policy may be applied to help allow the layer to be executed, rather than stalled.
At block 1106, the layer of the ML model is simulated executing on the target hardware with the adaptation applied to determine a second adaptation criterion, wherein the adaptation reduces an amount of a resource used by the layer. For example, layers of the ML model may be simulated with one or more adaptations applied. The resources used as well as performance of the layers of the ML with adaptations applied may be determined.
At block 1108, a determination that the adaptation may be applied to the layer based on a comparison of the first adaptation criterion and the second adaptation criterion, and an adaptation threshold is made. For example, the performance of layers of ML with adaptations applied are compared to the performance of corresponding layers of the ML without adaptations applied. As a more detailed example, for adaptations which alter the bit precision of the features and/or weights of the layer, a difference between output feature values and/or output of the ML model executed with and without the adaptation applied to the layer may be compared to a threshold to determine that the adaptation has a negligible affect on the ML model and that the adaptation may be applied to the layer. As another example, for the adaptation which slows down execution of the layer on the processing core, executes the layer on another processing core, or executes the layer from external memory, a performance of the layer, such as a number of times the ML model or layer may be executed per second, how long layers take to run, etc. may be determined in context with one or more other ML models simulated executing on the target hardware. This, in turn, may cause layers of the ML model to be stalled waiting for access to one or more resources, thus reducing the performance of layers of the ML model. The ML model may then be simulated, in context with one or more other ML models with one or more adaptation applied, to determine the performance of the layer with adaptations. The performance of the layer with adaptations are then compared to the performance of the layer without adaptations to see if the performance of the layer with adaptations performs at least a threshold amount better than the performance of the layer without adaptations. In some cases, this threshold may be that there is some improvement. If there is at least a threshold amount of performance improvement, a determination is made that adaptation may be applied to the layer. In some cases, steps 1104-1108 may be repeated for the layers of the ML model using different adaptations and/or combinations of adaptations. In some cases, these steps may be repeated exhaustively for the layers of the ML and available adaptations.
At block 1110, an indication that the adaptation may be applied to the layer is output. For example, an indication of which adaptations may be applied to which layers may be output as a part of the runtime code and parameters associated with the ML model.
In this description, the term “couple” may cover connections, communications, or signal paths that enable a functional relationship consistent with this description. For example, if device A generates a signal to control device B to perform an action: (a) in a first example, device A is coupled to device B by direct connection; or (b) in a second example, device A is coupled to device B through intervening component C if intervening component C does not alter the functional relationship between device A and device B, such that device B is controlled by device A via the control signal generated by device A.
Modifications are possible in the described embodiments, and other embodiments are possible, within the scope of the claims.