System and method for determining symbolic style from data by using regression modelling
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- TOYOTA JIDOSHA KK
- Filing Date
- 2022-11-28
- Publication Date
- 2026-05-08
Smart Images
Figure 00000000_0000_ABST
Abstract
Description
[Technical Field]
[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Patent Application No. 63 / 285,761, filed December 3, 2021, which is incorporated herein by reference in its entirety.
[0002] The subject matter described herein relates generally to determining symbolic expressions from experimental data, and more particularly to determining interpretable models from experimental data and observations using tokenization in the models. [Background technology]
[0003] Equations can represent the behavior of scientific phenomena. Deriving accurate equations can require complex computations to predict phenomena. For example, large neural networks can accurately predict the dependent variable of an experiment, given values for the independent variables. Experiments can involve a variety of applications, such as identifying abnormal battery performance or driving behavior. However, the structure of the equations using these variables and corresponding parameters makes it difficult to understand the scientific theory behind the anomaly from the experimental data. In other words, researchers have difficulty exploring the network to derive other models for related scientific tasks, thereby hindering progress. Therefore, researchers can use simple regressions (e.g., linear, logistic, etc.) to interpret experimental data and derive symbolic equations at the expense of accuracy.
[0004] Further scientific advances include the discovery of parsimonious equations for data with predictive accuracy, such as the law of gravity or Maxwell's equations. Parsimonious equations can use minimal assumptions or steps to model experimental data. Systems can derive parsimonious equations using models that include genetic programming and domain heuristics that find symmetries in data variables. However, these systems are computationally expensive and generate non-intuitive parametric equations because the equations are strings of symbols and the number of potential strings grows exponentially with the length of the string. Summary of the Invention
[0005] In one embodiment, an example system and method relates to determining interpretable models from experimental data using tokenization in predictive models. In various implementations, systems that accurately derive parametric equations for scientific experiments are complex and generate unintuitive equations. For example, some neural networks perform computationally expensive operations to generate more accurate equations in various applications (e.g., battery performance, driving behavior, etc.) because the potential equations grow exponentially with additional symbols or parameters. Furthermore, the operation of neural networks can be difficult to understand for deriving other models associated with scientific theories. Therefore, in one embodiment, an observation system uses a model that directly maps experimental data (e.g., a table of battery voltages) to symbolic equations that describe the experimental data through supervised learning. In particular, the observation system uses the feedforward operation of a neural network (e.g., a deep neural network (DNN), perceptron, etc.) to generate or transform tokens representing parts of the symbolic equations. Feedforward operations simplify computation by allowing data to flow forward between function nodes and by avoiding circular or feedback loops. An observation system parses and adapts symbolic parameters from a symbolic expression, such as through regression, to accurately output a symbolic expression. The symbolic expression can then be interpreted by observing the feedforward operations and tokens through stages of computation.
[0006] In terms of application, a user can directly observe and understand the derivation of the determined model. For example, an observation system is applied to a potentially defective battery. Linear testing (e.g., battery cycling) on manufactured batteries can identify anomalous behavior as an outlier with little practical insight. Now, the observation system finds an accurate and interpretable model that explains why a new battery is flagged as an outlier. Insight from the model may be that an overshoot in the charge curve was due to a manufacturing defect. Insight can also accurately indicate that the effect was simply a testing anomaly.
[0007] In one approach, an observation system trains a model by generating variable-length noisy data tables. For example, parametric equations estimated from experiments have parameters randomized, sampled, and processed with Gaussian noise to generate the noisy data tables. The observation system processes the noisy data tables containing the observed variables and outputs symbolic equations using the models as supervised learning. In other words, models are trained to generate other models from experimental data using specialized training data. Thus, the observation system improves the derivation and interpretation of symbolic equations by training and implementing models that reduce computational complexity, such as through feedforward operations.
