Patent Application
20240054184
Certain aspects of the present disclosure generally relate to artificial neural networks and, more particularly, to multitask learning based on Hermitian operators.
An artificial neural network, which may include an interconnected group of artificial neurons, may be a computational device or may represent a method to be performed by a computational device. Artificial neural networks may have corresponding structure and/or function in biological neural networks. Artificial neural networks, however, may provide useful computational techniques for certain applications, in which traditional computational techniques may be cumbersome, impractical, or inadequate. Because artificial neural networks may infer a function from observations, such networks may be useful in applications where the complexity of the task and/or data makes the design of the function burdensome using conventional techniques.
Machine learning may be used to perform both materials discovery and predict properties of the materials faster than molecular simulations. Machine learning can help identify correlations between material features and target properties. Nevertheless, most material discovery and properties are determined by single task machine learning models. With regards to multitask machine learning for material discovery/properties, there are significant difficulties with training a multitask model, such as task interference training.
A method for multitask learning based on Hermitian operators is described. The method includes training a multitask machine learning (MTML) model to map an input representation of a material onto a complex wave function state vector. The method also includes inferring, by a trained, MTML model, observable property matrices for each observable property of the material. The method further includes converting the observable property matrices into complex Hermitian operators. The method also includes predicting target properties of the material according to the complex Hermitian operators and the complex wave function state vector.
A non-transitory computer-readable medium having program code recorded thereon for multitask learning based on Hermitian operators is described. The program code is executed by a processor. The non-transitory computer-readable medium includes program code to train a multitask machine learning (MTML) model to map an input representation of a material onto a complex wave function state vector. The non-transitory computer-readable medium also includes program code to infer, by a trained, MTML model, observable property matrices for each observable property of the material. The non-transitory computer-readable medium further includes converting the observable property matrices into complex Hermitian operators. The non-transitory computer-readable medium also includes predicting target properties of the material according to the complex Hermitian operators and the complex wave function state vector.
A system for multitask learning based on Hermitian operators is described. The system includes a multitask machine learning (MTML) model, trained to map an input representation of a material onto a complex wave function state vector. The trained MTML model to infer observable property matrices for each observable property of the material. The trained MTML model is further to convert the observable property matrices into complex Hermitian operators. The trained MTML model is further to predict target properties of the material according to the complex Hermitian operators and the complex wave function state vector.
This has outlined, rather broadly, the features and technical advantages of the present disclosure in order that the detailed description that follows may be better understood. Additional features and advantages of the disclosure will be described below. It should be appreciated by those skilled in the art that this disclosure may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the teachings of the disclosure as set forth in the appended claims. The novel features, which are believed to be characteristic of the disclosure, both as to its organization and method of operation, together with further objects and advantages, will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.
The features, nature, and advantages of the present disclosure will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout.
The detailed description set forth below, in connection with the appended drawings, is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of the various concepts. Nevertheless, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well-known structures and components are shown in block diagram form in order to avoid obscuring such concepts.
Based on the teachings, one skilled in the art should appreciate that the scope of the disclosure is intended to cover any aspect of the disclosure, whether implemented independently of or combined with any other aspect of the disclosure. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth. In addition, the scope of the disclosure is intended to cover such an apparatus or method practiced using other structure, functionality, or structure and functionality in addition to or other than the various aspects of the disclosure set forth. It should be understood that any aspect of the disclosure disclosed may be embodied by one or more elements of a claim.
Although particular aspects are described, many variations and permutations of these aspects fall within the scope of the disclosure. Although some benefits and advantages of the preferred aspects are mentioned, the scope of the disclosure is not intended to be limited to particular benefits, uses, or objectives. Rather, aspects of the disclosure are intended to be broadly applicable to different technologies, system configurations, networks, and protocols, some of which are illustrated by way of example in the figures and in the following description of the preferred aspects. The detailed description and drawings are merely illustrative of the disclosure, rather than limiting the scope of the disclosure being defined by the appended claims and equivalents thereof.
