DETAILED ACTION
This action is responsive to the application filed on 04/12/2023. Claims 1-9 are pending and have been examined.
This action is Non-final.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Priority
Applicant’s claim for the benefit of a prior-filed application under 35 U.S.C. 119(e) or under 35 U.S.C.
120, 121, 365(c), or 386(c) is acknowledged.
Response to Arguments
Argument 1: Applicant argues on page 5-8 amended claim 1 overcomes the 101 rejection because the amendments allegedly recite a specific data-processing pipeline that integrates the mathematical concepts into a practical application. Their main point is that claim 1 now requires: the first function to be a forward propagation neural network with a monotonically increasing activation function; the second function to be an RNN that takes covariates as input and outputs at least a non-negative weight and bias so the first function remains monotonically increasing; and calculating a quantile without Monte Carlo simulation by calculating a quantile of a normal distribution and converting it through an inverse of the first function solvable by root-finding. They argue this improves computer functionality by avoiding computationally expensive Monte Carlo simulations and reducing processor/memory load. For Step 2B, they argue the arrangement is non-conventional because the cited art does not show the specific architecture of dynamically generated non-negative weights ensuring monotonicity and enabling lightweight root-finding instead of Monte Carlo. Claims 6 and 7 are argued allowable for similar/dependent reasons.
Response to Argument 1: The applicant’s arguments have been considered but are not persuasive. As set forth in the rejection under 35 U.S.C. 101, amended claim 1 continues to recite mathematical concepts, including optimizing parameters of functions and a Gaussian-process kernel, non-linearly transforming observation values so that transformed values follow a Gaussian process, calculating a quantile of a value following a normal distribution, and converting that quantile using an inverse function solvable by a root-finding algorithm. The additional recitations of a forward propagation neural network, a recurrent neural network, a non-negative weight, a bias, and a monotonically increasing activation function do not integrate the judicial exception into a practical application because these features are used as part of the mathematical model itself to transform values and calculate a prediction quantile. The claim does not recite an improvement to computer hardware, processor operation, memory organization, network communication, data storage, or another technical field beyond using generic computer components to execute the claimed mathematical prediction model. The argument that the claim avoids Monte Carlo simulation is also not persuasive because “without using Monte Carlo simulation” merely identifies that one mathematical simulation technique is not used and that a different mathematical calculation, namely calculating a normal-distribution quantile and applying an inverse/root-finding calculation, is used instead. Any alleged reduction in computational burden arises from selecting one mathematical prediction technique over another, not from a claimed improvement to the functioning of the computer itself. Further, under Step 2B, the claimed ordered combination does not amount to significantly more than the abstract idea. The amended limitations remain directed to the same mathematical prediction model and are implemented using generic computer components. To the extent of the argument that the claimed arrangement is non-conventional, that argument is not persuasive because the updated prior-art rejection shows that the relevant features were known and at least obvious in the art, including warped Gaussian-process prediction, monotonic nonlinear transformations, feedforward neural-network structures with monotonic activation functions, hypernetwork/recurrent-network generation of weights and biases, joint optimization of recurrent-network and Gaussian-process kernel parameters, and direct/inverse calculation of prediction quantiles. Accordingly, claim 1 remains directed to an abstract idea without significantly more. Claims 6 and 7 are not separately persuasive for at least the same reasons because claim 6 is an apparatus counterpart to claim 1 and claim 7 merely recites a non-transitory computer-readable recording medium having instructions for performing the method of claim 1.
Argument 2: Applicant argues the 102 rejection over Snelson should be withdrawn because Snelson allegedly uses a static/global warping function and does not disclose the amended “second function” as an RNN dynamically taking covariates and outputting non-negative weights/biases for the first function, nor the claimed Monte-Carlo-free quantile calculation using the inverse of the monotonic first function. For 103, Applicant argues the Snelson/Williams/Ha/Al-Shedivat combinations still fail because Ha may generate weights dynamically, but does not require those weights to be non-negative or use them to ensure a separate forward-propagation neural network remains monotonic. Williams only generally teaches feedforward networks/sigmoids, and Al-Shedivat transforms input space with an LSTM for recurrent Gaussian-process kernels but does not generate non-negative parameters for a separate monotonic inverse-function calculation. Applicant also argues claims 8-9 are allowable because the prior art does not teach the newly claimed probability-density-distribution/probability calculation without Monte Carlo simulation or the specific bisection-method root-finding in the context of the amended neural-network architecture.
Response to Argument 2: The applicant’s arguments have been considered but are not persuasive. The prior 35 U.S.C. 102 rejection over Snelson should be withdrawn, and in light of the amendments, the current rejection has been updated under 35 U.S.C. 103 and does not rely on Snelson alone to teach every limitation of amended claim 1. Rather, Snelson is relied upon for the core warped Gaussian-process prediction framework, including non-linearly transforming observation values using a monotonic warping function, modeling the transformed values by a Gaussian process, optimizing transformation and covariance/kernel parameters, calculating Gaussian predictive values, converting median/percentile values through an inverse warping function, and solving the inverse by a root-finding method. Williams is relied upon for the feedforward neural-network structure, weighted combinations, bias, and monotonically increasing activation function. Ha is relied upon for the hypernetwork/recurrent-network technique in which a recurrent network takes input data and dynamically generates weights and bias parameters for another network. Al-Shedivat is relied upon for sequential input/covariate data and joint optimization of recurrent-network parameters and Gaussian-process kernel parameters. Thus, the argument that Snelson alone uses a static/global warping function does not overcome the rejection because the rejection relies on the combined teachings of the cited references, not Snelson alone. The argument that Ha does not require non-negative generated weights is also not persuasive because the rejection does not rely on Ha alone for the non-negative-weight/monotonicity feature. The rejection relies on Ha for the recurrent neural network/hypernetwork that generates weights and bias parameters for another network, and relies on Snelson for the teaching that the warping function must be constrained to be monotonic and that non-negative parameters are used in a neural-net style monotonic warping function. Therefore, it would have been obvious to constrain the weights generated by Ha’s recurrent/hypernetwork technique to the non-negative values taught by Snelson when those generated weights are used to parameterize Snelson’s monotonic neural-network warping function. The argument that Williams only generally teaches feedforward networks and sigmoids is likewise not persuasive because Williams is used for that exact limited purpose, namely to show the known feedforward neural-network structure, weighted combinations, bias, and monotonically increasing sigmoid activation. The argument regarding Al-Shedivat is also not persuasive because Al-Shedivat is not relied upon to teach the entire claimed architecture, but rather to show recurrent/sequential Gaussian-process modeling and joint optimization of recurrent-network parameters and Gaussian-process kernel parameters. The arguments regarding claims 8 and 9 are also not persuasive. For claim 8, the rejection relies on Snelson for calculating a predictive probability distribution in observation space, Williams for multiple test inputs and corresponding test targets, Al-Shedivat for target vectors and complete predictive densities in sequential prediction, and the no-Monte-Carlo/direct-calculation teachings set forth in the rejection. Thus, the claimed probability-density-distribution and probability-at-time-step features are taught or rendered obvious by the cited combination. For claim 9, the rejection relies on Snelson for using a root-finding algorithm to solve the inverse warping function and relies on Lopez Galvan for the bisection method as a known root-finding method that generates a root approximation. Substituting the known bisection method for the root-finding calculation required by Snelson would have been an obvious use of a known numerical root-finding technique to obtain the predictable result of approximating a root for the inverse-function calculation.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition
of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the
conditions and requirements of this title.