[0008] In one embodiment, an observation system for determining an interpretable model from experimental data using tokenization in a predictive model is disclosed. The observation system includes a processor and a memory storing instructions that, when executed by the processor, cause the processor to output bit patterns of estimated tokens generated from raw data using the model. The instructions also include instructions for using the model to convert the bit patterns to output tokens and parsing the output tokens into symbolic expressions. The instructions also include instructions for fitting symbolic parameters from the symbolic expressions to the interpretable model for accuracy. The instructions also include instructions for estimating vehicle system operational behavior and signal outputs according to the interpretable model.
[0009] In one embodiment, a non-transitory computer-readable medium is disclosed that includes instructions for determining an interpretable model from experimental data using tokenization in a predictive model and that, when executed by a processor, cause the processor to perform one or more functions. The instructions include instructions for outputting bit patterns of estimated tokens generated from raw data using the model. The instructions also include instructions for using the model to convert the bit patterns into output tokens and parsing the output tokens into symbolic expressions for accuracy. The instructions also include instructions for fitting symbolic parameters from the symbolic expressions to the interpretable model. The instructions also include instructions for predicting vehicle system operating behavior and signal outputs according to the interpretable model.
[0010] In one embodiment, a method for determining an interpretable model from experimental data using tokenization in a predictive model is disclosed. In one embodiment, the method includes outputting bit patterns of estimated tokens generated from raw data using the model. The method also includes converting the bit patterns into output tokens using the model and parsing the output tokens into symbolic expressions. The method also includes fitting symbolic parameters from the symbolic expressions to the interpretable model for accuracy. The method also includes predicting vehicle system operational behavior and signal outputs according to the interpretable model. [Brief explanation of the drawings]
[0011] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate various systems, methods, and other embodiments of the disclosure. It will be appreciated that the boundaries of elements illustrated in the drawings (e.g., boxes, groups of boxes, or other shapes) represent one embodiment of the boundaries. In some embodiments, one element can be designed as multiple elements, or multiple elements can be designed as one element. In some embodiments, an element shown as an internal component of another element can be realized as an external component, and vice versa. Additionally, elements may not be drawn to scale.
[0012] [Figure 1] FIG. 1 illustrates one embodiment of an observation system that determines an interpretable model of experimental data using tokenization in the model.
[0013] [Figure 2] FIG. 2 illustrates one embodiment of an observation system associated with deriving an interpretable model of experimental data in a model.
[0014] [Figure 3]Figure 3 shows an example of a network architecture for the models used by the observing system.
[0015] [Figure 4] FIG. 4 illustrates one embodiment for generating variable length and noisy data tables for training a network model of an observation system.
[0016] [Figure 5] FIG. 5 illustrates one embodiment of a method associated with determining an interpretation model of experimental data using tokenization in the model and inferring behavioral behavior. DETAILED DESCRIPTION OF THE INVENTION
[0017] Systems, methods, and other embodiments associated with determining interpretable models from experimental data, such as for predicting operational behavior using tokenization in predictive models, are disclosed. Systems that accurately derive parametric equations for scientific observations from experimental data are complex and produce unintuitive equations. For example, test systems that use neural networks to observe battery behavior in factories are computationally expensive in generating accurate equations. Complexity increases because the potential equations grow exponentially with each additional parameter derived for the experimental data. Thus, in one embodiment, the observation system uses a model to generate and output estimated token bit patterns from the experimental data. In one approach, the model is a neural network (e.g., a deep neural network (DNN), multilayer perceptron, recurrent network, etc.) that performs meta-modeling by automatically predicting functions describing relationships from experimental data through transforms available for the domain (e.g., battery system, sensor system, etc.). The model may be a predictive model that uses feedforward operations to simplify computations by allowing data to flow forward between function nodes while avoiding circular or feedback loops. Thus, the model can receive noisy data tables from experiments as input and output symbolic expressions that are interpretable for various applications (e.g., battery manufacturing, autonomous driving, etc.). In particular, the observation system converts bit patterns into output tokens and parses the symbolic expressions accordingly, where the output tokens can represent variables, operators, etc., as decimal numbers. The observation system can then adapt symbolic parameters to improve the quality of the symbolic expressions before outputting a parsimonious model (i.e., minimal assumptions, steps, etc.) that is interpretable from the experimental data.