Machine learning is concerned with the automatic discovery of patterns in data through the use of computer algorithms. Once discovered, these patterns may be used to perform data classification and/or value prediction. With growing experimental and simulated dataset size for materials science research, the ability of algorithms to automatically learn and improve from data becomes increasingly useful. Various types of machine learning algorithms, such as neural networks, have recently been applied to materials research. Among these machine learning algorithms, convolutional neural networks (CNNs) have been very attractive in recent years due to their great success in image recognition.
A CNN may be composed of multilayer neural networks, of which at least one layer employs a mathematical operation called “convolution” to enable the CNN to extract high-level features directly from data. Compared to many other algorithms that specify artificial features based on domain knowledge, a CNN involves relatively little pre-processing, as the features can be directly learned from the data. This is particularly useful when the features are difficult to exactly define. Unlike their long-used basic forms, such as perceptron and fully connected neural networks, CNNs are very recently used for solving solid state problems, such as learning material property prediction, material classification, and material phase transition identification.
Another advantage of neural networks is that they are easy to utilize in transfer learning, which means that a neural network first learns from a large database with inexpensive labels (e.g., first principles calculation results), and then it is fine-tuned on a small dataset where much fewer labeled samples are available (e.g., experimental data). This technique can be used to overcome the data scarcity problem in materials research, and it is applied to property prediction of small molecules and crystalline compounds very recently as a tool for accelerated materials discovery.
The practical realization and sustainable future of emergent technologies is dependent on accelerating materials discovery. Data-driven methods are anticipated to play an increasingly significant role in enabling this desired acceleration. While the vision of accelerating materials discovery using data-driven methods is well-founded, practical realization is throttled due to challenges in data generation, ingestion, and materials state-aware machine learning. High-throughput experiments and automated computational workflows are addressing the challenge of data generation, and capitalizing on these emerging data resources involves ingestion of data into an architecture that captures the complex provenance of experiments and simulations.
In practice, machine learning may be used to perform both materials discovery and predict properties of the materials faster than molecular simulations. Machine learning can help identify correlations between material features and target properties. Nevertheless, most material discovery and properties are determined by single task machine learning models. At a top level, a multitask model can receive some information regarding a material, such as a formula or a material structure. In this example, the multitask model can output one or more predicted properties of the material, such as bandgap, a lattice constant, an elastic property, a formation energy, and the like. Unfortunately, multitask machine learning for material discovery/properties suffers from significant difficulties during training of the multitask model, such as task interference.
Some aspects of the present disclosure provide an improvement over current machine learning technology by enforcing a mathematical structure to machine learning of multiple properties of a material using a multitask model. In particular, some aspects of the present disclosure are directed to training of a multitask model by applying physical observables and quantum mechanics theory to enforce a mathematical structure on machine learning of multiple properties of materials. As a result, during training the model infers both the mapping of the input vectors to complex numbered state vectors and a set of complex Hermitian matrices (e.g., operators) for each observable that may or may not be input dependent. The target properties are calculated as expectation values of the respective operators of the Hermitian matrices given the state vectors.
The SoC 100 may also include additional processing blocks tailored to specific functions, such as a connectivity block 110, which may include fifth generation (5G) new radio (NR) connectivity, fourth generation long term evolution (4G LTE) connectivity, unlicensed Wi-Fi connectivity, USB connectivity, Bluetooth connectivity, and the like, and a multimedia processor 112 that may, for example, detect and recognize gestures. In one implementation, the NPU is implemented in the CPU, DSP, and/or GPU. The SoC 100 may also include a sensor processor 114 to provide sensor image data, image signal processors (ISPs) 116, and/or navigation module 120, which may include a global positioning system.
Deep learning architectures may perform an object recognition task by learning to represent inputs at successively higher levels of abstraction in each layer, thereby building up a useful feature representation of the input data. In this way, deep learning addresses a major bottleneck of traditional machine learning. Prior to the advent of deep learning, a machine learning approach to an object recognition problem may have relied heavily on human engineered features, perhaps in combination with a shallow classifier. A shallow classifier may be a two-class linear classifier, for example, in which a weighted sum of the feature vector components may be compared with a threshold to predict to which class the input belongs. Human engineered features may be templates or kernels tailored to a specific problem domain by engineers with domain expertise. Deep learning architectures, in contrast, may learn to represent features that are similar to what a human engineer might design, but through training. Furthermore, a deep network may learn to represent and recognize new types of features that a human might not have considered.
