DETAILED ACTION
This Office Action is sent in response to Applicant’s Communication received 7/13/2026 for application number 18/462,872.
Claims 1-30 are pending.
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 .
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 1-30 rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. Independent claim 1 (representative of independent claims 15, 29, and 30) recites:
A processing system, comprising: at least one memory having executable instructions stored thereon; and one or more processors configured to execute the executable instructions to cause the processing system to: generate a plurality of sample points from a multi-dimensional space representing a domain of a target function, each respective sample point of the plurality of sample points being generated based on one or more selected sampling rates for each dimension in the multi-dimensional space; generate a plurality of sparse matrices from the plurality of sample points, each respective sparse matrix of the plurality of sparse matrices being generated based on known locations of non-zero coefficients of the target function; generate a plurality of transformed sparse matrices representing a relationship between Chebyshev coefficients of the target function and the plurality of sparse matrices representing the plurality of sample points after applying a cosine transformation; generate an approximation of the target function based on the plurality of transformed sparse matrices; and take one or more actions based on the approximation of the target function
(2A, prong 1) The underlined portions of the claim recite an abstract idea, specifically mathematical calculations. Specifically, see paragraphs 24-44 of the specification (as filed) which shows the equations and calculations required to perform the steps in underlined portions of the claim.
(2A, prong 2) This judicial exception is not integrated into a practical application. The claims recite the additional element of (a) generic computer hardware like a processor, memory, etc. This additional element is a mere instruction to apply the exception because it is merely adding generic computer hardware after the fact to the mathematical calculations. Even when all of the additional elements are considered in ordered combination with the recited abstract idea, the claim as a whole does not integrate the abstract idea into a practical application because the additional elements only add mere instructions to apply the exception to the mathematical calculations.
(2B) The claim(s) does/do not include additional elements that are sufficient to amount to significantly more than the judicial exception. Additional elements (a) is a mere instruction to apply the exception as explained above. Even when all of the additional elements are considered in ordered combination with the recited abstract idea, the claim as a whole does not amount to significantly more than the abstract idea itself because the additional elements only add mere instructions to apply the exception to the mathematical calculations.
The Examiner notes he has considered if the claimed invention is an improvement to the functioning of a computer or other technology. When evaluating if an improvement provides an inventive concept, the specification must have a technical explanation of the improvement, the claim itself must reflect the disclosed improvement, and, “It is important to note, the judicial exception alone cannot provide the improvement. The improvement can be provided by one or more additional elements.” See MPEP 2106.05(a). Applicant’s specification at paragraphs 14-18 describe the invention can reduce the number of calculations needed to approximate a target function, and paragraphs 64 describe the outputs of the approximated target function can be used to control how an amplifier applied digital predistortion or amplification before outputting a signal for transmission. Here, for the rejected claims, the improvement is provided solely by the judicial exception, i.e. the mathematical calculations. Improved math alone is not patentable subject matter: ‘‘the discovery of [a mathematical formula] cannot support a patent unless there is some other inventive concept in its application.’’ See MPEP 2106.05(a)(2) citing Parker v. Flook, 437 U.S. 584, 594, 198 USPQ2d 193, 199 (1978).
With respect to dependent claims 2-9, 13-14, 16-23, and 27-28, these claims add additional mathematical calculations.
With respect to dependent claims 10-12 and 24-26 these claims add the additional element of, “identify parameters of one or more components of a signal amplifier based on test data associated with the signal amplifier, and configure the amplifier to generate an output signal for transmission via an antenna based on the identified parameters,” the parameters associated with a digital predistorter or power amplifier portion of the signal amplifier. The language of these limitations have no connection to any element of the parent independent claims: the claims recite identifying parameters based on test data to control the amplifier, but these limitations are not dependent on any limitation of the parent claim (that is to say, the way the claims are phrased, the control parameters for the amp are not dependent at all on what happens with the mathematical calculations; also see the 112(b) rejection below). (2A, prong 2) This additional element does not integrate the abstract idea into a practical application because it is insignificant extra-solution activity. Specifically, the limitation is not significant because it is only tangentially related to the invention: because these limitations are not connected to the mathematical calculations, they do not impose any meaningful limits on the claim. Even when all of the additional elements are considered in ordered combination with the recited abstract idea, the claim as a whole does not amount to significantly more than the abstract idea itself because the additional elements only add mere instructions to apply the exception to the mathematical calculations and insignificant extra-solution activity the abstract idea. (2B) This limitation does not amount to significantly more than the abstract idea itself because it is well-understood, routine, and conventional, analogous to receiving or transmitting data over a network, e.g., using the Internet to gather data. See MPEP 2106.05(d) citing Intellectual Ventures v. Symantec, 838 F.3d 1307, 1321; 120 USPQ2d 1353, 1362 (Fed. Cir. 2016). Even when all of the additional elements are considered in ordered combination with the recited abstract idea, the claim as a whole does not amount to significantly more than the abstract idea itself because the additional elements only add mere instructions to apply the exception to the mathematical calculations and insignificant extra-solution activity that is well-understood, routine, and conventional to the abstract idea. (The Examiner notes that paragraph 64 of the specification, for example, states that the target function that is approximated is the output of an amplifier including a DPD and PA, and the optimal parameters for the DPD and PA correspond to the Chebyshev coefficients of target function and are used to control the amplifier’s signal transmission. Although these disclosed elements would clearly integrate the mathematical calculations into a practical application, they are not claimed.)
