Prosecution Insights
Last updated: July 17, 2026
Application No. 18/161,024

Computer-Implemented Symbolic Differentiation Using Chain Rule

Non-Final OA §101
Filed
Jan 27, 2023
Priority
Jan 28, 2022 — provisional 63/304,537 +1 more
Examiner
WAJE, CARLO C
Art Unit
Tech Center
Assignee
Skydio Inc.
OA Round
1 (Non-Final)
68%
Grant Probability
Favorable
1-2
OA Rounds
0m
Est. Remaining
99%
With Interview

Examiner Intelligence

Grants 68% — above average
68%
Career Allowance Rate
163 granted / 239 resolved
+8.2% vs TC avg
Strong +34% interview lift
Without
With
+34.4%
Interview Lift
resolved cases with interview
Typical timeline
3y 1m
Avg Prosecution
36 currently pending
Career history
275
Total Applications
across all art units

Statute-Specific Performance

§101
21.5%
-18.5% vs TC avg
§103
57.8%
+17.8% vs TC avg
§102
6.6%
-33.4% vs TC avg
§112
12.0%
-28.0% vs TC avg
Black line = Tech Center average estimate • Based on career data from 239 resolved cases

Office Action

§101
DETAILED ACTION 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 The present application, 18161024, filed 01/27/2023 Claims Priority from Provisional Application 63344755, filed 05/23/2022; 18161024 Claims Priority from Provisional Application 63304537, filed 01/28/2022. Information Disclosure Statement The information disclosure statement (IDS) submitted on 11/12/2024, 12/19/2024 and 05/15/2024 are 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 § 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 1-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. Under Step 1, claims 1-7 recite a series of steps and, therefore, is a process. Claims 8-14 recite a non-transitory computer-readable medium and, therefore, is an article of manufacture. Claims 15-20 recite a device and, therefore, is a machine. Under Step 2A prong 1, claim 15 recites A computing device comprising: multithreaded processing circuitry; and a memory storing instructions which, when executed by the processing circuitry, cause the processing circuity to: access a first symbolic expression for an output value as a function of an input value; compute, at a first thread of the multithreaded processing circuitry, a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition; compute, at a second thread of the multithreaded processing circuitry, a second symbolic Jacobian of the output value with respect to the input value; compute, at a third thread of the multithreaded processing circuitry, a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition; apply symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space; and provide a representation of the second symbolic expression. The above underlined limitations of computing a first, second and third symbolic Jacobian and applying symbolic matrix multiplication to the first, second and third symbolic Jacobian amounts processing amounts to processing mathematical relationships/calculations and falls within the “Mathematical Concepts” grouping of abstract ideas. Accordingly, the claim is directed to recite an abstract idea. Under step 2A prong 2, the claim recites the following additional elements: multithreaded processing circuitry; a memory storing instructions which, when executed by the processing circuitry, cause the processing circuity to: access a first symbolic expression for an output value as a function of an input value; a first thread; a second thread; a third thread; and provide a representation of the second symbolic expression. However, the additional elements of “a memory”, “multithreaded processing circuitry”, “a first thread”, “a second thread” and “a third thread” are recited at a high-level of generality (i.e., as a generic computer component for storing instructions; and as a generic multithreaded processing circuitry comprising a first thread, a second thread, and a third thread for executing the instructions to perform mathematical computations) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. At most, the additional elements of ““multithreaded processing circuitry”, “a first thread”, “a second thread” and “a third thread” are merely generally linking the use of a judicial exception to a particular technological environment or field of use where the computations of the first, second and third symbolic Jacobian are performed by a first, a second, and a third thread of a multithreaded processing circuitry respectively. See MPEP 2106.05(h) for more information. The additional elements of “access a first symbolic expression for an output value as a function of an input value” and “provide a representation of the second symbolic expression” are merely adding insignificant extra-solution activities. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application. Under step 2B, claim 15 does not include additional elements that, individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements of “a memory”, “multithreaded processing circuitry”, “a first thread”, “a second thread” and “a third thread” are recited at a high-level of generality (i.e., as a generic computer component for storing instructions; and as a generic multithreaded processing circuitry comprising a first thread, a second thread, and a third thread for executing the instructions to perform mathematical computations) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. At most, the additional elements of ““multithreaded processing circuitry”, “a first thread”, “a second thread” and “a third thread” are merely generally linking the use of a judicial exception to a particular technological environment or field of use where the computations of the first, second and third symbolic Jacobian are performed by a first, a