DETAILED ACTION
This nonfinal rejection is responsive to the amendment filed on April 2, 2026. Claims 1-17 are pending. Claims 1, 9, and 17 are independent.
Claim rejections under 35 USC §103 are withdrawn in light of applicant’s amendment. However, a new grounds of rejection under 35 USC §103 has been made. See sections Claim Rejections – 35 USC §103 and Response to Arguments below.
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 .
Continued Examination Under 37 CFR 1.114
A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this application is eligible for continued examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on April 2, 2026 has been entered.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
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.
Claims 1-4, 7-12, and 15-17 are rejected under 35 U.S.C. 103 as being unpatentable over Hsieh et al. (Functional Autoencoders for Functional Data Representation learning), hereinafter Hsieh, in view of Rao et al. (Modern Non-Linear Function-on-Function Regression), hereinafter Rao, in view of Wan et al. (Dimensionality Reduction for Multivariate Time-Series Data Mining), hereinafter Wan.
Regarding claim 1, Hsieh teaches the method:
training a functional encoder comprising a plurality of layers of continuous neurons, … from input time series data to learn a dimension reduced form of the input time series data (Hsieh, section 1, paragraph 1: “The acceleration of different joints can be naturally modelled by curves that denote continuous functions of time, yielding multi-dimensional functional data.” Section 1, paragraph 2: “However, because functional data are sampled from a continuum, they are intrinsically infinite dimensional. In contrast, the standard machine learning methods are designed to work with data that are encoded by finite dimensional feature vectors. Hence, there is a need for methods to extract and encode the relevant information from functional data into a finite dimensional embedding.” Section 2, paragraph 1: “Subscripts
j
,
k
denote nodes in the neural network and
i
will be used to identify samples. Superscript
I
indexes the layers of the neural network.” And section 2.1, paragraph 1: “An autoencoder is constructed by learning an encoder
ϕ
, i.e., a mapping from a P-dimensional vector valued input space
R
P
to a d-dimensional representation space
R
d
.” And Fig. 2 – the encoder is analogous to the functional encoder as the input is the multi-dimensional data which uses the continuous functions of time, which is the input time series data. As shown in figure 2, the encoder portion of the functional autoencoder includes a plurality of layers. Functional data being intrinsically infinite dimensional being encoded into a finite dimensional embedding show that mapping from a P-dimensional vector to a d- dimensional vector representation space is indicative that the encoder learns a dimension reduced form of the input time series data.) through forward propagation and back-propagation using functional gradients, … (Hsieh, page 667, column 1, paragraph 1: “We derive a functional gradient based learning algorithm to optimize the parameters of FAE so as to minimize the reconstruction error of the functional data;” and page 669, section 2.2.3: “Thereafter, the algorithm iterates between feedforward pass and back-propagation weight update pass until the specified termination criterion is satisfied.” – The feedforward pass and back-propagation weight update is analogous to forward propagation and back-propagation, the functional gradient based learning algorithm to optimize the parameters is used in the forward and back-propagation and is analogous to the forward propagation and back-propagation using functional gradients.)
training a functional decoder comprising another plurality of layers of continuous neurons to learn the input time series data from the dimension reduced form of the input time series data. (Hsieh, section 2.1, paragraph 1: “a decoder
ψ
, i.e., a mapping from the representation space
R
d
to a P-dimensional vector-valued output space so as to minimize over the training set, a measure of the reconstruction error, e.g., mean square error, of the output with respect to input.” And Fig. 2 – The mapping from the representation space to the P-dimensional vector-valued space is indicative of the decoder being trained to learn the input time series data and, as noted above, the d-dimensional space is the reduced dimension form of the input time series data. As shown in figure 2, the decoder portion of the functional autoencoder includes a plurality of layers.)
