DETAILED ACTION
1. The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
2. Applicant’s submission filed 04 May 2026 [hereinafter Response], where:
Claims 5, 9, and 16 have been amended.
Claims 1-20 are pending.
Claims 1-20 are rejected.
Claim Rejections – 35 U.S.C. § 112
3. 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.
4. The rejection to claims 5-7, 9, and 16-18 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point out and distinctly claim the subject matter which the inventor or a joint inventor regards as the invention is WITHDRAWN in view of the Applicant’s amendments to the claims.
Claim Rejections - 35 U.S.C. § 101
5. 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.
6. Claims 1-20 are rejected under 35 U.S.C. § 101 because the claimed invention is directed to an abstract idea without significantly more.
Claim 1 recites a device or system, which is a product, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101).
However, under Step 2A Prong One, the claim recites the limitations of “providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein,” “encoding the tensor into a tensor network in the form of a matrix product state,” and “computing at least one moment of the probability distribution by processing the tensor network for sampling of the probability distribution.” The limitations of “. . . a tensor codifying,” “encoding,” and “computing at least one moment,” contain activities that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groups of abstract ideas. (MPEP § 2106.04(a)(2)). Also, because “tensor networks” are mathematical frameworks that represents high-dimensional, correlated data as a network of smaller, interconnected “tensors.” “Tensors” are mathematical objects generalizing scalars, vectors, and matrices into a multilinear object, and accordingly, are mathematical concepts, (MPEP § 2106.04(a)(2) sub I), and is one of the groups of abstract ideas. The claim recites more details or specifics to the abstract idea of “providing a tensor codifying,” where “where all probabilities are greater than or equal to zero and a sum of all probabilities is equal to one,” and accordingly, is merely more specific to the abstract idea. Therefore, claim 1 is directed to an abstract idea.
Under Step 2A Prong Two, the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified abstract idea include “at least one processor,” “at least one memory comprising computer program code for one or more programs,” which are generic computer components using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is an pre-processing insignificant extra-solution activity of mere data gathering, (MPEP § 2106.05(g)), that does not serve to integrate the abstract idea into a practical application. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not serve to integrate the abstract idea into a practical application. Therefore, claim 1 is directed to the abstract idea.
Finally, under Step 2B, the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include “at least one processor,” “at least one memory comprising computer program code for one or more programs,” which are generic computer components using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is a well-understood, routine, and conventional activity of retrieving information in memory, (MPEP § 2106.05(d) sub II.iv), which does not amount to significantly more than the abstract idea. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not amount to significantly more than the abstract idea. Therefore, claim 1 is subject-matter ineligible.
Claim 12 recites a computer-implemented method, which is a process, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101).
However, under Step 2A Prong One, the claim recites the limitations of “providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein,” “encoding the tensor into a tensor network in the form of a matrix product state,” and “computing at least one moment of the probability distribution by processing the tensor network for sampling of the probability distribution.” The limitations of “. . . a tensor codifying,” “encoding,” and “computing at least one moment,” contain activities that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groups of abstract ideas. (MPEP § 2106.04(a)(2)). Also, because “tensor networks” are mathematical frameworks that represents high-dimensional, correlated data as a network of smaller, interconnected “tensors.” “Tensors” are mathematical objects generalizing scalars, vectors, and matrices into a multilinear object, and accordingly, are mathematical concepts, (MPEP § 2106.04(a)(2) sub I), and is one of the groups of abstract ideas. The claim recites more details or specifics to the abstract idea of “providing a tensor codifying,” where “where all probabilities are greater than or equal to zero and a sum of all probabilities is equal to one,” and accordingly, is merely more specific to the abstract idea. Therefore, claim 1 is directed to an abstract idea.
Under Step 2A Prong Two, the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified abstract idea include a “computer-implemented method,” which is a generic computer component using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is an pre-processing insignificant extra-solution activity of mere data gathering, (MPEP § 2106.05(g)), that does not serve to integrate the abstract idea into a practical application. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables about a target,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not serve to integrate the abstract idea into a practical application. Therefore, claim 12 is directed to the abstract idea.
Finally, under Step 2B, the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include “computer-implemented method,” which are generic computer components using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is a well-understood, routine, and conventional activity of retrieving information in memory, (MPEP § 2106.05(d) sub II.iv), which does not amount to significantly more than the abstract idea. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not amount to significantly more than the abstract idea. Therefore, claim 12 is subject-matter ineligible.
Claim 20 recites a non-transitory computer-readable medium, which is a product, and thus one of the statutory categories of patentable subject matter. (35 U.S.C. § 101).
However, under Step 2A Prong One, the claim recites the limitations of “providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein,” “encoding the tensor into a tensor network in the form of a matrix product state,” and “computing at least one moment of the probability distribution by processing the tensor network for sampling of the probability distribution.” The limitations of “. . . a tensor codifying,” “encoding,” and “computing at least one moment,” contain activities that can practically be performed in the human mind, including, for example, observations, evaluations, judgments, and opinions, and accordingly, are a mental process, (MPEP § 2106.04(a)(2) sub III), which is one of the groups of abstract ideas. (MPEP § 2106.04(a)(2)). Also, because “tensor networks” are mathematical frameworks that represents high-dimensional, correlated data as a network of smaller, interconnected “tensors.” “Tensors” are mathematical objects generalizing scalars, vectors, and matrices into a multilinear object, and accordingly, are mathematical concepts, (MPEP § 2106.04(a)(2) sub I), and is one of the groups of abstract ideas. The claim recites more details or specifics to the abstract idea of “providing a tensor codifying,” where “where all probabilities are greater than or equal to zero and a sum of all probabilities is equal to one,” and accordingly, is merely more specific to the abstract idea. Therefore, claim 20 is directed to an abstract idea.