[0018] For training, the observation system can generate synthetic datasets with data tables of varying lengths and noise levels for end-to-end supervised training. In particular, neural networks can use synthetic datasets to learn to derive accurate symbolic formulas through tokenized free-form manipulation. Here, data tables can be layered with randomized parameters and variables of parametric formulas with added Gaussian noise as input for more efficient training. In one approach, the observation system validates the model by running public datasets from behavioral science as teachers. Thus, the observation system improves symbolic formula derivation and interpretation by achieving models with reduced computational complexity through tokenized manipulation and supervised training.
[0019] Referring to FIG. 1 , an observation system 100 is illustrated that determines an interpretable model of experimental data using tokenization in the model. Here, the network model 110 may be an interpretable model in that scientists can explore the mechanisms of the network model 110 to construct other models from scientific theories. For example, the network model 110 may be a searchable feedforward neural or perceptron network that processes data in a table format collected from experiments associated with a battery system or a vehicle perception system. The data table may have columns corresponding to independent variables along with a dependent variable of a potential parametric equation (e.g., battery discharge). For example, assume that an experiment includes independent variables x1 and x2, and the observation system 100 performs operations to derive the effect of these variables on the dependent variable y. The data table may then include observed values of the variables x1, x2, and y. In one approach, the network model 110 may generate a parametric equation 120 as follows: y=(w1x1+w2x2)(w3x1+w4x2) Equation (1) where {w1, w2, w3, w4} are parameters. In some respects, variables represent placeholders for the data being modeled, and parameters represent values to be fitted.
[0020] The parameter adaptation 130 operation is performed by using the parameter w i The parameter fitting 130 operation is performed by the observation system 100 as a regression procedure (e.g., linear, polynomial, etc.) to fit values for mc. The result is an equation model of the data table. Here, the parameter fitting 130 operation determines specific parameter values since the output from the network model 110 may be a raw parameter relationship. For example, the network model 110 may fit e=mc without specifying c. 2 Therefore, equation (1) using the fit becomes (1.2x1+3.1x2)(0.0x1+0.7x2) Equation (2) Form. and the output and interpretable model 140 is 2.17x2 2 +0.84x1x2 equation (3) It can be expressed as: The parameters 2.17 and 0.84 can be stored as symbolic parameters 260 for other tasks by the observation system 100 .
[0021] In various implementations, the observation system 100 can model human behavior. For example, the observation system 100 models a series of gambles presented to participants in a survey. Each gamble corresponds to two possibilities. The first gamble is the possibility of winning dollar value V1 with probability p1. The second gamble is the possibility of winning dollar value V2 with probability p2. A dataset can include variations on this survey type. For example, a participant benefits from one gamble in one survey, and the next survey participant benefits from the second gamble. For both gambles to a survey participant, where V1 ≥ 0 and V2 ≥ 0 are non-negative, the probability of each choice (pi ,V i ) and the associated subjective value (SV) of the choice is SV i =p i V j α Equation (4) It may be. Here, the value α varies from person to person and may be a risk aversion parameter. A higher α is interpreted as a greater risk tolerance. A straightforward way to model the choice of options is to select the option with the greater subjective value. Select = arg max(SV1,SV2) Equation (5)
[0022] Furthermore, an additional "noise" parameter β can be added to scale the sigmoid as follows: Selection=σ(β(SV1-SV2))+1 Equation (6) Equation (6) outputs a number between 1 and 2, which can be rounded to 1 or 2 to make a prediction of the choice a participant will make. In this example, network model 110 processes data sets V1, p1, V2, and p2 to derive interpretable model 140. In particular, equation (5) is reverted to its original state.
