Patent Publication Number: US-2022215654-A1

Title: Fully attentional computer vision

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a non-provisional of and claims priority to U.S. Provisional Patent Application No. 62/852,277, filed on May 23, 2019, the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND 
     This specification relates to a neural network system for implementing a computer vision neural network model. 
     Neural networks are machine learning models that employ one or more layers of nonlinear units to predict an output for a received input. Some neural networks include one or more hidden layers in addition to an output layer. The output of each hidden layer is used as input to the next layer in the network, i.e., the next hidden layer or the output layer. Each layer of the network generates an output from a received input in accordance with current values of a respective set of parameters. 
     Examples of neural networks include convolutional neural networks. Convolutional neural networks generally include at least two kinds of neural network layers, convolutional neural network layers and fully-connected neural network layers. Convolutional neural network layers have sparse connectivity, with each node in a convolutional layer receiving input from only a subset of the nodes in the next lowest neural network layer. Some convolutional neural network layers have nodes that share weights with other nodes in the layer. Nodes in fully-connected layers, however, receive input from each node in the next lowest neural network layer. 
     SUMMARY 
     This specification describes a neural network system implemented as computer programs on one or more computers in one or more locations that implements a computer vision neural network. 
     The subject matter described in this specification can be implemented in particular embodiments so as to realize one or more of the following advantages. Convolutions are a fundamental building block of modern computer vision systems. The techniques described in this specification allow for a replacement of one or more convolutional layers in neural networks with a new building block based on self-attention, i.e., a positional local self-attention neural network layer. The resulting neural network can outperform conventional convolutional neural networks while requiring fewer parameters in computer vision tasks such as image classification and object detection. In particular, the positional local self-attention neural network layer uses a memory block that includes neighboring input elements around a given input element of an input feature map to perform local attention. Thus, the resulting neural network is more computationally efficient than prior models that use global attention between all input elements. This is because global attention can only be used after significant spatial down-sampling has been applied to the input due to its expensive computational cost, which prevents its usage across all neural network layers in a fully attentional model. Further, the positional local self-attention neural network layer encodes positional information of the input elements in attention, thus improving expressivity and resulting in outputs that have significantly better accuracies than those generated by neural networks that use conventional convolutions. 
     The details of one or more embodiments of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example neural network system that implements a computer vision neural network that has a positional local self-attention layer. 
         FIG. 2  illustrates an example of a memory block. 
         FIG. 3  is a flow diagram of an example process for generating an output element for an input element of an input feature map. 
         FIG. 4  illustrates an example of relative distance computation. 
         FIG. 5  is a flow diagram of an example process for transforming a convolutional neural network to a computer vision neural network having one or more positional local self-attention layers. 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     This specification describes a neural network system implemented as computer programs on one or more computers in one or more locations that implement a computer vision neural network that includes a positional local self-attention neural network layer. The positional local self-attention neural network layer can be used to replace one or more convolutional layers in conventional computer vision neural network models in order to obtain better performance in computer vision tasks such as image classification and object detection while requiring fewer parameters and computational resources. 
     Generally, the computer vision neural network can be configured to receive input image data and to generate any kind of score or classification output based on the input image, i.e., can be configured to perform any kind of image processing task. The score or classification output generated by the computer vision neural network depends on the task that the computer vision neural network has been configured to confirm. For example, for an image classification or recognition task, the output generated by the computer vision neural network for a given image may be scores for each of a set of object categories, with each score representing the likelihood that the image contains an image of an object belonging to the category. As another example, for an object detection task, the output generated by the computer vision neural network can identify a location, a size, or both, of an object of interest in the input image. 
       FIG. 1  illustrate an example neural network system. The neural network system  100  is an example of a system implemented as computer programs on one or more computers in one or more locations, in which the systems, components, and techniques described below can be implemented. The neural network system  100  implements a computer vision neural network  105  that includes a positional local self-attention layer  110  (also referred to as “the layer  110 ” for simplicity). Although only a single layer  110  is illustrated, the computer vision neural network  105  can include multiple such layers and/or other types of neural network layers, e.g., 1×1 convolutions, other convolutional layers, and fully-connected layers. 
     As a particular example described below, the computer vision neural network  105  can be generated from an existing convolutional neural network by replacing all, or a subset, of the spatial convolutional layers in the existing convolutional neural network with a positional local self-attention layer. 
     The positional local self-attention layer  110  is configured to receive an input feature map (e.g., of an input image) and to generate an output feature map that characterizes features of the input feature map using both local content and positional information of the input feature map. The positional local self-attention layer  110  may receive the input feature map from a previous layer of the computer vision neural network  105 , from a user of the system  100  or from another system. The output feature map can be provided as input to the next layer of the computer vision neural network  105  or outputted as an output of the computer vision neural network  105 . 
     For each input element (e.g., input element  102  which is a pixel) in the input feature map, the positional local self-attention layer  110  is configured to generate a respective output element for the output feature map using positional local self-attention. The input feature map can be denoted as x∈   h×w×d     in    with height h, width w, and input channels d in , and the output feature map can be denoted as y∈   h×w×d     out    with output channels d out . 
     To generate an output element y ij  for an input element x ij , the layer  110  first generates a memory block that includes neighboring input elements around the input element. In particular, given the input feature map x∈   h×w×d     in   , the layer  110  extracts a local neighborhood    k (i,j) around an input element (which is a vector x ij ∈   d     in   ) of the input feature map with spatial extent k centered around the input element x y , resulting in a region with shape k×k×d in  (gray region as shown in  FIG. 2 ). This region is called a memory block (e.g., memory block  104  of  FIG. 1 ). The memory block includes neighboring input elements (i.e., neighboring pixels around pixel  102 ) in position ab∈   k (i,j), where a and b are coordinates relative to (i,j). An example of a memory block around x ij  is illustrated by  FIG. 2 . In the example shown, k=3, though other values of k may alternatively be used. For example, k may lie in the range [2, 20], such as in the range [6, 11], e.g. k=7. 
     The layer  110  applies a learned query linear transformation to the input element x ij  to generate a query vector q ij  (e.g., query vector  106 ), for example, as shown in the following equation: 
         q   ij   =W   Q   x   ij , 
     where W Q ∈   d     out     ×d     in    is a learned query weight matrix. 
     For each of the neighboring elements x ab  around the input element x ij  in the memory block, the layer  110  applies a learned key linear transformation to the neighboring element to generate a respective key vector (e.g., key vector  108 ). For example, the layer  110  generates a respective key vector as follows: 
         k   ab   =W   K   x   ab , 
     where k ab  denotes the respective key vector, W K ∈   d     out     ×d     in    is a learned key weight matrix. 
     For each of the neighboring elements x ab  around the input element x ij  in the memory block, the layer  110  generates a positional value vector from the neighboring element and one or more positional value weight matrices. The one or more positional value weight matrices represent spatial distance between the input element to each of its neighboring input elements in the memory block. For example, the positional value vector, denoted as v ab , can be computed as follows: 
         v   ab =(Σ m   p ( a,b,m ) W   V   m ) x   ab ,
 