Under Step 2A Prong Two, the claim as a whole is not integrated into a practical application, because the additional elements recited in the claim beyond the identified abstract idea include a “non-transitory computer-readable medium encoded with instructions that, when executed by at least one processor or hardware, perform or make a device,” which is a generic computer component using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is an pre-processing insignificant extra-solution activity of mere data gathering, (MPEP § 2106.05(g)), that does not serve to integrate the abstract idea into a practical application. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not serve to integrate the abstract idea into a practical application. Therefore, claim 20 is directed to the abstract idea.
Finally, under Step 2B, the additional elements, taken alone or in combination, do not represent significantly more than the abstract idea itself. The additional elements include “non-transitory computer-readable medium encoded with instructions that, when executed by at least one processor or hardware, perform or make a device,” which are generic computer components using instructions to cause a system to implement the abstract idea, (MPEP § 2106.05(f)), that does not amount to significantly more than the abstract idea. The claim also recites the limitation of “receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target,” which is a well-understood, routine, and conventional activity of retrieving information in memory, (MPEP § 2106.05(d) sub II.iv), which does not amount to significantly more than the abstract idea. The claim also recites more details or specifics of the additional element of “receiving,” where “the probability distribution relating to a plurality of discrete random variables,” and accordingly, is merely more specific to the additional element. Further, that the “probability distribution . . . is about a target” is generally linking the use of the judicial exception to a particular technological environment or field of use (MPEP § 2106.05(h)), that does not amount to significantly more than the abstract idea. Therefore, claim 12 is subject-matter ineligible.
Claim 2 depends from claim 1. Claim 13 depends from claim 12. The claims further recite “at least carry out the following: providing a predetermined command at least based on the computed at least one moment.” The activity of “providing a predetermined command” is a post-processing insignificant extra-solution of transmitting data, (MPEP § 2106.05(f)), that does not serve to integrate the abstract idea into a practical application. Also, the activity of “providing a predetermined command” is a well-understood, routine, and conventional activity of transmitting a command over a network, (MPEP § 2106.05(d) sub II.i), that does not amount to significantly more than the abstract idea. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Therefore, claims 2 and 13 are subject-matter ineligible.
Claim 3 depends directly or indirectly from claim 1. Claim 14 depends directly or indirectly from claim 12. The claims recite more details or specifics to the additional element of “providing a predetermined command” where “wherein the predetermined command comprises one or both of: providing a notification indicative of the computed at least one moment to an electronic device; and providing a command to a controlling device or system associated with the target or to the target itself when the target is either a machine or a system, the predetermined command being for changing a behavior of the target,” and accordingly, are merely more specific to the additional element. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Therefore, claims 3 and 14 are subject-matter ineligible.
Claim 4, 5, and 8 depend directly or indirectly from claim 1. Claims 15, 16, and 19 depend directly or indirectly from claim 12. The claims recite more details or specifics to the abstract idea of “encoding the tensor,” (claims 4 and 15: “wherein encoding the tensor into the tensor network comprises factorizing the tensor into the tensors of the tensor network by processing the tensor so that the following equation is solved:
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where P is the resulting normalized factorization into the tensors of the tensor network, T is the encoded tensor, and ZT is a predetermined normalization factor ZT=ΣX1, . . . , xN TX 1 , . . . , xN, with X1, . . . , XN being respective N configurations of the plurality of discrete random variables of the probability distribution, TX 1 , . . . , xN being the tensor for the respective configuration,” and N being the number of discrete random variables in the plurality of discrete random variables”) and (claims 5 and 16: “wherein encoding the tensor into the tensor network further comprises minimizing the following negative log-likelihood function for each sample xi of a discrete multivariate distribution:
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where each sample xi has values for each of the discrete random variables, and TXi is the tensor for the sample xi”), and (claims 8 and 19: “wherein encoding the tensor into the tensor network further comprises compressing a probability mass function into a tensor that is not negative, and minimizing the following Kullback-Leibler divergence equation:
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where PX 1 , . . . , xN is a probability mass function corresponding to the probability distribution”), and accordingly, are merely more specific to the abstract idea. Therefore, claims 4, 5, 8, 15, 16, and 19 are subject-matter ineligible.
Claim 6 depends directly or indirectly from claim 1. Claim 17 depends directly or indirectly from claim 12. The claims recite more details or specifics to the abstract idea of “encoding the tensor,” “wherein the minimization of the negative log-likelihood function for each sample xi is calculated with local gradient-descent in which the gradient of the function is computed for all tensors of the tensor network,” and accordingly, are merely more specific to the abstract idea. Therefore, claims 6 and 17 are subject-matter ineligible.
Claim 7 depends directly or indirectly from claim 1. Claim 18 depends directly or indirectly from claim 12. The claims recite more details or specifics to the abstract idea of “encoding the tensor,” “wherein values of the tensors of the tensor network are modified iteratively to approximate the probability distribution therein,” and accordingly, are merely more specific to the abstract idea. Therefore, claims 6 and 17 are subject-matter ineligible.