[0023] Referring to Figure 2, one embodiment of the observation system 100 of Figure 1 is further illustrated. The observation system 100 is generally in an abstract form that can be implemented and includes a processor 210. In one embodiment, the observation system 100 includes a memory 220 that stores a prediction module 230. The memory 220 may be random access memory (RAM), read-only memory (ROM), a hard disk drive, flash memory, or other suitable memory for storing the prediction module 230. The prediction module 230 may be, for example, computer-readable instructions that, when executed by the processor 210, cause the processor 210 to perform various functions disclosed herein.
[0024] Additionally, in one embodiment, observation system 100 includes data storage 240. In one embodiment, data storage 240 is a database, which in one embodiment is an electronic data structure stored in memory 220 or other data storage device and is comprised of routines executable by processor 210 to analyze the stored data, present the stored data, organize the stored data, etc. Thus, in one embodiment, data storage 240 stores data used by prediction module 230 in performing various functions.
[0025] In various implementations, the prediction module 230 includes instructions that cause the processor 210 to derive the interpretable model 140 from data tables and variables while avoiding computationally expensive operations (e.g., genetic programming). An example of an interpretable model output by the observation system 100 is the parametric equation e=mc using a feedforward network, since the derivation is observable. 2 The data tables and variables can be processed by the network model 110 using a variety of network architectures. Figure 3 shows an example network architecture 300 for the network model 110.
[0026] In FIG. 3, X elements can be input to the neural network. In one approach, the observation system 100 uses a feedforward neural network if the connections between network nodes avoid cycles or loops. Here, data moves forward between input, hidden, or output nodes without cycles or feedback loops within the network to reduce computational complexity. Elements include input vectors in the form of a data table, the number of variables for the potential equation, and data iteration residuals. The number of variables can be provided to the observation system 100 to derive the form of the output equation. In various implementations, the data table includes measurements from cycling new batteries against defects. The measurements can include discharge current, maximum charge, voltage levels, etc., used by the observation system 100 to predict life for new batteries, thereby improving quality control.
[0027] Furthermore, both data tables and data iterations can be obtained by stacking columns containing raw data from an experiment. Here, the observation system 100 can repeat the stacked columns multiple times since the data table has a variable length, and truncate the results to output X elements. In one approach, the network architecture has Z layers (e.g., 10) as inputs to Y units (e.g., 200). The output can have the same or a different number of layers (e.g., 27) and W elements (e.g., 655). W can represent the number of elements at the end of the range of the parametric equation. The elements can be variables, parameters, or operators (e.g., sine, cosine, sigmoid, addition, subtraction, etc.) associated with a parametric equation or formula.
[0028] Furthermore, the nonlinearity found in the layers in the network architecture 300 for deriving various equations may be from a rectified linear unit (ReLU) encoder. In one approach, the final layer utilizes a sigmoid nonlinearity. The decoder 310 can output an equation-construction string associated with a bit pattern. For example, the string can represent x1 * x2 as "multiplication of arguments x1 and x2." In one approach, the constructed string is converted into tokens using decimal numbers to represent various elements and stored as symbolic tokens 250. The representation may be addition = 1, subtraction = 2, and termination = 0. Furthermore, one-hot encoding can also be used to convert the equation-construction string into a format suitable for machine processing, similar to tokenization. Therefore, the string is encoded and converted into a bit pattern, which is a set representing a token.
[0029] For training, the network architecture 300 can utilize a loss function that is trained through a penalty. For example, a binary cross-entropy (BCE) loss function compares the output bit pattern to a known formula. The network architecture 300 is adjusted or tuned according to the penalty. In various implementations, the network architecture 300 is a neural network structured as a transformer. In this way, a variable length of output instead of the set W can be output by the decoder 310 up to the final token. In this way, padding by the termination token can be eliminated.
[0030] FIG. 4 illustrates one embodiment for generating a variable-length, noisy data table 400 for training the network model 110 of the observation system 100. The data set can include a set of symbolic or parametric equations, including linear and polynomial equations, min / max, argmin / argumax functions, etc. The data set can also include transcendental functions such as exponential, logarithmic, sigmoid, sine, cosine functions, etc. The parametric equations can be collected according to models from behavioral science and can include linear, polynomial, sigmoid, sigmoid of polynomials, sums of polynomials and sigmoids, subjective value equations, etc. In this manner, the observation system 100 can be trained to model automated driving systems (ADS) that include direct human intervention.
