DETAILED ACTION
Notices to Applicant
This communication is a non-final rejection. Claims 17-31, as filed 05/23/2024, are currently pending and have been considered below.
Foreign priority is acknowledged to DE102023204154A1 which was filed 05/04/2023.
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon and the rationale supporting the rejection would be the same under either status.
Claim Objections
Claim 27 is objected to because of the following informalities. The preamble recites “the neural network as recited in claim 25”, but claim 25 recites “neural network architecture”. The claim also recites “an actuation signal” and “the control signal”. These are interpreted as the same element, so the second portion is interpreted as “the actuation signal”.
Claim 28 is objected to because of the following informalities. The preamble recites “the neural network archtechture including for processing measurement data, including a plurality of layers…”which is interpreted as “architecture for processing measurement data including a plurality of layers…”.
Claims 30-31 are objected to because of the following informalities. The claims recite “causing the one or more computer” which is interpreted as “causing the one or more computers”. Additionally, claim 31 lacks a final period.
Claim 29 is objected to because it would be allowable if written in independent form but, as written, it depends from rejected claims.
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.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claim 27 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor, or for pre-AIA the applicant regards as the invention. Specifically, the claim is a neural network architecture, i.e., an apparatus, that recites “wherein an actuation signal is formed…[and a machine] is controlled with the control signal”. Controlling the recited machines is a method step, thus the claim recites both apparatus and method steps, and it is unclear whether infringement occurs when the apparatus is made or only when it is used. MPEP 2173.05(p)(II). For purposes of examination, the claim is interpreted as generating a control signal that is capable of controlling one of the recited machines.
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 17-28, and 30-31 are rejected under 35 U.S.C. 101 because the claimed invention is directed to non-statutory subject matter. The claim(s) does/do not fall within at least one of the four categories of patent eligible subject matter because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more.
Step 1
Claims 17-27 are directed to a neural network architecture for processing measurement data, which is software per se and does not fall within any of the statutory categories. MPEP 2106.03.
For purposes of compact prosecution, claims 17-27 are further analyzed below in anticipation of amendments to overcome the software per se rejection.
The claims 28, 27, 30, and 31 recite subject matter within a statutory category as a process, machine, and/or article of manufacture.
Step 2A Prong One
Claim 17 recites, in relevant part: neurons that “a plurality of layers, each having a plurality of neurons, wherein each of the neurons is configured to process complex-valued inputs with a holomorphic calculation function to produce an activation and to ascertain an output of the activation by applying a non-linear activation function to the activation, wherein the activation function is also holomorphic.” The broadest reasonable interpretation of these steps includes abstract ideas, namely mathematical concepts. Claim 28 further recites providing training records and feeding them into the neural network. These steps amount to insignificant extra-solution activity, namely, mere data gathering. The valuing and optimizing steps of claim 28 are further mathematical concepts. Claims 30 and 31 add generic computing equipment which amounts to applying the abstract idea with a computer.
Dependent claims recite additional subject matter which further narrows or defines the abstract idea embodied in the claims. For example, claims 18-20 and 22-24 recite additional mathematical concepts but for recitation of generic computer components.
Step 2A Prong Two
This judicial exception is not integrated into a practical application. In particular, the additional elements do not integrate the abstract idea into a practical application, other than the abstract idea per se, because the additional elements:
amount to mere instructions to apply an exception. For example, the non-transitory machine-readable data carrier of claims 30 and 31 amounts to invoking computers as a tool to perform the abstract idea, see MPEP 2106.05(f).
add insignificant extra-solution activity to the abstract idea. For example, providing training record and feeding them into a neural network amounts to mere data gathering, recitation of electromagnetic interrogation radiation in claim 26 amounts to selecting a particular data source or type of data to be manipulated, see MPEP 2106.05(g). Similarly, outputting a control signal to control a system for quality control in claim 27amounts to general output of data or merely invoking generic computers
generally link the abstract idea to a particular technological environment or field of use such as the electromagnetic interrogation radiation of claims 25-26, see MPEP 2106.05(h))
Dependent claims recite additional subject matter which amount to limitations consistent with the additional elements in the independent claims. Looking at the limitations as an ordered combination adds nothing that is not already present when looking at the elements taken individually. There is no indication that the combination of elements improves the functioning of a computer or improves any other technology. Their collective functions merely provide conventional computer implementation and do not impose a meaningful limit to integrate the abstract idea into a practical application.
