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 .
This action is in response to the application and claims filed 6/23/2023. Claims 1-20 are pending and have been examined. Claims 1-20 are rejected.
Priority
Applicant’s claim for the benefit of a prior-filed application under 35 U.S.C. 119(e) or under 35 U.S.C. 120, 121, 365(c), or 386(c) is acknowledged. The present application claims priority to U.S. Provisional Application No. 63/354,725, filed on 6/23/2022.
Drawings
The drawings are objected to as failing to comply with 37 CFR 1.84(p)(5) because they include the following reference characters not mentioned in the description:
Reference characters 100, 101, 102, 106 and 108 shown in Figure 1 are not found in the detailed description (see, e.g., paragraph 38 describing FIG. 1);
Reference character 200 shown in Figure 2 is not found in the detailed description (see, e.g., paragraphs 53-54 describing FIG. 2);
Reference character 303 shown in Figure 3B is not found in the detailed description (see, e.g., paragraphs 18 and 108-120 describing FIG. 3B); and
Reference characters 800, 801, 802, 803, 806 and 808 shown in Figure 8 are not found in the detailed description (see, e.g., paragraphs 144-145 describing FIG. 8).
The drawings are further objected to as failing to comply with 37 CFR 1.84(p)(3) because Figures 1, 2, 3A, 3B, 8, 12, 14 and 15 include letters which do not measure at least .32 cm. (1/8 inch) in height (i.e., most of the subscript characters and exponents, and many of the lowercase characters in FIGs. 1, 2, 3A, 3B, 8, 12, 14 and 15).
Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Specification
The disclosure is objected to because of the following informalities:
Reference characters 100, 101, 102, 106 and 108 shown in Figure 1 are not found in the detailed description (see, e.g., paragraph 38 describing FIG. 1).
Reference character 200 shown in Figure 2 is not found in the detailed description (see, e.g., paragraphs 53-54 describing FIG. 2).
Reference character 303 shown in Figure 3B is not found in the detailed description (see, e.g., paragraphs 18 and 108-120 describing FIG. 3B).
Reference characters 800, 801, 802, 803, 806 and 808 shown in Figure 8 are not found in the detailed description (see, e.g., paragraphs 144-145 describing FIG. 8).
Appropriate correction is required.
Claim Objections
Claim 17 is objected to because of the following informalities:
In line 3 of claim 17, the recitation of “stochastic duel” contains a typographical error and it appears this claim should recite “stochastic dual” (see, e.g., paragraphs 19, 121 and 123-129 of applicant’s specification disclosing a “stochastic dual”. Appropriate correction is required.
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.
Claims 12 and 18 are rejected under 35 U.S.C. 112(b) as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention.
Claims 12 and 18 both recite “the input” (see, line 4 of claim 12 and line 3 of claim 18 at the end of both of these claims). There is insufficient antecedent basis for this term in these claims. No “input” was previously recited in these claims or in their respective base claims, independent claims 9 and 15. Applicant previously introduced “input parameters” in line 5 of claim 9 and line 4 of claim 15. However, it is unclear if the subsequently-recited “the input” refers to some or all of the previously-introduced “input parameters”, or to some other “input” values or data (see, e.g., the last lines of claims and 13 and 19, which depend directly from claims 9 and 16, respectively and both recite “the input parameters.”). For the purposes of determining patent eligibility and comparison with the prior art, the Examiner is interpreting “the input” as any input data or values, including, but not limited to, some or all of the previously-introduced “input parameters”. Appropriate correction is required.
Claims 12 and 18, which depend directly from independent claims 9 and 15 respectively, both recite “automatically augmenting an arbitrary stochastic program to return a stochastic derivative whose samples estimate the derivative of the stochastic program’s expectation”. The recitations of “the stochastic program’s expectation” are unclear. In particular, as applicant previously introduced “a user-provided stochastic program” (see, lines 3-4 of claims 9 and claim 15) and “an arbitrary stochastic program” (see, line 2 of claims 12 and 18), it is unclear if the subsequently-recited “stochastic program’s expectation” refers to an expectation of the previously-introduced “user-provided stochastic program” or an expectation of the previously-introduced “arbitrary stochastic program”. For examination purposes, “the stochastic program’s expectation” is being interpreted as an expectation, an expected output or an expected result of either of the previously-introduced “user-provided stochastic program” or an expectation, an expected output or an expected result of the previously-introduced “arbitrary stochastic program”. Appropriate correction is required.
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. The analysis below of the claims’ subject matter eligibility follows the 2019 Revised Patent Subject Matter Eligibility Guidance, 84 Fed. Reg. 50-57 (January 7, 2019) (“2019 PEG”). and the 2024 Guidance Update on Patent Subject Matter Eligibility, Including on Artificial Intelligence, 89 Fed. Reg. 58128-58138 (July 17, 2024) (“2024 AI SME Update”).
When considering subject matter eligibility under 35 U.S.C. 101, it must be determined whether the claim is directed to one of the four statutory categories of invention, i.e., process, machine, manufacture, or composition of matter (Step 1). If the claim does fall within one of the statutory categories, the second step in the analysis is to determine whether the claim is directed to a judicial exception (Step 2A). The Step 2A analysis is broken into two prongs. In the first prong (Step 2A, Prong 1), it is determined whether or not the claims recite a judicial exception (e.g., mathematical concepts, mental processes, certain methods of organizing human activity). If it is determined in Step 2A, Prong 1 that the claims recite a judicial exception, the analysis proceeds to the second prong (Step 2A, Prong 2), where it is determined whether or not the claims integrate the judicial exception into a practical application. If it is determined at step 2A, Prong 2 that the claims do not integrate the judicial exception into a practical application, the analysis proceeds to determining whether the claim is a patent-eligible application of the exception (Step 2B). If an abstract idea is present in the claim, any element or combination of elements in the claim must be sufficient to ensure that the claim integrates the judicial exception into a practical application, or else amounts to significantly more than the abstract idea itself.
