Patent Publication Number: US-2022229988-A1

Title: Touch Keyboard Using a Trained Model

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of and claims priority to U.S. application Ser. No. 16/683,895, filed Nov. 14, 2019, which in turn is a continuation of and claims priority to U.S. application Ser. No. 15/795,955, filed Oct. 27, 2017, now U.S. Pat. No. 10,528,663, issued Jan. 7, 2020, which in turn is a continuation of and claims priority to U.S. application Ser. No. 14/477,490, filed Sep. 4, 2014, now U.S. Pat. No. 9,830,311, issued Nov. 28, 2017, which in turn is a continuation of and claims priority to U.S. application Ser. No. 13/789,106, filed Mar. 7, 2013, now U.S. Pat. No. 8,832,589, issued Sep. 9, 2014, which in turn claims priority to U.S. Provisional Application No. 61/752,790, filed Jan. 15, 2013, the disclosures of which are incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     Some computing devices (e.g., mobile phones, tablet computers, etc.) may provide a graphical keyboard as part of a graphical user interface for composing text using a presence-sensitive display (e.g., a touchscreen). The graphical keyboard may enable a user of the computing device to enter text (e.g., an e-mail, a text message, or a document, etc.). For instance, a presence-sensitive display of a computing device may output a graphical (or “soft”) keyboard that enables the user to enter data by indicating (e.g., by tapping) keys displayed at the presence-sensitive display. 
     In some cases, the computing device may present a graphical keyboard with which the user can indicate a word by tapping individual keys displayed on the graphical keyboard or by successively sliding a finger over the regions associated with graphical keys representing characters of which the word is comprised. In this way, graphical keyboards provide an input method that allows the user to enter characters, words, or a group of words by one or more gestures. As such, a graphical keyboard may allow the user to achieve a certain degree of efficiency by quickly and accurately entering text. 
     However, graphical keyboards have certain drawbacks. For example, a computing device may receive a series of tap gestures or sliding gestures from a user paying little attention to accuracy. The characters inputted by the computing device, though, may be different than the characters that the user attempted to select. Consequently, the user may need to correct the inputted characters. As such, entering text with gestures using a graphical keyboard may be difficult and reduce the speed at which the user may interact with the computing device. 
     SUMMARY 
     In one example a method includes outputting, by a computing device and for display at a presence-sensitive display, a graphical keyboard comprising a plurality of keys, receiving, by the computing device, an indication of at least one gesture to select a group of keys of the plurality of keys, and determining, by the computing device, at least one characteristic associated with the at least one gesture to select the group of keys of the plurality of keys. The method further includes modifying, by the computing device and based at least in part on the at least one characteristic, a spatial model, determining, by the computing device, a candidate word based at least in part on data provided by the spatial model and a language model, wherein the spatial model provides a first portion of the data based at least in part on the indication of the at least one gesture and wherein the language model provides a second portion of the data based at least in part on a lexicon, and outputting, by the computing device and for display at the presence-sensitive display, the candidate word. 
     In another example a computer-readable storage medium is encoded with instructions that, when executed, cause one or more processors of a computing device to perform operations comprising: outputting, for display at a presence-sensitive display, a graphical keyboard comprising a plurality of keys, receiving an indication of at least one gesture to select a group of keys of the plurality of keys, and determining at least one characteristic associated with the at least one gesture to select the group of keys of the plurality of keys. The computer-readable storage medium may be encoded with further instructions that, when executed, cause the one or more processors of a computing device to perform operations comprising: modifying, based at least in part on the at least one characteristic, a spatial model, determining a candidate word based at least in part on data provided by the spatial model and a language model, wherein the spatial model provides a first portion of the data based at least in part on the indication of the at least one gesture and wherein the language model provides a second portion of the data based at least in part on a lexicon, and outputting, for display at the presence-sensitive display, the candidate word. 
     In another example a computing device includes at least one processor that is operatively coupled to a presence-sensitive display and at least one module operable by the at least one processor to output, for display at the presence-sensitive display, a graphical keyboard comprising a plurality of keys, receive, at the presence-sensitive display, an indication of at least one gesture to select a group of keys of the plurality of keys and determine at least one characteristic associated with the at least one gesture to select the group of keys of the plurality of keys. The at least one module may further be operable by the at least one processor to modify, based at least in part on the at least one characteristic, a spatial model, determine a candidate word based at least in part on data provided by the spatial model and a language model, wherein the spatial model provides a first portion of the data based at least in part on the indication of the at least one gesture and wherein the language model provides a second portion of the data based at least in part on a lexicon, and output, for display at the presence-sensitive display, the candidate word. 
     The details of one or more examples are set forth in the accompanying drawings and the description below. Other features, objects, and advantages will be apparent from the description and drawings, and from the claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram illustrating an example computing device and graphical user interfaces (GUIs) for providing text input, in accordance with one or more aspects of the present disclosure. 
         FIG. 2  is a block diagram illustrating further details of an example computing device for providing text input, in accordance with one or more aspects of the present disclosure. 
         FIGS. 3A and 3B  are block diagrams illustrating one example of modifying a spatial model to provide accurate text input, in accordance with one or more aspects of the present disclosure. 
         FIGS. 4A and 4B  are block diagrams illustrating example GUIs for modifying a spatial model to provide accurate text input, in accordance with one or more aspects of the present disclosure. 
         FIGS. 5A-C  are block diagrams illustrating further details of one example of a computing device shown in  FIG. 1 , in accordance with one or more aspects of the present disclosure. 
         FIG. 6  is a flow diagram illustrating example operations that may be used to provide text input, in accordance with one or more aspects of the present disclosure. 
         FIG. 7  is a block diagram illustrating an example computing device that outputs graphical content for display at a remote device, in accordance with one or more techniques of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     In general, this disclosure is directed to techniques for modifying a spatial model used by a computing device for input determination. The techniques may be based at least in part on a user&#39;s text input at a graphical keyboard, the graphical keyboard being outputted for display at a presence-sensitive display. Techniques of the disclosure are also directed to using the spatial model in conjunction with a language model to correct, complete, and/or predict text input based on the text input received. In some examples, mobile devices, such as tablets or smartphones, may provide a presence-sensitive display with which a user may interact. In some examples, the user may provide one or more touch inputs, such as sliding gestures, tap gestures, etc., at the presence-sensitive display. For example, a user may input text to the computing device by interacting with a graphical (i.e., soft) keyboard displayed at the presence-sensitive display. The user may interact with the graphical keyboard by performing touch gestures, such as tapping a finger at the presence-sensitive display or continuously sliding the finger to different locations of the presence-sensitive display. In response to the touch gestures, the computing device may perform one or more operations to generate, select, modify, delete, etc., input data. 
     A computing device (e.g., a smartphone) may determine text input in response to receiving indications of tapping or sliding gestures at a graphical keyboard to select a sequence of keys. In some examples, a computing device implementing techniques of the disclosure may modify a spatial model employed in correction, completion and/or prediction methods for text inputted via a graphical keyboard. Specifically, in some examples, a computing device may determine characteristics of received user inputs and modify values of a spatial model based on the determined characteristics, which may thereby enable a user to provide faster text input. In this way, a computing device implementing techniques of the disclosure may modify the location and/or area of a character&#39;s associated input zone to account for speed and inaccuracy based on the determined characteristics. Such techniques may thereby reduce the need for a user to slowly and accurately select each character, and may provide a more error-tolerant process for inputting text. In this way, techniques of the disclosure may modify various values of a spatial model and use the spatial model along with a language model to correct, complete, and/or predict text input based on previously inputted text. 
     In one aspect of the present disclosure, a computing device (e.g., a mobile phone, a tablet computer, etc.) may modify values of the spatial model based on prior text input. The computing device may also determine a correction, completion, and/or prediction of text using the spatial model in conjunction with a language model. In one example, a computing device may receive a sequence of indications of user input in response to a user tapping a number of locations at a presence-sensitive display. In some instances, the indications of user input may not accurately align with the locations of keys displayed as part of the graphical keyboard. As such, after receiving an indication of user input, the computing device may modify one or more values of the spatial model based on characteristics (e.g., the input speed, the location of the inputs, etc.) associated with the indications of user input. The computing device may subsequently employ the modified spatial model to determine text corresponding to subsequent inputs. The computing device may use the modified spatial model in conjunction with a language model to determine characters, completion of words, and/or predictions of words intended by subsequent user inputs. Modifying the spatial model based on received inputs may allow the computing device to more accurately determine, for example: which characters are more probable to be selected by a user in subsequently received inputs, which word is more probable given a selection of one or more characters, and which characters and/or words are more probable to be selected next. 
     The techniques of the present disclosure may improve the ease with which a user can input text at a computing device. For example, using techniques of this disclosure, a computing device may receive indications of tapping gestures and/or swiping gestures at a graphical keyboard at increased speeds (i.e., more characters per second) to enter text. In response to such indications, the computing device may output one or more characters, character strings, etc., for display at a presence-sensitive display. The user may review the characters and/or character strings displayed by the computing device, as well as any corrections or completions of the word (i.e., a candidate word) that are outputted for display by the computing device. In some examples, the computing device may commit a candidate word as text input in response to receiving an indication of user input that the user is satisfied with the correction and completion. For example, the computing device may receive an indication of a gesture at the graphical keyboard to select a space key and commit the candidate word. Furthermore, once the user has entered text, the computing device may output one or more predictions of future text for review by the user. In this way, the computing device may enable the user to select from the predictions instead of requiring the user to manually enter text through tapping or sliding gestures at the graphical keyboard. 
       FIG. 1  is a block diagram illustrating an example computing device  102  and graphical user interfaces (GUIs) for providing text input, in accordance with one or more aspects of the present disclosure. In some examples, computing device  102  may be associated with user  150 . A user associated with a computing device may interact with the computing device by providing various user inputs into the computing device. In some examples, user  150  may have one or more accounts with one or more services, such as a social networking service and/or telephone service, and the accounts may be registered with computing device  102 . 
     Examples of computing device  102  may include but are not limited to, portable or mobile devices such as mobile phones (including smartphones), laptop computers, desktop computers, tablet computers, smart television platforms, personal digital assistants (PDAs), servers, mainframes, etc. As shown in the example of  FIG. 1 , computing device  102  may be a smartphone. Computing device  102 , in some examples, can include user interface (UI) device  104 , UI module  106 , gesture module  108 , spatial model  110 , language model  111 , and application modules  112 A- 112 N (collectively “application modules  112 ”). Other examples of computing device  2  that implement techniques of the present disclosure may include additional components not shown in  FIG. 1 . 
     Computing device  2  may include UI device  104 . In some examples, UI device  104  is configured to receive tactile, audio, or visual input. Examples of UI device  104  may include a touch-sensitive and/or presence-sensitive display, or any other type of device for receiving user input. UI device  104  may output content such as GUIs  114  and  116  for display. In the example of  FIG. 1 , UI device  104  may be a presence-sensitive display that can display a GUI and receive user input though capacitive, inductive, or optical detection at or near the presence-sensitive display. 
     As shown in  FIG. 1 , computing device  102  may include UI module  106 . UI module  106  may perform one or more functions to receive input, such as user input, and send indications of such input to other components associated with computing device  102 , such as gesture module  108 . UI module  106  may also receive data from components associated with computing device  102  such as gesture module  108  or application modules  112 . Using the data received, UI module  106  may cause other components associated with computing device  102 , such as UI device  104 , to provide output based on the data. For instance, UI module  106  may receive data from one of application modules  112  to display GUIs  114  and  116 . 
     UI module  106  may be implemented in various ways. For example, UI module  106  may be implemented as a downloadable or pre-installed application or “app.” In another example, UI module  106  may be implemented as part of a hardware unit of computing device  106 . In another example, UI module  106  may be implemented as part of an operating system of computing device  102 . 
     Computing device  102 , in some examples, may include gesture module  108 . Gesture module  108  may include functionality to perform a variety of operations on computing device  102 . For instance, gesture module  108  may use a spatial model in conjunction with a language model to determine text input in accordance with the techniques described herein. Gesture module  108  may be implemented in various ways. For example, gesture module  108  may be implemented as a downloadable or pre-installed application or “app.” In another example, gesture module  108  may be implemented as part of a hardware unit of computing device  102 . In another example, gesture module  108  may be implemented as part of an operating system of computing device  102 . 
     Gesture module  108 , in some examples, may be configured to receive gesture data from UI module  106  and determine text from the gesture data. In some examples, gesture module  108  can determine one or more characteristics associated with a gesture, such as the Euclidean distance between a location of a touch gesture and a key location, the rate at which a plurality of gestures are received, the Euclidean distance between two points on a gesture path, the length of a gesture path, the direction of a gesture, the curvature of a gesture path, and maximum curvature of a gesture between points on the gesture path, speed of the gesture, etc. Gesture module  108  may send text determined from the gesture data to other components of computing device  102 , such as application modules  112 , UI module  106 , etc. For instance, gesture module  108  may send text determined from the received gesture data to UI module  106  that causes UI device  104  to display text as shown in GUI  114 . 
     As shown in  FIG. 1 , computing device  102  may include spatial model  110 . Spatial model  110  may store key data corresponding to one or more keys or “soft buttons” of a graphical keyboard (i.e., in contrast to a unique key that is declared and assigned to a data entity). Key data may include, in some examples, statistical values associated with a key of a keyboard, location values associated with the key in the keyboard, a mathematical definition of a key, etc. Spatial model  110  may be stored in one of a range of data structures, such as an array, a list, a structured file such as a file encoded using eXtensible Markup Language (XML), etc. 
     In one example, spatial model  110  may include values for a bivariate Gaussian distribution of touch points for each key of a graphical keyboard. In other examples, spatial model  110  may include any other means of defining an area of an input device to be associated with a key of a graphical keyboard, such as values defining the location and size of the key, values defining the location and space between the keys, etc. In the context of bivariate Gaussian models, the mean values, standard deviation values, and/or co-variance values for each key may be preset or learned from data. Such values for a key in spatial model  110  may also be adjusted based at least in part on the proceeding inputted character. For instance, spatial model  110  may receive modification data from other components of computing device  102 , such as gesture module  108 , or a network device to change one or more values associated with a key. That is, gesture module  108  or other components may modify the values or definitions associated with one or more keys that are stored in spatial model  110  to more accurately correct, complete, and/or predict text. 