The Examiner notes that the rejected claims do not improve the functioning of a computer or other technology. While the specification asserts improved generalization and smoothed decision boundaries arising from holomorphic processing (spec as published [0014] and the discussion of FIGs. 4A-4C), claims 17-20, 22-28, 30, and 31 recite mathematical properties themselves with generic computer components which is an asserted improvement of the abstract idea rather than of technology. The specific disclosed mechanism operating on the training process (i.e., monitoring the determinant of the activation-coefficient matrix and renormalizing it) is reflected only in claims 21 and 29.
Step 2B
The claim(s) does/do not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to discussion of integration of the abstract idea into a practical application, the additional elements amount to no more than mere instructions to apply an exception, add insignificant extra-solution activity to the abstract idea, and generally link the abstract idea to a particular technological environment or field of use. Additionally, the additional limitations, other than the abstract idea per se amount to elements that have been recognized as well-understood, routine, and conventional activity in particular fields. For example, amounts to receiving or transmitting data over a network, Symantec, MPEP 2106.05(d)(II)(i), performing repetitive calculations, Flook, MPEP 2106.05(d)(II)(ii), electronic recordkeeping, Alice Corp., MPEP 2106.05(d)(II)(iii), and/or storing and retrieving information in memory, Versata Dev. Group, MPEP 2106.05(d)(II)(iv). Additionally, the conventionality of elements such as training steps and backpropagation is supported by the La Corte and Amos references described in greater detail below.
Dependent claims recite additional subject matter which, as discussed above with respect to integration of the abstract idea into a practical application, amount to invoking computers as a tool to perform the abstract idea. Dependent claims recite additional subject matter which amount to limitations consistent with the additional elements in the independent claims. Looking at the limitations as an ordered combination adds nothing that is not already present when looking at the elements taken individually. There is no indication that the combination of elements improves the functioning of a computer or improves any other technology. Their collective functions merely provide conventional computer implementation.
Patent Eligible Subject Matter
Claim 29 is not rejected under 35 USC § 101.
While claim 29 recites further abstract ideas (Step 2A Prong One), namely checking a deviation of a matric determinant and performing a manipulation of the determinant if certain conditions obtain, the claim in Step 2A Prong Two. As the specification describes, during the optimization of the free activation coefficients in claim 28, nothing stops the coefficient matrix from drifting toward singularity. See [0030] of the specification as published. This is a technical failure of the training process. This claim goes beyond a generic solution to the problem (e.g., “performing computations to maintain activation stability”) to recite a specific mechanism for manipulating the determinants, thereby acting on the training process to resolve this failure.
Claim 21 similarly recites similar features related to the determinant, but unlike claim 29, it expressly defines the matrix A as the Mobius coefficients. The ordered combination of claim 21 comprises holomorphic activation, conformal mapping, Mobius forms, real coefficients, and a determinant tolerance band. This is a particular way of producing the activation which goes beyond reciting an intended result. This is distinct from claims 17-20 because those claims permit the determinant to be 0 or near-0, so those claims do not achieve the improvement described in the specification. This claim would not be rejected under 101 but for it being software per se.
Claim Rejections - 35 USC § 103
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.
The factual inquiries set forth in Graham v. John Deere Co., 383 U.S. 1, 148 USPQ 459 (1966), that are applied 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.
Claim 17 is rejected under 35 U.S.C. 103 as being unpatentable over La Corte (La Corte et al., “Newton's Method Backpropagation for Complex-Valued Holomorphic Multilayer Perceptrons,” arXiv:1406.5254).
