DETAILED ACTION
This action is responsive to the Application 18/125,027 filed on 03/22/2023. Claims 1-20 have been examined and are pending in the case. Claims 1, 6, 11 and 16 are independent claims.
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 .
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.
Domestic Benefit
Domestic Benefit of 04/30/2021 is acknowledged for Provisional 17/733,874.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 04/27/2023 and 07/25/2025 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(d):
(d) REFERENCE IN DEPENDENT FORMS.—Subject to subsection (e), a claim in dependent form shall contain a reference to a claim previously set forth and then specify a further limitation of the subject matter claimed. A claim in dependent form shall be construed to incorporate by reference all the limitations of the claim to which it refers.
The following is a quotation of pre-AIA 35 U.S.C. 112, fourth paragraph:
Subject to the following paragraph [i.e., the fifth paragraph of pre-AIA 35 U.S.C. 112], a claim in dependent form shall contain a reference to a claim previously set forth and then specify a further limitation of the subject matter claimed. A claim in dependent form shall be construed to incorporate by reference all the limitations of the claim to which it refers.
Claim 20 is rejected under 35 U.S.C. 112(d) or pre-AIA 35 U.S.C. 112, 4th paragraph, as being of improper dependent form for failing to further limit the subject matter of the claim upon which it depends, or for failing to include all the limitations of the claim upon which it depends. Claim 20 has the same limitations as claim 15 and both are dependent from claim 14. Applicant may cancel the claim(s), amend the claim(s) to place the claim(s) in proper dependent form, rewrite the claim(s) in independent form, or present a sufficient showing that the dependent claim(s) complies with the statutory requirements.
Claim 20 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claim 20 recites the limitation the non-transitory computer-readable medium of claim 14 in line 1 of claim 20. There is insufficient antecedent basis for this limitation in the claim.
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.
Claim 1-20 rejected under 35 U.S.C. 101 because the claims are directed towards abstract ideas without substantially more.
Regarding Claim 1:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites approximating an optimization problem…as a nested polynomial optimization problem which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user using judgment and choosing an equation using polynomials that estimates another problem. See 2106.04.(a)(2).III.C.
The claim recites dividing the nested polynomial optimization problem into a sequence of sub-problems which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation into multiple parts. See 2106.04.(a)(2).III.C.
The claim recites and hierarchically solving the sequence of sub-problems… which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))).
Subject Matter Eligibility Analysis Step 2A Prong 2:
processor-implemented(merely recites a generic computer on which to perform the abstract idea, e.g. "apply it on a computer" (see MPEP 2106.05(f)))
for training an artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
to train the artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
Subject Matter Eligibility Analysis Step 2B:
Additional elements (a) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation amount to no more than mere instructions to apply the exception using a generic computer component. Please see MPEP §2106.05(f).
Additional elements (b) and (c) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation merely specifies a field of use in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)).
The additional element(s) (a) (b) and (c) in the claim do/does not include any additional elements , when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor significantly more than the judicial exception for the reasons set forth in step 2A prong 2 analysis above. The claim is not patent eligible.
Regarding Claim 2:
The rejection of claim 1 is incorporated and further claim recites further additional
elements/limitations:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites in which the sequence of sub-problems comprises multidimensional polynomial optimization problems which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation and, when making that decision, choosing to use multidimensional polynomials . See 2106.04.(a)(2).III.C.
Subject Matter Eligibility Analysis Step 2A Prong 2:
The claim does not contain elements that would warrant a Step 2A Prong 2 analysis.
Subject Matter Eligibility Analysis Step 2B:
The claim does not include any additional element, when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding Claim 3:
The rejection of claim 1 is incorporated and further claim recites further additional
elements/limitations:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites the sequence of sub-problems comprises nested polynomials which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation and, when making that decision, choosing to use nested polynomials. See 2106.04.(a)(2).III.C.
Subject Matter Eligibility Analysis Step 2A Prong 2:
The claim does not contain elements that would warrant a Step 2A Prong 2 analysis.
Subject Matter Eligibility Analysis Step 2B:
The claim does not include any additional element, when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding Claim 4:
The rejection of claim 1 is incorporated and further claim recites further additional
elements/limitations:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites relaxing the global polynomial optimization problem including polynomial constraints with a plurality of semi-definite programs;
The claim recites solving the plurality of semi-definite programs based on a pre-defined structure which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))).