[0031] Along with the data variables, the formulas in the dataset can have placeholders for numeric parameters. Random parameter instantiation 410 can randomly select values for the parameters. A data table can then be generated for the formula by repeatedly applying random values to the data variables and evaluating the formula associated with random variable sampling 420. This operation allows for data tables of varying length, but various implementations can utilize a set number of dependent variables (e.g., 200). A Gaussian noise operator 430 adds noise to the values of the dependent variables to model the effects of measurement noise. Loopback 440 also applies the generated noisy data table to the parameter instantiation to improve randomization. For example, negative numbers can represent added noise associated with a sigmoid ranging from 0 to 1.
[0032] In one approach, the operation is repeated for a number of noise levels (e.g., 10) associated with each equation. By using different randomly selected parameter instantiations, the generation operation generates a substantial number of combinations between noisy data tables and corresponding equations. In this way, the observation system 100 learns a general mapping between data and symbolic structures across parameter values.
[0033] Additionally, the observation system 100 can utilize supervised learning through the generated variable-length, noisy data table 400. Here, learning computes training and cross-validation loss. Training continues past points that increase the cross-validation error, as the percentage of correctly parsed formulas can increase past levels of minimum cross-validation loss. Additional enhancements to the observation system 100 include deriving grammars through loose enforcement of logical formulas. In this way, the network model 110 is tasked with learning grammars. For example, training improves the accuracy of predicting grammars by parsing formulas after a number of training steps. In this way, the observation system 100 derives models from a broader collection of applications and scientific experiments.
[0034] Turning now to Figure 5, there is illustrated a flowchart of a method 500 associated with determining an interpretable model from experimental data using tokenization in a predictive model. Method 500 is discussed in terms of observation system 100 of Figures 1 and 2. While method 500 is discussed in combination with observation system 100, it should be appreciated that method 500 is not limited to being implemented within observation system 100, but rather observation system 100 is one example of a system in which method 500 may be implemented.
[0035] At 510, the observation system 100 outputs the bit pattern of the estimated token generated from the raw data using the model. As explained above, the prediction module 230 utilizes network models 110, which are built from feedforward neural networks, perceptrons, transformers, etc., to reduce computational complexity. Feedforward operations can simplify computation by allowing data to flow forward between function nodes and avoiding circular or feedback loops.
[0036] Additionally, the raw data may be in a data table having columns corresponding to the independent variables along with the dependent variables of the potential parametric equation, and may include the number of variables. Tokens may be decimal numbers representing various elements of the equation. For example, expressions may include addition = 1, subtraction = 2, and a termination token = 0.
[0037] At 520, the observation system 100 converts the bit pattern into output tokens and parses the symbolic expression. For example, an expression-building string associated with the bit pattern may represent x*x as "multiplication of arguments x and x." Here, the conversion may include having the set of tokens represented in the bits that the observation system parses to derive x*x and associated parameters. As explained above, a similar operation may be performed to derive y=(wx+wx)(wx+wx) from an experiment (e.g., a battery test, a perceptual system) with independent variables x and x and a dependent variable y.
[0038] For fitting, at 530, the observation system 100 fits symbolic parameters from the symbolic equation to the interpretable model. In one approach, the observation system 100 performs parameter fitting to determine specific parameter values, since the output from the network model 110 has raw parameter relationships. For example, the network model 110 fits e=mc without specifying c. 2Therefore, the parameter fitting operation is e=mc 2 When deriving , a regression procedure (e.g., linear, polynomial, etc.) can be used to fit a value for c.
[0039] In application, at 540, the observation system 100 estimates the operational behavior of the system according to the interpretable model, where the model derived by the observation system 100 and / or the prediction module 230 is interpretable in that scientists can explore the mechanisms of the network model 110 to construct other models from scientific theories. For example, the network model 110 may be an investigative feedforward neural or perceptron network.