     where m is a fixed integer greater than or equal to one and represents a number of mixture components used to generate the value vector, the one or more positional value weight matrices W V   m ∈   d     out     ×d     in   , i.e., a respective weight matrix for each mixture component m, are combined through a convex combination of positional coefficients p(a,b,m) for each mixture component m that are a function of the position of the neighboring element in its neighborhood. An example of such function is defined in the following equation which computes the logit between the absolute embedding for the coordinates (a,b) and the mixture embedding v m  for the mixture component m. 
         p ( a,b,m )=softmax m (( emb   row ( a )+ emb   col ( b )) T   v   m ), 
     where emb row (a) and emb col (b) are pooling-window aligned row and column embeddings and v m  is a per-mixture embedding. If the layer  110  uses multiple attention heads, the resulting p(a,b,m) are shared across all attention heads of the layer  110 . 
     The query weight matrix W Q , the key weight matrix W K , and one or more positional value weight matrices W V   m  can be obtained by training the computer vision neural network  105 . 
     The layer  110  generates a query-key product  112  by taking a product of the query vector and the key vector, such as a dot product of the query vector and the key vector: 
       Query-key product= q   ij   T     ab    
     The layer  110  generates a positional query-key product  114  by adding positional information  116  to the query-key product  112 , e.g.: 
       Positional query-key product= q   ij   T   k   ab   +q   ij   T   r   a−i,b−j , 
     wherein q ij   T r a−i,b−j  is a query-distance product that includes the positional information. The positional information is added to the query-key product to improve expressivity for computer vision tasks. r a−i,b−j  is a relative distance vector that represents the relative distance of ij to each position ab∈   k (i,j). The relative distance is factorized across dimensions, so each element ab∈   k (i,j) receives two distances: a row offset a−i and a column offset b−j. The row and column offsets are associated with an embedding r a −i and an embedding r b−j  respectively each with dimension ½ d out . The layer  110  concatenates the row and column offset embeddings to form the relative distance r a−i,b−j . An example of relative distance computation is shown in  FIG. 4 . 
     The layer  110  generates an intermediate output  118  by applying a softmax operation on the positional query-key product  114 , e.g.: 
       softmax ab ( q   ij   T   k   ab   +q   ij   T   r   a−i,b−j ) 
     The layer  110  generates a temporary output element  122  for the current neighboring element x ab  by computing a product of the intermediate output  118  and the positional value vector  120 , e.g.: 
       softmax ab ( q   ij   T   k   ab   +q   ij   T   r   a−i,b−j ) v   ab    
     The layer  110  generates the output element y ij  for the input element x ij  by summing temporary output elements generated for all neighboring elements in the memory block, e.g.: 
     