Subject Matter Eligibility Analysis Step 2A Prong 2:
receiving as input, a global polynomial optimization problem that approximates the optimization problem for training the artificial neural network(which amount to mere extra solution activity of obtaining and/or gathering data over a network, see MPEP §2106.05(g))
outputting a solution indicating a location of a global optimum of the optimization problem(which amount to mere extra solution activity of data output, see MPEP §2106.05(g))
training the artificial neural network based on the solution(merely recites a generic computer on which to perform the abstract idea, e.g. "apply it on a computer" (see MPEP 2106.05(f)))
Subject Matter Eligibility Analysis Step 2B:
Additional element (a) obtaining a network input is well understood, routine, and conventional activity of “transmitting or receiving data over a network" (see MPEP 2106.05(d)(II)(i) using the Internet to gather data, Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362 ).
Additional element (b) recites receiving and sending inputs/outputs which is a well-understood, routine, and conventional activity of “transmitting or receiving data over a network" (see MPEP 2106.05(d)(II)(i) using the Internet to gather data, buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014) (computer receives and sends information over a network))
Additional elements (c) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation amount to no more than mere instructions to apply the exception using a generic computer component. Please see MPEP §2106.05(f).
The additional element(s) (a) (b) and (c) in the claim do/does not include any additional elements , when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor significantly more than the judicial exception for the reasons set forth in step 2A prong 2 analysis above. The claim is not patent eligible.
Regarding Claim 5:
The rejection of claim 4 is incorporated and further claim recites further additional
elements/limitations:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites pre-defined structure comprises at least one of a sparse structure, a hierarchical structure, a block Hankel-plus-Toeplitz structure, a low-rank structure, or an underlying geometry structure which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))) as the pre-defined structure is used with calculating a solution for a plurality of semi-definite programs.
Subject Matter Eligibility Analysis Step 2A Prong 2:
The claim does not contain elements that would warrant a Step 2A Prong 2 analysis.
Subject Matter Eligibility Analysis Step 2B:
The claim does not include any additional element, when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor to significantly more than the judicial exception. The claim is not patent eligible.
Regarding Claim 6:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites approximate an optimization problem…as a nested polynomial optimization problem which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user using judgment and choosing an equation using polynomials that estimates another problem. See 2106.04.(a)(2).III.C.
The claim recites divide the nested polynomial optimization problem into a sequence of sub-problems which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation into multiple parts. See 2106.04.(a)(2).III.C.
The claim recites and to hierarchically solve the sequence of sub-problems… which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))).
Subject Matter Eligibility Analysis Step 2A Prong 2:
a memory; and at least one processor coupled to the memory, the at least one processor configured(merely recites a generic computer on which to perform the abstract idea, e.g. "apply it on a computer" (see MPEP 2106.05(f)))
for training an artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
to train the artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
Subject Matter Eligibility Analysis Step 2B:
Additional elements (a) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation amount to no more than mere instructions to apply the exception using a generic computer component. Please see MPEP §2106.05(f).
Additional elements (b) and (c) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation merely specifies a field of use in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)).
The additional element(s) (a) (b) and (c) in the claim do/does not include any additional elements , when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor significantly more than the judicial exception for the reasons set forth in step 2A prong 2 analysis above. The claim is not patent eligible.
Regarding Claim 7:
The rejection of claim 6 is incorporated and further claim recites further additional elements/limitations:
Claim 7 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 2 found in claim 7.
Regarding Claim 8:
The rejection of claim 6 is incorporated and further claim recites further additional elements/limitations:
Claim 8 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 3 found in claim 8.
Regarding Claim 9:
The rejection of claim 6 is incorporated and further claim recites further additional elements/limitations:
Claim 9 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 4 found in claim 9.
Regarding Claim 10:
The rejection of claim 9 is incorporated and further claim recites further additional elements/limitations:
Claim 10 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 5 found in claim 10.
Regarding Claim 11:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites means for approximating an optimization problem…as a nested polynomial optimization problem which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user using judgment and choosing an equation using polynomials that estimates another problem. See 2106.04.(a)(2).III.C.