     Computing device  102 , in some examples, includes language model  111 . Language model  111  may include a lexicon. In some examples, a lexicon may include a listing of words and may include additional information about the listed words, such as relationships between words, grammar contexts, frequency of use, etc. A lexicon may be represented by a range of data structures, such as an array, a list, and/or a tree. For example, language model  111  may include a lexicon stored in a trie data structure. A lexicon trie data structure may contain a plurality of nodes, each node may represent a letter. The first node in a lexicon trie may be called the entry node, which may not correspond to a letter. In other examples, the entry node may correspond to a letter. Each node may have one or more child nodes. For instance, the entry node may have twenty-six child nodes, each corresponding to a letter of the English alphabet. 
     A subset of the nodes in a lexicon trie may each include a flag, which indicates that the node is a terminal node. Each terminal node of a lexicon trie may indicate a complete word (e.g., a candidate word). The letters indicated by the nodes along a path of nodes from the entry node to a terminal node may spell out a word indicated by the terminal node. In some examples, language model  111  may be a default dictionary installed on computing device  102 . In other examples, language model  111  may include multiple sources of lexicons, which may be stored at computing device  102  or stored at one or more remote computing devices and are accessible to computing device  102  via one or more communication channels. In some examples, language model  111  may be implemented in the firmware of computing device  102 . 
     Language model  111  may include language model frequency information such as word-level n-gram language models or dictionaries. An n-gram language model may provide a probability distribution for an item x i  (e.g., a letter or word) in a contiguous sequence of items based on the previous items in the sequence (i.e., P(x i |x i-(n-1) , . . . , x i-1 )). For instance, a word-level bigram language model (an n-gram language model where n=2) may provide a probability that the word “snow” follows the word “white”. 
     Techniques of the present disclosure may improve the speed and accuracy with which a user can enter text into a computing device. Using techniques of this disclosure, a computing device may receive an indication of one or more gestures performed by a user to indicate text. As the user performs the gesture or gestures, the computing device may modify the spatial model based on the gesture or gestures received. The computing device may employ a unified model including the spatial model and the language model to incrementally determine the text input indicated by the gesture or gestures. By incrementally decoding the gestures as they are being performed and updating the spatial model appropriately, the computing device may more accurately determine text correction, text completion, and/or text prediction with reduced post-gesture entry processing time. Moreover, by enabling the user to easily enter more accurate text with less error, techniques of this disclosure enable the user to increase the rate at which text is entered. Techniques of the disclosure are now further described herein with respect to components of  FIG. 1 . 
     As shown in the example of  FIG. 1 , GUI  114  may be a user interface generated by UI module  106  that allows user  150  to interact with computing device  102 . GUI  114  may include graphical content. Graphical content, generally, may include text, images, a group of moving images, etc. As shown in  FIG. 1 , graphical content may include graphical keyboard  128 , text entry area  126 , and word suggestion areas  122 A-C (collectively “word suggestion areas  122 ”). Graphical keyboard  128  may include a plurality of keys, such as “R” key  123 A, “E” key  123 B, “P” key  123 C, and space key  123 D. In some examples, each of the plurality of keys included in graphical keyboard  128  represents a single character. In other examples, one or more of the plurality of keys included in graphical keyboard  128  may respectively represent a group of characters selected based on a plurality of modes. 
     In some examples, text entry area  126  may include characters or other graphical content that are included in, for example, a text-message, a document, an e-mail message, a web browser, or any other situation where text entry is desired. For instance, text entry area  126  may include characters or other graphical content that are selected by user  150  via gestures performed at UI device  104 . As shown in GUI  114 , text entry area  126  includes inputted text  118  and predicted text  120 . Inputted text  118  may represent text already inputted by user  150  (e.g., via tapping or sliding gestures). 
     UI module  106  may cause UI device  104  to display graphical keyboard  128  and detect a series of tap gestures performed at UI device  104 . A tap gesture may include an input unit (e.g., user  3 &#39;s finger, a pen, a stylus, etc.) moving into proximity with UI device  104  such that the input unit is temporarily detected by UI device  4  and then moving away from UI device  104  such that the input unit is no longer detected. In other examples, UI device  104  may detect a sliding gesture. Sliding gestures may be continuous motion gestures that include a motion of the input unit from a first location of UI device  104  to a second location of UI device  104  such that the gesture performed from the first location to the second location is detected by UI device  104  throughout the performance of the gesture. 
     User  150  may perform tap gestures  124 A,  124 B,  124 C, and  124 D (collectively “tap gestures  124 ”) to select a number of keys of the plurality of keys. UI module  106  may detect each of tap gestures  124  as performed at UI device  104 . Gesture module  108  may receive data indicating each of tap gestures  124  from UI module  106 . For instance, gesture module  108  may receive a coordinate pair indicating a location of UI device  104  at which a gesture was received. In response to receiving an indication of a tap gesture, gesture module  108  may determine one or more characteristics associated with the tap gesture. For instance, in response to receiving an indication of tap gesture  124 A, gesture module  108  may access spatial model  110  to retrieve statistical location values (e.g., mean or average values of the bivariate Gaussian distribution associated with the key) associated with “R” key  123 A, “E” key  123 B, and others. Gesture module  108  may determine the Euclidian distance between the location of tap gesture  124 A and each of the retrieved statistical locations. Other examples of determined characteristics include an input speed (e.g., of a sliding gesture or multiple tap gestures), a duration, a pressure, and others. 
     Based at least in part on the determined characteristics, gesture module  108  may modify values of spatial model  110 . In some examples, gesture module  108  may determine characteristics and modify spatial model  110  after each indication is received. In other examples, gesture module  108  may determine characteristics and modify spatial model  110  at other intervals, such as after multiple indications are received. Gesture module  108  may modify values of spatial model  110  in order to improve determination for a specific character. That is, gesture module  108  may learn from received tap gestures. For instance, after receiving tap gesture  124 A, gesture module  108  may modify the statistical location value of “R” key  123 A as defined in spatial model  110 . Subsequently, gesture module  108  may use the updated statistical location of “R” key  123 A to calculate Euclidian distances between, e.g., first and second locations of a gesture and/or a first location of a gesture and a location associated with a given key. 
     Additionally, gesture module  108  may modify values of spatial model  110  in order to improve the determination for specific user inputs (e.g., the next user input to be received). For example, after receiving an indication of tap gesture  124 A, gesture module  108  may decrease a vertical standard deviation value associated with “E” key  123 B and/or increase a horizontal standard deviation value associated with “E” key  123 B. Modifications to spatial model  110 , in some examples, may be temporary. That is, gesture module  108  may return the modified values of spatial model  110  to their original state. In other examples, modifications may not be returned to their previous states. In either case, gesture module  110  may change various values of spatial model  110  associated with keys of a displayed graphical keyboard, to more accurately process subsequently received gestures. 
     Gesture module  108  may employ spatial model  110 , as modified, in conjunction with language model  111  to determine text input. Based at least in part on a received indication of a gesture, gesture module  108  may use spatial model  110  to determine a set of candidate strings. Gesture module  108  may determine a set of candidate strings upon receiving a first indication of a tap gesture (e.g., an indication of tap gesture  124 A). As gesture module  108  receives subsequent indications, gesture module  108  may modify spatial model  110 , and use spatial model  110 , as modified, to update the set of candidate strings based on the received indications (e.g., adding candidate strings, modifying candidate strings, removing candidate strings, etc.). 
     Candidate strings may represent hypotheses based on user  150 &#39;s input when performing tap gestures  124 . A candidate string may contain a string of characters, a single word, or multiple words as part of a phrase. For instance, as gesture module  108  begins receiving indications correlating to tap inputs  124 , gesture module  108  may create a set of character strings and, as gesture module  108  receives subsequent indications, gesture module  108  may modify spatial model  110  based on the indication. Gesture module  108  may then employ spatial model  110 , as modified, to add, remove, and/or update characters in one or more of the candidate strings. 
     Each candidate string may have an associated physical cost value. The physical cost value may be based at least in part on spatial model  110 , and may represent the likelihood (e.g., a probability) that the associated candidate string represents the user&#39;s intended input. In the example of  FIG. 1 , a lower physical cost value may indicate a higher likelihood that the associated candidate string represents the user&#39;s intended input. In other implementations, however, a higher physical cost value may indicate a higher likelihood. In any case, the physical cost value of a candidate string may be the sum of the physical cost values for each character in the candidate string. 
     In the example of  FIG. 1 , after receiving an indication of tap input  124 A, gesture module  108  may temporarily increase the horizontal standard deviation value associated with “E” key  123 B in accordance with techniques of the present disclosure. Consequently, the physical cost value of tap input  124 B representing an “e” character may be lower (i.e., better) than the physical cost value of tap input  124 B representing a “w” character. Responsive to receiving indications of tap inputs  124 , gesture module  108  may perform additional modifications to spatial model  110 . Gesture module  108  may use spatial model  110  to determine a set of candidate strings including, for example, the strings “revo”, “rwvo”, “reco”, “rwco”, “revp”, “rwvp”, and others. By employing a modifiable version of spatial model  110 , gesture module  108  may, for example, determine that the candidate strings beginning with “re”, such as “revo”, have a lower physical cost value than the candidate strings beginning with “rw”, such as “rwvp”. That is, despite the fact that tap gesture  124 B may be equidistant between the “W” key and “E” key  123 B, due to the modifications of spatial model  110 , gesture module  108  may determine that “revo”, “reco”, and “revp” have lower associated physical cost values. Gesture module  108  may determine that, given the received indications of tap gestures  124 , the candidate string “revp” has the lower physical cost value (and therefore a higher likelihood in the current example). 
     Gesture module  108  may employ a lexicon of language model  111  to determine one or more candidate words based at least in part on the candidate strings. Candidate words may be corrections and/or completions of determined candidate strings. Gesture module  108  may compare a candidate string with words contained in the lexicon of language model  111  in order to determine likely candidate words, based at least in part on the sequence of characters contained in the candidate string. For example, gesture module  108  may compare the candidate strings “revo”, “rwvo”, “reco”, “rwco”, “revp”, “rwvp” to words in language model  111 . For some candidate strings, such as “revo” or “reco”, gesture module  108  may determine one or more candidate words, such as “revolution”, “revolutionary”, “revolt”, “record”, and “recompense”, among others. In some examples, gesture module  108  may determine candidate words after user  150  indicates a completion of tap inputs  124  (e.g., a pause in performing tap inputs). In other examples, gesture module  108  may incrementally determine candidate words as indications of tap inputs  124  are received from UI module  106 . 
     In examples where a candidate string does not correspond to a beginning portion (e.g., prefix) of any word in the lexicon with a sufficient probability or where the candidate string itself is a word in the lexicon, gesture module  8  may determine that the candidate string is a candidate word itself (e.g., a candidate word “revp” for the candidate string “revp”). That is, the lexicon of language model  111  may not contain a word which begins with the prefix “revp”. In other examples, candidate words may include more characters, fewer characters, and/or different characters than the candidate string. For instance, a candidate word may contain fewer characters than the candidate string when gesture module  8  determines that the candidate string may contain an error (e.g., a candidate word of “dog” for the candidate string “doig”). 
     Words in the lexicon of language module  111  may be associated with a frequency value. The frequency value may represent the prevalence of the word in common usage. In some examples, the frequency value may be a predefined, static value stored in language model  111 . In other examples, frequency values may be dynamic and modifiable by, for instance, other components of computing device  102 , other devices, or based on past user input behavior. A higher frequency value may correspond to the associated word being used more often in the language and, thus, the associated word may have a higher likelihood of being a correct prediction of the user&#39;s input. 
     In some examples, gesture module  108  may employ a word-level n-gram language model in language model  111  to determine candidate words based at least in part on previously entered text. For instance, gesture module  108  may use a word-level bigram language model contained in language model  111 . The word-level bigram language model may provide frequency values associated with word pairs. Gesture module  108  may determine candidate words based at least in part on the word-level frequency values. That is, gesture module  108  may determine candidate words based at least in part on inputted text for the current word as well as inputted text from a previous word or words. In some examples, gesture module  108  may determine candidate words based on inputted text from a previous word, or words without requiring any inputted text for the current word. That is, gesture module  108  may predict a candidate word based on a word-level language model and/or a lexicon contained within language model  111 , without utilizing spatial model  110 . 
     In the example of  FIG. 1 , gesture module  108  may determine that “revolution” has a higher likelihood of representing user  150 &#39;s intended input than “revolutionary”, “revolt”, “record”, “recompense”, etc. That is, the lexicon of language model  111  may indicate that “revolution” is more frequently used in the language and/or the word-level bigram language model of language model  111  may indicate that “French revolution” is more frequently used, and thus “revolution” is more likely to appear in a user&#39;s text input. Consequently, though the candidate string “revp” may have a lowest physical cost value (as determined using spatial model  110 ), gesture module  108  may determine that “revo” has the highest likelihood of representing user  150 &#39;s intended input because “revp” is not a prefix of any word in language model  111 . Furthermore, because the candidate word “revolution”, resulting from the candidate string “revo”, has a highest frequency value of those candidate words based on the candidate string “revo”, gesture module  108  may determine that “revolution” has the highest likelihood of representing user  150 &#39;s intended future input. 
     Gesture module  108  may cause UI device  104  to display the candidate word having the highest probability as a soft commit word in text entry area  126 . A soft commit word may function as a placeholder and, if user  150  provides an input to select the soft commit word, gesture module  108  sends the soft commit word as text to, for example, application modules  112 . In response to receiving data indicating a soft commit word, UI device  104  may display the soft commit word as predicted text  120 . As shown in  FIG. 1 , UI module  106  may receive data indicating the soft commit word “revolution”, and UI device  104  may display the soft commit word as predicted text  120  such that the underlying candidate string, “revo”, is followed immediately by the remainder of the determined candidate word, “lution”, as included in GUI  114 . In some examples, UI module  106  may cause the entered characters and the predicted portion of a candidate word or candidate phrase to be displayed in different shades, formatting, or colors in order to indicate to the user what text has already been inputted by gestures, and what text is part of the prediction. 
     In some examples, gesture module  108  may also cause UI device  104  to output one or more candidate words as auto-completion suggestions. Auto-completion suggestions may be outputted to word suggestion areas  122 . Gesture module  108  may send to UI module  106  those candidate words that have been determined to have higher probabilities than other candidate words, thereby indicating the more likely intended input of user  150 . For instance, UI device  104  may output the two candidate words having the second and third highest probabilities in word suggestion areas  122 B and  122 C. For example the second most probable candidate word may be located at the center of GUI  114 , with the less probable candidate word located on the right side of GUI  114 . 
     Gesture module  108  may also cause UI device  104  to output one or more candidate strings as auto-completion suggestions. For example, gesture module  108  may send to UI module  106  the candidate string having the lowest physical cost value as determined using spatial model  110 . That is, gesture module  108  may output an auto-completion suggestion which allows user  150  to choose the string most likely to represent user  150 &#39;s literal input. In the example of  FIG. 1 , gesture module  108  may determine, after receiving data corresponding to tap gestures  124 , that the candidate words with the second and third highest probabilities of representing user  150 &#39;s intended input are “revolutionary”, and “revolt”. As previously stated, gesture module  108  may determine that the candidate string having the lowest physical cost value is “revp.” Based on these determinations, gesture module  108  may send data to UI module  106 , and the candidate words and candidate string may be outputted at UI device  104  as shown in GUI  114 . Thus, after user  150  has performed tap gestures  124 , UI device  104  may display GUI  114 . 