       
         
           
             
               
                 
                   
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     The above process for computing an output element for an input element is called a single-headed positional local self-attention process and is repeatedly performed by the layer  110  for every input element ij in the input feature map. 
     In some implementations where the layer  110  uses multiple attention heads to learn multiple distinct representations of the input feature map, the layer  110  may partition the input element x /ij  depthwise into N sub-input elements x ij   n ∈   d     in     /N , compute single-headed positional local self-attention on each sub-input element separately as above with different linear transformations W Q   n , W K   n , W V   n ∈   d     out     /N×d     in     /N  per head in order to generate a respective sub-output element, and then concatenate the sub-output elements into the final output element y ij ∈   d     out    for input element x ij . In some implementations, the sub-output elements for sub-input elements can be generated in parallel. 
     Because the positional local self-attention layer  110  performs local self-attention on pixels in the memory block  104 , the positional local self-attention layer  110  differs from conventional neural network layers exploring attention in vision which have performed global (i.e., all-to-all) attention between all pixels. Global attention can only be used after significant spatial down-sampling has been applied to the input because it is computationally expensive, which prevents its usage across all layers in a fully attentional model. 
     By performing local self-attention, the layer  110  can be used to replace spatial convolutions and build a fully attentional model that is more computationally efficient than prior models that use spatial convolutions. This is because the parameter count of attention is independent of the size of spatial extent, whereas the parameter count for convolution grows quadratically with spatial extent. The computational cost of attention also grows slower with spatial extent compared to convolution with typical values of d in  and d out . For example, if d in =d out =128, a convolution layer with k=3 has the same computational cost as an attention layer with k=19. 
     Further, the positional local self-attention neural network layer  110  encodes positional information of the input elements in attention, thus improving expressivity and resulting in outputs that have significantly better accuracies than those generated by neural networks that use only conventional convolutions. 
       FIG. 3  is a flow diagram of an example process for generating an output element for an input element in an input feature map. For convenience, the process  300  will be described as being performed by a system of one or more computers located in one or more locations. For example, a neural network system, e.g., the network system  100  of  FIG. 1 , appropriately programmed in accordance with this specification, can perform the process  300 . 
     The system generates a memory block for the input element including neighboring input elements around the input element in the input feature map (step  302 ). For example, given the input feature map x∈   h×w×d     in   , the system extracts a local neighborhood    k (i,j) around an input element x ij ∈   d     in    of the input feature map with spatial extent k centered around the input element x ij , resulting in a memory block with shape k×k×d in  The memory block includes neighboring input elements x ab  in position ab∈   k (i,j). 
     The system generates a query vector using the input element and a query weight matrix (step  304 ). For example, the system applies a learned query linear transformation to the input element x ij  to generate a query vector q ij  as follows: 
         q   ij   =W   Q   x   ij , 
     where W K ∈   d     out     ×d     in    is a learned query weight matrix. 
     For each neighboring element x ab  in the memory block, the system performs steps  306 - 310  as follows. 
     The system generates a respective key vector using the neighboring element and a key weight matrix (step  306 ). For example, the system applies a learned key linear transformation to the neighboring element to generate the respective key vector as follows: 
           ab   =W   K   x   ab , 
     where W K ∈   d     out     ×d     in    is a learned key weight matrix. 
     The system generates a positional value vector using the neighboring element and one or more positional value weight matrices (step  308 ). The one or more positional value weight matrices represent spatial distance between the input element to each of its neighboring input elements in the memory block. For example, the positional value vector, denoted as v ab , can be computed as follows: 
         v   ab =(Σ m   p ( a,b,m ) W   V   m ) x   ab ,
 