Regarding claim 17, La Corte discloses: A neural network architecture for processing measurement data, comprising:
--a plurality of layers, each having a plurality of neurons (“A well-used type of artificial neural network is the multilayer perceptron (MLP). An MLP is built of several layers of single neurons hooked together by a network of weight vectors,” page 4; “There are L-1 hidden layers of neurons, and the pth (1 ≤ p ≤ L - 1) hidden layer contains Kp nodes,” page 5),
--wherein each of the neurons is configured to process complex-valued inputs (“The use of fully complex-valued neural networks to solve real-valued as well as complex-valued problems in physical applications has become increasingly popular,” page 1; “The input layer has m = K_0 input nodes denoted z_1 = x_1^(0),…” page 5; complex training date on page 6)
--with a holomorphic (The Examiner construes “holomorphic” as complex-differentiable on the function’s domain of definition, not as pole-free on all of the complex plane. This is supported by [0050] of the spec which defines “the holomorphic Mobius transformation” as f(z) = 1 – 1/z which has a pole at z = 0) calculation function (The Examiner construes this function in light of the specification which identifies in [0041]: “a holomorphic calculation function, here: a weighted sum,” to encompass a complex-valued weighted sum)
--to produce an activation and to ascertain an output of the activation by applying a non-linear activation function to the activation (each neuron forms the complex weighted net sum on page 5
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; “g_L is holomorphic” on page 11; “Usually the activation function is taken to be the same among a single layer of the network; the defining characteristic of the MLP is that in at least one layer, the activation function must be nonlinear,” page 4)
--wherein the activation function is also holomorphic (A holomorphic MLP is a complex-valued MLP in which the activation function in the layer indexed by p of the network is holomorphic on some domain Ω_p ⊆ C).
To the extent that the holomorphy of the weighted-sum calculation function is not expressly stated, it would have been obvious to a POSITA before the effective filing date that La Corte’s complex-linear net sums are holomorphic, because La Corte’s backpropagation formulas derive from that property (i.e., “the Cauchy-Riemann condition” on page 11). MPEP 2144.01. An express mathematical property of a disclosed function yields a predictable result.
Claims 18 is rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Ozdemir (“Complex valued neural network with Mobius activation function” cited in IDS from 9/16/2025).
Regarding claim 18, La Corte does not expressly disclose but Ozdemir teaches: wherein the activation function, and/or a differential of the activation function, is a conformal mapping, after application of which to two complex numbers z_1 and z_2 the intermediate angle between the two complex numbers z_1 and z_2 is preserved in a complex plane (“To base on the observation of ‘‘fixed points of a neural network are determined by fixed points of the employed activation function’’ he deduced ‘the existence for fixed points of the activation function are guaranteed by the Möbius transformation’…[A Mobius transformation] is a conformal mapping of the complex plan and also known as linear fractional or bilinear transformation,” page 4699).
Thus Ozdemir explains that La Corte’s tanh transformations have the quality of being conformal. A POSITA before the effective filing date would have recognized that La Corte’s tanh-style activation functions (page 1) including a Mobius transformation is a conformal mapping as explained by Ozdemir because this is applying a known mathematical characterization of a known activation function to obtain a predictable result in the use of a known technique to improve a similar device.
Additionally, it can be seen that each element is taught by either La Corte or Ozdemir. The conformal property explanation does not affect the normal functioning of the elements of the claim which are taught by La Corte. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Ozdemir since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Claims 19-20 are rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Ozdemir and Mandic (“The use of Mobius transformations in neural networks and signal processing” cited in IDS from 9/16/2025).
Regarding claim 19, the Examiner first notes that the activation function here includes a Mobius transformation but the BRI of the activation function can also include other things. Nor does the claim require that the Mobius transformation act directly on the neuron’s activation variable. An activation function expressible as a composition containing a fractional-linear (Mobius) constituent includes a Mobius transformation. Further, “free coefficients” does not require trained coefficients. In fact, the specification states that “[t]hese coefficients can also be trained” in [0017], but the training is optional, so coefficients that are selectable parameters of the recited form satisfy the BRI of the limitation.
La Corte discloses complex networks whose activations are the “complex counterparts” of standard sigmoid functions, “an obvious choice is to use the complex counterparts of these real-valued functions,” La Corte displays the hyperbolic tangent on pages 1-2:
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La Corte does not expressly characterize this activation as including a Mobius transformation, but Mandic teaches: wherein the activation function includes a Möbius transformation of the form f(z) = ((a*z+b)/(c*z+d) with free coefficients a, b, c, and d (“It is first shown that both a nonlinear activation function of a neuron and a first order all-pass filter section can be considered as Mobius transformations,” page 185; see also Ozdemir’s description of Mandic: “He showed that sigmoidal or tanh types of activation functions for a RVNN satisfy the conditions of a Möbius transformation,” page 4699).