Hsieh does not explicitly teach:
… the continuous neurons configured to receive a function as an input and execute a non-linear transformation to generate an output function,…
…the dimension reduced form of the input time series data being a feature reduced and a time point reduced form of the input time series data
However, Rao teaches:
the continuous neurons configured to receive a function as an input and execute a non-linear transformation to generate an output function, (Rao, page 2, paragraph 2: “This expansion of the neural network to functional data is interesting, as it enables efficient non-linear learning when the predictions are functions.” And page 2, last paragraph: “Our framework consists of multiple continuous hidden layers consisting of continuous neurons that can learn functional representation from the functional inputs and functional outputs.” – The multiple hidden layers consists of continuous neurons that learn functional representations from the functional input is analogous to the continuous neurons receiving a function as an input and the non-linear learning is analogous to the non-linear transformation which results in a functional output.)
Rao is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Hsieh, which already teaches training a functional encoder comprising a plurality of layers of continuous neurons but does not explicitly teach that the continuous neurons are configured to receive a function as an input and execute a non-linear transformation to generate an output function, to include the teachings of Rao which does teach that the continuous neurons are configured to receive a function as an input and execute a non-linear transformation to generate an output function in order to model “a functional response using functional inputs, where we have a continuous mapping through the network.” (Rao, page 2, last paragraph)
Hsieh and Rao do not explicitly teach:
…the dimension reduced form of the input time series data being a feature reduced and a time point reduced form of the input time series data
However, Wan teaches:
the dimension reduced form of the input time series data being a feature reduced and a time point reduced form of the input time series data; and (Wan, page 9868, paragraph 3: “Because the local information is important for a long MTS, we can segment the original MTS
X
n
x
m
along with the time direction into several short sequences
X
^
=
X
^
1
,
X
^
2
,
⋯
,
X
^
n
.” And page 9869, paragraph 3: “Finally, SVD can be used to decompose
Σ
a
and obtain the transformation space U according to Eq. (8).
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43
426
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Thus, we can use Eq. (4) to reduce the dimensionality and obtain the feature sequences of MTS. The algorithm of PPCA can be described by the pseudo-code in Table 1.” – The segmentation along the time direction is analogous to the time reduced form with each sequence then being used to reduce the dimensionality and obtain the feature sequences being analogous to a feature reduction.)
Wan is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Hsieh and Rao, which already teaches reducing dimensionality of time series data but does not explicitly teach that the dimensionality reduction is both a feature reduction and time point reduction, to include the teachings of Wan which does teach that the dimensionality reduction is both a feature reduction and time point reduction in order to better consider local features and handle drift phenomena better. (Wan, page 9871, paragraph 2)
Regarding claim 2, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
learning a machine learning model for a downstream analytics task from the dimension reduced form of the input time series data. (Hsieh, section 2.1, paragraph 2: “The resulting finite dimensional encoding of functional data makes it possible to apply existing machine learning algorithms on downstream tasks, e.g., clustering, classifications.” – As noted in claim 1, the finite dimensional encoding of functional data is analogous to the dimension reduced form of the input time series data, applying existing algorithms on the downstream tasks is analogous to learning a machine learning model for a downstream task.)
Regarding claim 3, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
executing the trained functional decoder to obtain the input time series data from the dimension reduced form of the input time series data. (Hsieh, section 2.1, paragraph 1: “where the encoder is a mapping from a P-dimensional functional space to a d-dimensional vector space back to a P-dimensional functional space as follows:” – The decoder maps d-dimensional vector space, i.e., the dimension reduced form of the input time series data, back to P-dimensional functional space is analogous to executing the training decoder to obtain the input time series data from the dimension reduced form.)
Regarding claim 4, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
receiving an input defining at least one of feature reduction or time point reduction for the dimension reduced form of the input time series data; (Hsieh, section 1, paragraph 3: “In many real-world applications, each dimension of the functional data, i.e. each feature function, can be a complex nonlinear curve.” And section 3.2, paragraph 1: “In this experiment, we set d to 10, and use batch update.” And algorithm 1 – The dimension of the data, d, is analogous to the features and therefore being able to set d as an input is analogous to receiving an input defining feature reduction for the dimension reduced form of the input time series data.)
wherein the functional encoder is trained to learn the dimension reduced form of the time series data according to the at least one of the feature reduction or the time point reduction defined by the received input. (Hsieh, section 3.2, paragraph 1 and algorithm 1: “we train an FAE on each data set with the functional variant of the standard gradient descent (GD) and the proposed functional extension of the Adam optimizer and empirically demonstrate their convergence. In this experiment, we set d to 10, and use batch update.” – The training using d, the dimension, as an input and used to train the functional autoencoder is analogous to the functional encoder being trained according to the feature reduction defined by the received input.)