Regarding independent claim 1, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 1 is directed to a method, corresponding to a process, which is one of one of the four statutory categories of invention.
Step 2A Prong One Analysis: The claim is directed to an abstract idea. In particular, the claim recites mathematical concepts (including mathematical relationships, mathematical formulas or equations, and mathematical calculations). Claim 1 recites:
generating a stochastic derivative based on the user-provided stochastic program; and
generating an estimator for the user-provided stochastic program using the stochastic derivative,
wherein the estimator determines an estimate of a derivative of the user-provided stochastic program.
The above-noted generating limitations, as drafted, are a process that, under its broadest reasonable interpretation (BRI), covers mathematical concepts (i.e., mathematical relationships and calculations to generate a stochastic derivative based on a user-provided stochastic program/instructions; and to generate an estimator for the user-provided stochastic program using/applying the stochastic derivative where the estimator determines an estimate of a derivative of the stochastic program).
Under their BRI, in light of the specification, the generating limitations encompass mathematical concepts as described in the specification in paragraphs 39, 48, 87, 89 and 92. For example, paragraphs 39, 48, 87, 89 and 92 which state, inter alia, “construct a stochastic program X̃(p) whose expectation satisfies E[X̃(p)] =
d
E
[
X
p
]
d
p
. This is derived by performing a “stochastic derivative” technique, which includes propagating the proportional probability of differing event outcomes due to infinitesimal changes in p.”, “augment an arbitrary stochastic program, besides the output, to also return a stochastic derivative, whose samples serve as an estimate of the derivative of the program’s expectation with respect to the input. This means:
∂
E
X
p
∂
p
≈
1
n
∑
i
=
1
n
∂
X
i
where ∂X(1),∂X(2), . . . ,∂X(n) denote samples of such a stochastic derivative, just as similar as samples of a stochastic gradient on average corresponds to the actual gradient.”, “Consider stochastic programs X1(p) and X2(x1), where X1 has a stochastic derivative given by (δ1, w1, Y1) and X2 has a derivative (δ2, 0, 0), as discussed above. Then X2 ◦ X1 has a stochastic derivative given by (X2(δ), 0, 0).”, “Consider stochastic programs X1(p) and X2 (x1), where X1 has a stochastic derivative given by (δ1, w1, Y1) and X2 has a derivative (0, w2, Y2), as discussed above. Then the stacked program [X1; X2 ◦ X1] has a stochastic derivative given by ([δ; 0], w, Y) where
Y
=
Y
1
;
X
2
Y
1
w
i
t
h
p
r
o
b
a
b
i
l
i
t
y
w
1
w
1
+
w
2
X
1
X
1
;
Y
2
X
1
w
i
t
h
p
r
o
b
a
b
i
l
i
t
y
w
2
X
1
w
1
+
w
2
X
1
and w = w1 + w2(X1).”) and “Smoothed stochastic derivatives enjoy limited composition properties. For example, assuming w1 = 0, let
δ
2
=
w
2
X
1
E
Y
2
X
1
p
|
X
1
p
. Then for functions f that are linear:
∂
∂
p
E
f
X
2
∘
X
1
p
=
E
f
'
X
2
∘
X
1
p
δ
~
2
” further provide evidence that the claimed “generating a stochastic derivative based on the user-provided stochastic program; and generating an estimator for the user-provided stochastic program using the stochastic derivative” are mathematical concepts.
If the claim limitations, under their broadest reasonable interpretations, cover mathematical relationships, mathematical formulas or equations, or mathematical calculations, then they fall within the “Mathematical Concepts” grouping of abstract ideas. See MPEP 2106.04(a)(2) § I. But for the recitation of generic computer components (i.e., the “programmatic method” of claim 1), the limitations of claim 1 cover mathematical relationships, mathematical formulas or equations, and mathematical calculations. Accordingly, claim 1 recites an abstract idea.
Therefore, the claim is directed to an abstract idea (mathematical concept).
Step 2A Prong Two Analysis: This judicial exception is not integrated into a practical application. Claim 1 does not recite any additional limitations or elements which integrate the abstract idea into a practical application.
The claim recites these additional elements:
A programmatic method for performing language-level automatic differentiation of a stochastic program, the programmatic method comprising: receiving a user-provided stochastic program.
These additional limitations do nothing to alter the fundamental nature of the claim as a mathematical concept.
The recitation of “A programmatic method for performing language-level automatic differentiation of a stochastic program” amounts to recitation of the words "apply it" (or an equivalent) or are mere instructions to implement an abstract idea or other exception on a computer, which does not integrate a judicial exception into a practical application. See MPEP 2106.05(f).
The recitation of “receiving a user-provided stochastic program” limitation is adding insignificant extra-solution activity (amounts to necessary data gathering) to the judicial exception, as discussed in MPEP § 2106.05(g).
Accordingly, the additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea. See MPEP 2106.04(d).
Step 2B Analysis: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Receiving and communicating data are insignificant extra-solution activities that are well-understood, routine, and conventional. See MPEP2106.05(d)(II) (“The courts have recognized the following computer functions as well‐understood, routine, and conventional functions… i. Receiving or transmitting data over a network…iv. Storing and retrieving information in memory”) (citing OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015)). Therefore, the recitation of “receiving a user-provided stochastic program” is the well-understood, routine, conventional activity of receiving or transmitting data over a network, as discussed in MPEP § 2106.05(d).