Claims 1-9 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Regarding claim 1,
Step 1: The claim is directed to a prediction method, which is one of the four statutory categories. Therefore, claim 1 satisfies Step 1.
Step 2A Prong 1:
(a) “optimizing a parameter of a second function that outputs parameters of a first function from covariates, and optimizing a parameter of a kernel function of a Gaussian process, by using a series of observation values observed in a past and a series of the covariates observed simultaneously with the observation values” - This limitation is to optimizing parameters of functions, including a kernel function of a Gaussian process, and it involves mathematical relationships, mathematical formulas, and/or mathematical calculations performed on observation values and covariates. Thus, the limitation is directed to math.
(b) “wherein values obtained by non-linearly transforming the observation values by the first function follow the Gaussian process” - This limitation is directed to non-linearly transforming observation values by a function and modeling the transformed values as following a Gaussian process recites mathematical relationships and mathematical modeling, and thus the limitation is directed to math.
(c) “calculating a quantile of a prediction distribution of observation values in a period in future to be predicted without using Monte Carlo simulation, by calculating a quantile of a value following a normal distribution obtained by using the second function and the kernel function having parameters optimized in the optimizing and a series of covariates in the period” - This limitation is directed to calculating a quantile of a prediction distribution and calculating a quantile of a value following a normal distribution, which is considered mathematical calculations involving probability distributions, and thus the limitation is directed to math.
(d) “converting the calculated quantile of the value following the normal distribution using an inverse function of the first function which is solvable by a root-finding algorithm due to the monotonic increasing property of the first function” - This limitation is directed to converting a value using an inverse function and solving the inverse function by a root-finding algorithm are considered mathematical operations, and thus the limitation is directed to math.
(e) “using an inverse function of the first function which is solvable by a root-finding algorithm due to the monotonic increasing property of the first function” - This limitation recites solving an inverse function using a root-finding algorithm, which is part of the mathematical calculation itself, and thus the limitation is directed to math.
Step 2A Prong 2 and Step 2B:
(a) “A prediction method executed by a computer including a memory and a processor, the method comprising” - This limitation merely recites using generic computer components to execute the claimed prediction method. The memory and processor are recited at a high level of generality and amount to no more than mere instructions to apply the judicial exception using generic computer components. Therefore, this limitation does not integrate the judicial exception into a practical application, nor does it provide significantly more than the judicial exception. (see MPEP 2106.05(f)).
(b) “wherein the first function is a forward propagation neural network having an activation function that is a monotonically increasing function, and the second function is a recurrent neural network that takes the covariates as input and outputs at least a weight of a non-negative value and a bias as the parameters of the first function to ensure that the first function is a monotonically increasing function” - This limitation recites neural-network functions used to parameterize and perform transformation and prediction calculations. The forward propagation neural network, recurrent neural network, non-negative weight, bias, and monotonic activation function are used as part of the mathematical model for transforming observation values and calculating the prediction quantile. These limitations do not impose a meaningful limit on the judicial exception or apply the exception in a manner that improves another technology or technical field, which do not integrate the judicial exception into a practical application, nor do they provide significantly more than the judicial exception. See MPEP 2106.05(h)).
(c) “without using Monte Carlo simulation” - This limitation merely indicates that one mathematical calculation technique is not used when calculating the claimed prediction quantile. Avoiding Monte Carlo simulation, without more, does not apply the judicial exception to a particular machine/environment, and thus it does not integrate to a practical application, nor provide significantly more than the judicial exception (see MPEP 2106.05(h)).
Thus, claim 1 is non-patent eligible. Claim 6 is analogous to claim 1, aside from claim type, and thus faces the same rejection under 35 U.S.C. 101. Claim 7 merely recites a non-transitory computer-readable recording medium having instructions that cause a computer to perform the prediction method according to claim 1, and thus also faces the same rejection under 35 U.S.C. 101.
Regarding claim 2,
Step 1: The claim is directed to a method, which falls under the category of process. The claim satisfies Step 1.
Step 2A Prong 1:
“The prediction method according to claim 1, the method further comprising: calculating a statistic of the observation values in the period by using the calculated prediction distribution” -- The limitation is directed to a method that further comprises calculating an observation value statistic by using calculated distribution of the predictions. The limitation is directed to the use mathematical operations/calculations/operations, and thus the limitation is directed to math.
There are no elements to be evaluated under Step 2A Prong 2 and Step 2B.
Thus, claim 2 is non-patent eligible.
Regarding claim 3,
Step 1: The claim is directed to a method, which falls under the category of process. The claim satisfies Step 1.
There are no elements to be evaluated under Step 2A Prong 1.