Regarding claim 7, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
the dimension reduced form of the input time series data is a non-linear dimension reduced form. (Hsieh, section 2, paragraph 2: “Given
X
=
x
1
,
x
2
,
⋯
,
x
n
with
x
i
as a multidimensional functional data, i.e.,
x
i
∈
H
P
, learn a non-linear function
f
that can encode
x
i
as a d-dimensional vector, i.e.,
y
i
=
f
x
i
.” – As noted in claim 1, the d-dimensional vector is the dimension reduced form of the input time series data, thus the non-linear function encoding x as a d-dimensional vector is analogous to the dimension reduced form of the input time series data being a non-linear dimension reduced form.)
Regarding claim 8, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh does not explicitly teach:
each continuous neuron of the functional encoder computes an output using an integration operation over a bivariate parameter function.
However, Rao further teaches:
each continuous neuron of the functional encoder computes an output using an integration operation over a bivariate parameter function. (Rao, page 4, section 2.2: “The
l
t
h
continuous hidden layer and its
k
t
h
continuous neuron is defined as:
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66
600
media_image2.png
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where
l
=
1
,
2
,
3
,
…
,
L
,
H
j
0
s
=
X
j
s
,
H
L
t
=
E
Y
t
|
X
,
b
k
l
∈
L
2
(
T
)
is the unknown intercept function,
w
(
j
,
k
)
l
∈
L
2
(
T
×
T
)
is the bivariate parameter function for the
k
t
h
continuous neuron in the
l
t
h
hidden layer coming from the
j
t
h
continuous neuron of the
(
l
-
1
)
t
h
hidden layer and
σ
(
∙
)
is a non-linear activation function.” -
H
k
l
s
is the output of each continuous neuron of the functional encoder for the hidden layer which computes the output using the integration operation over the bivariate parameter function
w
(
j
,
k
)
l
.)
Regarding claim 9, Claim 9 has all the same limitations of claim 1 which are taught by Hsieh, Rao, and Wan – see claim 1 above.
Hsieh and Rao do not explicitly teach:
A non-transitory computer readable medium, storing instructions for executing a process, the instructions comprising:
However, Wan teaches:
A non-transitory computer readable medium, storing instructions for executing a process, the instructions comprising: (Wan, page 9870, section 4, paragraph 4: “The experiments were implemented with a Windows 7 system and a one quad-core Intel i7-2640 M clocked at 2.80 GHz with 8 GB of memory. Moreover, the related programs were compiled with Matlab R2012b.”)
Regarding claim 10, Hsieh, Rao, and Wan teach the non-transitory computer readable medium of claim 9, as cited above.
Claim 10 additionally has the same limitations of claim 2 which are taught by Hsieh, Rao, and Wan – see claim 2 above.
Regarding claim 11, Hsieh, Rao, and Wan teach the non-transitory computer readable medium of claim 9, as cited above.
Claim 11 additionally has the same limitations of claim 3 which are taught by Hsieh, Rao, and Wan – see claim 3 above.
Regarding claim 12, Hsieh, Rao, and Wan teach the non-transitory computer readable medium of claim 9, as cited above.
Claim 12 additionally has the same limitations of claim 4 which are taught by Hsieh, Rao, and Wan – see claim 3 above.
Regarding claim 15, Hsieh, Rao, and Wan teach the non-transitory computer readable medium of claim 9, as cited above.
Claim 15 additionally has the same limitations of claim 7 which are taught by Hsieh, Rao, and Wan – see claim 7 above.