     In some examples, responsive to user  150 &#39;s selection of an auto-completion suggestion (e.g., in one of word suggestion areas  122 ) or acceptance of the soft commit word included in GUI  114 , gesture module  108  may send data corresponding to the selected auto-completion suggestion and/or the selected soft commit word to other components associated with device  102  as text (i.e., a hard commit word). That is, gesture module  108  may determine a hard commit word in response to user  150 &#39;s selection of the soft commit word or an auto-completion suggestion. In other examples, gesture module  108  may determine a hard commit word without user  150 &#39;s selection, such as when there is a high likelihood that a candidate word is the intended input of user  150 . Generally, in the present example, a hard commit word may refer to a word and/or character string that is selected by the user and which may have previously been outputted for display as a soft commit word. 
     Other examples of possible situations include gesture module  108  determining a hard commit word when user  150  includes specific actions during the performance of a gesture, when user  150  performs a specific gesture, etc. In some examples, after sending text input as a hard commit word to an application, gesture module  108  may discard or otherwise cease to store the determined set of candidate strings. That is, after determining a hard commit word, any subsequent input may cause gesture module  108  to start anew, determining a new set of candidate strings. In this manner, gesture module  108  may control data associated with user inputted gestures and text prediction until a trigger of a hard commit word occurs, at which point, gesture module  108  may send the hard commit word to other components of computing device  102  (e.g., one of application modules  112 ). 
     In the example of  FIG. 1 , when presented with GUI  114  (i.e., after performing tap gestures  124 ), user  150  may perform tap gesture  125  to select space key  123 D. User  150  may perform tap gesture  125  as an indication that he or she is satisfied with predicted text  120  as displayed in GUI  114 . In response to user  150  performing tap gesture  125  at UI device  104 , UI module  106  may receive data corresponding to tap gesture  125 . UI module  106  may provide an indication of the tap gesture to gesture module  108 . 
     In accordance with one or more techniques of the present disclosure, gesture module  108  may determine one or more characteristics associated with tap gesture  125  and may modify spatial model  110  accordingly. Gesture module  108  may use spatial model  110 , as modified, to determine the most likely key intended by user  150  in his or her performance of tap gesture  125 . Based on the received indication of tap gesture  125  (e.g., the location of the performed gesture), gesture module  108  may determine that the most likely key is associated with a space character. Responsive to the determination, gesture module  108  may determine a hard commit. That is, gesture module  108  may send predicted text  120  to other components associated with computing device  102 , such as UI device  106  or one of applications  112 . 
     In response to receiving tap gesture  125 , components associated with computing device  102  may cause UI device  104  to display GUI  116 . As shown in  FIG. 1 , GUI  116  includes text entry area  126  and graphical keyboard  128 . Text entry area  126  includes inputted text  130  and predicted text  132 . In other words, after providing an input that causes computing device  102  to perform a hard commit by entering a space character, UI device  104  may present user  150  with a prediction of future input without performing any further gestures. 
     Predicted text  132  may be a prediction of user  150 &#39;s future input based at least in part on language model  111 . That is, in response to performing a hard commit, gesture module  108  may use spatial model  110  and language model  111  to determine a set of candidate words in accordance with one or more aspects of the present disclosure. However, in the example of  FIG. 1 , there may be no tap inputs or sliding inputs for which spatial model  110  may be used. Consequently, gesture module  108  may determine the candidate words based on language model  111  alone. 
     For instance, gesture module  108  may use a word-level bigram dictionary of language model  111  to determine the most likely word to follow “revolution”. In other examples, the language model used may be a trigram or a 4-gram dictionary. In such instance, gesture module  108  may determine the most likely word to follow “French revolution” or “The French revolution” respectively. In the example of  FIG. 1 , gesture module  108  may access the word-level bigram dictionary within language model  111  and determine that the pair of words “revolution timeline” has the highest frequency value, out of all pairs beginning with the word “revolution”. Based on this determination, gesture module  108  may send cause UI device  104  to output “timeline” as a soft commit. Gesture module  108  may, in some examples, provide other candidate words in word suggestion areas  122 . In other words, after causing a hard commit by selecting space key  123 D, user  150  may be presented with one or more options predicting future text input without being required to enter any further input. 
     In some examples, techniques of the present disclosure provide for improved correction, completion, and/or prediction of text input using a graphical keyboard. Techniques of this disclosure may also increase input accuracy by modifying a spatial model used to determine likely text input, and using the modified spatial model to determine text inputted from gestures. In this way, techniques of this disclosure may reduce the time requirement of text input by allowing users to input text using one or more gestures and providing users with corrections, completions, and/or predictions of text input, without requiring the user to pay close attention to gesture accuracy. 
       FIG. 2  is a block diagram illustrating an example computing device  102  for providing text input, in accordance with one or more aspects of the present disclosure.  FIG. 2  illustrates only one particular example of computing device  102 , and many other examples of computing device  102  may be used in other instances. 
     As shown in the specific example of  FIG. 2 , computing device  102  includes one or more processors  200 , one or more input devices  202 , one or more communication units  204 , one or more output devices  206 , one or more storage devices  210 , and user interface (UI) device  104 . Computing device  102 , in the specific example of  FIG. 2 , further includes operating system  212 , UI module  106 , gesture module  108 , application modules  112 , spatial model  110 , language model  111 , active beam  220 , and next beam  222 . Each of components  200 ,  202 ,  204 ,  206 ,  210 , and  104  may be interconnected (physically, communicatively, and/or operatively) for inter-component communications. As one example in  FIG. 2 , components  200 ,  202 ,  204 ,  206 ,  210 , and  104  may be coupled by one or more communication channels  208 . In some examples, communication channels  208  may include a system bus, network connection, interprocess communication data structure, or any other channel for communicating data. Modules  106 ,  108 , and  112 , as well as operating system  212 , spatial model  110 , language model  111 , active beam  220 , and next beam  222  may also communicate information with one another as well as with other components in computing device  102 . 
     Processors  200 , in one example, are configured to implement functionality and/or process instructions for execution within computing device  102 . For example, processors  200  may be capable of processing instructions stored in storage devices  210 . Examples of processors  200  may include, any one or more of a microprocessor, a controller, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or equivalent discrete or integrated logic circuitry. 
     One or more storage devices  210  may be configured to store information within computing device  102  during operation. Storage devices  210 , in some examples, are described as a computer-readable storage medium. In some examples, storage devices  210  are a temporary memory, meaning that a primary purpose of storage devices  210  is not long-term storage. Storage devices  210 , in some examples, are described as a volatile memory, meaning that storage devices  210  do not maintain stored contents when the computer is turned off. Examples of volatile memories include random access memories (RAM), dynamic random access memories (DRAM), static random access memories (SRAM), and other forms of volatile memories known in the art. In some examples, storage devices  210  are used to store program instructions for execution by processors  200 . Storage devices  210 , in one example, are used by software or applications running on computing device  102  (e.g., modules  106 ,  108 ,  112 , etc.) to temporarily store information during program execution. 
     Storage devices  210 , in some examples, also include one or more computer-readable storage media. Storage devices  210  may be configured to store larger amounts of information than volatile memory. Storage devices  210  may further be configured for long-term storage of information. In some examples, storage devices  210  include non-volatile storage elements. Examples of such non-volatile storage elements include magnetic hard discs, optical discs, floppy discs, flash memories, or forms of electrically programmable memories (EPROM) or electrically erasable and programmable memories (EEPROM). 
     Computing device  102 , in some examples, also includes one or more communication units  204 . Computing device  102 , in one example, utilizes communication unit  204  to communicate with external devices via one or more networks, such as one or more wireless networks. Communication unit  204  may be a network interface card, such as an Ethernet card, an optical transceiver, a radio frequency transceiver, or any other type of device that can send and receive information. Other examples of such network interfaces may include Bluetooth, 3G and WiFi radio components as well as Universal Serial Bus (USB). In some examples, computing device  102  utilizes communication unit  204  to wirelessly communicate with an external device such as other instances of computing device  102  of  FIG. 1 , or any other computing device. 
     Computing device  102 , in one example, also includes one or more input devices  202 . Input device  202 , in some examples, is configured to receive input from a user through tactile, audio, or video feedback. Examples of input device  202  include a presence-sensitive display, a mouse, a keyboard, a voice responsive system, video camera, microphone or any other type of device for detecting a command from a user. In some examples, a presence-sensitive display includes a touch-sensitive screen. 
     One or more output devices  206  may also be included in computing device  102 . Output device  206 , in some examples, is configured to provide output to a user using tactile, audio, or video stimuli. Output device  206 , in one example, includes a presence-sensitive display, a sound card, a video graphics adapter card, or any other type of device for converting a signal into an appropriate form understandable to humans or machines. Additional examples of output device  206  include a speaker, a cathode ray tube (CRT) monitor, a liquid crystal display (LCD), or any other type of device that can generate intelligible output to a user. 
     In some examples, UI device  104  may include functionality of input device  202  and/or output device  206 . In the example of  FIG. 2 , UI device  104  may be a presence-sensitive display. In some examples, a presence-sensitive display may detect an object at and/or near the screen of the presence-sensitive display. As one example range, a presence-sensitive display may detect an object, such as a finger or stylus that is within 2 inches or less of the physical screen of the presence-sensitive display. In another example range, a presence-sensitive display may detect an object 6 inches or less from the physical screen of the presence-sensitive display. Other exemplary ranges are also possible. The presence-sensitive display may determine a location (e.g., an (x,y) coordinate) of the presence-sensitive display at which the object was detected. The presence-sensitive display may determine the location of the display selected by a user&#39;s finger using capacitive, inductive, and/or optical recognition techniques. In some examples, the presence-sensitive display provides output to a user using tactile, audio, or video stimuli as described with respect to output device  206 . 
     Computing device  102  may include operating system  212 . Operating system  212 , in some examples, controls the operation of components of computing device  102 . For example, operating system  212 , in one example, facilitates the communication of modules  106 ,  108 , and  112  with processors  200 , communication units  204 , storage device  210 , input devices  202 , and output devices  206 . Modules  106 ,  108 , and  112  may each include program instructions and/or data that are executable by computing device  102 . As one example, UI module  106  may include instructions that cause computing device  102  to perform one or more of the operations and actions described in the present disclosure. 
     In the example of  FIG. 2 , computing device  102  may include spatial model  110 . As previously described in  FIG. 1 , spatial model  110  may store key data corresponding to one or more keys “or soft buttons” of a graphical keyboard (i.e., in contrast to a unique key that is declared and assigned to a data entity). Key data may include, in some examples, statistical values associated with a key of a keyboard, location values associated with a key of a keyboard, a mathematical definition of a key, etc. Spatial model  110  may be stored in one of a range of data structures, such as an array, a list, a structured file such as a file encoded using eXtensible Markup Language (XML), etc. 
     In one example, spatial model  110  may include values for a bivariate Gaussian distribution of touch points for each key of a graphical keyboard. The mean values, standard deviation values, and/or co-variance values for each key may be preset or learned from data. Such values for a key in spatial model  110  may also be adjusted based at least in part on the proceeding inputted character. For instance, spatial model  110  may receive modification data from other components of computing device  102 , such as gesture module  108 , or a network device to change one or more values associated with a key. That is, gesture module  108  or other components may modify the values or definitions associated with one or more keys that are stored in spatial model  110  to more accurately correct, complete, and/or predict text input. 
     Computing device  102 , in some examples, includes language model  111 . Language model  111  may include a lexicon. In some examples, a lexicon may include a listing of words and may include additional information about the listed words, such as relationships between words, grammar contexts, frequency of use, etc. A lexicon may be represented by a range of data structures, such as an array, a list, and/or a tree. For example, language model  111  may include a lexicon stored in a trie data structure. A lexicon trie data structure may contain a plurality of nodes, each node may represent a letter. The first node in a lexicon trie may be called the entry node, which may not correspond to a letter. In other examples, the entry node may correspond to a letter. Each node may have one or more child nodes. For instance, the entry node may have twenty-six child nodes, each corresponding to a letter of the English alphabet. 
     A subset of the nodes in a lexicon trie may each include a flag, which indicates that the node is a terminal node. Each terminal node of a lexicon trie may indicate a complete word (e.g., a candidate word). The letters indicated by the nodes along a path of nodes from the entry node to a terminal node may spell out a word indicated by the terminal node. In some examples, language model  111  may be a default dictionary installed on computing device  102 . In other examples, language model  111  may include multiple sources of lexicons, which may be stored at computing device  102  or stored at one or more remote computing devices and are accessible to computing device  102  via one or more communication channels. In some examples, language model  111  may be implemented in the firmware of computing device  102 . 
     As previously described in  FIG. 1 , language model  111  may include language model frequency information such as word-level n-gram dictionaries. An n-gram dictionary may provide a probability distribution for an item x i  (e.g., a letter or word) in a contiguous sequence of items based on the previous items in the sequence (i.e., P(x i |x i-(n-1) , . . . , x i-1 )). For instance, a word-level bigram dictionary (an n-gram language model where n=2) may provide a probability that the word “snow” follows the word “white”. 
     Computing device  102  may include active beam  220 . Active beam  220 , in some examples, is configured to store one or more candidate strings (e.g., as tokens) generated by gesture module  108 . Active beam  220  may be included within storage devices  210 . Active beam  220  may be represented by a range of data structures and/or software objects, such as an array object, a list object, a database, a table, a tree, etc. Active beam  220  is further described in the description of  FIG. 5 , below. 
     Computing device  102  may also include next beam  222 . Next beam  222 , in some examples, is configured to store one or more candidate strings (e.g., as tokens) generated by gesture module  108 . Next beam  222  may be included within storage devices  210 . Next beam  222  may be represented by a range of data structures and/or software objects, such as an array object, a list object, a database, a table, a tree, etc. Next beam  222  is further described in the description of  FIG. 5 , below. 
     In accordance with techniques of the present disclosure, computing device  102  may output a graphical keyboard comprising a plurality of keys at output device  206 . User  150  may perform a series of tap gestures to select a number of keys of the plurality of keys at input device  202 . In response to user  3  performing a tap gesture, input device  202  may detect the user input, such as tap gesture  124 A of  FIG. 1 , which may be received by UI module  106 . Gesture module  108  may receive an indication of the tap gesture from UI module  106 . In some examples, UI module  106  may send an indication of each tap gesture as it is received. In other examples, UI module  106  may send indications at different intervals. 