Applying this characterization to the tanh activation function quoted above from La Corte whose fractional linear constituent, f(z) = ((1*z-1)/(1*z+1) when a = 1, b = -1, c = 1, and d = 1.
Thus Mandic and Ozdemir explain that La Corte’s tanh activation function has the quality of including a Mobius transformation when the coefficients are a = 1, b = -1, c = 1, and d = 1. A POSITA before the effective filing date would have recognized that La Corte’s tanh-style activation functions (page 1) including a Mobius transformation as explained by Mandic and Ozdemir because this is applying a known mathematical characterization of a known activation function to obtain a predictable result in the use of a known technique to improve a similar device.
Additionally, it can be seen that each element is taught by either La Corte, Ozdemir, or Mandic. The Mobius transformation explanation of Mandic does not affect the normal functioning of the elements of the claim which are taught by La Corte and Ozdemir. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Ozdemir and Mandic since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Regarding claim 20, The claim is substantially similar to claim 19 and is rejected with the same reasoning. The Examiner further notes that the coefficients in claim 19, 1, -1, 1, and 1, are real numbers.
Claims 22, 25, and 26 are rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Fuchs (Fuchs et al., “Complex-valued Convolutional Neural Networks for Enhanced Radar Signal Denoising and Interference Mitigation,” https://arxiv.org/abs/2105.00929)
Regarding claim 22, the Examiner notes that the specification describes the feature extractor by example in [0020]: “An example of a feature extractor is a convolutional neural network (CNN), which generates feature maps by smoothly applying filter kernels to the measurement data.” Thus the BRI of feature extractor includes a multi-layer convolutional network whose layers output feature maps.
La Corte does not expressly disclose but Fuchs teaches: wherein the neural network architecture is at least partially formed as a feature extractor, wherein outputs of neurons in different layers of the feature extractor indicate an expression of features of different scales and/or complexities in the measurement data (“The model architecture implements a fully convolutional NN; it consists exclusively of convolutions, BN operations and the ReLU activation function… The first layer performs a complex-convolution followed by a CReLU non-linearity” page 3; K_x and K_y represent the spatial size of the kernel, whereas C_in indicates the number of input filter channels,” page 2).
One of ordinary skill in the art before the effective filing date would have been motivated to expand the holomorphic complex-valued network of La Corte to include the radar range-Doppler measurement data and complex-valued convolutional architecture of Fuchs because it “increases data efficiency, but also improve the conservation of phase information during filtering, which is crucial for further processing such as angle estimation,” (Fuchs page 1).
Additionally, it can be seen that each element is taught by either La Corte or Fuchs. The complex-valued radar network of Fuchs does not affect the normal functioning of the elements of the claim which are taught by La Corte. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Fuchs since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Regarding claim 25, La Corte does not expressly disclose but Fuchs teaches: wherein the neural network architecture is configured to process measurement data that indicates a spatial and/or temporal distribution of at least one electromagnetic field (“The CNN input is a noisy range-Doppler map, which is a complex-valued two dimensional matrix,” page 3; “This complex-valued spectrum is represented as a 2D matrix with signal peaks corresponding to the distances and velocities of objects,” page 1; “The range-Doppler (RD) processing chain of a common FMCW/CS radar is depicted in Fig. 2. The radar sensor transmits a set of linearly modulated radio frequency (RF) chirps, also termed ramps. Object reflections are perceived by the receive antennas and mixed with the transmit signal resulting in the Intermediate Frequency (IF) Signal,” page 2).
The motivation to combine is the same as in claim 22.
Regarding claim 26, La Corte does not expressly disclose but Fuchs teaches: wherein the electromagnetic field originates at least partially from reflections of an electromagnetic interrogation radiation on one or more objects (“The range-Doppler (RD) processing chain of a common FMCW/CS radar is depicted in Fig. 2. The radar sensor transmits a set of linearly modulated radio frequency (RF) chirps, also termed ramps. Object reflections are perceived by the receive antennas and mixed with the transmit signal resulting in the Intermediate Frequency (IF) Signal,” page 2).