A deep learning architecture may learn a hierarchy of features. If presented with visual data, for example, the first layer may learn to recognize relatively simple features, such as edges, in the input stream. In another example, if presented with auditory data, the first layer may learn to recognize spectral power in specific frequencies. The second layer, taking the output of the first layer as input, may learn to recognize combinations of features, such as simple shapes for visual data or combinations of sounds for auditory data. For instance, higher layers may learn to represent complex shapes in visual data or words in auditory data. Still higher layers may learn to recognize common visual objects or spoken phrases.
Deep learning architectures may perform especially well when applied to problems that have a natural hierarchical structure. For example, the classification of motorized vehicles may benefit from first learning to recognize wheels, windshields, and other features. These features may be combined at higher layers in different ways to recognize cars, trucks, and airplanes.
Neural networks may be designed with a variety of connectivity patterns. In feed-forward networks, information is passed from lower to higher layers, with each neuron in a given layer communicating to neurons in higher layers. A hierarchical representation may be built up in successive layers of a feed-forward network, as described above. Neural networks may also have recurrent or feedback (also called top-down) connections. In a recurrent connection, the output from a neuron in a given layer may be communicated to another neuron in the same layer. A recurrent architecture may be helpful in recognizing patterns that span more than one of the input data chunks that are delivered to the neural network in a sequence. A connection from a neuron in a given layer to a neuron in a lower layer is called a feedback (or top-down) connection. A network with many feedback connections may be helpful when the recognition of a high-level concept may aid in discriminating the particular low-level features of an input.
The DCN 200 may be trained with supervised learning. During training, the DCN 200 may be presented with an image, such as the image 201 of a speed limit sign, and a forward pass may then be computed to produce an output 222. The DCN 200 may include a feature extraction section 210 and a classification section 220. Upon receiving the image 201, a convolutional layer 212 may apply convolutional kernels (not shown) to the image 201 to generate a first set of feature maps 214. As an example, the convolutional kernel for the convolutional layer 212 may be a 5×5 kernel that generates 28×28 feature maps. In the present example, because four different convolutional kernels were applied to the image 201 at the convolutional layer 212, four different feature maps are generated in the first set of feature maps 214. The convolutional kernels may also be referred to as filters or convolutional filters.
The first set of feature maps 214 may be subsampled by a max pooling layer (not shown) to generate a second set of feature maps 216. The max pooling layer reduces the size of the first set of feature maps 214. That is, a size of the second set of feature maps 216, such as 14×14, is less than the size of the first set of feature maps 214, such as 28×28. The reduced size provides similar information to a subsequent layer while reducing memory consumption. The second set of feature maps 216 may be further convolved via one or more subsequent convolutional layers (not shown) to generate one or more subsequent sets of feature maps (not shown).
In the example of
In the present example, the probabilities in the output 222 for “sign” and “60” are higher than the probabilities of the others of the output 222, such as “30,” “40,” “50,” “70,” “80,” “90,” and “100.” Before training, the output 222 produced by the DCN 200 is likely to be incorrect. Thus, an error may be calculated between the output 222 and a target output. The target output is the ground truth of the image 201 (e.g., “sign” and “60”). The weights of the DCN 200 may then be adjusted so the output 222 of the DCN 200 is more closely aligned with the target output.
As shown in
The DCN 200 shown in
Another advantage of neural networks is that they are easy to utilize in transfer learning, which means that a neural network first learns from a large database with inexpensive labels (e.g., first principles calculation results), and then it is fine-tuned on a small dataset where much fewer labeled samples are available (e.g., experimental data). This technique can be used to overcome the data scarcity problem in materials research, and it is applied to property prediction of small molecules and crystalline compounds very recently as a tool for accelerated materials discovery.