Also, mere instructions to apply the abstract idea (mathematical concept) electronically (i.e., using “A programmatic method for performing language-level automatic differentiation of a stochastic program, the programmatic method comprising:” <the above-noted operations>) do not amount to significantly more than the judicial exception.
This claim does not include additional elements that 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, there are no additional elements recited that impose any meaningful limits on practicing the abstract idea. Therefore, the additional element of this claim is not sufficient to amount to significantly more than the abstract idea.
As an ordered whole, the claim is directed to a method of generating a stochastic derivative based on a received, user-provided stochastic program/instructions; and generating an estimator for the user-provided stochastic program by using/applying the stochastic derivative, the estimator determining an estimate of a derivative of the stochastic program. Nothing in the claim provides significantly more than this. As such, the claim is not patent eligible.
Regarding claim 2, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 2 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: See claim 1 above.
Step 2A Prong Two Analysis: The judicial exceptions are not integrated into a practical application.
The claim recites the additional element: outputting the estimate of the derivative of the user-provided stochastic program.
This is an insignificant extra-solution activity that is not integrated into the claim as a whole and does not add a meaningful limitation to the above-noted abstract idea (mathematical concepts) specified in this claim. That is, “outputting the estimate of the derivative of the user-provided stochastic program” amounts to necessary data outputting (See MPEP § 2106.05(g)).
Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. The claim is directed to an abstract idea.
Step 2B Analysis: The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Receiving, transmitting and communicating data are insignificant extra-solution activities that are well-understood, routine, and conventional. See MPEP2106.05(d)(II) (“The courts have recognized the following computer functions as well‐understood, routine, and conventional functions… i. Receiving or transmitting data over a network”) (citing OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015)). Therefore, recitation of “outputting the estimate of the derivative of the user-provided stochastic program” is the well-understood, routine, conventional activity of receiving or transmitting data over a network, as discussed in MPEP § 2106.05(d).
This claim does not include additional elements that 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, there are no additional elements recited that impose any meaningful limits on practicing the abstract idea. Therefore, the additional element of the claim is not sufficient to amount to significantly more than the abstract idea. This claim is not patent eligible.
Regarding claim 3, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 3 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: The claim recites wherein computation of a primal and computation of a derivative are coupled to reduce variance in the estimate of the derivative.
The additional limitation added by this claim covers a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations –“computation of a primal and computation of a derivative are coupled”). Such computations are mathematical calculations, as suggested in paragraphs 75, 84 and 101-102 of applicants’ specification.
Thus, this limitation does nothing to alter the fundamental nature of the claim as a mathematical concept.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claim does not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claim is subject-matter ineligible.
Step 2B: The claim does not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
This claim is not patent eligible.
Regarding claim 4, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 4 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: The claim recites wherein the estimate of the derivative is a primal-conditioned derivative.
The additional limitation added by this claim covers a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – to estimate the derivative as a primal-conditioned derivative). Such a primal-conditioned derivate calculation and derivative estimation is a mathematical concept.
For example, paragraphs 50-52, 93-95 and 98-102 of applicants’ specification, which state, inter alia “Primal-conditioned derivatives can be understood as taking derivatives averaged over all possible evaluations of the primal program that give rise to observable behavior”, “To motivate primal-conditioned derivatives, the classical quantities
∂
E
X
p
∂
p
a
n
d
∂
∂
p
X
p
can both be expressed as conditional expectations
∂
p
±
|
F
X
p
∶
=
∂
∂
p
±
E
X
p
|
F
” and “both primal-conditioned derivatives are unbiased with variance:
V
a
r
∂
p
+
|
Y
p
Y
p
=
n
p
1
-
p
,
a
n
d
V
a
r
∂
p
-
|
Y
p
Y
p
=
n
1
-
p
p
"
further provide evidence that the claimed “the estimate of the derivative is a primal-conditioned derivative” is itself a mathematical concept.
Thus, this limitation does nothing to alter the fundamental nature of the claim as a mathematical concept.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claim does not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claim is subject-matter ineligible.
Step 2B: The claim does not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
This claim is not patent eligible.
Regarding claim 5, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 5 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: The claim recites wherein the stochastic derivative is composable.
The additional limitation added by this claim covers a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations –the stochastic derivative being composable). Such a composable stochastic derivative is a mathematical concept.
For example, paragraphs 61 and 85-92 of applicants’ specification, which state, inter alia, “if the stochastic program X(p) represents the computation of an intermediate value of a larger program, or a single random building block of a program such as a draw from a Bernoulli variable, it does not suffice to compute just E[dX]. In order to develop a composable notion of derivative for stochastic programs, more information is needed about the distribution of dX. These distributional properties are also used to create unbiased estimators.”, “Consider stochastic programs X1(p) and X2(x1), where X1 has a stochastic derivative given by (δ1, w1, Y1) and X2 has a derivative (δ2, 0, 0), as discussed above. Then X2 ◦ X1 has a stochastic derivative given by (X2(δ), 0, 0)”, “consider stochastic programs X1(p) and X2 (x1), where X1 has a stochastic derivative given by (δ1, w1, Y1) and X2 has a derivative (0, w2, Y2), as discussed above. Then the stacked program [X1; X2 ◦ X1] has a stochastic derivative given by ([δ; 0], w, Y) where
Y
=
Y
1
;
X
2
Y
1
w
i
t
h
p
r
o
b
a
b
i
l
i
t
y
w
1
w
1
+
w
2
X
1
X
1
;
Y
2
X
1
w
i
t
h
p
r
o
b
a
b
i
l
i
t
y
w
2
X
1
w
1
+
w
2
X
1
and w = w1 + w2(X1).” and “smoothed stochastic derivatives enjoy limited composition properties. For example, assuming w1 = 0, let
δ
2
=
w
2
X
1
E
Y
2
X
1
p
|
X
1
p
. Then for functions f that are linear:
∂
∂
p
E
f
X
2
∘
X
1
p
=
E
f
'
X
2
∘
X
1
p
δ
~
2
” further provide evidence that the claimed “the stochastic derivative is composable” is itself a mathematical concept.