[0040] In various implementations, the raw data represents test results from newly manufactured batteries. The observation system 100 uses the raw data to identify the cause of abnormal battery behavior. Uninterpretable black-box models (e.g., DNNs) can identify abnormal behavior as an outlier with raw accuracy and little insight. Here, the observation system 100 finds an accurate and interpretable model that explains the cause for flagging a battery as an outlier. For example, insight from the interpretable model could be that an overshoot in the charge curve was caused by a manufacturing defect. The insight could also pinpoint that the impact was simply a test anomaly, without impacting the battery's lifespan.
[0041] The observation system 100 can also model raw data to understand operator behavior on the road. For example, the ADS estimates the intention-driven movements of other traffic participants (e.g., pedestrians, other vehicles, etc.). Black-box models (e.g., DNNs) can be accurate but may be uninterpretable because they are difficult to study or directly observe. Linear models may be interpretable but have low accuracy. The observation system 100 derives highly accurate yet interpretable models to understand the characteristics of traffic-related behavior, including behaviors that are prone to ADS errors.
[0042] Detailed embodiments are disclosed herein. However, it should be understood that the disclosed embodiments are intended to be examples. Accordingly, the specific structural and functional details disclosed herein should not be construed as limiting, but merely as a basis for the claims and as a representative basis for teaching those skilled in the art how to variously employ the aspects herein in substantially any appropriately detailed structure. Furthermore, the terms and phrases used herein are not intended to be limiting, but rather to provide an understandable description of possible implementations. While various embodiments are shown in Figures 1-5, the embodiments are not limited to the illustrated structures or applications.
[0043] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments. In this regard, blocks in the flowcharts or block diagrams may represent modules, segments, or portions of code, comprising one or more executable instructions for implementing specified logical functions. It should also be noted that in some alternative implementations, the functions shown in the blocks may occur in a different order than that shown in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may be executed in the reverse order, depending on the functionality involved.
[0044] The above systems, components, and / or processes can be realized in hardware or a combination of hardware and software, centralized in one processing system, or distributed with different elements spread across several interconnected processing systems. Any type of processing system or other device adapted to perform the methods described herein is suitable. A combination of hardware and software can be a processing system having computer-usable program code that, when loaded and executed, controls the processing system to perform the methods described herein. The systems, components, and / or processes can also be embodied in a computer-readable storage device, such as a computer program product or other data program storage device, that is machine-readable and tangibly contains a program of machine-executable instructions for performing the methods and processes described herein. These elements can also be embodied in an application product that comprises features enabling implementation of the methods described herein and that, when loaded in a processing system, can perform these methods.
[0045] Furthermore, the arrangements described herein may take the form of a computer program product embodied in one or more computer-readable media having computer-readable program code embodied therein, e.g., stored thereon. Any combination of one or more computer-readable media may be utilized. The computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. The phrase "computer-readable storage medium" refers to a non-transitory storage medium. The computer-readable medium may take forms including, but not limited to, non-volatile media and volatile media. Non-volatile media may include, for example, optical disks, magnetic disks, and the like. Volatile media may include, for example, semiconductor memory, dynamic memory, and the like. Examples of such computer-readable media include, but are not limited to, floppy disks, flexible disks, hard disks, magnetic tape, other magnetic media, application-specific integrated circuits (ASICs), CDs, other optical media, RAM, ROM, memory chips or cards, memory sticks, and other media readable by a computer, processor, or other electronic device. In the context of this document, a computer-readable medium may be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device.
[0046] The following contains definitions of selected terms employed herein. The definitions include various examples and / or forms of components within the scope of the terms, which may be used in various implementations. The examples are not intended to be limiting. Both singular and plural forms of terms may be included within the definitions.
[0047] References to "one embodiment," "an embodiment," "one example," "an example," etc. indicate that the embodiment or example so described may include a particular feature, structure, attribute, property, element, or limitation, but not all embodiments or examples necessarily include that particular feature, structure, attribute, property, element, or limitation. Furthermore, repeated use of the phrase "in one embodiment" does not necessarily refer to the same embodiment, although it may.