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-6, 8-20, 22-30 are 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. The term “sparse matrix” is a term of art which is ordinarily definite (meaning a matrix with primarily zeros, or with a large number of zeros such that special techniques can be used to take advantage of the sparseness). However, dependent claims 7 and 21 define “sparse matrix” as “a matrix including a majority of zero values.” Thus, the broadest reasonable interpretation of “sparse matrix” in the independent claims is a matrix including either a majority or a minority of zero values. (Otherwise dependent claims 7 and 21 would be improperly interpreted to not further limit the parent claim.) A matrix with a minority of zero values would not typically be considered “sparse” by one of ordinary skill in the art. Therefore, the term “sparse matrix” as it is used and defined by the claims is indefinite.
Response to Arguments
Applicant’s arguments with respect to the 112(b) rejection for lack of antecedent basis of claims 10, 13-14, 24, and 26-28 have been fully considered and are persuasive. The 112(b) rejection for lack of antecedent basis of claims 10, 13-14, 24, and 26-28 has been withdrawn.
Applicant's arguments with respect to the 112(b) rejection of claims 1-6, 8-20, and 22-30 have been fully considered but they are not persuasive. Applicant argues that “sparse matrix” is definite because matrices with a minority of zero values can “sparse” in the sense that they have a “large number of zero values.” The Examiner disagrees.
For determining the scope of the term “sparse matrix,” applicant’s specification generally states that a sparse matrix has “a large number of zero values,” para. 0018. Other outside definitions of “sparse matrix” generally do not specify an exact proportion of zero to nonzero values. For example, see Filippone et al., Sparse Matrix-Vector Multiplication on GPGPUs, pages 1-2 (NPL [U], see Notice of References Cited) setting forth a number of definitions, including: “Any matrix with enough zeros that it pays to take advantage of them,” and for an MxN matrix, the number of nonzeroes being much less than M x N; “Indeed, it is quite common for
A
∈
R
n
x
n
to have a number of nonzeros that is O(n); that is, the average number of nonzero elements per row (column) is bounded independently of the total number of rows (columns).” Applicant’s specification does not discuss or give any examples or guidance of how many zeros are needed in relation to the claimed sparse matrices that correspond to of the plurality of sample points in order to take advantage of the zero values computationally.
Dependent claims 7 and 21 also provide context on the scope of the term “sparse matrix”; they require the sparse matrix to be a matrix with a majority of zero values. These dependent claims imply that the independent claims more broadly cover matrices with a majority or minority zero values, otherwise claims 7 and 21 would improperly be read as redundant. See Dow Chem. Co. v. United States, 226 F.3d 1334, 1341-42 (Fed.Cir.2000) (holding an independent claim should be interpreted more broadly than a dependent claim so the dependent claim was not rendered redundant).
Because of how the term “sparse matrix” is defined and used in the independent claim and specification, “sparse matrix” is indefinite because it is unclear how many zeros the matrix must have to be sparse. It is unclear, for example, if an 8x8 matrix with 20 zero values is “sparse.” Applicant simply argues that the term is definite because a matrix with a minority of zero values can still have a “large number” of zero values. However, it is unclear if, for an 8x8 matrix, which of 15/64, 20/64, 28/64, and 31/64 zero values are a large number of zero values, making the matrix sparse; essentially this judgment would be a matter of opinion. In the Examiner’s opinion, an 8x8 matrix with 20 zeroes out of 64 total values does not seem to be a sparse matrix, although reasonable people could disagree about whether 20 zeroes is a “large number” of zero values. While a more typical definition of sparse matrix would define the number of zeroes as “enough zeros that it pays to take advantage of them,” rendering the term definite, this is not the definition used by the specification or claim (which is based on the number of proportion of zeroes) or in Applicant’s arguments.
Applicant's arguments with respect to the 101 rejection have been fully considered but they are not persuasive. Applicant argues that the claims are directed to a technical improvement of improved machine learning based on sparse Chebyshev interpolation of a target function, pointing to paragraphs 14, 18, and 63 of the specification, and therefore are integrated into a practical application at step 2A, prong 2 or amount to significantly more than the abstract idea itself at step 2B. The Examiner respectfully disagrees.
For an improvement to the functioning of a computer to furnish an inventive concept, “It is important to note, the judicial exception alone cannot provide the improvement. The improvement can be provided by one or more additional elements. … In addition, the improvement can be provided by the additional element(s) in combination with the recited judicial exception.” See MPEP 2106.05(a). Here, the improvement stems entirely from the mathematical calculations themselves: the specification at paragraphs 17-18 state the calculations can reduce computational complexity from
O
(
2
n
)
or
O
(
n
2
)
(n being the input dimensions) to
O
(
N
p
o
l
y
l
o
g
(
N
)
)
(N being the number of non-zero Chebyshev coefficients). The entirety of the improvement is derived from the mathematical calculations. In contrast, the improvements to machine learning in Ex parete Desjardins, Appeal No. 2024-000567 (PTAB September 26, 2025, Appeals Review Panel Decision) (precedential) were directed to preventing catastrophic forgetting when learning multiple tasks, and therefore, “Such improvements were tantamount to how the machine learning model itself would function in operation and therefore not subsumed in the identified mathematical calculation.” Charles Kim, Advance Notice of Changes to the MPEP in light of Ex Parte Desjardin (Dec. 5, 2025). Even when considering the additional elements of generic computer hardware in combination with the recited mathematical calculations, the improvements to computational complexity are derived entirely from the advances in the mathematical calculations themselves; running improved mathematical calculations on generic computer hardware does not furnish an inventive concept, or amount to improved machine learning or computers performance.
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.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Andrew T. Chiusano whose telephone number is (571)272-5231. The examiner can normally be reached M-F, 10am-6pm.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Tamara Kyle can be reached at 571-272-4241. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/ANDREW T CHIUSANO/Primary Examiner, Art Unit 2144
Prosecution Insights