The practical realization and sustainable future of emergent technologies is dependent on accelerating materials discovery using neural networks. Data-driven methods are anticipated to play an increasingly significant role in enabling this desired acceleration. While the vision of accelerating materials discovery using data-driven methods is well-founded, practical realization is throttled due to challenges in data generation, ingestion, and materials state-aware machine learning. High-throughput experiments and automated computational workflows are addressing the challenge of data generation, and capitalizing on these emerging data resources involves ingestion of data into an architecture that captures the complex provenance of experiments and simulations.
In practice, machine learning may be used to perform both materials discovery and predict properties of the materials faster than molecular simulations. Machine learning can help identify correlations between material features and target properties. Nevertheless, most material discovery and properties are determined by single task machine learning models. At a top level, a multitask model that can receive some information regarding a material, such as a formula or a material structure. In this example, the multitask model can output one or more predicted properties of the material, such as bandgap, a lattice constant, elastic properties, formation energies, and the like. Unfortunately, multitask machine learning for material discovery/properties suffers from significant difficulties during training of the multitask model, such as task interference.
Some aspects of the present disclosure provide an improvement over current machine learning technology by enforcing a mathematical structure to machine learning of multiple properties of a material using a multitask model. In particular, some aspects of the present disclosure are directed to training of a multitask model by applying physical observables and quantum mechanics theory to enforce a mathematical structure on machine learning of multiple properties of materials. As a result, during training the model infers both the mapping of the input vectors to complex numbered state vectors and a set of complex Hermitian matrices (e.g., operators) for each observable that may or may not be input dependent. The target properties are calculated as expectation values of the respective operators of the Hermitian matrices given the state vectors, for example, as shown in
In some aspects of the present disclosure, a multitask model is trained using the physical observables, and quantum mechanics theory is applied to enforce a mathematical structure to machine learning of the multiple properties Y of the materials X. As shown in
As further illustrated in
At block 340, the complex wave function of block 330 is normalized to form a complex, normalized wave function vector, having m-data rows and n-column components of complex wave functions. At block 350, during training of the MTML model, input vectors are mapped onto complex number state vectors at block 340, which may or may not be dependent on the input vectors. In addition, complex Hermitian matrices (operators) are converted from observable property square matrices interred at block 350 for each of the observables 360 of the material. Also, predicted properties (e.g., Ypred) for a material are calculated as expectation values of the respective Hermitian operators and as a function of the complex number state vectors at block 370. At block 390, a loss function is performed between the target properties Y of block 380 and the predicted properties Ypred of block 370. In one example of the MTML model, a formula or structure of a material is provided as input and one or more predicted properties of the material such as bandgap, lattice constant, elastic modulus, among others, are provided as output.
E[obs]=<psi|OP|psi> (1)
<psi|OP|psi>=psi*.Mop.PSI (2)
where E is the expected value, OP is the observable parameter, PSI is a complex wave function state vector, and Mop refers to an observable parameters matrix, such as the complex Hermitian matrix of block 430.