[0048] As used herein, a "module" includes computer or electronic hardware components, firmware, non-transitory computer-readable media storing instructions, and / or combinations of these components configured to perform a function or action and / or cause a function or action from other logic, methods, and / or systems. A module may include a microprocessor controlled by an algorithm, discrete logic (e.g., an ASIC), analog circuitry, digital circuitry, programmable logic devices, memory devices containing instructions that, when executed, perform an algorithm, etc. In one or more embodiments, a module includes one or more complementary metal-oxide-silicon (CMOS) gates, combinations of gates, or other circuit components. Where multiple modules are described, one or more embodiments include incorporating multiple modules into one physical modular component. Similarly, where a single module is described, one or more embodiments distribute the single module among multiple physical components.
[0049] Additionally, as used herein, a module includes a routine, program, object, component, data structure, etc. that performs a particular task or implements a particular data type. In a further aspect, a memory generally stores the described modules. The memory associated with a module may be a buffer or cache embedded within a processor, RAM, ROM, flash memory, or other suitable electronic storage medium. In a further aspect, a module as contemplated in this disclosure is implemented as an ASIC, a system-on-chip (SoC) hardware component, a programmable logic array (PLA), or other suitable hardware component embedded with a defined configuration set (e.g., instructions) to perform the disclosed functions.
[0050] In one or more arrangements, one or more of the modules described herein may include artificial or computational intelligence elements, such as, for example, neural networks, fuzzy logic, or other machine learning algorithms. Further, in one or more arrangements, one or more of the modules may be distributed among multiple modules described herein. In one or more arrangements, two or more of the modules described herein may be combined into a single module.
[0051] The program code contained on the computer-readable medium can be transmitted using any suitable medium, including, but not limited to, wireless, wireline, fiber optic, cable, radio frequency (RF), etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present arrangements can be written in any combination of one or more programming languages, including object-oriented programming languages such as Java®, Smalltalk®, C++, etc., and conventional procedural programming languages such as the “C” programming language or similar programming languages. The program code can execute entirely on the user's computer, partially on the user's computer as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter scenario, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can provide a connection to an external computer (e.g., through the Internet using an Internet service provider).
[0052] The term "a" as used herein is defined as one or more than one. The term "plurality" as used herein is defined as two or more than two. The term "another" as used herein is defined as at least a second or more. The terms "including" and / or "having" as used herein are defined as "comprising" (i.e., open language). The phrase "and at least one of" as used herein refers to and includes any and all possible combinations of one or more of the associated listed items. By way of example, the phrase "at least one of A, B, and C" includes A, B, C, or any combination thereof (e.g., AB, AC, BC, or ABC).
[0053] The embodiments herein may be embodied in other forms without departing from the spirit or essential attributes thereof, and reference should accordingly be made to the following claims, rather than to the foregoing specification, which indicate their scope.
Claims
1. A system, Processor and The system includes a memory that stores instructions, and when an instruction is executed by the processor, the processor receives the instructions. The model is used to generate the bit patterns associated with tokens from the raw data. Using the aforementioned model, the bit pattern is converted into a symbolic expression. The parameter values for the symbolic expression are derived, and an interpretable model of the raw data is generated. A system characterized by the following features.
2. The instruction is, Using the converter, the model calculates a variable number of estimated tokens up to the end token associated with the bit pattern, Using the aforementioned model, the bit pattern is converted into an output token, and the output token is parsed into a symbolic expression. Further instructions for, The system according to claim 1, characterized in that the symbolic expression is the interpretable model.
3. The instruction is, The data table is sampled and computed according to an equation with randomized parameters containing Gaussian noise. The model is trained using the data table which contains the randomized parameters and variables of the equation as input, The model is trained by fitting the parameter values such that the symbolic expression generates the interpretable model. The system according to claim 1, further comprising instructions for the purpose of
4. The instruction further includes instructions for predicting the operating behavior and signal output of a vehicle battery using the interpretable model, The system of 3, characterized in that the interpretable model has a set length of the parameter value, and the parameter value is a symbolic parameter.