     Gesture module  108  may determine characteristics associated with the received indications. Gesture module  108  may, in various examples, determine a Euclidian distance between the location of a received tap gesture and one or more keys of the graphical keyboard, determine a speed (e.g., in characters per second) at which tap gestures are being performed, and/or determine the size of contact area between an input unit (e.g., user  150 &#39;s finger) and input device  202 . Based at least in part on the determined characteristics, gesture module  108  may modify one or more values of spatial model  110 . For instance, gesture module  108  may modify a vertical or horizontal standard deviation value associated with keys of the graphical keyboard, based at least in part on the physical location of the preceding tap input. In another example, gesture module  108  may modify a statistical location of a key to include the physical location of the preceding tap input. In other words, gesture module  108  may modify spatial model  110  based on a received tap input, in order to more accurately determine text from subsequent user inputs. 
     Gesture module  108  may use spatial model  110 , as modified, as well as language model  111  to determine one or more candidate strings (e.g., as tokens) by determining, for each received tap gesture, a composite cost value for each of at least two keys of the plurality of keys, and comparing the respective composite cost values for each of at least two keys, as further described below. A composite cost value may include a physical cost value and a lexical cost value. While described in terms of tap gestures  124  of  FIG. 1 , gesture module  108  may determine characteristics, modify spatial model  110 , and determine composite cost values based on other received gestures as well, such as sliding or swipe gestures. 
     In some examples, gesture module  108  may use spatial model  110 , as modified, to determine respective physical cost values for each of at least two keys of the plurality of keys included in keyboard  128 . Each of the respective physical cost values may represent a probability that a performed tap gesture indicates a key of the graphical keyboard. In some examples, the respective physical cost values may be based on characteristics, such as physical features of the tap gesture and/or physical and statistical features of the key. For instance, the respective physical cost values may be based on the physical location of the tap gesture with reference to a statistical location of the key, as stored in spatial model  110 . 
     In some examples, lexical cost values may be based on language model  111 . For instance, the respective lexical cost values may be based on the probability that a second key will be selected after a first key (e.g., the probability that the “o” key will be selected after the “c” key). In other examples, the respective lexical cost values may be based on the probability that a second candidate word will follow a first candidate word, or on the frequency values of language model  111 . In certain examples, the keys for which respective lexical cost values are determined are selected based at least in part on language model  111 . In some examples, the lexical cost values are lower where there is a greater likelihood that a tap gesture indicates a key. In other examples, the lexical cost values are higher where there is a greater likelihood that the tap gesture indicates a key. 
     In  FIG. 2 , as described with respect to  FIG. 1 , a user may intend to type “revolution”. Gesture module  108  may determine a first composite cost value representing a probability that tap gesture  124 A indicates “R” key  123 A and a second composite cost value representing a probability that the tap gesture indicates “E” key  123 B. Similarly, gesture module  108  may determine a third composite cost value representing a probability that tap gesture  124 B indicates “E” key  123 B and a fourth composite cost value representing a probability that tap gesture  124 B indicates the “W” key (which may be another of the multiple keys in proximity to the location of the tap gesture performed near “E” key  123 B). In this way, gesture module  108  may incrementally determine composite cost values, each representing a probability that a tap gesture indicates a key of the plurality of keys included in graphical keyboard  128 . For instance, gesture module  108  may determine composite cost values representing probabilities that tap gestures indicate “P” key  123 C, space key  123 D, or other keys included in the plurality of keys, such as an “0” key that is in proximity to the tap gesture performed near “P” key  123 C). 
     Gesture module  108  may compare the respective composite cost values for at least two keys of the plurality of keys to determine a combination of keys having a combined composite cost value that satisfies a threshold. A combined composite cost value for a combination of keys may represent a probability that tap gestures  124 , together, indicate the combination of keys. Gesture module  108  may compare the respective composite cost values for at least two keys of the plurality of keys to determine which of the at least two keys is indicated by a tap gesture. Gesture module  108  may determine a combination of keys by determining which keys are indicated by each tap gesture. 
     In some examples, gesture module  108  may compare the combined composite cost value of a determined combination of keys with a threshold value. In some examples, the threshold value is the combined composite cost value of a different determined combination of keys. For instance, gesture module  108  may determine a first combination of keys having a first combined composite cost value and a second combination of keys having a second combined composite cost value. In such an instance, gesture module  108  may determine one or more candidate words based on the combination of keys with the lower combined composite cost value. In  FIG. 2 , as described with respect to  FIG. 1 , gesture module  108  may compare the determined respective composite cost values to determine a combination of keys (i.e., “R”, “E”, “V”, and “P”) having a combined composite cost value. 
     In response to receiving the tap gesture data from UI module  106 , gesture module  108  may create a set of candidate strings. Each candidate string may be stored in a token. A token may be used to store a candidate string and append characters as subsequent indications of gestures are received by gesture module  108 . As an example, gesture module  108  may create a token at the entry node of a lexicon which may be included in language model  111 . In some examples, language module  111  may be implemented as a trie data structure. Each movable token may represent a partial alignment between a node in the lexicon (i.e., a partial word and/or phrase) and a received tap gesture. A token may advance to child nodes in the lexicon (i.e., next letters in the word) as gesture module  108  receives subsequent indications of tap gestures. 
     As described, a lexicon trie data structure may contain a plurality of nodes, each node representing a letter. Gesture module  108  may push the created token into active beam  220 . Gesture module  108  may create a token copy on each of the token&#39;s child nodes. In the example of  FIG. 2 , gesture module  108  may create a first token copy on the child node representing the letter “R” (e.g., corresponding to a predicted key selection of “R” key  123 A) and a second token copy on the child node representing the letter “E” (e.g., corresponding to a predicted key selection of “E” key  123 B). Each of the tokens may include a single string of predicted characters. 
     For each tap gesture received, gesture module  108  may determine respective composite cost values for each of at least two keys of the plurality of keys. Each of the respective composite cost values may represent a probability that the tap gesture indicates a key of the plurality of keys. Gesture module  108  may determine a first composite cost value representing a probability that the first tap gesture indicates the node representing the letter “R” and a second composite cost value representing a probability that the tap gesture indicates the node representing the letter “E”. In some examples, gesture module  108  may then update the token copy with the respective composite cost value and push the token copy in to next beam  222 . Gesture module  108  may add the first composite cost value to the first token copy and the second composite cost value to the second token copy. 
     In some examples, gesture module  108  determines the respective cost values by including respective physical cost values and respective lexical cost values, as further described below. For instance, gesture module  108  may determine composite cost value by summing a physical cost value and a lexical cost value. In some examples, gesture module  108  may apply one or more weighting factors to the respective physical cost values by modifying specific values of spatial model  110 . For example, by increasing a standard deviation value, stored in spatial model  110  and associated with a key, gesture module  108  may decrease the relative importance of the physical cost value as compared to the lexical cost value. By decreasing a standard deviation value, gesture module  108  may increase the relative importance of the physical cost value. 
     In some examples, gesture module  108  may weigh one or more of the lexical cost values higher than the respective physical cost values, such as where the tap gestures are detected at a high rate of speed. For instance, gesture module  108  may determine that a characteristic associated with a gesture (e.g., speed) satisfies one or more thresholds, such as when a global speed of the tap gestures is greater than or equal to a threshold value, less than or equal to a threshold value, etc. In response to the determination, gesture module  108  may weigh the lexical cost values of respective candidate strings higher than the respective physical cost values. In some examples, gesture module  108  may use statistical machine learning to adapt to the style of the user and modify the weighting over time. For instance, gesture module  108  may, in response to determining that the user is inaccurate while performing gestures, weigh the lexical cost values higher than the physical cost values. 
     In some examples, gesture module  108  may weigh physical cost values higher than the lexical cost values. Gesture module  108  may weigh the physical cost values higher than the lexical cost values where there is an indication that the lexical cost values may be unreliable, such as where the user has a history of entering words not included in the lexicon. In some examples, the relative weights may be estimated and optimized heuristically, such as by measuring accuracy from a plurality of computing devices. 
     In one example, gesture module  108  may determine a first physical cost value based on the Euclidian distance between the first tap gesture  124 A and “R” key  123 A, as shown in  FIG. 1 . In some examples, gesture module  108  may determine the physical cost values by comparing the Euclidian distance between a first tap gesture and a second tap gesture with the Euclidian distance between a first letter indicated by the first tap gesture and a second letter which may be represented by the second tap gesture. Gesture module  108  may determine that the cost value of the second letter is inversely proportional to the difference between the distances (i.e., that the second letter is more probable where the distances are more similar). That is, in some examples, physical cost values may be calculated on the geometry of the tap gestures instead of the location of the tap gestures. For instance, a smaller difference in distances may indicate a better likelihood that the second gesture was a selection of the second letter. 
     Gesture module  108  may also determine the composite cost values for respective keys by determining lexical cost values for each of the at least two keys of the plurality of keys. Each of the respective lexical cost values may represent a probability that a letter represented by a key of the plurality of keys is included in a candidate word based on the token. The lexical cost values may be based on language model  111 . For instance, the lexical cost values may represent the likelihood that a given letter is selected based on probable words included in a lexicon of language model  111 . Gesture module  108  may determine a first lexical cost value based on an entry in the lexicon indicating a frequency that the letter “R” is the first letter in a word. 
     As an example, gesture module  108  may receive an indication of tap gestures  124 A and  124 B. In response, gesture module  108  may determine a first token including the single string of predicted characters “re”. Gesture module  108  may determine one or more candidate words indicated by the gesture using the first token. For instance, gesture module  108  may determine one or more candidate words for which the single string of predicted characters is a prefix, such as the words “rest”, “rend”, and the like. 
     In the present example, as user  150  continues to perform the tap gestures, gesture module  108  may receive an indication of tap gesture  124 C. In response, gesture module  108  may create a token copy on each of the token&#39;s child nodes to include a predicted character indicated by the received portion of the gesture, such as the letter “v” corresponding to a predicted selection of the “V” key. As such, gesture module  108  may advance the first token to include the single string of predicted characters “rev”. Based on the first token, gesture module  108  may determine one or more candidate words indicated by the gesture, such as words included in the lexicon for which the single string of predicted characters “rev” is a prefix (e.g., the words “review”, “revolve”, and the like). 
     In certain examples, gesture module  108  may maintain a threshold number of tokens (e.g., fifty tokens, one hundred tokens, two hundred tokens, or other numbers of tokens) and discard the rest. For instance, gesture module  108  may maintain a group of the one hundred tokens that include the most likely words indicated by the received gestures, as determined based on spatial model  110  and language model  111 . In this way, gesture module  108  may efficiently scale to large lexicons. 
     Gesture module  108  may determine whether UI module  106  has completed receiving tap gestures  124 . Where UI module  106  continues to receive tap gestures on character keys, gesture module  108  may continue to incrementally process the gesture data. In some examples, gesture module  108  may output one or more predictions prior to UI module  106  completing receipt of the tap gestures. 
     After receiving an indication of each tap gesture, gesture module  108  may determine one or more candidate words for display at the presence-sensitive display as auto-completion suggestions and/or a soft commit word. After UI module  106  has completed receiving the gesture path data corresponding to tap gestures  124 , gesture module  108  may determine candidate words of “revolutionary” and “revolt” for display as auto-completion suggestions as seen in GUI  114  of  FIG. 1 . Gesture module  108  may further determine the candidate word “revolution” for display as a soft commit word, as seen in text entry area  126 . 
     Gesture module  108  may retain one or more of the determined tokens. That is, gesture module  108  may maintain tokens after receiving an indication of a tap gesture, and may modify the tokens in response to receiving gesture data corresponding to a subsequent gesture being received at input device  202 . As such, in response to receiving an indication of a next gesture to select a next character key of the plurality of keys, gesture module  108  may create a token copy on each of the previously determined token&#39;s child nodes to include a predicted character indicated by the received gesture. 
     If a next gesture is determined to be a selection of space key  123 D, gesture module  108  may perform a hard commit. That is, gesture module  108  may send the displayed soft commit to other components associated with computing device  102  (e.g., applications  112 ). Gesture module  108  may perform a hard commit in response to receiving a selection of a displayed auto-complete suggestion (i.e., a candidate word displayed in one of word suggestion areas  122 ). In such case, gesture module  108  may send the displayed auto-complete suggestion to one or more components associated with computing device  102 . In some examples, gesture module  108  may discard the determined candidate strings and/or candidate words after performing a hard commit. Upon receiving an indication of a subsequent gesture, gesture module  108  may create a new set of candidate strings. In other examples, gesture module  108  may not discard candidate strings or candidate words. 
     According to techniques of the present disclosure, gesture module  108  may dynamically modify values of a spatial model used in conjunction with a language model to determine one or more tokens based on received indications of one or more gestures to select one or more keys of a graphical keyboard. Gesture module  108  may thereby enable a user to accurately enter a word or phrase by providing a series of tapping or sliding gestures without requiring the user to accurately and precisely perform the gesture or gestures. In addition, by using the spatial model, as modified, along with the language model, gesture module  108  may dynamically vary the weighting of the models, thereby enabling more accurate text input. Moreover, by allowing the user to input gestures at higher speeds and less accuracy, techniques of the present disclosure may increase typing speed and efficiency by allowing a user to enter characters without requiring as much attention to precise inputs. 
       FIGS. 3A and 3B  are block diagrams illustrating one example of modifying a spatial model to provide text input, in accordance with one or more aspects of the present disclosure. For purposes for illustration only, the example operations are described below within the context of computing device  102 , as shown in  FIGS. 1 and 2 . 
       FIGS. 3A and 3B  include an example graph of distribution models  302 A and  302 B (collectively “distribution models  302 ”), respectively, each displaying the expected distribution of touch points along a horizontal or x-axis for “E” key  123 B. Distribution models  302  may be stored in spatial model  110 . Though not shown in  FIGS. 3A and 3B , spatial model  110  may also include a distribution model of expected touch point distribution along a vertical, or y-axis for “E” key  123 B. Though the example of  FIGS. 3A and 3B  show a distribution model for “E” key  123 B, distribution models for the other keys of, for example, graphical keyboard  128  may have similar characteristics. 
     Distribution models  302  may adhere to a Gaussian distribution pattern. Distribution models  302  may include a statistical average or mean, μ, and a standard deviation value, σ. The mean value may represent the statistical, horizontal location of “E” key  123 B. Initially, the mean value may be centered on “E” key  123 B as displayed in graphical keyboard  128 . The standard deviation value may be defined with respect to the physical size of “E” key  123 B as displayed by graphical keyboard  128 . The standard deviation value may represent the horizontal variability in expected touch point distribution. That is, a larger standard deviation value with respect to the physical size of “E” key  123 B may indicate a wider variability in expected touch point distribution (i.e., more of the received touch points are expected to be received further from the mean). A smaller standard deviation value with respect to the physical size of “E” key  123 B may indicate a narrower variability in expected touch point distribution (i.e., a larger number of the received touch points are expected to be received closer to the mean). 
     In either case, distribution models  302  may be defined by the probability distribution function of a Gaussian distribution, 
     