According to Equation (1), the expectation value E of the observable (e.g., E[obs] may refer to Hermitian operators determined from expectation values and matrix products. According to Equation (2) of a first matrix, multiplication is performed between the observable parameters matrix Mop and the complex wave function state vector PSI (e.g., block 340) to form a matrix product. Next a complex conjugate operation is performed between the complex wave function state vector PSI and the matrix product to form the expected value of the observable parameters to predict a property (e.g., Ypred). As shown
In the multitask learning process overview 500, a vector form is used to represent complex wave functions (PSI) as complex vectors. In addition, the vector form is computed with complex Hermitian matrices as operators. These can optionally be constrained to have non-negative eigenvalues by computing them as M.M{circumflex over ( )}*) to compute Hermitian matrices with positive Eigen values. In particular, this vector form enables training of a multitask model by applying physical observables and quantum mechanics theory to enforce a mathematical structure on machine learning of multiple properties of materials. As a result, during training the model infers both the mapping of the input vectors to complex numbered state vectors and a set of complex Hermitian matrices (e.g., operators) for each observable that may or may not be input dependent. The target properties are calculated as expectation values of the respective operators of the Hermitian matrices given the state vectors, according to Equations (1) and (2). This process is further illustrated, for example, according to a method as shown in
At block 604, observable property matrices are inferred for each observable property of the material inferred using a trained, MTML model. For example, as shown in the multitask learning process framework 300 of
At block 606, the observable property matrices are converted into complex Hermitian operators. For example, as shown in
At block 608, target properties of the material are predicted according to the complex Hermitian operators and the complex wave function state vector. For example, as shown in
The method of 600 may include predicting target properties by calculating a product of the complex Hermitian operators and the complex wave function state vector. The method of 600 may also include predicting target properties of the material as expectation values of a complex conjugate operation between the calculated product and the complex wave function state vector. The method 600 may further include predicting the target properties by performing a loss function between the predicted target properties (Ypred) and the observable target properties (Y) of the material. The method may also include training by learning parameters of the multitask model for mapping an input formula/structure of the material to the complex wave function state vector. The method 600 may further include dividing the learned parameters into rows and columns according to a predetermined format. The method 600 may also include normalizing the predetermined format of the learned parameters to form the complex wave function state vector.
The method 600 may include training by applying physical observables and quantum mechanics theory to enforce a mathematical structure on machine learning of multiple properties of materials. The observable property matrices comprise square matrices. The method 600 may further include predicting the observable properties of target properties of the material, including a bandgap, a lattice constant, an elastic property, and/or a formation energy. The method 600 may also include predicting the target properties by calculating expectation values of respective operators of Hermitian matrices given the complex wave function state vector, for example, as shown in
In some aspects, the method 600 may be performed by the SoC 100 (
The various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and/or software component(s) and/or module(s), including, but not limited to, a circuit, an application specific integrated circuit (ASIC), or processor. Generally, where there are operations illustrated in the figures, those operations may have corresponding counterpart means-plus-function components with similar numbering.
As used, the term “determining” encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Additionally, “determining” may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Furthermore, “determining” may include resolving, selecting, choosing, establishing, and the like.
As used, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c.
The various illustrative logical blocks, modules and circuits described in connection with the present disclosure may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array signal (FPGA) or other programmable logic device (PLD), discrete gate or transistor logic, discrete hardware components or any combination thereof designed to perform the functions described. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any commercially available processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.
The steps of a method or algorithm described in connection with the present disclosure may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in any form of storage medium that is known in the art. Some examples of storage media that may be used include random access memory (RAM), read-only memory (ROM), flash memory, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, a hard disk, a removable disk, a CD-ROM, and so forth. A software module may comprise a single instruction, or many instructions, and may be distributed over several different code segments, among different programs, and across multiple storage media. A storage medium may be coupled to a processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor.
The methods disclosed, include one or more steps or actions for achieving the described method. The method steps and/or actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is specified, the order and/or use of specific steps and/or actions may be modified without departing from the scope of the claims.
The functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in hardware, an example hardware configuration may comprise a processing system in a device. The processing system may be implemented with a bus architecture. The bus may include any number of interconnecting buses and bridges depending on the specific application of the processing system and the overall design constraints. The bus may link together various circuits including a processor, machine-readable media, and a bus interface. The bus interface may be used to connect a network adapter, among other things, to the processing system via the bus. The network adapter may be used to implement signal processing functions. For certain aspects, a user interface (e.g., keypad, display, mouse, joystick, etc.) may also be connected to the bus. The bus may also link various other circuits such as timing sources, peripherals, voltage regulators, power management circuits, and the like, which are well known in the art, and therefore, will not be described any further.
The processor may be responsible for managing the bus and general processing, including the execution of software stored on the machine-readable media. The processor may be implemented with one or more general purpose and/or special-purpose processors. Examples include microprocessors, microcontrollers, DSP processors, and other circuitry that can execute software. Software shall be construed broadly to mean instructions, data, or any combination thereof, whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise. Machine-readable media may include, by way of example, random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, magnetic disks, optical disks, hard drives, or any other suitable storage medium, or any combination thereof. The machine-readable media may be embodied in a computer-program product. The computer-program product may comprise packaging materials.