The motivation to combine is the same as in claim 22.
Claims 23, 24, and 27 are rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Fuchs and Amos (US20200364553A1).
Regarding claim 23, La Corte does not expressly disclose but Amos teaches: a task head that is configured to ascertain a solution of a predefined task from one or more outputs of the feature extractor with respect to the measurement data (“the projection layer may be the final layer of the sequence of neural network layers. The earlier layers may be conventional neural network layers, e.g., convolutional layers, ReLu layers, dense layers, softmax layers, pooling layers, etc,” [0013]).
One of ordinary skill in the art before the effective filing date would have been motivated to expand the radar network analysis of La Corte and Fuchs to include the classification head and control signal generation of Amos because “[u]sing a projection layer increases the robustness of the classification,” (Amos [0016]).
Additionally, it can be seen that each element is taught by either La Corte, Fuchs, or Amos. The classification head and control signals of Amos do not affect the normal functioning of the elements of the claim which are taught by La Corte and Fuchs. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Fuchs and Amos since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Regarding claim 24, La Corte does not expressly disclose but Amos teaches: wherein the task head is configured to ascertain classification scores with regard to one or more classes of a predefined classification for the measurement data (“the final output of the neural network may be a vector with entries between 0 and 1, each entry corresponding to a label, and the value indicating a likelihood that an object with the corresponding label was recognized in the input,” [0048]).
The motivation to combine is the same as in claim 23.
Regarding claim 27, La Corte does not expressly disclose but Amos teaches: wherein an actuation signal is formed from one or more outputs provided by the neural network architecture, and a vehicle, and/or a driver assistance system, and/or a robot, and/or a system for quality control, and/or a system for monitoring regions, and/or a system for medical imaging, is controlled with the control signal (“the controller may use the neural network to classify objects in the sensor data, and to generate a control signal for controlling the autonomous device using the classification,” [0017]).
The motivation to combine is the same as in claim 23.
Claim 28 is rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Hanna (Hanna et al., “A complex-valued nonlinear neural adaptive filter with a gradient adaptive amplitude of the activation function,” Neural Networks Letter, March 2003, Volume 16, Issue 2, pages 155-159).
Regarding claim 28, the recited neural network architecture (i.e., plurality of layers of neurons processing complex-valued inputs with a holomorphic calculation function and a holomorphic non-linear activation function) is taught by La Corte as described above for claim 17 (incorporated herein).
La Corte further discloses:
--providing training records of measurement data (“To train the network, we use a training set with N data points,” page 6);
--feeding the training records to the neural network architecture, and processing the training records by the neural network architecture into outputs (“As the input vector (z_t1,…, z_tm) of the tth training point is propagated throughout the network we update the subscripts of the network calculations with an additional t subscript to signify that those values correspond to the tth training point,” page 6);
--valuing the outputs using a predefined real-valued cost function (“Finally, we train the network by minimizing the standard sum-of-squares error function,” page 6); and
--optimizing parameters that characterize a behavior of the neural network architecture with an aim of improving the valuation by the cost function during further processing of training records (“Minimization of the error function can be achieved through the use of the backpropagation algorithm,” page 6).
La Corte does not expressly disclose but Hanna teaches: wherein the parameters also include free coefficients of a parameterized approach for the holomorphic activation function (“the amplitude of the complex-valued analytic nonlinear activation function of a neuron in the learning algorithm is made gradient adaptive,” page 155. Under the BRI, the gradient-adaptive amplitude is a free coefficient of the parameterized form of a holomorphic activation function, optimized together with the other parameters during the training.).
One of ordinary skill in the art before the effective filing date would have been motivated to expand training method of La Corte to include the gradient-adaptive activation coefficients of Hanna because “Such an algorithm is beneficial when dealing with signals that have rich dynamical behavior” (Hanna Abstract).
Additionally, it can be seen that each element is taught by either La Corte or Hanna. The activation coefficients of Hanna do not affect the normal functioning of the elements of the claim which are taught by La Corte. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Hanna since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Claims 30-31 are rejected under 35 U.S.C. 103 as being unpatentable over La Corte in view of Amos.