Claims 9 and 10 depend directly or indirectly from claim 1. The claims recite more details or specifics to the abstract idea of “computing at least one moment,” (claim 9: “wherein computing the at least one moment comprises computing any one of the first, second, third and fourth moments of the probability distribution by processing the tensor network; claim 10: “wherein computing the at least one moment comprises computing a contraction of the tensor network”), and accordingly, are merely more specific to the abstract idea. Therefore, claims 9 and 10 are subject-matter ineligible.
Claim 11 depends from claim 1. The claim recites more details or specifics to the additional element of “receiving data,” “wherein the target comprises: an electrical grid, an electricity network, a portfolio of financial derivatives, a stock market, a set of patients of a hospital unit, or a system comprising one of: one or more devices, one or more machines, or a combination thereof,” and accordingly, is merely more specific to the additional element. The abstract idea of these claims are not integrated into a practical application, (see MPEP § 2106.04(d)), nor do they amount to significantly more than the abstract idea, (MPEP § 2106.05 sub I; see also MPEP § 2106.05(a) – (h)), because the claims recite no more than the abstract idea. Therefore, claim 11 is subject-matter ineligible.
Claim Rejections – 35 U.S.C. § 102
7. The following is a quotation of the appropriate paragraphs of 35 U.S.C. § 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
(a)(2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention.
8. Claims 1-3, 9, 10, 12-14, and 20 are rejected under 35 U.S.C. § 102(a)(1) as being anticipated by Gillman et al., "A Tensor Network Approach to Finite Markov Decision Processes," arXiv (2020) [hereinafter Gillman].
Regarding claims 1, 12, and 20, Gillman teaches [a] device or system (Gillman, left column of p. 2, “2.1. Finite Markov Decision Processes,” first paragraph, teaches “the state of the system is a terminal state [(that is, a device or system)]”) of claim 1, [a] computer-implemented method (Gillman, right column of p. 1, “1. Introduction,” second paragraph, teaches “[g]iven the nature of the problems tackled by TNs in physics, it is natural to consider them for machine learning problems [(that is, “machine learning problems” are inherently a computer-implemented method)]”) of claim 12, and [a] non-transitory computer-readable medium encoded with instructions that, when executed by at least one processor or hardware (Gillman, right column of p. 1, “1. Introduction,” second paragraph, teaches “[g]iven the nature of the problems tackled by TNs in physics, it is natural to consider them for machine learning problems [(that is, “machine learning problems” inherently includes a non-transitory computer-readable medium encoded with instructions, when executed by at least one processor or hardware )]”) of claim 20, comprising:
at least one processor; and at least one memory comprising computer program code for one or more programs; the at least one processor, the at least one memory, and the computer program code (Gillman, right column of p. 1, “1. Introduction,” second paragraph, teaches “[g]iven the nature of the problems tackled by TNs in physics, it is natural to consider them for machine learning problems [(that is, “machine learning problems” inherently includes the at least one processor, the at least one memory, and the computer program code)]”) being configured to cause the device or system (Gillman, left column of p. 2, “2.1. Finite Markov Decision Processes,” first paragraph, teaches “the state of the system is a terminal state [(that is, a device or system)]”) to at least carry out the following:
receiving data including a probability distribution of a dataset or a multivariate probability distribution about a target (Gillman, Abstract, teaches “[a]s an application [of a general tensor network formulation of finite, episodic and discrete Markov decision processes (MDPs),] we consider the issue - formulated as an RL problem - of finding a stochastic evolution that satisfies specific dynamical conditions [(that is, a probability distribution of a dataset . . . about a target)], using the simple example of random walk excursions as an illustration”; Gillman, left column of p. 3, “2.2 Tensor Networks for Hidden Markov Models,” first paragraph, teaches “[a]s suggested by the chosen notation, Eq. (11) [(that is, since the matrices are rank-2 tensors and the vector a rank-1 tensor, this can be considered a TN consisting of T + 1 tensors, where the contraction pattern is given by the usual matrix products. Performing such a contraction produces a new vector,
|
p
T
, with components,
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where
|
p
0
=
∑
s
c
s
|
s
for some coefficients cs and the vectors
|
s
associated to each state s form a basis of a vector space VS),] is exactly the [tensor network representation (TNR)] for a probability distribution over states produced by a Markovian dynamics [(that is, receiving data including a probability distribution of a dataset)]. In that case, the components of Mt are equal to the probabilities of state transitions,
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while the components of
|
p
0
give the initial probabilities distribution over states [(that is, receiving data including a probability distribution of a dataset)]”; Gillman, right column of p. 1, “1. Introduction,” second paragraph, teaches “using the formalism of Markov decision processes (MDPs), consisting of repeated updates according to an agent’s decision making policy and the dynamics of an environment it inhabits [(that is, “dynamics of an environment” is receiving data including a probability distribution of a dataset . . . about a target)]”;
[Examiner notes that the plain meaning of term “target” pertains to an environment in which the system is deployed, and accordingly, the broadest reasonable interpretation of the term “target” covers the teachings of Gillman, which is not inconsistent with the Applicant’s disclosure. (MPEP § 2111.01).]),
the probability distribution relating to a plurality of discrete random variables (Gillman, left column of p. 2, “2.1 Finite Markov Decisions Processes,” first paragraph, teaches “[i]n a discrete-time, episodic, MDP, individual trajectories take the form,