Regarding claim 16, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
receiving an input defining … a number of features … for the dimension reduced form of the input time series data, (Hsieh, algorithm 1 -– the input including dimension of embedding d is analogous to the input defining the number of features for the dimension reduced form of the input time series data.)
Hsieh and Rao do not explicitly teach:
receiving an input defining both a number of features and a number of timepoints for the dimension reduced form of the input time series data, wherein the functional encoder is trained to generate the dimension reduced form having the defined number of features observed at the defined number of timepoints.
However, Wan teaches:
receiving an input defining both a number of features and a number of timepoints for the dimension reduced form of the input time series data, (Wan, table 1 – The w number of segments is analogous to the number of timepoints for the dimension reduced form while the MTS
X
n
×
m
, where the output also has dimension nxm means that the input defines the number of features for the dimension reduced form.)
wherein the functional encoder is trained to generate the dimension reduced form having the defined number of features observed at the defined number of timepoints. (Wan, table 1 – The feature sequence being returned is based off the nxm dimensions and the w number of segments, thus the functional encoder generates the dimension reduced form having the defined number of features observed at the defined number of timepoints.)
Regarding claim 17, Claim 17 has all the same limitations of claim 1 which are taught by Hsieh, Rao, and Wan – see claim 1 above.
Hsieh and Rao do not explicitly teach:
An apparatus, comprising: a processor, configured to:
However, Wan teaches:
An apparatus, comprising: a processor, configured to: (Wan, page 9870, section 4, paragraph 4: “The experiments were implemented with a Windows 7 system on a one quad-core Intel i7-2640 M clocked at 2.80 GHz with 8 GB of memory. Moreover, the related programs were compiled with Matlab R2012b.”)
Claims 5 and 13 are rejected under 35 U.S.C. 103 as being unpatentable over Hsieh in view of Rao in view of Wan in view of Brownlee (How to Configure the Number of Layers and Nodes in a Neural Network), hereinafter Brownlee.
Regarding claim 5, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
wherein the functional encoder is constructed according to the another input, (Hsieh, section 3.4, paragraph 2: “To examine the sensitivity of clustering performance to the number of hidden layers, we set the embedding dimensionality to 10 and experiment with the number of hidden layers ranging from 1 to 4.” – The experiment using the number of hidden layers ranging from 1 to 4 indicates that the another input includes the number of layers which is used to construct the function encoder in the experiments.)
Hsieh does not explicitly teach:
receiving another input defining at least one of a number of the plurality of layers of continuous neurons or a number of the continuous neurons, … and wherein the continuous neurons of the functional encoder use bivariate parameter functions.
However, Rao further teaches:
and wherein the continuous neurons of the functional encoder use bivariate parameter functions. (Rao, page 4, paragraph 2: “We learn using the functional (univariate and bivariate) weights that are continuous over time (or some other continuum).” And equation 8:
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600
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– The functional weights that are continuous over time are analogous to the continuous neurons of the functional encoder, while the functional weights being univariate and bivariate indicates that there is bivariate parameter function which is shown in equation (8) above.)
Hsieh, Rao, and Wan do not explicitly teach:
receiving another input defining at least one of a number of the plurality of layers of continuous neurons or a number of the continuous neurons, …
However, Brownlee teaches:
receiving another input defining at least one of a number of the plurality of layers of continuous neurons or a number of the continuous neurons, … (Brownlee, page 1, paragraphs 1 and 2: “Artificial neural networks have two main hyperparameters that control the architecture or topology of the network: the number of layers and the number of nodes in each hidden layer. You must specify values for these parameters when configuring your network.” – The artificial neural network is analogous to the functional encoder of Hsieh, the hyperparameters being the number of layers and the number of nodes of each layer indicates that here is an input defining at least one of a number of the plurality of layers or number of neurons, wherein the neurons being continuous is taught by Hsieh in claim 1.)