The claim recites means for dividing the nested polynomial optimization problem into a sequence of sub-problems which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation into multiple parts. See 2106.04.(a)(2).III.C.
The claim recites and means for hierarchically solving the sequence of sub-problems… which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))).
Subject Matter Eligibility Analysis Step 2A Prong 2:
for training an artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
to train the artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
Subject Matter Eligibility Analysis Step 2B:
Additional elements (a) and (b) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation merely specifies a field of use in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)).
The additional element(s) (a) and (b) in the claim do/does not include any additional elements , when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor significantly more than the judicial exception for the reasons set forth in step 2A prong 2 analysis above. The claim is not patent eligible.
Regarding Claim 12:
The rejection of claim 11 is incorporated and further claim recites further additional elements/limitations:
Claim 12 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 2 found in claim 12.
Regarding Claim 13:
The rejection of claim 11 is incorporated and further claim recites further additional elements/limitations:
Claim 13 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 3 found in claim 13.
Regarding Claim 14:
The rejection of claim 11 is incorporated and further claim recites further additional elements/limitations:
Claim 14 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 4 found in claim 14.
Regarding Claim 15:
The rejection of claim 14 is incorporated and further claim recites further additional elements/limitations:
Claim 15 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 5 found in claim 15.
Regarding Claim 16:
Subject Matter Eligibility Analysis Step 2A Prong 1:
The claim recites approximate an optimization problem…as a nested polynomial optimization problem which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user using judgment and choosing an equation using polynomials that estimates another problem. See 2106.04.(a)(2).III.C.
The claim recites divide the nested polynomial optimization problem into a sequence of sub-problems which, under the broadest reasonable interpretation, covers performance of the limitation in the mind. The limitations encompass a user making a decision on dividing an equation into multiple parts. See 2106.04.(a)(2).III.C.
The claim recites and hierarchically solving the sequence of sub-problems… which is an abstract idea (Mathematical Calculations (see MPEP 2106.04(a)(2)(I)(C))).
Subject Matter Eligibility Analysis Step 2A Prong 2:
A non-transitory computer-readable medium having program code recorded thereon, the program code executed by a processor(merely recites a generic computer on which to perform the abstract idea, e.g. "apply it on a computer" (see MPEP 2106.05(f)))
for training an artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
to train the artificial neural network(merely specifies a particular technological environment in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)))
Subject Matter Eligibility Analysis Step 2B:
Additional elements (a) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation amount to no more than mere instructions to apply the exception using a generic computer component. Please see MPEP §2106.05(f).
Additional elements (b) and (c) do not integrate the abstract idea into a practical application nor do the additional limitation provide significantly more than the abstract idea because the limitation merely specifies a field of use in which the abstract idea is to take place, i.e. a field of use (see MPEP 2106.05(h)).
The additional element(s) (a) (b) and (c) in the claim do/does not include any additional elements , when considered separately and in combination, that amount to an integration of the judicial exception into a practical application, nor significantly more than the judicial exception for the reasons set forth in step 2A prong 2 analysis above. The claim is not patent eligible.
Regarding Claim 17:
The rejection of claim 16 is incorporated and further claim recites further additional elements/limitations:
Claim 17 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 2 found in claim 17.
Regarding Claim 18:
The rejection of claim 16 is incorporated and further claim recites further additional elements/limitations:
Claim 18 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 3 found in claim 18.
Regarding Claim 19:
The rejection of claim 16 is incorporated and further claim recites further additional elements/limitations:
Claim 19 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 4 found in claim 19.
Regarding Claim 20:
The rejection of claim 14 is incorporated and further claim recites further additional elements/limitations:
Claim 20 is rejected under that same 101 claim analysis due to the substantially similarity of the limitations and additional elements of claim 5 found in claim 20.
Claim Rejections - 35 USC § 102
The following is a quotation of the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
(a)(2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention.