second, and a third thread of a multithreaded processing circuitry respectively. See MPEP 2106.05(h) for more information. The additional elements of “access a first symbolic expression for an output value as a function of an input value” and “provide a representation of the second symbolic expression” are merely adding insignificant extra-solution activities. See MPEP 2106.05(d)(II) which states that the courts have recognized computer functions such as “Receiving or transmitting data over a network” and “Storing and retrieving information in memory” as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. The claim does not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claim does not amount to significantly more than the abstract idea. Under step 2A prong 1, claims 16-20 recite the same abstract idea as claim 15 by reason of dependence. Further, claim 16 recites further details of computing the first, second and third symbolic Jacobian; claim 17 recites further details of the first symbolic expression; and claim 18 recites further of the second symbolic expression which falls within the “Mathematical Concepts” grouping of abstract ideas. Accordingly, the claims are directed to recite an abstract idea. Under step 2A prong 2, claim 16 recites the following additional elements: wherein the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian are computed in parallel; claim 17 recites the following additional elements: wherein accessing the first symbolic expression comprises accessing a cost function for operating an unmanned aerial vehicle; claim 18 recites the following additional elements: control operation of the unmanned aerial vehicle; claim 19 recites the following additional elements: a flight control subsystem of the unmanned aerial vehicle, and wherein controlling operation of the unmanned aerial vehicle comprises transmitting instructions to a motor of the unmanned aerial vehicle; claim 20 recites the following additional elements: wherein the first thread comprises one or more first threads, wherein the second thread comprises one or more second threads, wherein the third thread comprises one or more third threads. However, the additional elements of “a flight control subsystem” in claim 19 is recited at a high-level of generality (i.e., as a generic flight control subsystem for controlling operations of a uav) such that it amounts to no more than mere instructions using a generic computer component or merely as a tool to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. The additional elements of “wherein the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian are computed in parallel” in claim 16; “wherein accessing the first symbolic expression comprises accessing a cost function for operating an unmanned aerial vehicle” in claim 17; “control operation of the unmanned aerial vehicle” in claim 18; wherein controlling operation of the unmanned aerial vehicle comprises transmitting instructions to a motor of the unmanned aerial vehicle” in claim 19; and “wherein the first thread comprises one or more first threads, wherein the second thread comprises one or more second threads, wherein the third thread comprises one or more third threads” in claim 20 are merely generally linking the use of a judicial exception to a particular technological environment or field of use (i.e., where the computations of the first, second and third symbolic Jacobian are performed in parallel; where the first symbolic expression is part of a cost function for operating an unmanned aerial vehicle; where the result is used to control operation of the unmanned aerial vehicle without providing any specific details of the operations of the uav; by limiting the transmitting of instructions to a motor of the uav without providing specific details of the instructions to control the operations of the uav; and wherein the first, second and third threads each comprises one or more respective threads). See MPEP 2106.05(h) for more information. The additional elements of “accessing a cost function” in claim 17; and “transmitting instructions” in claim 20 are merely adding insignificant extra-solution activities. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claims are not integrated into a practical application. Under step 2B, claims 16-20 do not include additional elements that, individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements of “a flight control subsystem” in claim 19 is recited at a high-level of generality (i.e., as a generic flight control subsystem for controlling operations of a uav) such that it amounts to no more than mere instructions using a generic computer component or merely as a tool to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. The additional elements of “wherein the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian are computed in parallel” in claim 16; “wherein accessing the first symbolic expression comprises accessing a cost function for operating an unmanned aerial vehicle” in claim 17; “control operation of the unmanned aerial vehicle” in claim 18; wherein controlling operation of the unmanned aerial vehicle comprises transmitting instructions to a motor of the unmanned aerial vehicle” in claim 19; and “wherein the first thread comprises one or more first threads, wherein the second thread comprises one or more second threads, wherein the third thread comprises one or more third threads” in claim 20 are merely generally linking the use of a judicial exception to a particular technological environment or field of use (i.e., where the computations of the first, second and third symbolic Jacobian are performed in parallel; where the first symbolic