Step 2A Prong 2 and Step 2B:
“wherein the first function is a forward propagation neural network having a weight and a bias as parameters and a monotonically increasing function as an activation function,” -- The limitation is directed to the forward propagation NN (computer/network) that will have weight/bias parameters and an increasing function that will act as an activation function. The limitation is directed to no more than mere instructions to apply onto a computer, and does not integrate to a practical application, nor provides significantly more than the judicial exception (see MPEP 2106.05(f)).
“the second function is a recurrent neural network that outputs at least the weight of a non-negative value and the bias.” -- The limitation recites a second function that is a recurrent (repetitive) NN that will output the weight of the non-negative ones and the bias value. The limitation is directed to an insignificant, extra-solution activity that cannot be integrated to a practical application (see MPEP 2106.05(g)). Furthermore, under Step 2B, the act of a NN performing repetitive calculations as well as inputting/outputting gathered data over a network is a well-understood, routine, and conventional activity (WURC) that cannot provide significantly more than the judicial exception (see MPEP 2106.05(d)(II)).
Thus, claim 3 is non-patent eligible.
Regarding claim 4,
Step 1: The claim is directed to a method, which falls under the category of process. The claim satisfies Step 1.
There are no elements to be evaluated under Step 2A Prong 1.
Step 2A Prong 2 and Step 2B:
“The prediction method according to claim 3, wherein the second function further outputs a real value to be taken as input of the kernel function.” -- The limitation recites that the second function will further output a real value to be taken as the input of the kernel function. The limitation amounts no more than mere further limiting to a field of use/environment and it does not integrate to a practical application, nor provides significantly more than the judicial exception (see MPEP 2106.05(h)).
Thus, claim 4 is non-patent eligible.
Regarding claim 5,
Step 1: The claim is directed to a method, which falls under the category of process. The claim satisfies Step 1.
Step 2A Prong 1:
“The prediction method according to claim 1, wherein, in the optimizing, the parameters of the second function and the kernel function are optimized by searching for parameters of the second function and the kernel function that minimize negative log marginal likelihood.” -- The limitation is directed to optimizing parameters by searching for parameters of the second and kernel function that minimize negative log marginal likelihood. The limitation is directed to a process that can be performed in the human mind using evaluation, observation, and judgement, with aid of pen and paper if needed, and thus the limitation is directed to a mental process.
There are no elements to be evaluated under Step 2A Prong 2 and Step 2B.
Thus, claim 5 is non-patent eligible.
Regarding claim 7,
Step 1: The claim is directed to a non-transitory CRM, which falls under the category of manufacture. The claim satisfies Step 1.
There are no elements to be evaluated under Step 2A Prong 1.
Step 2A Prong 2 and Step 2B:
“A non-transitory computer-readable recording medium having computer-readable instructions stored thereon. which when executed, cause a computer to perform the prediction method according to claim 1.” -- The limitation recites a CRM claim that will have instructions that will be executed to a computer to perform the method of claim 1. The limitation amounts to no more than mere instructions to apply onto a computer and it does not integrate to a practical application, nor provides significantly more than the judicial exception (see MPEP 2106.05(f)).
Thus, claim 7 is non-patent eligible.
Regarding claim 8,
Step 1: The claim is directed to a method, which falls under the category of process. The claim satisfies Step 1.
Step 2A Prong 1:
(a) “calculating a probability density distribution of a target value vector in the period” - This limitation is directed to calculating a probability density distribution involves mathematical relationships, probability calculations, and/or statistical modeling. The specification corroborates that this limitation is mathematical in nature because it describes the prediction unit as using the kernel function, forward propagation neural network, recurrent neural network, and covariates in the prediction period to calculate a probability density distribution of the target value vector, and then provides mathematical expressions for that distribution, including mean/covariance expressions and a multivariate normal distribution. (see spec [0060-0067])
(b) “obtaining a probability corresponding to a target value at any time step in the period from the probability density distribution without using Monte Carlo simulation” - This limitation is directed to obtaining a probability from a probability density distribution is a mathematical calculation involving probability and statistical distributions. The specification corroborates this characterization because it states that, with the probability density distribution, a probability corresponding to the target value yt at any time step in the prediction period can be obtained without using Monte Carlo simulation, thus the limitation is directed to math.
There are no elements to be evaluated Step 2A Prong 2 and Step 2B.
Thus, claim 8 is non-patent eligible.
Regarding claim 9,
Step 1: The claim is directed to a prediction method, which is one of the four statutory categories. Therefore, claim 9 satisfies Step 1.
Step 2A Prong 1:
(a) “The prediction method according to claim 1, wherein the root-finding algorithm is a bisection method” - This limitation is directed to a bisection method is a mathematical root-finding algorithm used to solve for a value of a function. The limitation therefore recites a mathematical operation/algorithm.
There are no elements to be evaluated under Step 2A Prong 2 and Step 2B.
Thus, claim 9 is non-patent eligible.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this
Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not
identically disclosed as set forth in section 102, if the differences between the claimed invention and the
prior art are such that the claimed invention as a whole would have been obvious before the effective filing
date of the claimed invention to a person having ordinary skill in the art to which the claimed invention
pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are
summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claim(s) 1-8 is/are rejected under 35 U.S.C. 103 as being unpatentable over NPL reference “Warped gaussian processes”, by Snelson et. al. (referred herein as Snelson) in view of NPL reference “Gaussian Processes for Machine Learning”, by Williams et. al. (referred herein as Williams) in view of NPL reference “Hypernetworks.”, by Ha et. al. (referred herein as Ha) further in view of NPL reference “Learning scalable deep kernels with recurrent structure.” (referred herein Al-Shevidet).