     where the one or more positional value weight matrices W V   m ∈   d     out     ×d     in    are combined through a convex combination of positional coefficients p (a,b,m) that are a function of the position of the neighboring element in its neighborhood. In other words, the system generates a combined value weight matrix Σ m p(a,b,m)W V   m  as a convex combination of the one or more positional value weight matrices W V   m  using the corresponding one or more positional coefficients p(a,b,m), and then generates the positional value vector using the neighboring element and the combined value weight matrix. 
     The system generates a temporary output element using the query vector, the key vector, and the positional value vector (step  310 ). 
     In particular, the system generates a query-key product by taking a product of the query vector and the key vector, such as a dot product of the query vector and the key vector: 
       Query-key product= q   ij   T     ab    
     The system generates a positional query-key product by adding positional information to the query-key product, e.g.: 
       Positional query-key product= q   ij   T     ab   +q   ij   T   r   a−i,b−j , 
     wherein q ij   T r a−i,b−j  is a query-distance product that includes the positional information. The positional information is added to the query-key product to improve expressivity for computer vision tasks. r a−i,b−j  is a relative distance vector that represents the relative distance of ij to each position ab∈   k (i,j). The relative distance is factorized across dimensions, so each element ab∈   k (i,j) receives two distances: a row offset a−i and a column offset b−j. The row and column offsets are associated with an embedding r a −i and an embedding r b−j  respectively each with dimension ½ d out . The system concatenates the row and column offset embeddings to form the relative distance r a−i,b−j . 
     The system generates an intermediate output by applying a softmax operation on the positional query-key product, e.g.: 
       softmax ab ( q   ij   T   k   ab   +q   ij   T   r   a−i,b−j ) 
     The system generates a temporary output element for the current neighboring element X ab  by computing a product of the intermediate output and the positional value vector, e.g.: 
       softmax ab ( q   ij   T   k   ab   +q   ij   T   r   a−i,b−j ) v   ab    
     The system generates the respective output element by summing the temporary output elements generated for the neighboring elements in the memory block (step  312 ). For example, the system generates the respective output element y ii  as follows: 
     
       
         
           
             
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       FIG. 5  is a flow diagram of an example process for transforming a convolutional neural network to a computer vision neural network having one or more positional local self-attention layers. For convenience, the process  500  will be described as being performed by a system of one or more computers located in one or more locations. For example, a neural network system, e.g., the network system  100  of  FIG. 1 , appropriately programmed in accordance with this specification, can perform the process  500 . 
     The system receives as input data specifying a convolutional neural network (step  502 ). 
     The system replaces spatial convolutional neural network layers in the convolutional neural network by a positional local self-attention layer (step  504 ). A spatial convolution is defined as a convolution with spatial extent k&gt;1. This definition excludes 1×1 convolutions, which may be viewed as a standard fully connected layer applied to each pixel independently. The system replaces every instance of a spatial convolution with a positional local self-attention layer as defined in Equation (*). 
     Optionally, the system determines when spatial down-sampling is required and in response, the system appends a 2×2 average pooling layer with stride  2  operation following the respective positional local self-attention layer (step  506 ). Spatial down-sampling decreases the spatial size of an input in order to reduce the computational cost and increase the “receptive field,” which generally refers to how many pixels in the input image affect a specific output of a neural network layer. The choice of when to spatially down-sample is typically made through a combination of human-designed heuristics and experimental tuning, where one tries out many locations to place down-sampling and chooses the best performing one. In the following example, the system determines when spatial down-sampling is required based on the spatial down-sampling design choices made by the network designer of the received convolutional neural network. Then the system appends a 2×2 average pooling layer with stride  2  operation after the respective positional local self-attention layer whenever spatial down-sampling is required. 
     For example, the convolutional neural network is a ResNet neural network. Examples of ResNet neural network architectures are described in K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in IEEE Conference on Computer Vision and Pattern Recognition, 2016. The core building block of a ResNet neural network is a bottleneck block with a structure of a 1×1 down-projection convolution, a 3×3 spatial convolution, and a 1×1 up-projection convolution, followed by a residual connection between the input of the block and the output of the last convolution in the block. The bottleneck block is repeated multiple times to form the ResNet, with the output of one bottleneck block being the input of the next bottleneck block. The transform described in steps  502 - 506  swaps the 3×3 spatial convolution with a positional local self-attention layer as defined in Equation (*). All other structure, including the number of layers and when spatial down-sampling is applied can be preserved. 
     This specification uses the term “configured” in connection with systems and computer program components. For a system of one or more computers to be configured to perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by data processing apparatus, cause the apparatus to perform the operations or actions. 
     Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non transitory program carrier for execution by, or to control the operation of, data processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. The computer storage medium is not, however, a propagated signal. 
     The term “data processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. 
     A computer program (which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     As used in this specification, an “engine,” or “software engine,” refers to a software implemented input/output system that provides an output that is different from the input. An engine can be an encoded block of functionality, such as a library, a platform, a software development kit (“SDK”), or an object. Each engine can be implemented on any appropriate type of computing device, e.g., servers, mobile phones, tablet computers, notebook computers, music players, e-book readers, laptop or desktop computers, PDAs, smart phones, or other stationary or portable devices, that includes one or more processors and computer readable media. Additionally, two or more of the engines may be implemented on the same computing device, or on different computing devices. 
     The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). For example, the processes and logic flows can be performed by and apparatus can also be implemented as a graphics processing unit (GPU). 
     Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few. 
     Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user&#39;s client device in response to requests received from the web browser. 
     Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), e.g., the Internet. 
     The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. 
     Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.