       
         
           
             
               
                 
                   
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     In adherence with the Gaussian distribution, distribution models  302  may include approximately 68.2% of all expected touch points within one standard deviation of the mean. Distribution models  302  may include approximately 95.4% of all expected touch points within two standard deviations of the mean, and so on. Thus, by modifying the mean value and/or standard deviation value, gesture module  108  may more accurately determine a set of candidate strings in accordance with one or more techniques of the present disclosure. For instance, gesture module  108  may modify the horizontal mean value of “E” key  123 B to account for a user regularly attempting to select “E” key  123 B by tapping slightly to the right or left of the center of the key. In another example, gesture module  108  may modify the horizontal standard deviation value as described below. Further details of how gesture module  108  may utilize spatial model  110  are described with respect to  FIG. 5  below. 
       FIG. 3A  includes distribution model  302 A. Distribution model  302 A may represent a default or initial state of the horizontal model for “E” key  123 B. For instance, spatial model  110  may contain distribution model  302 A prior to receipt of any user input by computing device  102 . As shown, distribution model  302 A may include a mean value and standard deviation value. The standard deviation value may be twice the physical width of “E” key  123 B, as displayed (i.e., the width of “E” key  123 B is 0.5σ). In other words, based on distribution model  302 A, roughly 38.2% of touch inputs would be expected to fall within the left and right boundaries of “E” key  123 B. In some examples, the standard deviation value may be based on the physical size of the keys of graphical keyboard  128 . For example, when computing device  102  is a tablet, the keys may be relatively large and the width of a key may be roughly 4.13σ. That is, approximately 96% of selections of “E” key  123 B may fall within the left and right boundaries of the key. When the key is smaller, such as when computing device  102  is a smartphone, the width of “E” key  123 B may be equal to 2σ. In one example implementation, for a key width of 48 pixels, the horizontal standard deviation may be 1.2 times the width of the key. Various standard deviation values may be preset or experimentally determined in different situations. 
     The standard deviation value of  302 A may represent the expected horizontal variability in received tap gestures when “E” key  123 B is selected as a first character. However, in some situations, different standard deviation values may more accurately represent the expected variability. For instance, when a user selects a key that is located in the same row as “E” key  123 B within graphical keyboard  128  (e.g., the “P” key or the “T” key), the variability in tap gestures to select “E” key  123 B may increase in the horizontal direction. That is, after selecting a key in the same row, a user may be more likely to tap to the left or the right of the center of “E” key  123 B compared to when tapping after selecting a key in a different row or when tapping “E” key  123 B without tapping any other keys. In order to account for the increase in variability (i.e., tap gestures that are more sloppy in the horizontal direction), gesture module  108  may modify the horizontal standard deviation value of “E” key  123 B. 
       FIG. 3B  includes distribution model  302 B. Distribution model  302 B may represent a modified state of the horizontal model for “E” key  123 B. As shown in  FIG. 3B , the standard deviation value of distribution model  302 B may be increased by two-and-a-half times. In some examples, increases and decreases in standard deviation values may be predetermined values for various criteria. For instance, while an increase of two-and-a-half times is shown in  FIG. 3B , other increases or decreases may be larger or smaller in size in various situations. In other examples, standard deviation changes may be experimentally determined by computing device  102 , or may be determined by a central server from a large number of devices and received by computing device  102  (e.g., via communication unit  204 ). 
     By increasing the standard deviation value for “E” key  123 B, distribution model  302 B may reduce the need for the user to accurately tap within the horizontal boundaries of “E” key  123 B. That is, by using distribution model  302 B, gesture module  108  may assign a lower cost value to an “e” character when receiving a tap input than would be assigned if gesture module  108  were using distribution model  302 A. In this way, modification of spatial model  110  by gesture module  108  may increase the accuracy of text input. 
       FIGS. 4A and 4B  are block diagrams illustrating example GUIs of modifying a spatial model to provide accurate text input, in accordance with one or more aspects of the present disclosure. For purposes for illustration only, the example operations are described below within the context of computing device  102 , as shown in  FIGS. 1 and 2 . GUIs  402  and  404  may be displayed by UI device  104  as described in  FIG. 1 . 
     In some example techniques, gesture module  108  may enable a user to enter text input and receive improved correction, completion, and/or prediction services without requiring improved accuracy by modifying a spatial model used in character determination. That is, computing device  102  may modify one or more attributes of spatial models for characters of a graphical keyboard in response to received text input, and may employ the modified spatial models to more accurately determine which characters were intended by a user as text input, which words are likely to be intended by the text input, and what text input may be next inputted. Such techniques are further illustrated in  FIGS. 4A and 4B . 
     As shown in  FIG. 4A , GUI  402  may include text entry area  426  and graphical keyboard  428 . Initially, text entry area  426  may not include text. Each of the keys of graphical keyboard  428  may be associated with a statistical distribution model of a respective key. For instance, prior to receiving any text input, “W” key  406 A, “G” key  406 B, and “L” key  406 C (collectively “keys  406 ”) may be associated with statistical models  408 A,  408 B, and  408 C, respectively. In the example of  FIGS. 4A and 4B , statistical models  408 A,  408 B, and  408 C (collectively “statistical models  408 ”) may be default, or initial statistical models of the respective keys. That is, statistical models  408  may be predefined and stored in spatial model  110  before computing device  102  has received any text input. 
     Each of statistical models  408  may include one or more statistical locations of the associated key, a standard deviation value for both the horizontal (x) and vertical (y) axis, and a co-variance value for both the horizontal and vertical axis. In some examples, statistical models  408  may include other data about the associated key, such as the number of times the associated key has been pressed, a record of recent selections of the key, or other information. As displayed in  FIGS. 4A and 4B , the location of statistical models  408  may represent the statistical location of the associated key, and the size and shape of statistical models  408  may represent the standard deviation values of the associated key. As seen in  FIG. 4A , the statistical locations associated with keys  406  may be centered over their respective keys. Both the horizontal and vertical standard deviation values of statistical models  408  may be approximately equal to the height of the respective keys. In some examples, the horizontal and vertical standard deviations may not be the same. 
     A user of computing device  102  (e.g., user  150 ), may perform tap gesture  410  to input an “1” character. Tap gesture  410  may not be exactly at the center of “L” key  406 C. Instead, tap gesture  410  may be on the upper right corner of the key. UI device  104  may receive tap gesture  410 , and UI module  106  may send an indication of tap gesture  410  to gesture module  108 . In accordance with one or more aspects of the present disclosure, gesture module  108  may modify spatial model  110  based on the received indication. The modification of spatial model  110  may, in some examples, include a modification of values associated with “L” key  406 C (e.g., statistical model  408 C). In some examples, gesture module  108  may modify other values stored in spatial model  110 , such as statistical models  408 A,  408 B, as well as spatial models of other keys. 
       FIG. 4B  includes GUI  404  which may represent the state of statistical models  408  after user  150  performs a second tap gesture  412 . User  150  may perform tap gesture  412  to input an “o” character. Gesture module  108  may receive an indication of tap gesture  412 , and modify spatial model  110  accordingly. The modifications to spatial model  110  performed by Gesture module  108  may result in statistical models  408  as shown in GUI  404 . For example, gesture module  108  may receive an indication of tap gesture  412 , and determine one or more characteristics based on the received indication. The characteristics may include a location of input device  202  at which tap gesture  412  was received. For example, the input location may include an x-coordinate of input device  202  and a y-coordinate of input device  202 . Based on the input location, gesture module  108  may determine a row of keys of graphical keyboard  428  within which tap gesture  412  was received. In the example of  FIG. 4B , this may be the row of keys including “W” key  406 A. 
     In response to determining the row of keys, gesture module  108  may modify the statistical model of keys in the row of keys. For example, gesture module  108  may increase the horizontal standard deviation value of statistical model  408 A, associated with “W” key  406 A, thereby accounting for the possibility that a next tap gesture to select “W” key  406 A, located mostly horizontally (i.e., as opposed to both horizontally and vertically) from the current tap gesture  412 , may include increased horizontal error. In another example, gesture module  108  may decrease the vertical standard deviation value of statistical model  408 A, thereby accounting for the possibility that the next tap gesture will include decreased vertical error. That is, when a user selects a key and then slides a finger substantially directly to the left or the right, the tap gesture may be more likely to “overshoot” or “undershoot” (e.g., to the left or right) the horizontal location of the next intended key, but may be more accurately placed vertically with respect to the next intended key. In some examples, gesture module  108  may both increase the horizontal standard deviation value for a key and decrease the vertical standard deviation value for the key. 
     As shown in  FIG. 4B , statistical model  408 A may continue to have a mean value centered over “W” key  406 A. However, in response to receiving an indication of tap gesture  412 , gesture module  108  may reduce the vertical standard deviation value of statistical model  408 A. Additionally, gesture module  108  may increase a horizontal standard deviation value of statistical model  408 A. The modifications of statistical model  408 A may account for the higher likelihood that user  150  will make a straight, horizontal motion from the “0” key to “W” key  406 A, and thus may increase likely error in the horizontal direction, while decreasing likely error in the vertical direction. 
     In another example, gesture module  108  may modify statistical model  406 B based on the received indications of tap gestures  410  and  412 . In accordance with one or more aspects of the present disclosure, gesture module  108  may determine one or more characteristics associated with the received tap gestures. As previously described, the characteristics may include a location of input device  202  at which the tap gestures were received. Based on the determined location characteristics, gesture module  108  may determine that an “1” character and an “o” character were inputted by the tap gestures  410  and  412 , respectively. In response to a high probability that the characteristics of a tap gesture indicates a specific key, gesture module  108  may use language model  111  to determine the likelihood of one or more keys being the next key selected, and modify spatial model  110  accordingly. For example, gesture module  108  may determine that there is a high probability that the location of tap gesture  410  indicates “L” key “ 406 C and that the location of tap gesture  412  indicates an “O” key. Based on these high probabilities, gesture module  108  may use language model  111 , and determine that there is a high likelihood that a “g” character will follow the “1” and “o” characters inputted, because there are a number of words beginning with “log” in the lexicon and/or the words beginning with “log” have a high frequency value. 
     Based on this determination, gesture module  108  may increase the vertical and/or horizontal standard deviation values of statistical model  408 B in order to increase the likelihood that a selection near “G” key  406 B will result in a lowest cost value being associated with adding a “g” character to the set of candidate strings. In some examples, gesture module  108  may decrease the vertical and/or horizontal standard deviation values of statistical models for keys associated with unlikely next characters, such as a “y” character. That is, based on the location of the previously received tap gestures, gesture module  108  may use language model  111  to determine likely next keys and increase the standard deviation values. Gesture module  108  may also determine unlikely next keys and decrease the standard deviation values. In this way, gesture module  108  may, in some examples, the importance of spatial model  110  when receiving a next tap input. 
     The modifications of statistical models  408 A and  408 B may be temporary. That is, upon receiving a third tap gesture, gesture module  108  may modify spatial model  110  to change the standard deviation values of statistical models  408 A and  408 B back to a previous state. In this way, gesture module  108  may enable computing device  102  to more accurately determine text input by using previous text input to estimate future text input error. 
     Gesture module  108  may also perform non-temporary modifications. As one example, in response to receiving an indication of tap gesture  410 , gesture module  108  may modify spatial model  110  to change the statistical location of statistical model  408 C associated with “L” key  206 C. For instance, in response to receiving an indication of tap gesture  410 , gesture module  108  may determine one or more characteristics associated with tap gesture  410 . The characteristics may include a location of input device  202  at which tap gesture  410  was received. The location may include a vertical and horizontal location, such as pair of coordinate values in an x, y plane. In response to determining the location, gesture module  108  may modify a statistical location value of spatial model  110  associated with one or more keys of graphical keyboard  428 . 
     Modifying the statistical location may include changing the vertical and horizontal components of the statistical location by a value determined based on the location of tap gesture  410 . For example, gesture module  108  may calculate the horizontal and vertical distances between the statistical location of “L” key  406 C and tap gesture  410 . Gesture module  108  may then apply a multiplier (e.g.,  0 . 5 ,  0 . 1 ,  0 . 01 , etc.) to the calculated distances, and add the result to the statistical location values. In the example of  FIG. 4A , the difference between the statistical location of statistical model  408 C and tap gesture  410  may be 0.6 in the y-direction, and 0.4 in the x-direction. Based on this difference, gesture module  108  may determine a new statistical location for statistical model  408 C by adding, for example, 0.06 to the y-value of the statistical location, and adding 0.04 to the x-value of the statistical location. In some examples, gesture module  108  may determine a new statistical location for the statistical model by calculating an average of previous values. For instance, a statistical model may represent the average of the previous horizontal values and the previous vertical values for the key. In response to determining a location characteristic, gesture module  108  may take a weighted average of the statistical location and the characteristic location by, for example, multiplying the horizontal and vertical statistical locations by 9, adding the respective horizontal and vertical characteristic locations, and dividing the result by 10. 
     As shown in  FIG. 4B , the resultant statistical model  408 C may be located slightly above and slightly to the right of the center of “L” key  206 C. This modification may persist through the receipt of subsequent tap gestures. That is, gesture module  108  may not return statistical model  408 C back to a previous state. In some examples, modifying the statistical location of a statistical model may be performed on more than one key for each tap gesture received, such as where physical cost values do not clearly indicate which key was intended. In this way, gesture module  108  may enable computing device  102  to account for repetitive errors in user input, such as those caused by how user  150  is holding computing device  102 , what fingers user  150  is using to input text, etc. 
     In some examples, gesture module  108  may modify spatial model  110  in response to a determined input speed of text input. That is, when a user enters a number of tap inputs at a high rate of speed, gesture module  108  may increase the vertical and/or horizontal standard deviation values of one or more keys of keyboard  428 . For instance, gesture module  108  may receive a series of indications of tap gestures performed by user  150 . In accordance with one or more aspects of the present invention, gesture module  108  may determine an input speed characteristic of the received tap gestures. In some examples, the determined input speed (e.g., in taps per second) may be based on a certain number of the most recently received tap gestures (e.g., the last  3  tap gestures, the last  5  tap gestures, etc.). In other examples, the input speed may be determined based on all tap gestures received since the most recent hard commit. In any case, gesture module  108  may compare the input speed to a threshold value. The threshold value may be a predetermined value stored at computing device  102 , or may be based on previous input received from users. In some examples, if the input speed of the tap gestures is less than the threshold value, gesture module  108  may refrain from modifying any standard deviation values stored in spatial model  110  based on the determined speed characteristic. In other examples, responsive to determining that the input speed is less than the threshold value, gesture module  108  may reduce one or more standard deviation values stored in spatial model  110 . That is, when gesture module  108  determines an input speed below the threshold, gesture module  108  may reduce a horizontal and/or vertical standard deviation value of one or more keys of graphical keyboard  428 , thereby increasing the importance of spatial model  110  in determining composite cost values. 
     If, however, gesture module  108  determines that the determined input speed is greater than or equal to the threshold, gesture module  108  may increase standard deviation values of one or more keys of graphical keyboard  428 . Increasing standard deviation values may reduce the importance of spatial model  108  in determining a composite cost value for various candidate strings. In other examples, gesture module  108  may modify one or more standard deviation values of spatial model  110  by a factor proportionate to the determined speed characteristic. For instance, given a preset average input speed (in characters per second), S, a determined input speed, S′, and a default standard deviation, a′, gesture module  108  may calculate a modified standard deviation value, 
     