Regarding claim 1, Snelson teaches:
A prediction method executed by a computer including a memory and a processor, ([Snelson, page 1-2] “We wish to predict the value of an observation tN+1 given a new input vector x(N+1) … the calculation of the mean and variance of this distribution involves doing a matrix inversion of the covariance matrix CN of the training inputs, which using standard exact methods incurs a computational cost of order N³ “, wherein the examiner interprets “predict the value of an observation” to be the same as a prediction method because they are both directed to a methodology for forecasting observation values. The examiner further interprets “calculation” involving “matrix inversion” with “computational cost of order N³” to be the same as executed by a computer including a memory and a processor because they are both directed to computational operations that inherently require computer hardware with processing and memory capabilities to perform intensive matrix calculations.)
the method comprising: optimizing a parameter of a second function that outputs parameters of a first function from covariates, ([Snelson, page 3] “Learning in this extended model is achieved by simply taking derivatives of the negative log likelihood function (6) with respect to both Θ and Ψ parameter vectors, and using a conjugate gradient method to compute ML parameter values” and [Snelson, page 2] “The covariance between the function value of y at two points x and x′ is modelled with a covariance function C(x, x′), which is usually assumed to have some simple parametric form”, wherein the examiner interprets “taking derivatives” with respect to “Ψ parameter vectors” where “covariance function C(x, x′)” operates on input covariates x to be the same as “optimizing a parameter of a second function that outputs parameters of a first function from covariates” because they are both directed to optimizing parameters where a covariance function uses covariates to define the structure that governs the warping function parameters.)
and optimizing a parameter of a kernel function of a Gaussian process, ([Snelson, page 2] “Learning, or 'training', in a GP is usually achieved by finding a local maximum in the likelihood using conjugate gradient methods with respect to the hyperparameters Θ of the covariance matrix”, wherein the examiner interprets “finding a local maximum in the likelihood” with respect to “hyperparameters Θ of the covariance matrix” to be the same as “optimizing a parameter of a kernel function of a Gaussian process” because they are both directed to optimizing parameters of a covariance/kernel function within a Gaussian process framework.)
by using a series of observation values observed in a past and a series of the covariates observed simultaneously with the observation values, ([Snelson, page 2] “Suppose we are given a dataset D, consisting of N pairs of input vectors XN ≡ {x(n)} N n=1 and real-valued targets tN ≡ {tn} N n=1. We wish to predict the value of an observation tN+1 given a new input vector x^(N+1).” wherein the examiner interprets “real-valued targets” in the already-given “dataset D” to be the same as “a series of observation values observed in a past” because they are both directed to previously obtained (historical) observed target/observation values used as the known data for predicting a new/future observation. The examiner further interprets “N pairs of input vectors XN ≡ {x(n)}Nn=1” to be the same as a series of the covariates observed simultaneously with the observation values because they are both directed to input covariates that are paired with and collected at the same time as the corresponding observation values.)
wherein values obtained by non-linearly transforming the observation values by the first function follow the Gaussian process; ([Snelson, page 3] “Now we make a transformation from the true observation space to the latent space by mapping each observation through the same monotonic function f, zn = f(tn; Ψ) ∀n” and “Let us consider a vector of latent targets zN and suppose that this vector is modelled by a GP”, wherein the examiner interprets “transformation from the true observation space to the latent space” through “monotonic function f” where the resulting “latent targets zN” is “modelled by a GP” to be the same as “values obtained by non-linearly transforming the observation values by the first function follow the Gaussian process” because they are both directed to applying a nonlinear transformation to observations such that the transformed values conform to a Gaussian process model.)
optimizing a parameter of a kernel function of a Gaussian process, by using a series of observation values observed in a past and a series of the covariates observed simultaneously with the observation values, ([Snelson, page 2] “Suppose we are given a dataset D, consisting of N pairs of input vectors XN ≡ {x(n)}Nn=1 and real-valued targets tN ≡ {tn}Nn=1.” and [Snelson, page 3] “Learning, or ‘training’, in a GP is usually achieved by finding a local maximum in the likelihood using conjugate gradient methods with respect to the hyperparameters Θ of the covariance matrix.”, wherein the examiner interprets “real-valued targets tN” to be the same as “a series of observation values observed in a past” because they are both directed to previously observed target/observation values used for prediction. The examiner interprets “input vectors XN” to be the same as “a series of the covariates observed simultaneously with the observation values” because they are both directed to input/covariate values paired with corresponding target/observation values. The examiner interprets “finding a local maximum in the likelihood” with respect to “hyperparameters Θ of the covariance matrix” to be the same as “optimizing a parameter of a kernel function of a Gaussian process” because they are both directed to optimizing parameters of a covariance/kernel function in a Gaussian process.)
wherein values obtained by non-linearly transforming the observation values by the first function follow the Gaussian process; ([Snelson, page 1] “The learning algorithm chooses a nonlinear transformation such that transformed data is well-modelled by a GP.” and [Snelson, page 3] “Now we make a transformation from the true observation space to the latent space by mapping each observation through the same monotonic function f, zn = f(tn; Ψ) ∀n.”, wherein the examiner interprets “nonlinear transformation” and “mapping each observation through the same monotonic function f” to be the same as “non-linearly transforming the observation values by the first function” because they are both directed to applying a nonlinear function to observation values. The examiner interprets “transformed data is well-modelled by a GP” to be the same as “values obtained by non-linearly transforming the observation values by the first function follow the Gaussian process” because they are both directed to transformed observation values being modeled by or following a Gaussian process.)
calculating a quantile of a prediction distribution of observation values in a period in future to be predicted, by calculating a quantile of a value following a normal distribution obtained by using the kernel function having parameters optimized in the optimizing and a series of covariates in the period, and converting the calculated quantile of the value following the normal distribution using an inverse function of the first function which is solvable by a root-finding algorithm due to the monotonic increasing property of the first function, at least with respect to calculating a quantile/percentile of a Gaussian predictive distribution and converting the value using an inverse monotonic function solvable by a root-finding algorithm; ([Snelson, page 4, sec 3.2] “For a particular setting of the covariance function hyperparameters Θ (for example ΘML or ΘMAP), in latent variable space the predictive distribution at a new point is just as for a regular GP: a Gaussian whose mean and variance are calculated as mentioned in section 2…The median is particularly easy to calculate: tmedN+1 = f-1(ẑN+1)… Notice we need to compute the inverse warping function. In general we are unlikely to have an analytical form for f-1, because we have parameterised the function in the opposite direction. However since we have access to derivatives of f, a few iterations of Newton-Raphson with a good enough starting point is enough….These points in observation space are calculated in exactly the same way as the median - simply pass the values through the inverse function: tmed±2σN+1 = f−1(ẑN+1 ± 2σN+1).”, wherein the examiner interprets “predictive distribution at a new point is just as for a regular GP: a Gaussian whose mean and variance are calculated” to be the same as “a value following a normal distribution” because they are both directed to a Gaussian/normal predictive value. The examiner interprets “median” and “‘2σ’ either side of the median” to be the same as “quantile” because they are both directed to values corresponding to specified portions of a probability distribution. The examiner interprets “f−1” and “inverse warping function” to be the same as “inverse function of the first function” because they are both directed to the inverse of the nonlinear warping/transformation function. The examiner interprets “Newton-Raphson” to be the same as “root-finding algorithm” because they are both directed to numerically solving for an inverse-function value.)