Thus, this limitation does nothing to alter the fundamental nature of the claim as a mathematical concept.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claim does not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claim is subject-matter ineligible.
Step 2B: The claim does not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
This claim is not patent eligible.
Regarding claim 6, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 6 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: See claim 1 above.
Step 2A Prong 1: The judicial exceptions are not integrated into a practical application.
The claim recites the additional element: wherein the programmatic method preserves structure of the user-provided stochastic program.
The recitation of “the programmatic method preserves structure of the user-provided stochastic program” amounts to recitation of the words "apply it" (or an equivalent) or are mere instructions to implement an abstract idea or other exception on a computer, which does not integrate a judicial exception into a practical application. See MPEP 2106.05(f).
Also, the “method preserves structure of the user-provided stochastic program” is insignificant extra-solution activity that is not integrated into the claim as a whole and does not add a meaningful limitation to the above-noted abstract idea specified in this claim. That is, the method “preserves structure of the user-provided stochastic program” is intended use language with no patentable weight - aside from this recitation, no “structure of the user-provided stochastic program” is recited elsewhere in the claim or any of its dependent claims (this claim has no dependent claims).
Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. The claim is directed to an abstract idea.
Step 2B: The claim does not recite additional elements that 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, there are no additional elements recited that impose any meaningful limits on practicing the abstract idea. Therefore, the additional element of the claim is not sufficient to amount to significantly more than the abstract idea. This claim is not patent eligible.
Regarding claim 7, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 7 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: The claim recites wherein the estimator includes a differentiable particle filter. This limitation does nothing to alter the fundamental nature of the claim as an abstract idea (mathematical concept). This is because the additional limitation merely limits the invention to a narrower abstract idea by further narrowing what the generically-recited “estimator” includes i.e., a “differentiable particle filter.”
Dependent claim 7, when analyzed as a whole, is not patent eligible under 35 U.S.C. 101 because the additional recited limitation fails to establish that the claim is not directed to an abstract idea. The additional limitation added by this claim covers a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – estimation of a derivative by using an “estimator” that “includes a differentiable particle filter.”). Such estimation with a filter encompasses a mathematical concept, as suggested in paragraphs 225-227 and 253 of applicants’ specification. For example, paragraphs 225-227 and 253 of the specification, which state, inter alia, “Differentiable Particle Filter … In a particle sampler, particles are resampled with particles with high weight having proportionally higher chance to be selected”, “A similar effect may be achieved by retaining each particle independently with probability proportional to its weight. Again, a particle with zero weight is dropped from further computations. But an infinitesimal increment to the probability argument, such as h in a random variable X(h) ∼ Ber(h), has an infinitesimal (not negligible) probability of turning a zero weight positive.” and “systems and methods described herein may use a differentiable particle filter … particle filters can be used for Bayesian estimation.” further provide evidence that the claimed “estimator” that “includes a differentiable particle filter” is itself a mathematical concept.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claim does not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claim is subject-matter ineligible.
Step 2B: The claim does not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
This claim is not patent eligible.
Regarding claim 8, this claim is rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 8 is directed to a method as depending from claim 1, thus the analysis for patent eligibility of claim 1 is incorporated herein.
Step 2A Prong 1: The claim recites wherein the estimator performs forward-mode automatic differentiation or reverse-mode automatic differentiation. This limitation does nothing to alter the fundamental nature of the claim as an abstract idea (mathematical concept). This is because the additional limitation merely limits the invention to a narrower abstract idea by further narrowing what the generically-recited “estimator” performs i.e., “forward-mode automatic differentiation or reverse-mode automatic differentiation.”
Dependent claim 8, when analyzed as a whole, is not patent eligible under 35 U.S.C. 101 because the additional recited limitation fails to establish that the claim is not directed to an abstract idea. The additional limitation added by this claim covers a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – estimation of a derivative by performing forward or reverse-mode automatic differentiation). Such estimation by forward or reverse-mode automatic differentiation encompasses a mathematical concept, as suggested in paragraphs 33-34, 152, 177 and 230 of applicants’ specification. For example, paragraphs 33, 177 and 230 of the specification, which state, inter alia, “the systems and methods described herein also demonstrate various applications including, for example, unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway’s Game of Life, and unbiased reverse-mode AD of a particle filter.”, “The systems and methods described herein incorporate the notion of linking into stochastic derivatives. With this innovation included, an unbiased estimate for the derivative of an arbitrary stochastic program is computed via forward-mode AD.” and “Because of the similarity of smoothed stochastic dual numbers and standard dual numbers, reverse-mode AD can also be used instead of forward-mode AD. This is convenient, as eventually reverse-mode AD becomes superior than forward-mode AD for functions f: Rn 7→ Rm with m ≫ n.” further provide evidence that the claimed “estimator” that “performs forward-mode automatic differentiation or reverse-mode automatic differentiation” is itself a mathematical concept.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claim does not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claim is subject-matter ineligible.
Step 2B: The claim does not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
This claim is not patent eligible.