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where St; At and Rt are random variables for the state, action and reward, taking values st, at, and rt respectively [(that is, the probability distribution relating to a plurality of discrete random variables)]”);
providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein (Gillman, right column of p. 2, “2.2 Tensor Networks for Hidden Markov Models,” second paragraph, teaches in a diagrammatic notation, “rank-K tensors are represented as shapes with K legs, and contractions are indicated by joining the appropriate legs together. In this notation, Eq. (11) for T = 3 [(that is, each “termination time T” is each configuration of the plurality of discrete random variables)] reads,
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As suggested by the chosen notation, Eq. (11) is exactly the TNR for a probability distribution over states produced by a Markovian dynamics. In that case, the components of Mt are equal to the probabilities of state transitions,
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while the components of
|
p
0
give the initial probability distribution over states”; moreover, Gillman, left column of p. 3, “2.2 Tensor Networks for Hidden Markov Models,” fourth paragraph, teaches “[t]aking tensor products of these vectors produces an encoding [(that is, codifying)] for the possible observations over time,
|
r
, which form a basis of the vector space
V
R
T
=
⊗
t
=
1
T
V
R
. The vectors representing the probability distributions over observations are elements of this space,
|
p
r
∈
V
R
T
[(that is, providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein)], and obey the normalization
-
r
p
r
=
1
),
where all probabilities are greater than or equal to zero and a sum of all probabilities is equal to one (Gillman, left column of p. 3, “2.2 Tensor Networks for Hidden Markov Models,” first paragraph, teaches “Any vector
|
p
t
∈
V
S
, that is a convex combination of the particular basis
|
s
, can be interpreted as a probability distribution over states via their components
s
p
t
=
p
t
s
. This implies their normalization as
-
s
p
t
=
1
, where
-
s
|
is the flat-vector for the basis,
-
s
|
=
∑
s
s
|
”) [(that is, “normalization” is where all probabilities are greater than or equal to zero)]”;
[Examiner notes the plain meaning of the term “greater than or equal to zero and a sum of all probabilities is equal to one” is that of a normalized data where data values are transformed to a specific range, such as 0 to 1, based on the minimum and maximum values in the dataset, and accordingly, the broadest reasonable interpretation of “greater than or equal to zero and a sum of all probabilities is equal to one” covers the teachings of Gillman, which is not inconsistent with the Applicant’s disclosure. (MPEP § 2111.01)];
encoding the tensor into a tensor network in the form of a matrix product state (Gillman, left column of p. 3, “2.2 Tensor Networks for Hidden Markov Models,” second paragraph, teaches “[a] more complicated [tensor network representation (TNR)] relevant for dynamics is offered by the matrix product state (MPS) representation [(that is, encoding the tensor into a tensor network in the form of a matrix product state)] - also known as the tensor train decomposition (Oseledets, 2011) – of HMMs”),
where an external index of each tensor of the tensor network represents one discrete random variable of the plurality discrete random variables, and an internal index or internal indices of each tensor of the tensor network represents correlation between the tensor and the corresponding adjacent tensor of the tensor network (Specification at p. 2, lines 20-23, teaches “[a]s known in the art, the tensors of an [matrix product state (MPS)] have an external index, and one or two internal indices, depending on whether the tensor is at an end of the MPS or not. The external index, also referred to as physical dimension, of each tensor is representative of a respective discrete random variable, hence the MPS has as many tensors as discrete random variables are in the probability distribution. Further, the internal index or indices, also referred to as virtual dimension or dimensions, are representative of the correlation between adjacent tensors;
[Examiner notes that, in view of Applicant’s disclosure, the term “matrix product state” inherently includes “an external index” and “an internal index or internal indices”]); and
computing at least one moment of the probability distribution (Gillman, right column of p. 3, “2.3 Tensor Networks for Time Integrated Observables,” first paragraph, teaches that “[w]hen considering dynamics described by an [Hidden Markov Model (HMM)], one is often interested in time integrated observables. Such objects can be represented easily in terms of [tensor networks (TNs)], which in turn allows for the [tensor network representation (TNR)] of averages or higher-order moments [(that is, computing at least one moment of the probability distribution)]”).
[Examiner notes that the Specification at p. 2, lines 28-29, teaches “[b]y operating the tensor network as known in the art, different data can be sampled from the probability distribution since it is encoded in the tensor network itself [(that is, processing the tensor network for sampling of the probability distribution)]”).
Regarding claims 2 and 13, Gillman teaches all of the limitations of claims 1 and 12, respectively, as described above in detail.
Gillman teaches -
wherein the at least one processor, the at least one memory, and the computer program code are configured to further cause the device or system to
at least carry out the following: providing a predetermined command at least based on the computed at least one moment (Gillman, left column of p. 7, “5.1 Conditioned Dynamics and FMDPs,” first & second paragraphs, teaches that “[a]n elementary example of rare events are \stochastic excursions’ (Majumdar & Orland, 2015), where a simple random walker is conditioned to stay above a certain line and at a given time must return to this line. . . . For an episode with fixed termination time, T, the positions of the random walker are encoded in S={-T, . . . , -1, 0, 1, +T} such that |S| = 2T+1. The action space is Α = {0; 1}, where a = 0, 1 [(that is, “action a = 0, 1” is at least carry out the following: providing a predetermined command at least based on the computer at least one moment)] correspond to a down/up move of the walker, respectively”).
Regarding claims 3 and 14, Gillman teaches all of the limitations of claims 2 and 13, respectively, as described above in detail.