Brownlee is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Hsieh, Rao, and Wan, which already teaches training the functional encoder but does not explicitly teach that the number of layers or neurons is specified as an input, to include the teachings of Brownlee which does teach that the number of layers or neurons is specified as an input in order to “see what works best for your specific dataset.” (Brownlee, page 4, paragraph 3)
Regarding claim 13, Hsieh, Rao, and Wan teach the non-transitory computer readable medium of claim 9, as cited above.
Claim 13 additionally has the same limitations of claim 5 which are taught by Hsieh, Rao, Wan, and Brownlee – see claim 5 above.
Claims 6 and 14 are rejected under 35 U.S.C. 103 as being unpatentable over Hsieh in view of Rao in view of Wan in view of Quanz et al. (US20220138537), hereinafter Quanz.
Regarding claim 6, Hsieh, Rao, and Wan teach the method of claim 1, as cited above.
Hsieh further teaches:
wherein the dimension reduced form of the additional input time series data is generated through the forward propagation and back-propagation using the functional gradients. (Hsieh, page 670, algorithm 1 – Quanz teaches the additional input time series data below, thus the input of algorithm 1 would include the additional input time series data and the output being the embedding representation which is the dimension reduced form. Algorithm 1 additionally shows that the output is generated through the forward propagation and back-propagation using the functional gradients.)
Hsieh, Rao, and Wan do not explicitly teach:
for receipt of additional input time series data from a same source of the input time series data, executing the trained functional encoder on the additional input time series data to generate a dimension reduced form of the additional input time series data,
However, Quanz teaches:
for receipt of additional input time series data from a same source of the input time series data, executing the trained functional encoder on the additional input time series data to generate a dimension reduced form of the additional input time series data, (Quanz, paragraph 0018: “According to one embodiment, a computer-implemented method of multivariate time series modeling and forecasting, the computer-implemented method includes encoding a plurality of inputs of multivariate time series data, mapping the encoded multivariate time series data to a lower-dimensional latent space, predicting the next values in time of the encoded multivariate time series data in the lower dimensional latent space, and mapping the predicted next values and a random noise back to an input space to provide a predictive distribution sample for a next time points of the multivariate time series data. There is an output of one or more time series forecasts based on the predictive distribution sample.” And paragraph 0040: “The term “input space” is understood in machine learning as all the possible inputs.” – The plurality of inputs being encoded to a lower-dimensional latent space is analogous to receipt of additional input time series data and executing the trained encoder to generate a dimension reduced form of the additional input time series data. Wherein the input coming from the “input space” is analogous to the data being from the same source.)
Quanz is considered analogous to the claimed invention as it is in the same field of endeavor, machine learning. Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date to have modified Hsieh, Rao, and Wan, which already teaches training a functional encoder to learn a dimension reduced form of the input data but does not explicitly teach generating a dimension reduced form of additional input data from a same source, to include the teachings of Quanz which does teach generating a dimension reduced form of additional input data from a same source since “there is an improvement in accuracy and in the time to process the time series modeling and forecasting.” (Quanz, paragraph 0018)
Regarding claim 14, Hsieh, Rao, and Wan teach the non-transitory machine readable medium of claim 9, as cited above.
Claim 14 additionally has the same limitations of claim 6 which are taught by Hsieh, Rao, Wan, and Quanz – see claim 6 above.
Response to Arguments
Applicant's arguments filed April 2, 2026 have been fully considered but they are not persuasive. In particular, applicant argues on page 7 that “none of the cited references teach or suggest training a functional encoder ‘through forward propagation and back-propagation using functional gradients’. However, this is taught by Hsieh as one of the major contributions of their paper, see page 667, bullet 3 and Claim Rejections – 35 USC 103 above. Applicant further argues that the amendments to claims 5 and 13, 6 and 14, 8, and 16 are not taught or suggested by the cited references, examiner disagrees and notes that they are taught by the cited references as shown in Claim Rejections – 35 USC 103 above.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Dang et al. (US20210350225)
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/J.C.M./Examiner, Art Unit 2144
/SHOURJO DASGUPTA/Primary Examiner, Art Unit 2144
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