expression is part of a cost function for operating an unmanned aerial vehicle; where the result is used to control operation of the unmanned aerial vehicle without providing any specific details of the operations of the uav; by limiting the transmitting of instructions to a motor of the uav without providing specific details of the instructions to control the operations of the uav; and wherein the first, second and third threads each comprises one or more respective threads). See MPEP 2106.05(h) for more information. The additional elements of “accessing a cost function” in claim 17; and “transmitting instructions” in claim 20 are merely adding insignificant extra-solution activities. See MPEP 2106.05(d)(II) which states that the courts have recognized computer functions such as “Receiving or transmitting data over a network” and “Storing and retrieving information in memory” as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. The claims do not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claims do not amount to significantly more than the abstract idea. Regarding claims 1-6, they are directed to a method practiced by the device of claims 15-20 respectively. All steps performed by the method of claims 1-6 would be practiced by the device of claims 15-20 respectively. Claims 15-20 analysis applies equally to claims 1-6 respectively. Regarding claims 8-13, they are directed to a non-transitory computer-readable medium storing instructions to execute the operations of the device of claims 15-20 respectively. All steps of the operations stored in the non-transitory computer-readable medium claims 8-13 would be executed by the device of claims 15-20 respectively. Claims 15-20 analysis applies equally to claims 8-13 respectively. Under step 2A prong 2, claim 7 recites the following additional elements: wherein the one or more first threads, the one or more second threads, and the one or more third threads are mutually exclusive; claim 14 recites the following additional elements: wherein the one or more first threads, the one or more second threads, and the one or more third threads are mutually exclusive. However, the additional elements of “wherein the one or more first threads, the one or more second threads, and the one or more third threads are mutually exclusive” in claims 7 and 14 are merely generally linking the use of a judicial exception to a particular technological environment or field of use. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claims are not integrated into a practical application. Under step 2B, claims 7 and 14 do not include additional elements that, individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements of “wherein the one or more first threads, the one or more second threads, and the one or more third threads are mutually exclusive” in claims 7 and 14 are merely generally linking the use of a judicial exception to a particular technological environment or field of use. The claims do not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claims do not amount to significantly more than the abstract idea. Allowable Subject Matter Claims 1-20 would be allowable if rewritten to overcome the 35 U.S.C. 101 rejection discussed above. The following is a statement of reasons for the indication of allowable subject matter: Robenack et al. (NPL – “LIEDRIVERS — A Toolbox for the Efficient Computation of Lie Derivatives Based on the Object-Oriented Algorithmic Differentiation Package ADOL-C”) discloses computing Lie derivatives using symbolic computation which includes accessing a first symbolic expression for an output value as a function of an input value; computing a first symbolic Jacobian of the input value with respect to an input tangent space from a symbolic Lie group definition; computing a second symbolic Jacobian of the output value with respect to the input value; applying symbolic matrix multiplication to the first symbolic Jacobian and the second symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space and providing a representation of the second symbolic expression. Further, Robenack discloses using the Lie derivatives in control-related task such as nonlinear control systems. However, Robenack fails to explicitly teach or suggest at least the features of computing a third symbolic Jacobian of an output tangent space with respect to the input value from the symbolic Lie group definition; and applying symbolic matrix multiplication to the first symbolic Jacobian, the second symbolic Jacobian, and the third symbolic Jacobian to obtain a second symbolic expression for the output tangent space with respect to the input tangent space as recited in claims 1, 8 and 15. Conclusion Any inquiry concerning this communication or earlier communications from the examiner should be directed to Carlo Waje whose telephone number is (571)272-5767. The examiner can normally be reached 9:00-6:00 M-F. 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, James Trujillo can be reached at (571) 272-3677. 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. /Carlo Waje/Examiner, Art Unit 2151 (571)272-5767
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Prosecution Timeline

Jan 27, 2023
Application Filed
Apr 20, 2023
Response after Non-Final Action
Jul 08, 2026
Non-Final Rejection mailed — §101 (current)

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Prosecution Projections

1-2
Expected OA Rounds
68%
Grant Probability
99%
With Interview (+34.4%)
3y 1m (~0m remaining)
Median Time to Grant
Low
PTA Risk
Based on 239 resolved cases by this examiner. Grant probability derived from career allowance rate.

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