Regarding independent claims 9 and 15 these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 9 is directed to a system comprising a memory and at least one processor, corresponding to a machine, and claim 15 is directed to a method, corresponding to a process, which are each one of one of the four statutory categories of invention.
Step 2A Prong One Analysis: The claims are directed to an abstract idea. In particular, the claims recite mathematical concepts (including mathematical relationships, mathematical formulas or equations, and mathematical calculations). Claims 9 and 15 both recite:
automatically determining a derivative of an expectation of a user-provided stochastic program based on input parameters of the user-provided stochastic program, wherein the user-provided stochastic program includes continuous and discrete sources of randomness.
The above-noted determining limitation, as drafted, is a process that, under its BRI, covers mathematical concepts (i.e., mathematical relationships and calculations to determine a derivative of an expectation of a user-provided stochastic program based on its input parameters, the user-provided stochastic program including continuous and discrete sources of randomness).
Under its BRI, in light of the specification, the determining limitation encompasses mathematical concepts as described in the specification in paragraphs 74, 94, 102, 109, 113, 195 and 223.
For example, paragraphs 74, 94, 102, 109, 113, 195 and 223, which state, inter alia, “a stochastic program X(p) produces a non-deterministic quantity depending on input parameters p using a source of randomness. Formally, X : p → X(p) is a random map. Repeatedly sampling the output of a stochastic program allows estimation of quantities of interest, which can be formulated as expected value EX(p) of its output.”, “Imagine a noise z, representing all randomness involved in the program, being drawn a noise space to produce a deterministic output X(p)(z).”, “Using the accuracy and precision the primal derivatives ∂p±|Y(p)Y(p) as estimators of the derivative of the expectation, in this example
∂
∂
p
E
Y
p
= n, both primal-conditioned derivatives are unbiased with variance:
V
a
r
∂
p
+
|
Y
p
Y
p
=
n
p
1
-
p
,
a
n
d
V
a
r
∂
p
-
|
Y
p
Y
p
=
n
1
-
p
p
”, “Let p ∈ R be real and h an infinitesimal change. If f is a differentiable function, then ∆f = f(p + h) − f(p) represents an infinitesimal change in f, so that ∆f / h = f ʹ (p). Analogously,
E
X
=
X
p
+
h
-
X
p
defines a stochastic differential ƐX, which depends on p and h. Here, X(p + h) and X(p) belong to a joint distribution with the same noise space (whereas in finite differences, the samples from each would be independent). With that,
E
X
h
is an unbiased estimator for the derivative of the expectation of X(p),
E
E
X
h
=
∂
∂
p
E
X
p
”, “To make sampling tractable in the case of discrete randomness, ƐX is coarsened. This motivates, for h > 0 (or h < 0), the primal-conditioned differential
E
E
X
|
X
p
=
h
∂
p
+
|
σ
X
o
r
p
-
X
p
”, “Quantifying the uncertainty related to estimating the derivative of an expectation from its primal-conditioned derivative in the case of a mixed Bernoulli process is described below. Let (pi, hi)i=1,... a sequence of independent identically distributed random dual probabilities with pi real, hi infinitesimal and Epi = µ and Ehi = µ∂ and Var(hi) = σ∂2 and Xi(pi) the dependent process of conditionally independent Bernoulli draws with conditionally expected left derivatives
H
i
=
1
X
i
p
i
=
1
h
i
p
i
” and “Then, writing Y(p) for the program rejection_sampler, with
H
=
h
∂
f
p
x
∂
p
f
p
x
=
h
∂
∂
p
l
o
g
f
p
x
the primal-conditioned derivative of the last Bernoulli random variable of the loop depending on the sample x, for infinitesimal h the program Y (p+h) returns a dual
X
p
+
H
X
p
which gives an unbiased estimate of the derivative of the expectation,
E
H
X
(
p
)
/
h
=
E
X
∂
∂
p
log
f
↓
p
X
p
=
∫
x
∂
∂
p
f
p
x
∂
x
=
∂
∂
p
E
X
p
” further provide evidence that the claimed “determining a derivative of an expectation of a user-provided stochastic program based on input parameters of the user-provided stochastic program, wherein the user-provided stochastic program includes continuous and discrete sources of randomness” are mathematical concepts.
If the claim limitations, under their broadest reasonable interpretations, cover mathematical relationships, mathematical formulas or equations, or mathematical calculations, then they fall within the “Mathematical Concepts” grouping of abstract ideas. See MPEP 2106.04(a)(2) § I. But for the recitation of generic computer components (i.e., the “computer system … comprising: a memory and at least one processor” of claim 9 and the “programmatic method” of claim 15), the limitations of claims 9 and 15 cover mathematical relationships, mathematical formulas or equations, and mathematical calculations. Accordingly, claims 9 and 15 recite an abstract idea.
Therefore, the claims are directed to an abstract idea (mathematical concept).
Step 2A Prong Two Analysis: This judicial exception is not integrated into a practical application. Claims 9 and 15 do not recite any additional limitations or elements which integrate the abstract idea into a practical application.
The claims recite the additional limitations of “A computer system for computation of derivatives of stochastic programs, the computer system comprising: a memory and at least one processor, the at least one processor configured for:” <performing the above-noted operations> (claim 9) and “A programmatic method for computation of derivatives of stochastic programs, the programmatic method comprising:” <the above-noted operations> (claim 15).
The recitations of “A computer system for computation of derivatives of stochastic programs, the computer system comprising: a memory and at least one processor, the at least one processor configured for:” <performing the above-noted operations> and “A programmatic method for computation of derivatives of stochastic programs, the programmatic method comprising:” <the above-noted operations>” amount to recitation of the words "apply it" (or an equivalent) or are mere instructions to implement an abstract idea or other exception on a computer, which does not integrate a judicial exception into a practical application. See MPEP 2106.05(f).