5. The token is associated with a decimal number representing a variable, constant, operator, or one of the observed parameters associated with the interpretable model according to the symbolic expression, The system according to claim 1, characterized in that the token is an estimated token associated with the unprocessed data.
6. The system of claim 1, wherein the instruction further includes an instruction for estimating the output from the symbolic expression based on the first data received.
7. The system according to claim 1, characterized in that the parameter value is a symbolic parameter which is a constant of the symbolic expression, and the token corresponds to a latent expression received by the model.
8. A non-temporary computer-readable medium, The system includes instructions, and when these instructions are executed by the processor, the processor receives the instructions. The model is used to generate the bit patterns associated with tokens from the raw data. Using the aforementioned model, the bit pattern is converted into a symbolic expression. The parameter values for the symbolic expression are derived, and an interpretable model of the raw data is generated. A non-temporary computer-readable medium characterized by the following:
9. The instruction is, Using the converter, the model calculates a variable number of estimated tokens up to the end token associated with the bit pattern, Using the aforementioned model, the bit pattern is converted into an output token, and the output token is parsed into a symbolic expression. Further instructions for, The non-temporary computer-readable medium of 8, characterized in that the symbolic expression is the interpretable model.
10. The instruction is, The data table is sampled and computed according to an equation with randomized parameters containing Gaussian noise. The model is trained using the data table which contains the randomized parameters and variables of the equation as input, The model is trained by fitting the parameter values such that the symbolic expression generates the interpretable model. The non-temporary computer-readable medium of the 8th, further comprising instructions for the purpose of...
11. The instruction further includes instructions for predicting the operating behavior and signal output of a vehicle battery using the interpretable model, The non-temporary computer-readable medium of 10, characterized in that the interpretable model has a set length of the parameter value, and the parameter value is a symbolic parameter.
12. The token is associated with a decimal number representing a variable, constant, operator, or one of the observed parameters associated with the interpretable model according to the symbolic expression, The non-temporary computer-readable medium of 8, characterized in that the token is an estimated token associated with the unprocessed data.
13. The non-temporary computer-readable medium of 8, wherein the instruction further comprises an instruction for estimating an output from the symbolic expression based on the first data received.
14. The non-temporary computer-readable medium of 8, characterized in that the parameter value is a symbolic parameter which is a constant of the symbolic expression, and the token corresponds to a potential expression received by the model.
15. It is a method, The model is used to generate bit patterns associated with tokens from raw data, and Using the aforementioned model, the bit pattern is converted into a symbolic expression, The parameter values for the symbolic expression are derived, and an interpretable model of the raw data is generated. A method characterized by comprising the following features.
16. Using a converter, the model calculates a variable number of estimated tokens up to the end token associated with the bit pattern, Using the aforementioned model, the bit pattern is converted into an output token, and the output token is parsed into a symbolic expression. Furthermore, The method of 15, characterized in that the symbolic expression is the interpretable model.
17. The process involves calculating a data table according to an equation with randomized parameters that have been sampled and contain Gaussian noise, and The model is trained using the data table which contains the randomized parameters and variables of the equation as input, The model is trained by fitting the parameter values such that the symbolic expression generates the interpretable model. The method of 15 is further characterized by comprising the following:
18. Further comprising predicting the operating behavior and signal output of a vehicle battery using the interpretable model, The method of 17, characterized in that the interpretable model has a set length of the parameter value, and the parameter value is a symbolic parameter.
19. The token is associated with a decimal number representing a variable, constant, operator, or one of the observed parameters associated with the interpretable model according to the symbolic expression, The method of 15, characterized in that the token is an estimated token associated with the raw data.
20. The method of 15, characterized in that the parameter value is a symbolic parameter which is a constant of the symbolic expression, and the token corresponds to a latent expression received by the model.