       
         
           
             
               
                 
                   
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     In some examples, such as the case where a user is inputting gestures using a single finger, a more accurate adjustment can be made to spatial model  110  by determining what key is being tapped, what the last key was, and applying Fitts&#39;s law: T=a+b log (D/4σ′+1), where T is the time interval from the last key to the current key and D is the physical distance from the last key to the current key (i.e., the key associated with the standard deviation values being increased or decreased). In each case, gesture module  108  may increase the accuracy of predicted text input by modifying values of spatial model  110  for one or more keys, based on determined characteristics of received input, in order to weight the importance of spatial model  110  more or less heavily than the importance of language model  111 . This flexibility may allow computing device  2  to more accurately predict text input and increase the overall typing speed and accuracy of the user. 
       FIGS. 5A-C  are block diagrams illustrating further details of one example of a computing device shown in  FIG. 1 , in accordance with one or more aspects of the present disclosure. The example illustrated in  FIGS. 5A-C  describes one implementation of the underlying unified model for providing text input. Text error correction may rely on two types of knowledge that is represented herein by spatial model  110 , which models graphical keyboard  528  and relates received tap gestures or sliding gestures to the individual keys of graphical keyboard  528 , and language model  111 , which gives a probability distribution of what text input is likely to come next, given the received text input, as shown in  FIGS. 1-2 . Most generally, given a set of tap gestures, s 1 , s 2 , . . . , s N , performed at graphical keyboard  528 , error correction is achieved by determining the string of characters (i.e., a candidate string), c 1 , c 2 , . . . , c N , such that 
       argmax c     1     . . . ,C     N     P ( c   1   , . . . ,c   N   |s   1   , . . . ,s   N ).  (3)
 
     That is, error correction as implemented in computing device  102  may find the candidate string which has a best probability value, given the sequence of tap gestures received. For instance, computing device  102  may apply Bayes&#39; theorem to the conditional probability of equation (3) above to obtain 
       argmax c     1     . . . ,C     N     P ( s   1   , . . . ,s   N   |c   1   , . . . ,c   N ) P ( c   1   , . . . ,c   N ).  (4)
 
     In other words, the “best” candidate string may be the candidate string which results in a maximum value when taking the product of two probability values. The first probability value may represent the probability of receiving the sequence of performed tap gestures, given the characters of the candidate string are the intended input. The second probability value may represent the probability that the characters of the candidate string are the intended input. In accordance with the techniques of the present disclosure, the first value may be determined by reference to spatial model  110  and the second value may be determined by reference to language model  111 . 
     The number of tap inputs, N, at which to determine the respective probability values may be based on the indications of received tap gestures. In one example, gesture module  108  may access spatial model  110  and language model  111  only after receiving certain indicators, such as a selection of space key  123 D. Rather than limiting the ability of the user to receive immediate text correction when, for example, the user is unsure about the number of characters in an intended word (e.g., attempting to enter “acess” for the word “access”), gesture module  108  may incrementally update the set of candidate strings after each received indication of a tap gesture. In this way, computing device  102  may provide the user with the immediate opportunity to review likely corrections and select a desired correction. In other words, because the user may desire to review suggestions after each tap gesture performed, gesture module  108  may use a value of N as small as one. In accordance with techniques of the present disclosure, gesture module  108  may predict a next word, and thus, N may be zero. 
     In some examples, gesture module  108  may retain a set of candidate strings, and update one or more strings as new indications are received, performing new determinations after each received indication. This process may continue until gesture module  108  performs a hard commit, as previously described. Examples which may cause gesture module  108  to perform a hard commit include a candidate string passing a threshold confidence value, the user&#39;s selection of a word delimiter, such as a space character or punctuation, or when the length of the candidate strings passes a threshold number of characters. 
     As described, language model  111  may include a lexicon and a word-level N-gram dictionary. Language model  111  may allow the user to enter non-words (i.e., words not in the lexicon) by allows providing the literal string of letters as a suggestion (e.g., in one of word suggestion areas  122 ). In some examples, once a non-word is entered a threshold number of times, the non-word may be added to the lexicon. The lexicon and word-level N-gram dictionary may provide more efficient storage requirements and better performance when compared to a character-level N-gram dictionary, for example. 
     Using the lexicon and word-level N-gram dictionary of language model  111 , gesture module  108  may unify correction and word completion tasks by determining 
       argmax w     N     P ( w   1   , . . . ,w   N   |s   1   , . . . ,s   M ).  (5)
 
     In equation (5), (w 1 , . . . , w N-1 ) may represent a sequence of N−1 words already entered, w N  may represent the current word being entered, and (s 1 , . . . , s M ) may be a sequence of M tap gestures performed in an attempt to enter w N . In such instance, the value of M may be between one and the character length of w N . Computing device  102  may apply Bayes&#39; theorem to equation (5) resulting in 
       argmax w     N     P ( s   1   , . . . ,s   M   |w   1   , . . . ,w   N ) P ( w   1   , . . . ,w   N ).  (6)
 
     That is, computing device  102  may determine that the best candidate word is the word which results in a maximum product of the two probability values of equation (6). The first probability value may represent the likelihood of receiving the inputted tap gestures, given that the intended sequence of words is (w 1 , . . . , w N ). Gesture module  108  may determine the first probability value of equation (6) based on spatial model  110  as described. The second probability value may represent the likelihood (i.e., the frequency value) of the sequence of words, (w 1 , . . . , w N ). Gesture module  108  may determine the second probability value of equation (6) based on a word-level N-gram dictionary of language model  111  as described. In some examples, the tap gestures performed in order to input w N  may be independent of the preceding words. That is, how gesture module  108  determines the current word may not be affected by what the preceding words are. In other words, P(s 1 , . . . , s M |w 1 , . . . , w N ) may be simplified to P(s 1 , . . . , s M |w N ). Consequently, for a current word, w N , which consists of L characters, c 1 , . . . , c L , the probability P(s 1 , . . . , s M |w N ) may be represented by computing device  102  as P(s 1 , . . . , s M |c 1 , . . . , c L ). 
     In the present example of  FIGS. 5A-C , gesture module  108  may be modeled on the assumption that a user&#39;s tap gesture is independent of his or her future tap gestures. Thus, the probability, P(s 1 , . . . , s M |c 1 , . . . , c L ) can be simplified to P(s 1 , . . . , s M |c 1 , . . . , c M ). That is, gesture module  108  may use spatial model  110  to determine the probability of receiving the performed tap gestures, assuming the user intended to input the corresponding characters. This probability may depend on a user&#39;s input method. For example, a user typing on graphical keyboard  528  using both thumbs may perform tap gestures differently than a user typing with only one thumb, or with an index finger on the hand opposite the hand holding computing device  102 . Additionally, tap gestures to select certain characters may, as described, be dependent on one or more previously performed tap gestures. Gesture module  108  may account for such dependencies by determining characteristics of one or more received tap gestures, and modifying spatial model  110  accordingly. In some examples, however, spatial model  110  may be predetermined based on the assumption that each inputted gesture is independent from the others. That is, P(s 1 , . . . , s M |c 1 , . . . , c M ) may be approximated by P(s 1 |c 1 ) P(s 2 |c 2 ) . . . P(s M |c M ). In other words, for each candidate string, gesture module  108  may use spatial model  110  to determine a cost value by determining 
       Π i=1   M   P ( s   i   |c   i ).  (7)
 
     In accordance with techniques of the present disclosure, spatial model  110  may store statistical models associated with keys of graphical keyboard  528 . Each statistical model may adhere to a bivariate Gaussian distribution. In some examples, the vertical and horizontal Gaussian probabilities may be dependent. That is, the covariance may be non-zero. In other examples, the Gaussian probabilities may be independent, and thus the covariance may be zero. For ease of understanding only, the example described in  FIGS. 3A, 3B, and 3C  assume a covariance of 0. Therefore, the probability of receiving a given tap gesture, given the intended key, c i , may be determined by gesture module  108  by using: 
     
       
         
           
             
               
                 
                   
                     P 
                     ⁡ 
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                         s 
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                     ) 
                   
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                   8 
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     In equation (8), (x i , y i ) may represent the location of the performed tap gesture, and (μ xi , μ yi ) may represent the statistical location associated with the key for character c i . As previously described, statistical models of spatial model  110  may include values for μ xi , μ yi , σ xi , and σ yi . Consequently, gesture module  108  may receive an indication of a tap gesture including a location of a performed tap gesture, (x i , y i ). In response to receiving an indication, gesture module  108  may access spatial model  110  to retrieve the relevant values, μ xi , μ yi , σ xi , and σ yi , associated with one or more keys of graphical keyboard  528 . For each key, gesture module  108  may apply equation (8) to determine a probability that the performed tap gesture was intended to select the key. This probability value may represent the physical cost value of adding a character associated with the key to a candidate string. Gesture module  108  may, based on equations (8) and (6), determine a composite cost value: 
     
       
         
           
             
               
                 
                   arg 
                   
                     max 
                     
                       w 
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                   9 
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     Gesture module  108  may perform the analysis of equation (9) after each indication received, in order to determine physical cost values for the group of received tap inputs and lexical cost values (e.g., frequency values) for each candidate string. 
     In some examples, gesture module  108  may operate at a logarithmic scale. By applying a log function to equation (9), the computation may become a series of additions and subtractions, such that: 
     
       
         
           
             
               
                 
                   
                     arg 
                     
                       max 
                       
                         w 
                         N 
                       
                     
                     
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                       10 
                     
                     ⁢ 
                     
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                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     For ease of understanding, s W     N    (the physical cost value of the word w N ) can be defined as the second half of equation (10), and L WN  (i.e., the lexical cost value of the word w N ) can be defined as the first half of equation (10) (i.e., the lexical cost value). Thus, a composite cost value or “total cost” value, T WN , may be determined by gesture module  108  as 
         T   WN   =L   WN   +s   WN .  (11)
 
     Equation (11) may provide gesture module  108  with an accurate approximation for determining correction and completion of inputted text. Gesture module  108  may unify the correction and completion model with a prediction model by, in some examples, adding an additional cost (e.g., 0.6σ) to each candidate string&#39;s physical cost value for each additional key for which a tap gesture was not performed. In other examples, gesture module  108  may multiply a current spatial score by a factor of (L−M)/M where L is the number of characters in word w N , and M is the number of tap gestures inputted. That is, each additional key for which a tap gesture was not performed may be given a physical cost value equal to the average physical cost value of those characters already contained in a candidate string. In other words, gesture module  108  may predict that the user will continue to input tap gestures at the same average level of precision. In other examples, gesture module  108  may assign other cost values to not-yet-selected characters of each word prediction, such as an additional lexical cost value, or total cost value. By adding a cost value for predicted characters, longer words may get proportionately ranked lower, before factoring in the lexical cost value. 
     Gesture module  108  may account for insertion and omission errors. Insertion errors may represent those errors where one or more additional characters are selected, but do not belong in a word (e.g., tap gestures inputting “abourt” for “about”). Omission errors may represent errors in which one or more characters are accidentally not selected (e.g., tap gestures inputting “abot” for “about”). Instead of using deterministic mapping from a word, w, to a character sequence, spelling(w), gesture module  108  may employ probabilistic mapping that includes insertions/deletions. In one example, once a number of received tap gestures (e.g., 2-4) have been entered for a current word, if the total cost value of the best candidate word, T C1 , minus the total cost value of the second best candidate word, T C2 , is lower than a specified threshold, gesture module  108  may run alternative insertion/omission alternative hypotheses. For instance, gesture module  108  may insert one or more wild card characters. Wild card characters may also account for an omitted or inserted space character. If a hypothesis has a much higher total score than T C1  and T C2 , the hypothesis may be presented to the user (e.g., in one of word suggestion areas  122 ). Spelling errors may be accounted for in a similar manner. That is, in some examples, gesture module  108  may account for spelling errors, insertion errors, and omission errors by employing a probabilistic model instead of a deterministic model. 
     The process of  FIGS. 5A-C  may represent one example of operations performed by gesture module  108 . In the example of  FIGS. 5A-C  computing device  102  receives a series of tap gestures. In other examples, techniques of the present disclosure may be applied to sliding or “swiping” gestures. For example, computing device  102  may determine a group of keys in response to receiving a gesture path. Gesture module  108  may determine a candidate word by determining a group of alignment points traversed by the gesture path. An alignment point is a point along the gesture path that may indicate a key of the plurality of keys. An alignment point may include one or more coordinates corresponding to the determined position of the alignment point. For instance, an alignment point may include Cartesian coordinates corresponding to a point on input device  202 . That is, techniques of the present disclosure are described herein in relation to tap gestures, but may readily be applied to sliding gestures by using alignment points of the gesture path instead of locations of the tap gestures. 
     As shown in the example of  FIG. 5A , at time  560 , computing device  102  may include GUI  512 , active beam  220 A, and next beam  222 A. GUI  512  may include graphical keyboard  528  which may include “N” key  520 A, “B” key  520 D, and a received tap gesture  526 A. While shown in  FIG. 5A , tap gesture  526 A may not be visible during the performance of the techniques described herein. 
     A user (e.g., user  150 ) may desire to enter text into computing device  102  by performing a series of tap gestures at graphical keyboard  528 . As previously discussed, as user  150  performs the tap gestures, computing device  102  may detect each gesture at UI device  104 . In the example of  FIG. 3A , computing device  102  is shown as having detected tap gesture  526 A. 
     In response to detecting tap gesture  526 A, computing device  102  may determine one or more characteristics associated with the received indication. Based on the characteristics, computing device  102  may, in some examples, modify values of spatial model  110 . For ease of understanding, in the example of  FIGS. 5A-C , computing device  102  may determine that no modification is required. In response to detecting tap gesture  526 A, computing device  102  may create a token and push the token into active beam  220 A. At time  560 , the contents on active beam  220 A may be represented by Table 1 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Parent 
                 Letter Key of 
                 Letter 
                 Cost 
               