Gillman teaches -
wherein the predetermined command comprises one or both of:
providing a notification indicative of the computed at least one moment to an electronic device; and
providing a command to a controlling device or system associated with the target or to the target itself when the target is either a machine or a system, the predetermined command being for changing a behavior of the target (Gillman, left column of p. 7, “5.1 Conditioned Dynamics and FMDPs,” first & second paragraphs, teaches that “[a]n elementary example of rare events are \stochastic excursions’ (Majumdar & Orland, 2015), where a simple random walker is conditioned to stay above a certain line and at a given time must return to this line. . . . For an episode with fixed termination time, T, the positions of the random walker are encoded in S={-T, . . . , -1, 0, 1, +T} such that |S| = 2T+1. The action space is Α = {0; 1}, where a = 0, 1 [(that is, “action a = 0, 1” is providing a command to a controlling device or system associated with the target itself)] correspond to a down/up move of the walker, respectively [(that is, “the down/up move of the walker” is the predetermined command being for changing a behavior of the target)]”).
Regarding claim 9, Gillman teaches all of the limitations of claim 1, as described above in detail.
Gillman teaches -
wherein computing the at least one moment comprises
computing any one of the first, second, third and fourth moments of the probability distribution by processing the tensor network (Gillman, right column of p. 3, “2.3 Tensor Networks for Time Integrated Observables,” first paragraph, teaches “When considering dynamics described by an HMM, one is often interested in time integrated observables. Such objects can be represented easily in terms of TNs, which in turn allows for the TNR of averages or higher-order moments”).
Regarding claim 10, Gillman teaches all of the limitations of claim 1, as described above in detail.
Gillman teaches -
wherein computing the at least one moment comprises
computing a contraction of the tensor network (Gillman, right column of p. 2, “2.2. Tensor Networks for Hidden Markov Models,” first paragraph, teaches “A TN is a collection of tensors contracted together in a given pattern, typically specified by a graph. . . . Since the matrices are rank-2 tensors and the vector a rank-1 tensor, this can be considered a [tensor network (TN)] consisting of T + 1 tensors, where the contraction pattern is given by the usual matrix products. Performing such a contraction produces a new vector,
|
P
T
[(that is, computing a contraction of the tensor network )]”).
Claim Rejections – 35 U.S.C. § 103
9. The following is a quotation of 35 U.S.C. § 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
10. The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. § 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
11. This application currently names joint inventors. In considering patentability of the claims the Examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the Examiner to consider the applicability of 35 U.S.C. § 102(b)(2)(C) for any potential 35 U.S.C. § 102(a)(2) prior art against the later invention.
12. Claims 4-8 and 15-19 are rejected under 35 U.S.C. § 103 as being unpatentable over Gillman et al., "A Tensor Network Approach to Finite Markov Decision Processes," arXiv (2020) [hereinafter Gillman] in view of Glasser et al., “Expressive power of tensor-network factorizations for probabilistic modeling,” arXiv (2019) [hereinafter Glasser].
Regarding claims 4 and 15, Gillman teaches all of the limitations of claims 1 and 12, respectively, as described above in detail.
Though Gillman teaches a tensor network representation for dynamics of a matrix product state (MPS) representation (also known as the tensor train decomposition), Gillman, however, does not explicitly teach -
wherein encoding the tensor into the tensor network comprises
factorizing the tensor into the tensors of the tensor network by processing the tensor so that the following equation is solved:
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where P is the resulting normalized factorization into the tensors of the tensor network, T is the encoded tensor, and ZT is a predetermined normalization factor ZT=ΣX1, . . . , xN TX 1 , . . . , xN, with X1, . . . , XN being respective N configurations of the plurality of discrete random variables of the probability distribution, TX 1 , . . . , xN being the tensor for the respective configuration, and N being the number of discrete random variables in the plurality of discrete random variables
But Glasser teaches -
wherein encoding the tensor into the tensor network comprises
factorizing the tensor into the tensors of the tensor network by processing the tensor so that the following equation is solved:
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where P is the resulting normalized factorization into the tensors of the tensor network, T is the encoded tensor, and ZT is a predetermined normalization factor ZT=ΣX1, . . . , xN TX 1 , . . . , xN, with X1, . . . , XN being respective N configurations of the plurality of discrete random variables of the probability distribution, TX 1 , . . . , xN being the tensor for the respective configuration, and N being the number of discrete random variables in the plurality of discrete random variables (Glasser at p. 2, “2. Tensor-Network Models of Probability Distributions,” second paragraph, teaches “we are interested in the case where N is large. Since the number of elements of this tensor scales exponentially with N, it is quickly impossible to store. In cases where there is some structure to the variables, one may use a compact representation of P which exploits this structure, such as Bayesian networks or Markov random fields [p(that is, discrete random variables of the probability distribution)] defined on a graph. In the following we consider models, known as tensor networks, in which a tensor T [(that is, the encoded tensor)] is factorized into the contraction of multiple smaller tensors. As long as T is non-negative, one can model P as P = T/ZT [(that is, factorizing the tensor into the tensors of the tensor network by processing the tensor so that the following equation is solved: P=T/ZT)], where ZT = ∑ X1,.,XN TX1,.,XN is a normalization factor”).