a weight of a non-negative value and to ensure that the first function is a monotonically increasing function ([Snelson, page 4, sec 3.3] “We wish to design a warping function that will allow for complex transformations, but we must constrain the function to be monotonic. There are various ways to do this, an obvious one being a neural-net style sum of tanh functions, f(t; Ψ) = t + ΣIi=1 ai tanh (bi(t + ci)) ai, bi ≥ 0 ∀i.” AND [Snelson page 3, sec 3] “warping the observation space through a nonlinear monotonic function to a latent space, whilst retaining the full probabilistic framework to enable learning and prediction to take place consistently.”, wherein the examiner interprets “ai, bi ≥ 0 ∀i” to be the same as “a weight of a non-negative value” because they are both directed to non-negative parameters/weights used in a neural-net style nonlinear function. Furthermore, the examiner interprets “must constrain the function to be monotonic” to be the same as “to ensure that the first function is a monotonically increasing function” because they are both directed to maintaining monotonic behavior of the nonlinear transformation.)
Snelson does not teach wherein the first function is a forward propagation neural network having an activation function that is a monotonically increasing function, and the second function is a recurrent neural network that takes the covariates as input and outputs at least a weight of a non-negative value and a bias as the parameters of the first function to ensure that the first function is a monotonically increasing function,…without using Monte Carlo simulation.
Williams teaches:
wherein the first function is a forward propagation neural network having an activation function that is a monotonically increasing function, ([Williams, page 166] “in artificial neural networks (ANNs), which are feedforward networks consisting of an input layer, followed by one or more layers of non-linear transformations of weighted combinations of the activity from previous layers” and [Williams, page 56] “A sigmoid function is a monotonically increasing function mapping from R to [0, 1].”, wherein the examiner interprets “feedforward networks” to be the same as “forward propagation neural network” because they are both directed to neural networks in which information propagates from an input layer through later layers. The examiner interprets “non-linear transformations of weighted combinations” to be the same as neural-network activations because they are both directed to applying nonlinear functions to weighted neural-network inputs. The examiner interprets “sigmoid function is a monotonically increasing function” to be the same as “activation function that is a monotonically increasing function” because they are both directed to a nonlinear neural-network function that increases monotonically.)
a bias as the parameters of the first function; ([Williams, page 8] “Often a bias weight or offset is included”, wherein the examiner interprets “bias weight or offset” to be the same as “bias” because they are both directed to an offset parameter included in a neural-network or weighted-function model.)
Snelson and Williams do not teach and the second function is a recurrent neural network that takes the covariates as input and outputs at least a weight of a non-negative value and a bias as the parameters of the first function to ensure that the first function is a monotonically increasing function…optimizing a parameter of a second function that outputs parameters of a first function from covariates.
Ha teaches the second function is a recurrent neural network that takes the covariates as input and outputs at least a weight and a bias as the parameters of the first function, ([Ha, page 1] “In this work, we consider an approach of using a small network (called a ‘hypernetwork’) to generate the weights for a larger network (called a main network).”, AND [Ha, page 1] “In addition, our embedding vectors can also be generated dynamically by our hypernetwork, allowing the weights of a recurrent network to change over timesteps and also adapt to the input sequence” AND [Ha, page 1] “Figure 1: A hypernetwork generates the weights for a feedforward network.”, AND [Ha, page 4] “At every time step t, a HyperRNN takes as input the concatenated vector of input xt and the hidden states of the main RNN ht-1, it then generates as output the vector hˆt. This vector is then used to generate the weights for the main RNN at the same timestep.”, AND [Ha, page 5] “the parameters Wh, Wx, b of the main RNN are different at different time steps” AND [Ha, page 3] “The first layer of the hypernetwork takes the input vector zj and linearly projects it into the Nin inputs, with Nin different matrices Wi ∈ Rd× Nz and bias vectors Bi ∈ Rd, where d is the size of the hidden layer in the hypernetwork”, wherein the examiner interprets “hypernetwork” to be the same as “second function” because they are both directed to a network/function that generates parameters for another network/function. The examiner further interprets “feedforward network” and “main network” to be the same as “first function” because they are both directed to a network/function whose parameters are generated by another network/function. The examiner further interprets “HyperRNN takes as input the concatenated vector of input xt and the hidden states of the main RNN ht-1” to be the same as “the second function is a recurrent neural network that takes the covariates as input” because they are both directed to a recurrent neural network receiving time-indexed input data. The examiner interprets “This vector is then used to generate the weights” to be the same as “outputs at least a weight” because they are both directed to generating/outputting weights for another network/function. The examiner interprets “b” to be the same as “bias” because they are both directed to a bias parameter of the main network.)
optimizing a parameter of a second function that outputs parameters of a first function from covariates, ([Ha, page 4] “Both the HyperRNN and the main RNN are trained jointly with backpropagation and gradient descent.” AND [Ha, page 22] “We will use the same model architecture described in (Graves, 2013) and use a Mixture Density Network layer (Bishop, 1994) to generate a mixture of bi-variate Gaussian distributions to model at each time step to model the pen location.”, wherein the examiner interprets “trained jointly with backpropagation and gradient descent” to be the same as “optimizing a parameter” because they are both directed to adjusting/optimizing network parameters during training. The examiner further interprets “HyperRNN” to be the same as “second function” because they are both directed to the network/function that generates parameters for another network/function. The examiner further interprets “generate a mixture of bi-variate Gaussian distributions to model at each time”, the same as “output parameters of a first function from covariates”, because they are both directed to variate outputting using a model.)