Claim(s) 1-20 is/are rejected under 35 U.S.C. 102(a)(1) as being anticipated by Bartan et al.(“Neural Spectrahedra and Semidefinite Lifts: Global Convex Optimization of Polynomial Activation Neural Networks in Fully Polynomial-Time” henceforth known as Bartan)
Regarding claim 1:
Bartan discloses A processor-implemented method (Bartan, ABSTRACT, "Remarkably, we show that semidefinite lifting is always exact and therefore computational complexity for global optimization is polynomial in the input dimension and sample size for all input data" where using computation complexity as a measurement implies the method is completed on a computer/processor)
Bartan discloses approximating an optimization problem for training an artificial neural network as a nested polynomial optimization problem and dividing the nested polynomial optimization problem into a sequence of sub-problems and hierarchically solving the sequence of sub-problems(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
x
T
u
j
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a nested polynomial optimization that is used to train a neural network and the separate a b and c correspond to a sequence of sub-problems) to train the artificial neural network(Bartan, Page 27, Paragraph 3, “The optimal neural network weights are determined from the solution of the convex problem via the neural decomposition” where determined from the optimal neural network weights corresponds to training the artificial neural network)
Regarding claim 2:
The rejection of claim 1 with prior art Bartan is incorporated and further:
Bartan discloses in which the sequence of sub-problems comprises multidimensional polynomial optimization problems(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
x
T
u
j
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a multidimensional sequence of sub-problems as it’s a multivariate polynomial)
Regarding claim 3:
The rejection of claim 1 with prior art Fang is incorporated and further:
Bartan discloses in which the sequence of sub-problems comprises nested polynomials(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
(
x
T
u
j
)
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a nested polynomial sequence of sub-problems as there is a structure of nested parentheses)
Regarding claim 4:
The rejection of claim 1 with prior art Bartan is incorporated and further:
Bartan discloses receiving as input, a global polynomial optimization problem that approximates the optimization problem for training the artificial neural network(Bartan, Page 7, Paragraph 4, “We will show that polynomial activation neural networks can be represented via a class of simple linear matrix inequalities, dubbed neural spectrahedra (see Figure 2 for an example), and enables global optimization in fully polynomial time and elucidates their parameterization in convex analytic terms.”)
Bartan discloses relaxing the global polynomial optimization problem(Bartan, Page 6, Paragraph 3, “This problem can be relaxed by replacing the equality by the matrix inequality U
PNG
media_image1.png
20
18
media_image1.png
Greyscale
uuT . Re-writing the expression U
PNG
media_image1.png
20
18
media_image1.png
Greyscale
uuT as a linear matrix inequality via the Schur complement formula yields the following SDP”) including polynomial constraints with a plurality of semi-definite programs(Bartan, Page 14, Theorem 3.1, Equation 21, where the constraints the SDP is subject to contain polynomial constraints corresponds to polynomial constraints with a plurality of semi-definite program)
Bartan discloses solving the plurality of semi-definite programs based on a pre-defined structure and outputting a solution indicating a location of a global optimum of the optimization problem and training the artificial neural network based on the solution(Bartan, Page 6, Paragraph 4, “…it can be shown that the original non-convex problem…can be solved exactly by solving the convex SDP…This shows that the SDP relaxation is exact in this problem, returning a globally optimal solution when one exists” where solving the SDP and returning a globally optimal solution and the neural decomposition recovers the neural network weights(See Also Bartan, Page 15, Paragraph 5, “In the next section, we introduce a method for decomposing the solution of this convex program… into feasible neural network weights” ))
Regarding claim 5:
The rejection of claim 4 with prior art Bartan is incorporated and further:
in which the pre-defined structure comprises at least one of a sparse structure, a hierarchical structure, a block Hankel-plus-Toeplitz structure, a low-rank structure, or an underlying geometry structure(Bartan, Page 7, Paragraph 4, “In convex geometry, a spectrahedron is a convex body that can be represented as a linear matrix inequality which are the feasible sets of semidefinite programs.”)
Regarding claim 6:
Bartan discloses a memory; and at least one processor coupled to the memory, the at least one processor configured to (Bartan, ABSTRACT, "Remarkably, we show that semidefinite lifting is always exact and therefore computational complexity for global optimization is polynomial in the input dimension and sample size for all input data" where using computation complexity as a measurement implies the method is completed on a computer/processor with memory)
Bartan discloses approximate an optimization problem for training an artificial neural network as a nested polynomial optimization problem and divide the nested polynomial optimization problem into a sequence of sub-problems and hierarchically solving the sequence of sub-problems(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
x
T
u
j
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a nested polynomial optimization that is used to train a neural network and the separate a b and c correspond to a sequence of sub-problems) to train the artificial neural network(Bartan, Page 27, Paragraph 3, “The optimal neural network weights are determined from the solution of the convex problem via the neural decomposition” where determined from the optimal neural network weights corresponds to training the artificial neural network)
Regarding Claim 7:
The rejection of claim 6 incorporated in claim 7. Claim 7 is rejected under the same rationale as set forth in the rejection of claim 2.