Gillman and Glasser are from the same or similar field of endeavor. Gillman teaches a general tensor network formulation of finite, episodic and discrete Markov decision processes. Glasser teaches various tensor-network factorizations of discrete multivariate probability distributions, these factorizations including non-negative tensor-trains/MPS, which are in correspondence with hidden Markov models used to model probability distributions.
Thus, it would have been obvious to a person having ordinary skill in the art to modify Gillman pertaining to tensor network representation for dynamics of a matrix product state (MPS) representation with the tensor network factorizations of Glasser.
The motivation to do so is because “results indicate that despite rather small differences between HMM and non-negative MPS on the training set, the differences on the test set are important and non-negative MPS are able to reach a better accuracy at larger ranks.” (Glasser at p. 28, “3.3 Generalization Performance,” first paragraph).
Regarding claims 5 and 16, the combination of Gillman and Glasser teaches all of the limitations of claims 4 and 15, respectively, as described above in detail.
Glasser teaches –
wherein encoding the tensor into the tensor network further comprises
minimizing the following negative log-likelihood function for each sample xi of a discrete multivariate distribution:
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where each sample xi has values for each of the discrete random variables, and TXi is the tensor for the sample xi (Glasser at p. 8, “5. Learning Algorithm,” second paragraph, teaches “given samples {xi = (Xi1 , . . . ,XiN)} from a discrete multivariate distribution, they can be trained to approximate this distribution through maximum likelihood estimation. Specifically, this can be done by minimizing the negative log-likelihood,
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where i indexes training samples and Txi is given by the contraction of one of the tensor-network models we have introduced [(that is, minimizing the following negative log-likelihood function for each sample xi of a discrete multivariate distribution)]”).
Regarding claims 6 and 17, the combination of Gillman and Glasser teaches all of the limitations of claims 5 and 16, respectively, as described above in detail.
Glasser teaches -
wherein the minimization of the negative log-likelihood function for each sample xi is calculated with local gradient-descent in which the gradient of the function is computed for all tensors of the tensor network (Glasser at p. 8, “5. Learning Algorithm,” second paragraph, teaches “[t]he negative log-likelihood can be minimized using a mini-batch gradient-descent algorithm [(that is, “mini-batch” is wherein the minimization . . . is calculated with local gradient-descent)]. At each step of the optimization, the sum is computed over a batch of training instances [(that is, as noted above, “i indexes training samples,” where the gradient of the function is computed for all tensors of the tensor network )]”).
Regarding claims 7 and 18, the combination of Gillman and Glasser teaches all of the limitations of claims 6 and 17, respectively, as described above in detail.
Glasser teaches -
wherein values of the tensors of the tensor network are modified iteratively to approximate the probability distribution therein (Glasser at p. 8, “5. Learning Algorithm,” second paragraph, teaches “[t]he negative log-likelihood can be minimized using a mini-batch gradient-descent algorithm. At each step of the optimization, the sum is computed over a batch of training instances. The parameters in the tensor network are then updated by a small step [(that is, “updated” is values of the tensors of the tensor network are modified iteratively to approximate the probability distribution therein)] in the inverse direction of the gradient”).
Regarding claims 8 and 19, the combination of Gillman and Glasser teaches all of the limitations of claims 4 and 15, respectively, as described above in detail.
Glasser teaches -
wherein encoding the tensor into the tensor network further comprises
compressing a probability mass function into a tensor that is not negative, and minimizing the following Kullback-Leibler divergence equation:
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where PX 1 , . . . , xN is a probability mass function corresponding to the probability distribution (Glasser at p. 9, “5. Learning Algorithms,” fourth paragraph, teaches “Instead of approximating a distribution from samples, it might also be useful to compress a probability mass function P given in the form of a non-negative tensor [(that is, compressing a probability mass function into a tensor that is not negative)]. Since the original probability mass function has a number of parameters that is exponential in N, this is only possible for a small number of variables. It can be done by minimizing the Kullback–Leibler (KL) divergence
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where T is represented by a tensor-network model. The gradient of the KL-divergence can be obtained in the same way as the gradient of the log-likelihood and gradient-based optimization algorithms can then be used to solve this optimization problem [(that is, compressing a probability mass function into a tensor that is not negative and minimizing the following Kullback-Leibler divergence equation)]”).
13. Claim 11 is rejected under 35 U.S.C. § 103 as being unpatentable over Gillman et al., "A Tensor Network Approach to Finite Markov Decision Processes," arXiv (2020) [hereinafter Gillman] in view of US Published Application 20210398621 to Stojevic et al. [hereinafter Stojevic].
Regarding claim 11, the combination of Gillman teaches all of the limitations of claims 1 and 12, respectively, as described above in detail.
Though Gillman teaches a probability distribution over states produced by a Markovian dynamics from an environment, Gillman, however, does not explicitly teach -
[(a.2)] wherein the target comprises: an electrical grid, an electricity network, a portfolio of financial derivatives, a stock market, a set of patients of a hospital unit, or a system comprising one of: one or more devices, one or more machines, or a combination thereof.
But Stojevic teaches -
wherein the target comprises: an electrical grid, an electricity network, a portfolio of financial derivatives, a stock market, a set of patients of a hospital unit, or a system comprising one of: one or more devices, one or more machines, or a combination thereof (Stojevic ¶ 0243 teaches “[f]urther use cases include . . . Beyond quantum simulation: ML for effectively infinite systems, such as NLP, audio, stock market prediction [(that is, the target comprises . . . . a stock market)]”).