In a hardware implementation, the machine-readable media may be part of the processing system separate from the processor. However, as those skilled in the art will readily appreciate, the machine-readable media, or any portion thereof, may be external to the processing system. By way of example, the machine-readable media may include a transmission line, a carrier wave modulated by data, and/or a computer product separate from the device, all which may be accessed by the processor through the bus interface. Alternatively, or in addition, the machine-readable media, or any portion thereof, may be integrated into the processor, such as the case may be with cache and/or general register files. Although the various components discussed may be described as having a specific location, such as a local component, they may also be configured in various ways, such as certain components being configured as part of a distributed computing system.
The processing system may be configured as a general purpose processing system with one or more microprocessors providing the processor functionality and external memory providing at least a portion of the machine-readable media, all linked together with other supporting circuitry through an external bus architecture. Alternatively, the processing system may comprise one or more neuromorphic processors for implementing the neuron models and models of neural systems described. As another alternative, the processing system may be implemented with an application specific integrated circuit (ASIC) with the processor, the bus interface, the user interface, supporting circuitry, and at least a portion of the machine-readable media integrated into a single chip, or with one or more field programmable gate arrays (FPGAs), programmable logic devices (PLDs), controllers, state machines, gated logic, discrete hardware components, or any other suitable circuitry, or any combination of circuits that can perform the various functionality described throughout this disclosure. Those skilled in the art will recognize how best to implement the described functionality for the processing system depending on the particular application and the overall design constraints imposed on the overall system.
The machine-readable media may comprise a number of software modules. The software modules include instructions that, when executed by the processor, cause the processing system to perform various functions. The software modules may include a transmission module and a receiving module. Each software module may reside in a single storage device or be distributed across multiple storage devices. By way of example, a software module may be loaded into RAM from a hard drive when a triggering event occurs. During execution of the software module, the processor may load some of the instructions into cache to increase access speed. One or more cache lines may then be loaded into a general register file for execution by the processor. When referring to the functionality of a software module below, it will be understood that such functionality is implemented by the processor when executing instructions from that software module. Furthermore, it should be appreciated that aspects of the present disclosure result in improvements to the functioning of the processor, computer, machine, or other system implementing such aspects.
If implemented in software, the functions may be stored or transmitted over as one or more instructions or code on a non-transitory computer-readable medium. Computer-readable media include both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage medium may be any available medium that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage, or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Additionally, any connection is properly termed a non-transitory computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared (IR), radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used herein, include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray® disc, where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Thus, in some aspects computer-readable media may comprise non-transitory computer-readable media (e.g., tangible media). In addition, for other aspects computer-readable media may comprise transitory computer-readable media (e.g., a signal). Combinations of the above should also be included within the scope of computer-readable media.
Thus, certain aspects may comprise a computer program product for performing the operations presented. For example, such a computer program product may comprise a non-transitory computer-readable medium having instructions stored (and/or encoded) thereon, the instructions being executable by one or more processors to perform the operations described herein. For certain aspects, the computer program product may include packaging material.
Further, it should be appreciated that modules and/or other appropriate means for performing the methods and techniques described herein, may be downloaded and/or otherwise obtained by a user terminal and/or base station as applicable. For example, such a device can be coupled to a server to facilitate the transfer of means for performing the methods described herein. Alternatively, various methods described herein, may be provided via storage means (e.g., RAM, ROM, a physical storage medium such as a compact disc (CD) or floppy disk, etc.), such that a user terminal and/or base station can obtain the various methods upon coupling or providing the storage means to the device. Moreover, any other suitable technique for providing the methods and techniques described herein to a device can be utilized.
It is to be understood that the claims are not limited to the precise configuration and components illustrated above. Various modifications, changes, and variations may be made in the arrangement, operation, and details of the methods and apparatus described above without departing from the scope of the claims.