Snelson, Williams, and Ha do not teach optimizing a parameter of a second function that outputs parameters of a first function from covariates, and optimizing a parameter of a kernel function of a Gaussian process, by using a series of observation values observed in a past and a series of the covariates observed simultaneously with the observation values, in the full claimed sequential Gaussian-process setting, including joint optimization of recurrent-network parameters and Gaussian-process kernel parameters.
Al-Shedivat teaches optimizing a parameter of a second function that outputs parameters of a first function from covariates, and optimizing a parameter of a kernel function of a Gaussian process, by using a series of observation values observed in a past and a series of the covariates observed simultaneously with the observation values, ([Al-Shedivat, page 3] “We consider the problem of learning a regression function that maps sequences to real-valued target vectors.” AND [Al-Shedivat, page 3] “Recurrent neural networks (RNNs) model recurrent processes by using linear parametric maps followed by nonlinear activations”, [Al-Shedivat, page 8] “we apply the same technique to learn kernels with recurrent structure by transforming input sequences with a recurrent neural network that acts as φ(·).”, AND [Al-Shedivat, page 8] “and the parameters of the recurrent neural transformation, φ(·), denoted W and further referred as the transformation hyperparameters. Our goal is to optimize L with respect to both θ and W.”, wherein the examiner interprets “sequences”, “recurrent processes by using linear parametric maps” and “input sequences” to be the same as “a series of the covariates”, at least with respect to recurrent sequential covariates and joint optimization of recurrent-network and Gaussian-process kernel parameters, because they are both directed to input/covariate values arranged over time. The examiner further interprets “real-valued target vectors” to be the same as “observation values” because they are both directed to target/observed output values used for prediction. The examiner interprets “θ” to be the same as “a parameter of a kernel function of a Gaussian process” because Al-Shedivat identifies θ as the base kernel hyperparameters. The examiner interprets “W” to be the same as “a parameter of a second function” because W is the parameter of the recurrent neural transformation. The examiner interprets “optimize L with respect to both θ and W” to be the same as optimizing the kernel-function parameter and the recurrent-function parameter because they are both directed to jointly optimizing Gaussian-process kernel parameters and recurrent-network parameters.)
in a period in future to be predicted; ([Al-Shedivat, page 3] “Assuming that only the most recent L steps of a sequence are predictive of the targets, the goal is to learn a function, f : XL ↦ Rd, from some family, F, based on the available data.” AND [Al-Shedivat, page 3] “This task is a classical instance of the sequence-to-reals regression, where a temporal sequence of measurements is regressed to the future position estimates.” AND [Al-Shedivat, page 7] “Figure 1: (a) Graphical representation of a recurrent model (RNN/LSTM) that maps an input sequence to a target value in one-step-ahead prediction manner. Shaded variables are observable, diamond variables denote deterministic dependence on the inputs. (b) Graphical model for GP LSTM with a time lag, L = 3, two training time points, t = 3 and t = 4,”, wherein the examiner interprets “future position estimates… a target value in one-step-ahead prediction manner… with a time lag, L = 3, two training time points, t = 3 and t = 4” to be the same as “observation values in a period in future to be predicted” because they are both directed to future target values predicted from sequential input/covariate data.)
Snelson, Williams, Ha, Al-Shedivat, and the instant application are analogous art because they are all directed to machine-learning prediction/regression using Gaussian processes, neural networks, recurrent neural networks, learned model parameters, nonlinear transformations, and predictive distributions for target/observation values.
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the prediction method disclosed by Snelson to include the feedforward neural-network structure and monotonically increasing activation functions disclosed by Williams, to further generate the weights and bias parameters of the neural-network warping function using the hypernetwork/recurrent-network parameter-generation technique disclosed by Ha, to further jointly optimize the recurrent-network parameters and Gaussian-process kernel parameters using the recurrent Gaussian-process training framework disclosed by Al-Shedivat, One would be motivated to make these modifications to effectively adapt the monotonic warping function to sequential covariate information while preserving the Gaussian-process predictive-distribution framework and reducing the computational burden associated with sampling-based prediction, as suggested by Snelson ([Snelson, page 3] “We require f to be monotonic and mapping on to the whole of the real line; otherwise probability measure will not be conserved in the transformation, and we will not induce a valid distribution over the targets tN.”), Williams ([Williams, page 166] “feedforward networks consisting of an input layer, followed by one or more layers of non-linear transformations of weighted combinations of the activity from previous layers”), Ha ([Ha, page 2] “allowing the weights of a recurrent network to change over timesteps and also adapt to the input sequence.”), Al-Shedivat ([Al-Shedivat, page 8] “Our goal is to optimize L with respect to both θ and W.”). Claim 6 is analogous to claim 1, aside from claim type and minute differences, thus the same rejection can apply to both. Furthermore, claim 7 merely states it is going to apply claim 1’s method onto non-transitory CRM with instructions, and thus claim 7 is also analogous to claim 1.
Regarding claim 2, Snelson, Williams, Ha, and Al-Shedivat teaches The prediction method according to claim 1, (see rejection for claim 1).
Snelson further teaches the method further comprising: calculating a statistic of the observation values in the period by using the calculated prediction distribution ([Snelson, page 4] “To calculate the mean, we need to integrate tN+1 over the density (8). Rewriting this integral back in latent space we get E(tN+1) = ∫dzf−1(z)Nz(ẑN+1, σ²N+1) = E(f−1) … The median is particularly easy to calculate: tmedN+1 = f−1(ẑN+1)” and [Snelson, page 2] “It is simple to show that the predictive distribution for a new point given the observed data, P(tN+1|tN , XN+1), is Gaussian. The calculation of the mean and variance of this distribution”, wherein the examiner interprets “calculate the mean” and “median is particularly easy to calculate” applied to “tN+1” to be the same as” calculating a statistic of the observation values” because they are both directed to computing statistical measures such as the mean and median from the predictive distribution for future observation values. The examiner further interprets “the predictive distribution for a new point given the observed data … is Gaussian” to be the same as “calculating a statistic … by using the calculated prediction distribution” because they are both directed to calculating statistics (mean and variance) of a predictive distribution for an observation/target.)