Gillman and Stojevic are from the same or similar field of endeavor. Gillman teaches a general tensor network formulation of finite, episodic and discrete Markov decision processes. Stojevic teaches methods for periodic systems, such as iMPS, iPEPS, or uniform cMPS are regularly used to simulate effectively infinite systems.
Thus, it would have been obvious to a person having ordinary skill in the art to modify Gillman pertaining to tensor network representation for dynamics of a matrix product state (MPS) representation with the further use cases, including stock markets, of Stojevic.
The motivation to do so is because “description of both the environment and the local region of interest of an infinite tensor network is computed on a quantum computer by optimising appropriate quantum circuits. The methods are also amenable to classical data that has a naturally repeating structure or is effectively infinite in extent.” (Stojevic ¶ 0084).
Response to Arguments
14. Examiner has fully considered Applicant’s arguments, and responds below accordingly.
Section 101
15. Applicant submits that “the claims as a whole result in a specific improvement in technology. The claims are patent eligible under 35 U.S.C. § 101, because they are directed to a device or system (claim 1), a computer-implemented method (claim 12), and a non-transitory computer-readable medium encoded with instructions that, when executed by at least one processor or hardware, perform or make a device to at least perform a sequence of steps (claim 20). Specifically, the claims allow for performing a sampling which enhances accuracy of representation of behavior of the target associated with the probability distribution because it minimizes the issue of lack of uncorrelation present in techniques like MCMC (Markov Chain Monte Carlo). Therefore, the claimed invention allows dispensing with the need to generate a large number of samples from which a portion has to be removed because said portion of samples does not satisfy the required conditions.” (Response at pp. 8-9 (quoting Specification at p. 1, lines 18-27)).
Applicant submits “it is clear that Applicant's claimed invention allows for decreasing the number of samples that need to be generated and hence allows decreasing energy consumption for generating the samples as well as the memory capacity required to store the generated samples. Advantageously, this clearly shows that the claimed invention is integrated into a practical application and results in improving existing technology.” (Response at p. 9).
Examiner’s Response:
Under Step 2A Prong Two, the rejection identifies any additional elements recited in the claim beyond the identified judicial exception (i.e., abstract idea); and evaluate the integration of the judicial exception into a practical application by explaining that the claim as a whole, looking at the additional elements individually and in combination, does not integrate the judicial exception into a practical application using the considerations set forth in MPEP §§ 2106.04(d), 2106.05(a)-(c) and (e)-(h).
“Integration” may be based on the improvements in the functioning of a computer or an improvement to any other technology or technical field. (MPEP § 2106.04(d)(1)). The evaluation requires, [i]n sum, that (1) the specification should be evaluated to determine if the disclosure provides sufficient details such that one of ordinary skill in the art would recognize the claimed invention as providing an improvement. Next, (2) if the specification sets forth such an improvement, the claim must be evaluated to ensure that the claim itself reflects the disclosed improvement.
By way of example to Desjardins, the MPEP provides under Step 2A Prong Two that “the [Desjardins] specification identified improvements as to how the machine learning model itself operates, including training a machine learning model to learn new tasks while protecting knowledge about previous tasks to overcome the problem of ‘catastrophic forgetting’ encountered in continual learning systems. Importantly, the [appeals review panel (ARP)] evaluated the claims as a whole in discerning at least the limitation ‘adjust the first values of the plurality of parameters to optimize performance of the machine learning model on the second machine learning task while protecting performance of the machine learning model on the first machine learning task’ reflected the improvement disclosed in the specification.” (MPEP § 2106.04(d) sub III; see “Advance Notice of Change to the MPEP in light of Ex Parte Desjardins” (05 December 2025) at p. 2)).
Regarding Leg 1 of MPEP § 2106.04(d)(1), the disclosure generally recites sampling based on a moment of a probability distribution of a target. In particular, the disclosure recites that “probability distribution represents different probabilities about the target, which has the plurality of discrete random variables defining the behavior or operation of the target. The probabilities can be set by way of a model of the target (e.g. a mathematical model describing the behavior or operation of the target with probability distributions) or by performing experimental tests that make possible to determine probabilities of occurrence of certain events. The probability distribution is included in the tensor provided, which is a probability tensor. Accordingly, the configurations of the discrete random variables, with respective probabilities thereof, are defined in the tensor. That way, the tensor includes all the information about the probability distribution so that data is extracted from the probability distribution by operating with the tensor.” (Specification at p. 2, lines 9-19).
Further, the disclosure recites the use of a machine learning approach, where a “probability distribution is encoded into the tensor network following a machine learning approach whereby, preferably in a plurality of iterations, the tensor network is provided as an approximation of the probability distribution as a result of the minimization of the [negative log-likelihood (NLL)] function. This technique progressively performs the approximation, which can be made more accurate by making the minimization more iterations, thus a trade-off can be established regarding the accuracy of the approximation and the time it takes to provide the tensor network.” (Specification at p. 3, lines 15).
The Specification appears to an improvement rooted in an “accuracy versus time” trade-off regarding the approximation of the received probability distribution; however, the improvement appears in a conclusory manner (i.e., a bare assertion of an improvement without the detail necessary to be apparent to a person of ordinary skill in the art), in which the claims would not improve the technology. (MPEP § 2106.04(d)(1)).
Accordingly, claims 1-20 are subject-matter ineligible, as set out above in detail.