Regarding Claim 8:
The rejection of claim 6 incorporated in claim 8. Claim 8 is rejected under the same rationale as set forth in the rejection of claim 3.
Regarding Claim 9:
The rejection of claim 6 incorporated in claim 9. Claim 9 is rejected under the same rationale as set forth in the rejection of claim 4.
Regarding Claim 10:
The rejection of claim 9 incorporated in claim 10. Claim 10 is rejected under the same rationale as set forth in the rejection of claim 5.
Regarding claim 11:
Bartan discloses approximating an optimization problem for training an artificial neural network as a nested polynomial optimization problem and dividing the nested polynomial optimization problem into a sequence of sub-problems and hierarchically solving the sequence of sub-problems(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
x
T
u
j
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a nested polynomial optimization that is used to train a neural network and the separate a b and c correspond to a sequence of sub-problems) to train the artificial neural network(Bartan, Page 27, Paragraph 3, “The optimal neural network weights are determined from the solution of the convex problem via the neural decomposition” where determined from the optimal neural network weights corresponds to training the artificial neural network)
Regarding Claim 12:
The rejection of claim 11 incorporated in claim 12. Claim 12 is rejected under the same rationale as set forth in the rejection of claim 2.
Regarding Claim 13:
The rejection of claim 11 incorporated in claim 13. Claim 13 is rejected under the same rationale as set forth in the rejection of claim 3.
Regarding Claim 14:
The rejection of claim 11 incorporated in claim 14. Claim 14 is rejected under the same rationale as set forth in the rejection of claim 4.
Regarding Claim 15:
The rejection of claim 14 incorporated in claim 15. Claim 15 is rejected under the same rationale as set forth in the rejection of claim 5.
Regarding claim 16:
Bartan discloses non-transitory computer-readable medium having program code recorded thereon, the program code executed by a processor(Bartan, ABSTRACT, "Remarkably, we show that semidefinite lifting is always exact and therefore computational complexity for global optimization is polynomial in the input dimension and sample size for all input data" where using computation complexity as a measurement implies the method is completed on a computer/processor with memory)
Bartan discloses program code to approximate an optimization problem for training an artificial neural network as a nested polynomial optimization problem and program code to divide the nested polynomial optimization problem into a sequence of sub-problems and program code to hierarchically solving the sequence of sub-problems(Bartan, Page 3, Paragraph 1, “We show that the standard optimization formulation for training neural networks fθ(x) =
∑
j
=
1
m
σ
x
T
u
j
α
j
with trainable parameters θ = (u1,...,um , α1,...,αm) and degree two polynomial activations σ(u) = au2 + bu + c” where substituting the activation gives
∑
j
=
1
m
a
x
T
u
j
2
+
b
x
T
u
j
+
c
α
j
corresponds to a nested polynomial optimization that is used to train a neural network and the separate a b and c correspond to a sequence of sub-problems) to train the artificial neural network(Bartan, Page 27, Paragraph 3, “The optimal neural network weights are determined from the solution of the convex problem via the neural decomposition” where determined from the optimal neural network weights corresponds to training the artificial neural network)
Regarding Claim 17:
The rejection of claim 16 incorporated in claim 17. Claim 17 is rejected under the same rationale as set forth in the rejection of claim 2.
Regarding Claim 18:
The rejection of claim 16 incorporated in claim 18. Claim 18 is rejected under the same rationale as set forth in the rejection of claim 3.
Regarding Claim 19:
The rejection of claim 16 incorporated in claim 19. Claim 19 is rejected under the same rationale as set forth in the rejection of claim 4.
Regarding Claim 20:
The rejection of claim 14 incorporated in claim 20. Claim 20 is rejected under the same rationale as set forth in the rejection of claim 5.
Conclusion
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/C.J.J./Examiner, Art Unit 2122
/KAKALI CHAKI/Supervisory Patent Examiner, Art Unit 2122
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