Regarding claim 3, Snelson, Williams, Ha, and Al-Shedivat teaches The prediction method according to claim 1, (see rejection for claim 1).
Snelson further teaches the weight of a non-negative value to ensure monotonicity of the first function, ([Snelson, page 4] “We wish to design a warping function that will allow for complex transformations, but we must constrain the function to be monotonic.” and [Snelson, page 4] “There are various ways to do this, an obvious one being a neural-net style sum of tanh functions,” and [Snelson, page 4] “f(t; Ψ) = t + ΣIi=1 ai tanh (bi(t + ci)) ai, bi ≥ 0 ∀i.”, wherein the examiner interprets “ai, bi ≥ 0 ∀i” to be the same as “the weight of a non-negative value” because they are both directed to non-negative parameters/weights used in a neural-net style nonlinear function. The examiner interprets “must constrain the function to be monotonic” to be the same as using the non-negative weight to maintain the monotonically increasing first function because they are both directed to constraining the nonlinear transformation so that the transformation remains monotonic.)
Williams further teaches wherein the first function is a forward propagation neural network having a weight and a bias as parameters, ([Williams, page 166] “in artificial neural networks (ANNs), which are feedforward networks consisting of an input layer, followed by one or more layers of non-linear transformations of weighted combinations of the activity from previous layers” and [Williams, page 8] “Often a bias weight or offset is included.”, wherein the examiner interprets “feedforward networks” to be the same as “forward propagation neural network” because they are both directed to neural networks in which values are propagated from an input layer through one or more later layers. The examiner interprets “weighted combinations of the activity from previous layers” to be the same as “having a weight” because they are both directed to neural-network computations that use weights to combine values from prior layers. The examiner interprets “bias weight or offset is included” to be the same as “a bias as parameters” because they are both directed to an offset/bias term used as part of the neural-network model parameterization.)
monotonically increasing function as an activation function, ([Williams, page 37] “A sigmoid function is a monotonically increasing function mapping from R to [0, 1].”, wherein the examiner interprets “sigmoid function” to be the same as “activation function” because they are both directed to a nonlinear function applied in a neural-network model. The examiner interprets “monotonically increasing function” to be the same as “monotonically increasing function” because they use the same terminology and are both directed to a function whose output increases monotonically with its input.)
Ha further teaches and the second function is a recurrent neural network that outputs at least the weight and the bias, ([Ha, page 4] “In this section, we will use a recurrent network to dynamically generate weights for another recurrent network, such that the weights can vary across many timesteps.”, AND [Ha, page 4] “At every time step t, a HyperRNN takes as input the concatenated vector of input xt and the hidden states of the main RNN ht-1, it then generates as output the vector hˆt. This vector is then used to generate the weights for the main RNN at the same timestep.”, AND [Ha, page 5] “the parameters Wh, Wx, b of the main RNN are different at different time steps”, wherein the examiner interprets “recurrent network” and “HyperRNN” to be the same as “second function is a recurrent neural network” because they are both directed to a recurrent neural network used to generate parameters for another network. The examiner interprets “dynamically generate weights” and “used to generate the weights” to be the same as “outputs at least the weight” because they are both directed to producing weight parameters for another network. The examiner interprets “b” to be the same as “bias” because they are both directed to a bias parameter of the network.)
Snelson, Williams, Ha, Al-Shevidat, and the instant application are analogous art because they are all directed to machine-learning prediction using parameterized nonlinear functions, neural-network structures, recurrent neural networks, and learned model parameters.
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the method of claim 1 disclosed by Snelson, Williams, Ha, Al-Shevidat to include the monotonic neural-net style warping function using the feedforward neural-network structure, weighted combinations, bias term, and monotonically increasing activation function disclosed by Williams, and to further use the hypernetwork/recurrent-network parameter-generation technique disclosed by Ha to output the weight and bias parameters of the first function. One would be motivated to do so to effectively implement Snelson’s monotonic nonlinear transformation using a known feedforward neural-network structure and to adapt the generated weights across sequential timesteps, as suggested by Williams ([Williams, page 166] “feedforward networks consisting of an input layer, followed by one or more layers of non-linear transformations of weighted combinations of the activity from previous layers”) AND Ha ([Ha, page 4] “dynamically generate weights for another recurrent network, such that the weights can vary across many timesteps.”).
Regarding claim 4, Snelson, Williams, Ha, and Al-Shevidat teach The prediction method according to claim 3, (see rejection for claim 3).
Al-Shedivat further teaches wherein the second function further outputs a real value to be taken as input of the kernel function. ([Al-Shedivat, page 7] “Gaussian processes with different kernel functions correspond to different structured probabilistic models. For example, some special cases of the Matérn class of kernels induce models with Markovian structure (Stein, 1999). To construct deep kernels with recurrent structure we transform the original input space with an LSTM network and build a kernel directly in the transformed space,”, wherein the examiner interprets “transform the original input space with an LSTM network and build a kernel directly in the transformed space” to be the same as “the second function further outputs a real value to be taken as input of the kernel function” because they are both directed to a recurrent neural network producing an output (a transformed-space representation) that is used as the input space in which the kernel is evaluated.)
Snelson, Williams, Ha, Al-Shedivat, and the instant application are analogous art because they are all directed to a feature in which a recurrent neural network (RNN) produces an output that is used as an input representation for a kernel function of a Gaussian process (GP).
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the method claim 3 disclosed by Snelson, Williams, Ha, Al-Shevidat to include the kernel construction method disclosed by Al-Shedivat. One would be motivated to do so to effectively model recurrent structure, as suggested by Al-Shedivat ([Al-Shedivat, page 1, page 7] “To model such structure, we propose expressive closed-form kernel functions for Gaussian processes… To construct deep kernels with recurrent structure we transform the original input space with an LSTM network and build a kernel directly in the transformed space, as shown in Figure 1b.”).
Regarding claim 5, Snelson, Williams, Ha, and Al-Shevidat teaches The prediction method according to claim 1, (see rejection for claim 1).