Section 102 / 103
16. “Applicant submits that the claims presented herein include limitations which are neither taught nor suggested by Gillman. Thus, the novelty rejections are improper and may not be maintained.” (Response at p. 10).
Applicant submits that “Applicant respectfully asserts that these limitations are neither taught nor disclosed by Gillman.” (Response at p. 10).
In particular, Applicant submits that the limitations not taught nor disclosed be Gillman include:
"providing a tensor codifying the probability distribution such that each configuration of the plurality of discrete random variables has its respective probability codified therein, where all probabilities are greater than or equal to zero and a sum of all probabilities is equal to one;
encoding the tensor into a tensor network in the form of a matrix product state, . . . .“
(Response at p. 10).
Examiner’s Response:
Examiner respectfully disagrees because the Gillam prior art teaches all of the limitations of Applicant’s claim as set out above in detail. (see, e.g., Gillman, left column of p. 3, “2.2 Tensor Networks for Hidden Markov Models,” fourth paragraph ; Gillman, right column of p. 2, “2.2 Tensor Networks for Hidden Markov Models,” second paragraph; Gillam, right column of p. 3, “2.3 Tensor Networks for Time Integrated Observables,” first paragraph.
Accordingly, claims 1-3, 9, 10, 12-14, and 20 are anticipated by the cited prior art of Gillam, as set out above in detail.
With regards to the rejection to the remaining claims under Section 103 hereinabove, the rejection clearly sets forth which claim limitations are taught by each of the prior art references, and the reason why it would be obvious to a person having ordinary skill in the art as of the effective filing date of the Applicant's invention to combine their teachings, and Applicant has not explained why the cited prior art references cannot be combined in the manner set forth in the rejection.,
17. “Applicant respectfully points out that the above-cited claim limitations in combination with the additional claim limitations allow for performing a sampling which enhances accuracy of representation of behavior of the target associated with the probability distribution because minimizes the issue of lack of uncorrelation present in techniques like MCMC (Markov Chain Monte Carlo).” (Response at p. 11 (quoting Specification at p. 1, lines 18-27)).
Also, “Applicant respectfully notes that the encoding of the tensor into a tensor network in the form of a matrix product state allows decreasing the correlation among the tensors of the matrix product state accordingly to the bond dimensions of the matrix product state (e.g., by truncating the bond dimensions of the matrix product state), and hence allows decreasing the correlation among the random variables represented by the external indices of the tensors of the MPS.” (Response at p . 12).
Examiner’s Response:
Examiner respectfully disagrees because the claims are not so limited as suggested by Applicant. For example, the claim simply recites “encoding the tensor into a tensor network in the form of a matrix product state, . . . an internal index or internal indices of each tensor of the tensor network represents correlation between the tensor and the corresponding adjacent tensor of the tensor network, . . . .” (see, e.g., claim 1, lines 13-17). That is, the claim does not recite “a matrix product state . . . allows decreasing correlation among the tensors of the matrix product state accordingly to the bond dimensions . . .” as suggested by Applicant. (Response at p. 12). Also, the disclosure is silent reading “bond dimensions.” Incidentally, equation (12) of Gillam shows such “bond dimensions” forming a chain of matrices Mi, which is set out above in detail.
Also, though the Background recites that “[t]he Markov Chain MC has its limitations, one of which is that it cannot be guaranteed that the samples in the distribution are uncorrelated,” such language is admitted prior art to the claimed invention.
Accordingly, claims 1-3, 9, 10, 12-14, and 20 are anticipated by the cited prior art of Gillam, as set out above in detail.
With regards to the rejection to the remaining claims under Section 103 hereinabove, the rejection clearly sets forth which claim limitations are taught by each of the prior art references, and the reason why it would be obvious to a person having ordinary skill in the art as of the effective filing date of the Applicant's invention to combine their teachings, and Applicant has not explained why the cited prior art references cannot be combined in the manner set forth in the rejection.
Conclusion
18. 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.
19. The prior art made of record and not relied upon is considered pertinent to Applicant's disclosure:
(US Patent 12657453 to Finzi et al.) teaches that coherently defined networks on continuous functions should only depend on the input function ƒ, and not on spurious shortcut features, such as the sampling locations or sampling density, which enable overfitting and reduce robustness to changes in the sampling procedure. Each application of custom character in a standard neural network incurs some discretization error which is determined by the sampling resolution.
(Okada et al., "The reliability of observational measurements of column density probability distribution functions," arXiv (2016)) teaches We solve the integrals that describe the convolution of a cloud PDF with contaminating sources such as noise and line-of-sight emission and study the impact of missing information on the measured column density PDF. In this way we can quantify the effect of the different processes and propose ways to correct for their impact in order to recover the intrinsic PDF of the observed cloud.
20. Any inquiry concerning this communication or earlier communications from the Examiner should be directed to KEVIN L. SMITH whose telephone number is (571) 272-5964. Normally, the Examiner is available on Monday-Thursday 0730-1730.
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, KAKALI CHAKI can be reached on 571-272-3719. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of an application may be obtained from the Patent Application Information Retrieval (PAIR) system. Status information for published applications may be obtained from either Private PAIR or Public PAIR. Status information for unpublished applications is available through Private PAIR only. For more information about the PAIR system, see http://pair-direct.uspto.gov. Should you have questions on access to the Private PAIR system, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative or access to the automated information system, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/K.L.S./
Examiner, Art Unit 2122
/KAKALI CHAKI/Supervisory Patent Examiner, Art Unit 2122
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