Regarding claims 30 and 31, the recited neural network architecture (i.e., plurality of layers of neurons processing complex-valued inputs with a holomorphic calculation function and a holomorphic non-linear activation function) is taught by La Corte as described above for claim 17 (incorporated herein). La Corte does not expressly disclose, but Amos teaches:
--A non-transitory machine-readable data carrier on which is stored a computer program containing machine-readable instructions, the machine readable instructions, when executed by one or more computers, causing the one or more computer (“An embodiment of the methods may be implemented on a computer as a computer implemented method, or in dedicated hardware, or in a combination of both. Executable code for an embodiment of the method may be stored on a computer program product. Examples of computer program products include memory devices, optical storage devices, integrated circuits, servers, online software, etc. Preferably, the computer program product may include non-transitory program code stored on a computer readable medium for performing an embodiment of the method when the program product is executed on a computer,” [0020]; FIG. 6A; [0151]).
One of ordinary skill in the art before the effective filing date would have been motivated to realize the holomorphic network of La Corte on the computer components of Amos because this would make the functionality available to users (see Amos [0148]).
Additionally, it can be seen that each element is taught by either La Corte or Amos. The computer components Amos do not affect the normal functioning of the elements of the claim which are taught by La Corte. Because the elements do not affect the normal functioning of each other, the results of their combination would have been predictable. Therefore, before the effective filing date of the claimed invention, it would have been obvious to combine the teachings of La Corte with the teachings of Amos since the result is merely a combination of old elements, and, since the elements do not affect the normal functioning of each other, the results of the combination would have been predictable.
Subject Matter Free from Prior Art
Claims 21 and 29 are not anticipated or obvious in view of the prior art.
Regarding claim 21, no prior art of record teaches or suggests that the matrix A formed from the free coefficients has a determinant that deviates from a predefined value by at most a predefined amount in the context of the claim. This is particularly true in light of the specification which describes the coefficients as trainable.
Regarding claim 29, no prior art of record teaches or suggests, in the context of training the recited holomorphic complex-valued architecture, checking whether the determination det(A) of a matrix A formed from the coefficients of the parameterized activation function deviates from a predefined value by more than a predefined amount, and, based on the deviation exceeding that amount, dividing the elements of the matrix by the square root of the det(A). This is true even though, under Ex Parte Schulhauser, the conditional dividing step need not be performed under the BRI of the method claim. Even under that construction, monitoring the determinant of a trained activation-coefficient matrix as claimed is not taught by the art of record.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Kim (Kim, et al., "Approximation by Fully Complex Multilayer Perceptrons" Neural Computation 15, 1641–1666 (2003)) describes MLPs with analytic/holomorphic activations (“A number of elementary transcendental functions (ETFs) derivable from the entire exponential function e^z that are analytic are defined as fully complex activation functions”).
Zhou (Sharon Zhou et al, "Data augmentation with Mobius transformations" 2021 Mach. Learn.: Sci. Technol. 2 025016) describes four-coefficient Mobius maps and their conformal, angle-preserving character (“Möbius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space… We show that the inclusion of Möbius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes,” Abstract).
Scardapane (Scardapane et al., "Complex-Valued Neural Networks With Nonparametric Activation Functions" IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE, VOL.4, NO.2, APRIL 2020) describes a plurality of coefficients (“flexible activation functions (AFs) in the complex domain, i.e., AFs endowed with sufficient degrees of freedom to adapt their shape given the training data… Leveraging over the recently proposed kernel activation functions, and related advances in the design of complex-valued kernels, we propose the first fully complex, nonparametric activation function for CVNNs, which is based on a kernel expansion with a fixed dictionary that can be implemented efficiently on vectorized hardware,” Abstract).
Any inquiry concerning this communication or earlier communications from the examiner should be directed to JOSHUA BLANCHETTE whose telephone number is (571)272-2299. The examiner can normally be reached on Monday - Thursday 7:30AM - 6:00PM, EST.
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/JOSHUA B BLANCHETTE/Primary Examiner, Art Unit 3624
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