Accordingly, the additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea. See MPEP 2106.04(d).
Step 2B Analysis: The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception.
These claims do not include additional elements that 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, there are no additional elements recited that impose any meaningful limits on practicing the abstract idea. Therefore, the additional elements of these claims are not sufficient to amount to significantly more than the abstract idea.
Also mere instructions to apply the abstract idea (mathematical concept) electronically (i.e., using “A computer system for computation of derivatives of stochastic programs, the computer system comprising: a memory and at least one processor, the at least one processor configured for:” <performing the above-noted operations> of claim 9, and using “A programmatic method for computation of derivatives of stochastic programs, the programmatic method comprising:” <the above-noted operations>” of claim 15 do not amount to significantly more than the judicial exception.
As an ordered whole, the claims are directed to a method and system for determining/calculating a derivative of an expectation of a user-provided stochastic program based on its input parameters, where the received, user-provided stochastic program includes continuous and discrete sources of randomness. Nothing in the claims provide significantly more than this. As such, the claims are not patent eligible.
Regarding claims 10 and 16, these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 10 is directed to a system as depending from claim 9 and claim 16 is directed to a method as depending from claim 15, thus the analysis for patent eligibilities of claims 9 and 15 are incorporated herein.
Step 2A Prong 1: The claims both recite using a differentiable particle filter to accelerate the determination of the derivative of the expectation of the user-provided stochastic program.
These limitations do nothing to alter the fundamental nature of the claims as an abstract idea (mathematical concepts).
Dependent claims 10 and 16, when analyzed as a whole, are not patent eligible under 35 U.S.C. 101 because the additional recited limitations fail to establish that the claims are not directed to an abstract idea. The additional limitations added by these claims cover a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – estimation/determination of a derivative by using “a differentiable particle filter.”). Such estimation/determination by a filter encompasses a mathematical concept, as suggested in paragraphs 225-227 and 253 of applicants’ specification. For example, paragraphs 225-227 and 253 of the specification, which state, inter alia, “Differentiable Particle Filter … In a particle sampler, particles are resampled with particles with high weight having proportionally higher chance to be selected”, “A similar effect may be achieved by retaining each particle independently with probability proportional to its weight. Again, a particle with zero weight is dropped from further computations. But an infinitesimal increment to the probability argument, such as h in a random variable X(h) ∼ Ber(h), has an infinitesimal (not negligible) probability of turning a zero weight positive.” and “systems and methods described herein may use a differentiable particle filter … particle filters can be used for Bayesian estimation.” further provide evidence that the claimed “determination of the derivative” using “a differentiable particle filter” is itself a mathematical concept.
Also, the limitation of “to accelerate the determination of the derivative of the expectation of the user-provided stochastic program” is intended use language with no patentable weight - aside from this recitation, no speed or acceleration of “the determination of the derivative of the expectation of the user-provided stochastic program” is recited elsewhere in the claims or any of their dependent claims (these claims have no dependent claims).
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claims do not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claims are subject-matter ineligible.
Step 2B: The claims do not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
These claims are not patent eligible.
Regarding claims 11 and 17, these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 11 is directed to a system as depending from claim 9 and claim 17 is directed to a method as depending from claim 15, thus the analysis for patent eligibilities of claims 9 and 15 are incorporated herein.
Step 2A Prong 1: See claims 9 and 15 above.
Step 2A Prong Two Analysis: The judicial exceptions are not integrated into a practical application.
The claims recite, using respective similar language, the additional elements: generating a composable data structure configured to propagate through the discrete and continuous sources of randomness without accruing bias, wherein the composable data structure is a stochastic dual or a stochastic triple.
These additional limitations do nothing to alter the fundamental nature of the claims as an abstract idea (mathematical concepts).
Dependent claims 11 and 17, when analyzed as a whole, are not patent eligible under 35 U.S.C. 111 because the additional recited additional limitations fail to establish that the claims are not directed to an abstract idea.
The above-noted “generating a composable data structure” limitation is an insignificant extra-solution activity that is not integrated into the claims as a whole and does not add a meaningful limitation to the above-noted abstract idea (mathematical concepts) specified in these claims. That is, “generating a composable data structure configured to propagate through the discrete and continuous sources of randomness without accruing bias1, wherein the composable data structure is a stochastic dual or a stochastic triple” amounts to necessary data outputting (See MPEP § 2106.05(g)).
Accordingly, these additional elements do not integrate the abstract idea into a practical application because they do not impose any meaningful limits on practicing the abstract idea. The claims are directed to an abstract idea.
Step 2B Analysis: The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception.
Receiving, transmitting, forwarding, and communicating data are insignificant extra-solution activities that are well-understood, routine, and conventional. See MPEP2106.05(d)(II) (“The courts have recognized the following computer functions 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. i. Receiving or transmitting data over a network, e.g., using the Internet to gather data, Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362 (utilizing an intermediary computer to forward information); … iv. Storing and retrieving information in memory”) (citing OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015)) (sending messages over a network); 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)". Therefore, recitations of “generating a composable data structure configured to propagate through the discrete and continuous sources of randomness without accruing bias, wherein the composable data structure is a stochastic dual or a stochastic triple” are the well-understood, routine, conventional activities of forwarding (propagating), communicating or transmitting data over a network, as discussed in MPEP § 2106.05(d).