               
                 Index 
                 Index 
                 Current Node 
                 Chain 
                 Value 
               
               
                   
               
             
            
               
                 0 
                 — 
                 — 
                 — 
                 0 
               
               
                   
               
            
           
         
       
     
     In Table 1, each row represents an individual token, the index column represents a unique identifier for each token, the parent index column represents the index value of the token to which the listed token is a child, the letter key of the current node column represent the letter key represented by the current node of the token, the letter chain column represents all of the letter keys represented by the nodes from the entry node to the current node of the token (i.e., the candidate string), and the cost value column may represent the total cost value, T WN , of the token. As shown in Table 1, the created token has an index of 0 (i.e., token 0 ), no parent index, no letter key of the current node, no letter chain, and a total cost value of zero. 
     To determine the text indicated by the gesture, computing device  102  may create a copy of each token on its child nodes. In some examples, an entry node may have 26 child nodes (one for each letter of the English alphabet). For simplicity, in the example of  FIG. 5A , the entry node has only two child nodes on the letters “B” and “N”. Therefore, computing device  102  may create a copy of the token with index 0 on child node “N” (i.e. token 0 ) and child node “B” (i.e. token 2 ). For each created token copy, computing device  102  may determine a total cost value by, for example, applying equation (10) as described above. In other examples, computing device  102  may use other methods of computing the total cost value. Computing device  102  may push each token copy in to next beam  222 A, the contents of which may be represented by Table 2 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Parent 
                 Letter Key of 
                 Letter 
                 Cost 
               
               
                 Index 
                 Index 
                 Current Node 
                 Chain 
                 Value 
               
               
                   
               
             
            
               
                 1 
                 0 
                 N 
                 N 
                 CV1 
               
               
                 2 
                 0 
                 B 
                 B 
                 CV2 
               
               
                   
               
            
           
         
       
     
     The entries shown in Table 2 are identical in format to the entry shown in Table 1. In Table 2, token 1  has total cost value CV1 and token 2  has total cost value CV2. Computing device  102  may use the letter chain of individual tokens (i.e., the candidate strings) now in next beam  222 A to predict one or more candidate words. Computing device  102  may store the candidate words in a list of output predictions. As described, each candidate word may add the average total cost value per character of the underlying candidate string to the total cost value of the candidate word for each additional character. For example, Table 3 below may represent the list of output predictions determined from the tokens in active beam  220 A. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                   
                 Parent 
                 Letter 
                 Cost 
               
               
                   
                 Index 
                 Index 
                 Chain 
                 Value 
               
               
                   
                   
               
             
            
               
                   
                 p0 
                 0 
                 NO 
                 CV1 + CV1 
               
               
                   
                 p1 
                 0 
                 NET 
                 CV1 + CV1 + CV1 
               
               
                   
                 p2 
                 1 
                 BE 
                 CV2 + CV2 
               
               
                   
                 p3 
                 1 
                 BOY 
                 CV2 + CV2 + CV2 
               
               
                   
                   
               
            
           
         
       
     
     In Table 3, each row represents an output prediction. The index column represents a unique identifier for each item and may be separate from the index values of tokens. The parent index column represents the index value of the token upon which the listed candidate word is based, the letter chain column represents the candidate word, and the cost value column may represent the total cost value of the candidate word. As shown in Table 3, the created candidate word “NO” has an index of p0 (i.e., word p0 ), was predicted based on token 0 , and has a total cost value of two times CV1. 
     Computing device  102  may output the list of output predictions. In some examples, computing device  102  may determine a subset of the list of output predictions including candidate words which have the lowest cost values (i.e., the predictions with the best probability). Additionally, in some examples, computing device  102  may, after each subsequent received gesture, discard the list of output predictions and create a new list of output predictions based on the updated tokens. In other examples, computing device  102  may add to the list of output predictions. For instance, computing device  102  may modify the cost value of previously determined candidate words (e.g., make word p0  more or less probable) in response to detecting a subsequent tap gesture. 
     After creating the token copies and the list of output predictions, computing device  102  may determine that token 0  is not a terminal node and discard token 0 . Computing device  102  may subsequently determine whether active beam  220 A is empty (i.e., contains no tokens). In response to determining that active beam  220 A is empty, computing device  102  may copy the contents of next beam  222 A to active beam  220 B of  FIG. 5B  and discard the contents of next beam  222 A. 
     In the example of  FIG. 5B , computing device  102  is shown as having detected tap gesture  526 B at time  562 . As described above, the contents of active beam  220 B may be represented by Table 2. Computing device  102  may determine one or more characteristics associated with the received indications, and modify spatial model  110  based at least in part on the determined characteristics. For example, characteristics determined based on an indication of tap gesture  526 B may cause computing device  102  to modify the horizontal and vertical standard deviation values associated with other keys in the same row as “O” key  520 B. For instance, computing device  102  may increase the horizontal standard deviation value associated with “Q” key  520 F to more accurately represent a user&#39;s likely horizontal error as described with respect to  FIGS. 4A and 4B . In addition to modifying spatial model  110 , computing device  102  may, for each token in active beam  220 B, create a copy on each child node. In the example of  FIG. 5B , token 1  and token 2  each have child nodes with letter keys “0” and “P”. For each created token copy, computing device  102  may determine a total cost value as described above. That is, the total cost value may be determined using spatial model  110  and language model  111 . Computing device  102  may push each token copy in to next beam  222 B, the contents of which may be represented by Table 4 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                 Parent 
                 Letter Key of 
                 Letter 
                 Cost 
               
               
                 Index 
                 Index 
                 Current Node 
                 Chain 
                 Value 
               
               
                   
               
             
            
               
                 3 
                 1 
                 O 
                 NO 
                 CV1 + CV3 
               
               
                 4 
                 1 
                 P 
                 NP 
                 CV1 + CV4 
               
               
                 5 
                 2 
                 O 
                 BO 
                 CV2 + CV5 
               
               
                 6 
                 2 
                 P 
                 BP 
                 CV2 + CV6 
               
               
                   
               
            
           
         
       
     
     The entries shown in Table 4 are identical in format to the entries shown in Table 1 and Table 2. In Table 4, the total cost value for each token includes the total cost value for the previous letters and the total cost value for the current letter. Computing device  102  may determine which, if any, of the tokens are on terminal nodes. For instance, computing device  102  may determine that token 3  is on a terminal node because its letter chain “NO” is a word. In response to determining that a token is on a terminal node, computing device  102  may copy the token to the list of output predictions. In some examples, computing device  102  may copy only the letter chain of the token to the list of candidate words. 
     Computing device  102  may subsequently determine whether active beam  220 B is empty. In response to determining that active beam  220 B is empty, computing device  102  may copy the contents of next beam  222 B to active beam  220 C of  FIG. 5C  and discard the contents of next beam  222 B. 
     In the example of  FIG. 5C , computing device  102  is shown as having detected tap gesture  526 C at time  564 . As described above, the contents of active beam  220 C may be represented by table 4. Computing device  102  may determine characteristics of the received gestures, and may, in some examples, modify spatial model  110  in accordance with one or more aspects of the present disclosure. For ease of understanding, computing device  102  may determine no modification is needed. Computing device  102  may, for each token in active beam  220 C, create a copy on each child node. In the example of  FIG. 5C , token 3  through token 6  each have child nodes with letter keys “0” and “P”. For each created token copy, computing device  102  may determine a total cost value using spatial model  110  (as modified) and language model  111 , as described above. Computing device  102  may push each token copy in to next beam  222 C, the contents of which may be represented by Table 5 below. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                 Parent 
                 Letter Key of 
                 Letter 
                 Cost 
               
               
                 Index 
                 Index 
                 Current Node 
                 Chain 
                 Value 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 7 
                 3 
                 W 
                 NOW 
                 CV1 + CV3 + CV7  
               
               
                 8 
                 3 
                 Q 
                 NOQ 
                 CV1 + CV3 + CV8  
               
               
                 9 
                 4 
                 W 
                 NPW 
                 CV1 + CV4 + CV9  
               
               
                 10 
                 4 
                 Q 
                 NPQ 
                 CV1 + CV4 + CV10 
               
               
                 11 
                 5 
                 W 
                 BOW 
                 CV2 + CV5 + CV11 
               
               
                 12 
                 5 
                 Q 
                 BOQ 
                 CV2 + CV5 + CV12 
               
               
                 13 
                 6 
                 W 
                 BPW 
                 CV2 + CV6 + CV13 
               
               
                 14 
                 6 
                 Q 
                 BPQ 
                 CV2 + CV6 + CV14 
               
               
                   
               
            
           
         
       
     
     The entries shown in Table 5 are identical in format to the entries shown in Tables 1, 2, and 4. In Table 5, the total cost value for each token includes the total cost value for the previous letters and the total cost value for the current letter. Computing device  102  may determine the list of output predictions based on the tokens shown in Table 5. After determining one or more candidate strings, computing device  102  may determine which, if any, of the tokens are on terminal nodes. For instance, computing device  102  may determine that token 7  and token 11  are on terminal nodes because their respective letter chains “NOW” and “BOW” are words. In response to determining that a token is on a terminal node, computing device  102  may copy token 7  and token 11  to the list of output predictions as candidate strings. The list of output predictions may be represented by Table 6 below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                   
                 Parent 
                 Letter 
                 Cost 
               
               
                   
                 Index 
                 Index 
                 Chain 
                 Value 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 p0 
                 7 
                 NOWHERE 
                 CV1 + CV3 + CV7 + 
               
               
                   
                   
                   
                   
                 4*(CV1 + CV3 + CV7)/3 
               
               
                   
                 p1 
                 11 
                 BOWS 
                 CV2 + CV5 + CV11 + 
               
               
                   
                   
                   
                   
                 (CV2 + CV5 + CV11)/3 
               
               
                   
                 p2 
                 11 
                 BOWED 
                 CV2 + CV5 + CV11 + 
               
               
                   
                   
                   
                   
                 2*(CV2 + CV5 + CV11)/3 
               
               
                   