Al-Shedivat further teaches wherein, in the optimizing, the parameters of the second function and the kernel function are optimized. ([Al-Shedivat, page 8] “The negative log marginal likelihood of the Gaussian process has the following form: L(K) = y (Ky +σ2I)−1y+logdet(Ky +σ2I)+const, where Ky + σ²I (≜ K) is the Gram kernel matrix, Ky, is computed on {φ(xi)}Ni=1 and implicitly depends on the base kernel hyperparameters, θ, and the parameters of the recurrent neural transformation, φ(·), denoted W and further referred as the transformation hyperparameters. Our goal is to optimize L with respect to both θ and W.”, wherein the examiner interprets “Our goal is to optimize L with respect to both θ and W” where “θ” represents “base kernel hyperparameters” and “W” represents “parameters of the recurrent neural transformation” to be the same as “the parameters of the second function and the kernel function are optimized” because they are both directed to jointly optimizing the parameters of the recurrent neural network (W, the second function) and the parameters of the kernel function (θ) together.)
by searching for parameters of the second function and the kernel function that minimize negative log marginal likelihood. ([Al-Shedivat, page 8] “Therefore, we propose a semi-stochastic block-gradient optimization procedure which allows mini-batching weight updates and fully joint training of the model from scratch.”, AND [Al-Shedivat, page 23] “GPs with deep recurrent kernels are trained by minimizing the negative log marginal likelihood objective function.,” wherein, the examiner interprets “semi-stochastic block-gradient optimization procedure” to be the same as “optimized by searching for parameters” because they are both directed to an iterative optimization procedure that searches over parameter values. The examiner further interprets “trained by minimizing the negative log marginal likelihood objective function” to be the same as “minimize negative log marginal likelihood” because they are both directed to minimizing a negative log marginal likelihood objective.)
Snelson, Williams, Ha, Al-Shedivat, and the instant application are analogous art because they are all directed to prediction using a Gaussian process with optimizing parameters for prediction.
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the method claim 1 disclosed by Snelson, Williams, Ha, and Al-Shedivat to include the optimization procedure disclosed by Al-Shedivat. One would be motivated to do so to efficiently enable mini-batched updates and fully joint training from scratch when optimizing the relevant model parameters, as suggested by Al-Shedivat ([Al-Shedivat, page 8] “Therefore, we propose a semi-stochastic block-gradient optimization procedure which allows mini-batching weight updates and fully joint training of the model from scratch.”).
Regarding claim 8, Snelson, Williams, Ha, and Al-Shevidat teaches The prediction method according to claim 1, (see rejection for claim 1).
Snelson teaches calculating a probability density distribution of a target value in the period; and obtaining a probability corresponding to a target value at a time step from the probability density distribution; ([Snelson, page 2] “Suppose we are given a dataset D, consisting of N pairs of input vectors XN ≡ {x(n)}N n=1 and real-valued targets tN ≡ {tn}N n=1. We wish to predict the value of an observation tN+1 given a new input vector x(N+1), or rather the distribution P(tN+1|x(N+1),D).” AND [Snelson, page 4] “To find the distribution in the observation space we pass that Gaussian through the nonlinear warping function, giving P(tN+1|x(N+1), D, Θ, Ψ)…The shape of this distribution depends on the form of the warping function f, but in general it may be asymmetric and multimodal.”, wherein the examiner interprets “distribution in the observation space” and “P(tN+1|x(N+1), D, Θ, Ψ)… real-valued targets tN ≡ {tn}N n=1… rather the distribution P(tN+1|x(N+1),D)” to be the same as calculating “a probability density distribution…obtaining a probability corresponding to a target value at any time step in the period from the probability density distribution” because they are both directed to determining the predictive probability distribution for an observation/target value. The examiner interprets “tN+1” to be the same as “target value” because they are both directed to the predicted observation/target value.)
Claim 9 is rejected under 35 U.S.C. 103 as being unpatentable over Snelson in view of Williams in view of Ha in view of Al-Shevidat further in view of NPL reference “The multivariate bisection algorithm”, by Lopez Galvan et. al. (referred herein as Lopez Galvan.)
Regarding claim 9, Snelson, Williams, Ha, and Al-Shevidat teaches The prediction method according to claim 1, (see rejection for claim 1).
Snelson, Williams, Ha, and Al-Shevidat do not teach wherein the root-finding algorithm is a bisection method.
Lopez Galvan teaches wherein the root-finding algorithm is a bisection method. ([Lopez Galvan, Abstract] “In this work we propose a multivariate bisection method supported by the Poincare-Miranda theorem in order to solve non-linear system of equations. Given an initial cube verifying the hypothesis of Poincare-Miranda theorem the algorithm performs congruent refinements throughout its center by generating a root approximation. Throughout preconditioning we will prove the local convergence of this new root finder methodology”, wherein the examiner interprets “solve non-linear system of equations…the algorithm performs congruent refinements throughout its center by generating a root approximation …new root finder methodology” to be the same as “root-finding algorithm” because they are both directed to numerically finding a solution/root of a nonlinear equation. The examiner further interprets “algorithm performs congruent refinements throughout its center” to be the same as using bisection as the claimed root-finding algorithm because they are both directed to iteratively refining a search region to approximate a root.)
Snelson, Williams, Ha, Al-Shedivat, Lopez Galvan, and the instant application are analogous art because they are all directed to mathematical and computer-implemented prediction/modeling methods that use numerical calculations, including solving nonlinear functions or equations to obtain predicted values.
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the invention to modify the prediction method of claim 1 disclosed by Snelson, Williams, Ha, and Al-Shedivat to include the “bisection method” and the root-finding algorithm disclosed by Lopez Galvan. One would be motivated to do so to robustly and predictably approximate a root for the inverse-function calculation required by the prediction method, as suggested by Lopez Galvan ([Lopez Galvan, Abstract] “In this work we propose a multivariate bisection method supported by the Poincare-Miranda theorem in order to solve non-linear system of equations. Given an initial cube verifying the hypothesis of Poincare-Miranda theorem the algorithm performs congruent refinements throughout its center by generating a root approximation. Throughout preconditioning we will prove the local convergence of this new root finder methodology.”).
Conclusion
THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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/DEVAN KAPOOR/Examiner, Art Unit 2126
/DAVID YI/Supervisory Patent Examiner, Art Unit 2126
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