These claims do not include additional elements that 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, there are no additional elements recited that impose any meaningful limits on practicing the abstract idea. Therefore, the additional elements of the claims are not sufficient to amount to significantly more than the abstract idea. These claims are not patent eligible.
Regarding claims 12 and 18, these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 12 is directed to a system as depending from claim 9 and claim 18 is directed to a method as depending from claim 15, thus the analysis for patent eligibilities of claims 9 and 15 are incorporated herein.
Step 2A Prong 1: The claims both recite: automatically augmenting an arbitrary stochastic program to return a stochastic derivative whose samples estimate the derivative of the stochastic program’s expectation2 with respect to the input3.
The additional limitations added by these claims cover a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – to augment or add to a program/instructions so that the program returns/outputs a stochastic derivative whose samples estimate the derivative of the stochastic program’s expectation/expected result/output with respect to input data values). Such a stochastic derivate calculation and derivative estimation are mathematical concepts, as suggested in paragraphs 39 and 48 of applicants’ specification.
For example, paragraphs 39 and 48 applicants’ specification, which state, inter alia, “automatically construct a stochastic program X̃(p) whose expectation satisfies E[X̃(p)] =
d
E
[
X
p
]
d
p
. This is derived by performing a “stochastic derivative” technique, which includes propagating the proportional probability of differing event outcomes due to infinitesimal changes in p.” and “The systems and methods described herein automatically augment an arbitrary stochastic program, besides the output, to also return a stochastic derivative, whose samples serve as an estimate of the derivative of the program’s expectation with respect to the input. This means:
∂
E
X
p
∂
p
≈
1
n
∑
i
=
1
n
∂
X
i
where ∂X(1),∂X(2), . . . ,∂X(n) denote samples of such a stochastic derivative, just as similar as samples of a stochastic gradient on average corresponds to the actual gradient.” further provide evidence that the claimed “automatically augmenting an arbitrary stochastic program to return a stochastic derivative whose samples estimate the derivative of the stochastic program’s expectation with respect to the input” are mathematical concepts.
Thus, these limitations do nothing to alter the fundamental nature of the claims as mathematical concepts.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claims do not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claims are subject-matter ineligible.
Step 2B: The claims do not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
These claims are not patent eligible.
Regarding claims 13 and 19, these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 13 is directed to a system as depending from claim 9 and claim 19 is directed to a method as depending from claim 15, thus the analysis for patent eligibilities of claims 9 and 15 are incorporated herein.
Step 2A Prong 1: The claims both recite: performing forward and backward automatic differentiation to automatically differentiate the user-provided stochastic program in expectation based on the input parameters.
Dependent claims 13 and 19, when analyzed as a whole, are not patent eligible under 35 U.S.C. 101 because the additional recited limitations fail to establish that the claims are not directed to an abstract idea. The additional limitations added by these claims cover a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – performing forward and backward differentiation to differentiate the user-provided stochastic program in expectation based on input parameters/data values). Such differentiation by forward and backward/reverse-mode automatic differentiation encompasses a mathematical concept, as suggested in paragraphs 33-34, 52, 77, 152, 154, 177, 179 and 230 of applicants’ specification. For example, paragraphs 33, 177 and 230 of the specification, which state, inter alia, “the systems and methods described herein also demonstrate various applications including, for example, unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway’s Game of Life, and unbiased reverse-mode AD of a particle filter.”, “The systems and methods described herein incorporate the notion of linking into stochastic derivatives. With this innovation included, an unbiased estimate for the derivative of an arbitrary stochastic program is computed via forward-mode AD.” and “Because of the similarity of smoothed stochastic dual numbers and standard dual numbers, reverse-mode AD can also be used instead of forward-mode AD. This is convenient, as eventually reverse-mode AD becomes superior than forward-mode AD for functions f: Rn 7→ Rm with m ≫ n.” further provide evidence that the claimed “performing forward and backward automatic differentiation to automatically differentiate the user-provided stochastic program in expectation based on the input parameters” are mathematical concepts.
Thus, these limitations do nothing to alter the fundamental nature of the claims as mathematical concepts.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claims do not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claims are subject-matter ineligible.
Step 2B: The claims do not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
These claims are not patent eligible.
Regarding claims 14 and 20, these claims are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Step 1 Analysis: Claim 14 is directed to a system as depending from claim 9 and claim 20 is directed to a method as depending from claim 15, thus the analysis for patent eligibilities of claims 9 and 15 are incorporated herein.
Step 2A Prong 1: The claims both recite: determining conditional expectations of pathwise derivatives.
Dependent claims 14 and 20, when analyzed as a whole, are not patent eligible under 35 U.S.C. 101 because the additional recited limitations fail to establish that the claims are not directed to an abstract idea. The additional limitations added by these claims cover a mathematical concept (i.e., mathematical relationships, mathematical formulas or equations, and mathematical calculations – determining conditional expectations of pathwise derivatives). Such determination/calculation of conditional expectations of pathwise derivatives encompasses a mathematical concept, as suggested in paragraphs 77, 91, 95 and 126 of applicants’ specification. For example, paragraphs 77, 91, 95 and 126 of the specification, which state, inter alia, “Taking conditional expectations of pathwise derivatives enables the extension of forward and backward automatic differentiation to make stochastic programs automatically differentiable in expectation with respect to their parameters with minimal adaptions. The local smoothing properties of conditional expectations allows differentiating pathwise through important discrete stochastic transitions, such as the resampling step of a particle filter.”, “To motivate primal-conditioned derivatives, the classical quantities
∂
E
X
p
∂
p
a
n
d
∂
∂
p
X
p
can both be expressed as conditional expectations
∂
p
±
|
F
X
p
∶
=
∂
∂
p
±
E
X
p
|
F
for different choices of the σ-algebra F. Here, ∂p+|F and ∂p−|F are defined to represent right-sided and left-sided conditionally expected derivative operators.”, “By the tower property of conditional expectation, if δ + w(Y − X(p)) is an unbiased estimate of ∂pE[X(p)], then so is the random number δ̃ = E[δ + w(Y − X(p)) | X(p)]. If the function f is approximately linear in X(p) over the range of X(p) + Y , even ∂pEf(X(p)) ≈ Ef ′ (X(p))δ̃.” and “To perform forward differentiation, a stochastic dual with value p and infinitesimal part 1 are inputted into the program. After the stochastic dual propagates through the full program, the δ and ∆s components are collapsed into their expectation to form the derivative estimate. Thus, unbiasedness follows by the tower property of conditional expectations, E[E[dX| FX]] = E[dX], and thus stochastic duals produce unbiased derivative estimates.” further provide evidence that the claimed “determining conditional expectations of pathwise derivatives” are mathematical concepts.