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                   
                  p16 
                 7 
                 NOW 
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     Computing device  102  may subsequently determine whether active beam  220 C is empty. In response to determining that active beam  220 C is empty, computing device  102  may copy the contents of next beam  222 C to the active beam, and the process may continue as described. Upon receiving, for example, an indication of a selection of the space key, computing device  102  may perform a hard commit. That is, computing device  102  may use the candidate word having the best cost value as input, and may or may not discard all tokens in active beam  220  and next beam  222 . In this way, computing device  102  may use active beam  220  and next beam  222  to maintain tokens and associated total cost values, in order to correct, complete, and predict text input in accordance with one or more aspects of the present disclosure. 
       FIG. 6  is a flow diagram illustrating example operations that may be used to provide text input, in accordance with one or more aspects of the present disclosure. For purposes of illustration only, the example operations are described below within the context of computing device  102 , as shown in  FIGS. 1 and 2 . 
     In the example of  FIG. 6 , computing device  102  may initially output a graphical keyboard for display at a presence-sensitive display, the graphical keyboard having a plurality of keys ( 502 ). Computing device  102  may subsequently receive an indication of at least one gesture to select a group of keys of the plurality of keys ( 504 ). Computing device may determine at least one characteristic associated with the at least one gesture to select the group of keys of the plurality of keys ( 506 ). Based at least in part on the at least one characteristic, Computing device  102  may modify a spatial model ( 508 ). Computing device  102  may then determine a candidate word based at least in part on data provided by the spatial model and a language model ( 510 ). In some examples, the spatial model may provide a first portion of the data, based at least in part on the indication of the at least one gesture and the language model may provide a second portion of the data, based at least in part on a lexicon. Computing device  102  may output the candidate word for display at the presence-sensitive display ( 512 ). 
     In some examples, the at least one characteristic comprises an input speed associated with the at least one gesture, and modifying the spatial model comprises, in response to determining that the input speed satisfies a threshold value, modifying, by the computing device, a standard deviation value of the spatial model, wherein the standard deviation value is associated with a key of the plurality of keys. In some examples, the operations further include, in response to determining that the input speed is greater than the threshold value, increasing the standard deviation value. In some examples, the at least one characteristic comprises a location at the presence-sensitive display at which the at least one gesture is detected and modifying the spatial model comprises determining, by the computing device, a distance between the location of the at least one gesture and a statistical location of the spatial model, wherein the statistical location is associated with a key of the plurality of keys and in response to determining that the distance satisfies the threshold value, modifying the statistical location based at least in part on the determined location. 
     In some examples, the statistical location is a first statistical location, and modifying the first statistical location comprises determining, by the computing device, a vertical modifier value by dividing a vertical component of the location of the at least one gesture by a positive integer value, determining, by the computing device, a horizontal modifier value by dividing a horizontal component of the location of the at least one gesture by the positive integer value, and determining, by the computing device, a second statistical location by adding the vertical modifier value to a vertical component of the first statistical location and adding the horizontal modifier value to a horizontal component of the first statistical location. In some examples, the at least one characteristic comprises a location at the presence-sensitive display at which the at least one gesture is detected, and modifying the spatial model comprises determining, by the computing device, a distance between the location of the at least one gesture and a second location of a key of the plurality of keys and in response to determining that the distance satisfies a threshold value, modifying, by the computing device and based at least in part on the determined distance, a standard deviation value of the spatial model, wherein the standard deviation value is associated with the key. In some examples, the indication is a first indication, and the operations further include receiving, by the computing device and subsequent to the modifying, a second indication of a second gesture to select a key of the plurality of keys, and modifying, by the computing device and in response to the receiving the second indication, the standard deviation value associated with the next key. 
     In some examples, the at least one characteristic comprises a location at the presence-sensitive display at which the at least one gesture is detected, the location corresponding to a row of keys of the graphical keyboard, and modifying the spatial model comprises determining, by the computing device, whether a key of the plurality of keys is located in the row of keys of the graphical keyboard and in response to determining that key is located in the row of keys, modifying, by the computing device, a standard deviation value of the spatial model wherein the standard deviation value is associated with the key. In some examples, modifying the standard deviation value further comprises increasing, by the computing device, a horizontal standard deviation value associated with the key. In some examples, the candidate word is a first candidate word, the method further comprising determining, by the computing device, a second candidate word based at least in part on one or more words displayed in a text area of the presence-sensitive display, and outputting, for display at the presence-sensitive display, the second candidate word subsequent to the one or more words displayed in the text area. 
     In some examples, determining the second candidate word comprises determining, by the computing device and based at least in part on the language model, at least one frequency value, wherein the at least one frequency value is associated with a sequence of words, and wherein the frequency value represents a frequency of occurrence of the sequence of words in an n-gram dictionary of the language model, and selecting, by the computing device, the second candidate word based at least in part on the at least one frequency value. In some examples, determining the candidate word further comprises determining, by the computing device and based at least in part on the spatial model, at least one candidate string and at least one cost value and determining, by the computing device and based at least in part on the language model, the candidate word, wherein the candidate word includes the at least one candidate string as a prefix, and wherein the candidate word is associated with a predicted cost value, the predicted cost value being based at least in part on the at least one cost value of the at least one candidate string. In some examples, 
     In some examples, the at least one gesture comprises a plurality of tap gestures and determining a plurality of candidate strings and associated cost values comprises determining a plurality of tap locations each associated with a tap gesture of the plurality of tap gestures, determining respective cost values for each of at least two keys of the plurality of keys, wherein each of the respective cost values represents a probability that a tap location of the plurality of tap locations indicates a key of the plurality of keys, and comparing the respective cost values for each of at least two keys of the plurality of keys to determine a candidate string having a combined cost value. In some examples, determining a candidate word comprises determining, by the computing device and based at least in part on the language model, at least one frequency value, wherein the at least one frequency value is associated with a sequence of characters, and wherein the at least one frequency value represents a frequency of occurrence of the sequence of characters in the lexicon, and selecting, by the computing device and based at least in part on the determined at least one frequency value, the candidate word. In some examples, the language model further comprises a word-level n-gram dictionary. 
     In some examples, modifying the spatial model comprises modifying at least one of: a standard deviation value of the spatial model, a statistical location value of the spatial model, and a covariance value of the spatial model. In some examples, the at least one gesture comprises at least one sliding gesture. In some examples, outputting the candidate word comprises outputting, by the computing device and for display at the presence-sensitive display, characters of the candidate word associated with the group of keys in a first visual style, and outputting, by the computing device and for display at the presence-sensitive display; characters of the candidate word that are not associated with the group of keys in a second visual style. 
     In some examples, techniques of the present disclosure may include outputting, by a computing device and for display at a display device, a representation of a text area and receiving, by the computing device, a sequence of inputs from a user to select a plurality of characters. The techniques may also include, responsive to receiving the sequence of inputs, determining, by the computing device, a candidate word to output at a first position in the text area based at least in part on data provided by a spatial model and a language model, wherein the spatial model provides a first portion of the data used by the computing device to determine the candidate word based at least in part on spatial locations with respect to the computing device that are associated with the sequence of inputs, wherein the language model provides a second portion of the data used by the computing device to determine the candidate word based at least in part on one or more words displayed in the text area that precede the first position, and wherein the candidate word is not identical to the plurality of characters. The techniques may also include outputting, by the computing device and for display at the display device, a representation of the candidate word as a first word at the first position in the text area and, after outputting the representation of the first word, predicting, by the computing device, a second word that follows the first word at a second position in the text area based at least in part on additional data provided by the language model, wherein the additional data is based at least in part on one or more words displayed in the text area, including the first word, that precede the second position in the text area. The techniques may further include outputting, by the computing device and for display at the display device, a representation of the second word at the second position in the text area. 
       FIG. 7  is a block diagram illustrating an example computing device that outputs graphical content for display at a remote device, in accordance with one or more techniques of the present disclosure. Graphical content, generally, may include any visual information that may be output for display, such as text, images, a group of moving images, etc. The example shown in  FIG. 7  includes a computing device  700 , presence-sensitive display  701 , communication unit  710 , projector  720 , projector screen  722 , tablet device  726 , and visual display device  730 . Although shown for purposes of example in  FIGS. 1 and 2  as a stand-alone computing device  102 , a computing-device may, generally, be any component or system that includes a processor or other suitable computing environment for executing software instructions and, for example, need not include a presence-sensitive display. 
     As shown in the example of  FIG. 7 , computing device  700  may be a processor that includes functionality as described with respect to processor  200  in  FIG. 2 . In such examples, computing device  700  may be operatively coupled to presence-sensitive display  701  by a communication channel  703 A, which may be a system bus or other suitable connection. Computing device  700  may also be operatively coupled to communication unit  710 , further described below, by a communication channel  703 B, which may also be a system bus or other suitable connection. Although shown separately as an example in  FIG. 7 , computing device  700  may be operatively coupled to presence-sensitive display  701  and communication unit  710  by any number of one or more communication channels. 
     In other examples, such as illustrated previously in  FIGS. 1-2 , computing device  700  may be a portable or mobile device such as mobile phones (including smart phones), laptop computers, etc. In some examples, computing device  700  may be a desktop computers, tablet computers, smart television platforms, cameras, personal digital assistants (PDAs), servers, mainframes, etc. 
     As shown in  FIG. 7 , computing device  700  may also include and/or be operatively coupled with communication unit  710 . Communication unit  710  may include functionality of communication unit  204  as described in  FIG. 2 . Examples of communication unit  710  may include a network interface card, an Ethernet card, an optical transceiver, a radio frequency transceiver, or any other type of device that can send and receive information. Other examples of such communication units may include Bluetooth, 3G, and WiFi radios, Universal Serial Bus (USB) interfaces, etc. Computing device  700  may also include and/or be operatively coupled with one or more other devices, e.g., input devices, output devices, memory, storage devices, etc. that are not shown in  FIG. 7  for purposes of brevity and illustration. 
       FIG. 7  also illustrates a projector  720  and projector screen  722 . Other such examples of projection devices may include electronic whiteboards, holographic display devices, and any other suitable devices for displaying graphical content. Projector  720  and project screen  722  may include one or more communication units that enable the respective devices to communicate with computing device  700 . In some examples, the one or more communication units may enable communication between projector  720  and projector screen  722 . Projector  720  may receive data from computing device  700  that includes graphical content. Projector  720 , in response to receiving the data, may project the graphical content onto projector screen  722 . In some examples, projector  720  may determine one or more user inputs (e.g., continuous gestures, multi-touch gestures, single-touch gestures, etc.) at projector screen using optical recognition or other suitable techniques and send indications of such user input using one or more communication units to computing device  700 . 
     Projector screen  722 , in some examples, may include a presence-sensitive display  724 . Presence-sensitive display  724  may include a subset of functionality or all of the functionality of UI device  104  as described in this disclosure. In some examples, presence-sensitive display  724  may include additional functionality. Projector screen  722  (e.g., an electronic whiteboard), may receive data from computing device  700  and display the graphical content. In some examples, presence-sensitive display  724  may determine one or more user inputs (e.g., continuous gestures, multi-touch gestures, single-touch gestures, etc.) at projector screen  722  using capacitive, inductive, and/or optical recognition techniques and send indications of such user input using one or more communication units to computing device  700 . 
       FIG. 7  also illustrates tablet device  726  and visual display device  730 . Tablet device  726  and visual display device  730  may each include computing and connectivity capabilities. Examples of tablet device  726  may include e-reader devices, convertible notebook devices, hybrid slate devices, etc. Examples of visual display device  730  may include televisions, computer monitors, etc. As shown in  FIG. 5 , tablet device  726  may include a presence-sensitive display  728 . Visual display device  730  may include a presence-sensitive display  732 . Presence-sensitive displays  728 ,  732  may include a subset of functionality or all of the functionality of UI device  104  as described in this disclosure. In some examples, presence-sensitive displays  728 ,  732  may include additional functionality. In any case, presence-sensitive display  732 , for example, may receive data from computing device  700  and display the graphical content. In some examples, presence-sensitive display  732  may determine one or more user inputs (e.g., continuous gestures, multi-touch gestures, single-touch gestures, etc.) at projector screen using capacitive, inductive, and/or optical recognition techniques and send indications of such user input using one or more communication units to computing device  700 . 
     As described above, in some examples, computing device  700  may output graphical content for display at presence-sensitive display  701  that is coupled to computing device  700  by a system bus or other suitable communication channel. Computing device  700  may also output graphical content for display at one or more remote devices, such as projector  720 , projector screen  722 , tablet device  726 , and visual display device  730 . For instance, computing device  700  may execute one or more instructions to generate and/or modify graphical content in accordance with techniques of the present disclosure. Computing device  700  may output the data that includes the graphical content to a communication unit of computing device  700 , such as communication unit  710 . Communication unit  710  may send the data to one or more of the remote devices, such as projector  720 , projector screen  722 , tablet device  726 , and/or visual display device  730 . In this way, computing device  700  may output the graphical content for display at one or more of the remote devices. In some examples, one or more of the remote devices may output the graphical content at a presence-sensitive display that is included in and/or operatively coupled to the respective remote devices. 
     In some examples, computing device  700  may not output graphical content at presence-sensitive display  701  that is operatively coupled to computing device  700 . In other examples, computing device  700  may output graphical content for display at both a presence-sensitive display  701  that is coupled to computing device  700  by communication channel  703 A, and at one or more remote devices. In such examples, the graphical content may be displayed substantially contemporaneously at each respective device. For instance, some delay may be introduced by the communication latency to send the data that includes the graphical content to the remote device. In some examples, graphical content generated by computing device  700  and output for display at presence-sensitive display  701  may be different than graphical content display output for display at one or more remote devices. 
     Computing device  700  may send and receive data using any suitable communication techniques. For example, computing device  700  may be operatively coupled to external network  714  using network link  712 A. Each of the remote devices illustrated in  FIG. 7  may be operatively coupled to network external network  714  by one of respective network links  712 B,  712 C, and  712 D. External network  714  may include network hubs, network switches, network routers, etc., that are operatively inter-coupled thereby providing for the exchange of information between computing device  700  and the remote devices illustrated in  FIG. 7 . In some examples, network links  712 A- 712 D may be Ethernet, ATM or other network connections. Such connections may be wireless and/or wired connections. 
     In some examples, computing device  700  may be operatively coupled to one or more of the remote devices included in  FIG. 7  using direct device communication  718 . Direct device communication  718  may include communications through which computing device  700  sends and receives data directly with a remote device, using wired or wireless communication. That is, in some examples of direct device communication  718 , data sent by computing device  700  may not be forwarded by one or more additional devices before being received at the remote device, and vice-versa. Examples of direct device communication  718  may include Bluetooth, Near-Field Communication, Universal Serial Bus, WiFi, infrared, etc. One or more of the remote devices illustrated in  FIG. 7  may be operatively coupled with computing device  700  by communication links  716 A- 716 D. In some examples, communication links  712 A- 712 D may be connections using Bluetooth, Near-Field Communication, Universal Serial Bus, infrared, etc. Such connections may be wireless and/or wired connections. 
     In accordance with techniques of the disclosure, computing device  700  may be operatively coupled to visual display device  730  using external network  714 . Computing device  700  may output a graphical keyboard for display at presence-sensitive display  732 . For instance, computing device  700  may send data that includes a representation of the graphical keyboard to communication unit  710 . Communication unit  710  may send the data that includes the representation of the graphical keyboard to visual display device  730  using external network  714 . Visual display device  730 , in response to receiving the data using external network  714 , may cause presence-sensitive display  732  to output the graphical keyboard. In response to a user performing one or more gestures at presence-sensitive display  732  to select a group of keys of the keyboard, visual display device  730  may send an indication of the gestures to computing device  700  using external network  714 . Communication unit  710  may receive the indication of the gesture, and send the indication to computing device  700 . 
     Computing device  700  may determine a number of characteristics (e.g., speed, location, etc.) associated with the gestures. In some examples, computing device  700  may modify, based at least in part on the determined characteristics, one or more values of a spatial model used in determining which keys were selected by the one or more gestures. For instance, if the input speed is higher than a threshold value, computing device  700  may increase standard deviation values associated with at least one key of the graphical keyboard. If the input speed is below a certain threshold value, computing device  700  may decrease the standard deviation values. In any case, computing device  700  may use the modified spatial model in accordance with the present disclosure to determine at least one candidate word based. Computing device  700  may send data that includes the candidate word to communication unit  710 , which in turn sends the data to visual display device  730  using external network  714 . Upon receiving the data, visual display device  730  may cause presence-sensitive display  732  to display the candidate word. In this way, computing device  700  may output the candidate word for display at presence-sensitive screen  732 , in accordance with techniques of the disclosure. 
     The techniques described in this disclosure may be implemented, at least in part, in hardware, software, firmware, or any combination thereof. For example, various aspects of the described techniques may be implemented within one or more processors, including one or more microprocessors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or any other equivalent integrated or discrete logic circuitry, as well as any combinations of such components. The term “processor” or “processing circuitry” may generally refer to any of the foregoing logic circuitry, alone or in combination with other logic circuitry, or any other equivalent circuitry. A control unit including hardware may also perform one or more of the techniques of this disclosure. 
     Such hardware, software, and firmware may be implemented within the same device or within separate devices to support the various techniques described in this disclosure. In addition, any of the described units, modules or components may be implemented together or separately as discrete but interoperable logic devices. Depiction of different features as modules or units is intended to highlight different functional aspects and does not necessarily imply that such modules or units must be realized by separate hardware, firmware, or software components. Rather, functionality associated with one or more modules or units may be performed by separate hardware, firmware, or software components, or integrated within common or separate hardware, firmware, or software components. 
     The techniques described in this disclosure may also be embodied or encoded in an article of manufacture including a computer-readable storage medium encoded with instructions. Instructions embedded or encoded in an article of manufacture including a computer-readable storage medium encoded, may cause one or more programmable processors, or other processors, to implement one or more of the techniques described herein, such as when instructions included or encoded in the computer-readable storage medium are executed by the one or more processors. Computer readable storage media may include random access memory (RAM), read only memory (ROM), programmable read only memory (PROM), erasable programmable read only memory (EPROM), electronically erasable programmable read only memory (EEPROM), flash memory, a hard disk, a compact disc ROM (CD-ROM), a floppy disk, a cassette, magnetic media, optical media, or other computer readable media. In some examples, an article of manufacture may include one or more computer-readable storage media. 
     In some examples, a computer-readable storage medium may include a non-transitory medium. The term “non-transitory” may indicate that the storage medium is not embodied in a carrier wave or a propagated signal. In certain examples, a non-transitory storage medium may store data that can, over time, change (e.g., in RAM or cache). 
     Various examples have been described. These and other examples are within the scope of the following claims.