Thus, these limitations do nothing to alter the fundamental nature of the claims as mathematical concepts.
Step 2A Prong Two: The judicial exceptions are not integrated into a practical application.
The claims do not recite any additional elements that integrate the abstract idea into a practical application or provide significantly more than the abstract idea, and thus the claims are subject-matter ineligible.
Step 2B: The claims do not recite additional elements that are sufficient to amount to significantly more than the judicial exception.
These claims are not patent eligible.
Conclusion
The prior art made of record, listed on form PTO-892, and not relied upon, is considered pertinent to applicant's disclosure.
The references listed on form PTO-892 are all generally related to automated/automatic and algorithmic differentiation techniques, methods and systems using stochastic derivatives and techniques such as stochastic gradient descent.
For example, non-patent literature Oktay, Deniz, et al. (“"Randomized automatic differentiation." arXiv preprint arXiv:2007.10412 v2 (2021) hereinafter “Oktay”) discloses “a general framework and approach for randomized automatic differentiation (RAD), which can allow unbiased gradient estimates to be computed with reduced memory in return for variance.” and “RAD can be applied to scientific computing, and use it to develop a low-memory stochastic gradient method for optimizing the control parameters” (see, e.g., Abstract).
FIG. 1 of Oktay depicts a “Primal graph” as part of linearized computational graphs including “(a) a simple Python function with intermediate variables; (b) the primal computational graph, a DAG with variables as vertices and flow moving upwards to the output; (c) the linearized computational graph (LCG) in which the edges are labeled with the values of the local derivative”.
Oktay also discloses that “we replace deterministic AD with randomized automatic differentiation (RAD), trading off of computation for variance inside AD routines when imprecise gradient estimates are tolerable, while retaining unbiasedness.” and “Automatic (or algorithmic) differentiation is a family of techniques for taking a program that computes a differentiable function f : Rn [Wingdings font/0xE0] Rm, and producing another program that computes the associated derivatives” (see, page 2, Sects. 1-2).
Also, for example, non-patent literature Ruzayqat, Hamza, et al. (“Unbiased Estimation using a Class of Diffusion Processes." arXiv preprint arXiv:2203.03013 v1 (March 2022), hereinafter “Ruzayqat”) discloses that “We study the problem of unbiased estimation of expectations with respect to (w.r.t.)
π
a given, general probability measure on (Rd; B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure.” (see, e.g., Abstract).
Further, for example, non-patent literature Ketkar et al. ("Automatic differentiation in deep learning." Deep Learning with python: learn best practices of deep learning models with PyTorch. Berkeley, CA: Apress, 2021. 133-145 hereinafter “Ketkar”) discloses that “The first key intuition behind automatic differentiation is that all functions of interest (which we intend to differentiate) can be expressed as compositions of elementary functions for which corresponding derivative functions are known. Composite functions thus can be differentiated by applying the chain rule for derivatives. This intuition is also at the basis of symbolic differentiation. The second key intuition behind automatic differentiation is that rather than storing and manipulating intermediate symbolic forms of derivatives of primitive functions, we can simply evaluate them (for a specific set of input values) and thus address the issue of expression swell.” (see, e.g., page 137).
The examiner requests, in response to this office action, support be shown for language added to any original claims on amendment and any new claims. That is, indicate support for newly added claim language by specifically pointing to page(s) and line no(s) in the specification and/or drawing figure(s). This will assist the examiner in prosecuting the application.
When responding to this office action, Applicant is advised to clearly point out the patentable novelty which he or she thinks the claims present, in view of the state of the art disclosed by the reference cited or the objections made. He or she must also show how the amendments avoid such references or objections See 37 CFR 1.111 (c).
Any inquiry concerning this communication or earlier communications from the examiner should be directed to RANDY K BALDWIN whose telephone number is (571)270-5222. The examiner can normally be reached on Mon - Fri 9:00-6:00.
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If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Kamran Afshar can be reached at (571) 272-7796. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
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/RANDALL K. BALDWIN/Primary Examiner, Art Unit 2125
1 Also, the limitation includes intended use language with no patentable weight (e.g., “without accruing bias”).
2 As indicated in the section 112(b) rejections of these claims above, “the stochastic program’s expectation” has been interpreted as an expectation, an expected output or an expected result of either of the previously-introduced “user-provided stochastic program” or an expectation, an expected output or an expected result of the previously-introduced “arbitrary stochastic program”
3 As indicated in the section 112(b) rejections of these claims above, recitations of “the input” in these claims have been interpreted as any input data or values, including, but not limited to, some or all of the previously-introduced “input parameters”.
Prosecution Insights