DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after February 07, 2024, is being examined under the first inventor to file provisions of the AIA
Status of Claims
The present application is being examined under the claims filed on February 07, 2024.
Claims 1-20 are rejected.
Claims 1-20 are pending
Specification
The specification filed on February 07, 2024, is acceptable for examination purposes
Drawings
The drawings filed on February 07, 2024, is acceptable for examination purposes.
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 2, 4, 8, 13, 18 rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as failing to set forth the subject matter which the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the applicant regards as the invention.
Regarding claim 2,
Claim 2, row 3 recites ““the original hierarchical index space”
However, in claim 2, row 5 recites “the original hierarchical space” without “index".
Therefore, claim 2 lacks antecedent basis.
Regarding claim 4,
Claim 4 recite “
X
:
=
x
λ
:
λ
∈
Λ
,
x
λ
∈
R
D
”
However, these variables:
x
λ
,
λ
,
R
D
are not defined in claim 4 or claim 1 which claim 4 depend on.
Therefore, claim 4 lacks antecedent basis.
Regarding claim 5
Claim 5 recites “
Z
≔
z
τ
:
τ
∈
Λ
m
,
z
τ
∈
R
D
”
However, these variables:
z
τ
,
τ
,
R
D
are not defined in claim 5 or claim 4 which claim 5 depend on.
Claim 5 also recites
Λ
m
≔
τ
m
λ
:
λ
∈
Λ
However, these variables
τ
m
λ
,
λ
are not defined in claim 5 or claim 4 which claim 5 depend on.
Claim 5 also recites
Z
~
≔
z
~
t
:
τ
∈
Λ
m
,
z
~
t
∈
R
D
~
,
However, these variables
z
~
t
,
τ
, are not defined in claim 5 or claim 4 which claim 5 depends on.
Claim 5 also recites
Y
:
=
y
λ
:
λ
∈
Λ
,
y
λ
∈
R
D
~
However, these variables
y
λ
,
λ
are not defined in claim 5 or claim 4 which claim 5 depends on.
Therefore, claim 5 lacks antecedent basis.
Regarding claim 6,
z
τ
≔
ϕ
m
a
g
g
x
λ
:
λ
m
=
τ
wherein
λ
m
is an aggregation type of
λ
and is computed by
λ
m
≔
λ
m
'
:
m
'
∉
s
u
b
m
,
Claim 6 recites
z
τ
≔
ϕ
m
a
g
g
x
λ
:
λ
m
=
τ
However, these variables
x
λ
,
τ
are not defined in claim 6 or claim 5 which claim 6 depends on.
Claim 6 recites
λ
m
≔
λ
m
'
:
m
'
∉
s
u
b
m
However, these variables
λ
m
'
,
m
'
are not defined in claim 6 or claim 5 which claim 6 depends on.
Therefore, claim 6 lacks antecedent basis.
Regarding claim 7,
Claim 7 recites
z
~
τ
~
=
Σ
τ
ϵ
N
m
τ
~
W
τ
~
τ
m
z
τ
However, these variables
τ
,
τ
~
,
z
τ
are not defined in claim 7 or claim 5 which claim 7 depends on.
Therefore, claim 7 lacks antecedent basis.
Regarding claim 8,
Claim 8 depend on claim 1
Claim 8 recites “
y
λ
:
=
z
'
[
λ
]
m
”
However, these variables
z
'
[
λ
]
m
are not defined in claim 8 or claim 1 which claim 8 depends on.
Therefore, claim 8 lacks antecedent basis.
Regarding claim 13,
Claim 13, row 4 recites ““the original hierarchical index space”
However, in claim 13, row 6 recites “the original hierarchical space” without “index".
Therefore, claim 13 lacks antecedent basis.
Regarding claim 18,
Claim 18, row 4 recites ““the original hierarchical index space”
However, in claim 18, row 6 recites “the original hierarchical space” without “index".
Therefore, claim 18 lacks antecedent basis.
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.
Claims 1 – 6, 8 – 11, 12 - 20 are rejected under 35 U.S.C. 103 as being unpatentable over Wang et al (Equivariant Maps for Hierarchical Structures) in view of Hanselmann et al (US 20230032634 A1)
Regarding claim 1,
(preamble) - A computer-implemented method comprising.
Wang does not explicitly teach method can be performed on a computer.
Hanselmann teaches:
Hanselmann, paragraph [0039], “The method may be computer-implemented, especially in its entirety or in part.”
Examiner note:
A computer-implemented method i.e. The method can be performed using a computer.
Limitation 1a - receiving feature vectors whose indices are in an original hierarchical index space.
Wang teaches:
Wang, Page 7, Section 4.3, "let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form
Wang, Page 6, Secion 4.2.2, "Note that one instance of the hierarchy (e.g., a sequence of sets) belongs to
R
P
Q
, because each instance of the structure is in
R
Q
and the outer structure is of size P– that is vectorization of the input follows the hierarchy
Examiner note:
Wang recites a two level of hierarchy have: P x Q which P is outer structure and Q is inner structure.
Wang recites that Input signal
x
∈
R
P
×
Q
which vectorization of the input follows the hierarchical structure that have dimension of P x Q
receiving feature vectors receiving feature vectors whose indices are in an original hierarchical index space. i.e. Input signal
x
∈
R
P
×
Q
which vectorization of the input follows the hierarchical structure with P x Q is the original hierarchical index space
Limitation 1b - generating a transformation of each mode of the feature vectors
Wang teaches:
Wang, Page 2, Figure 1, "Figure 1: Wreath product can express the symmetries of hierarchical structures: wreath product of three groups U~K~H acting on the set of elements P × Q × R, can be seen as independent copies of groups, H, K and U at different level of hierarchy acting on copies of P;Q and R. Intuitively, a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H, performs pooling over leaves under each inner node , applies equivariant map for each inner structure (i.e.,WU, WK, WH respectively), and broadcasting the output back to the leaves. A U~K~H-equivariant map can be constructed as the sum of these three contributions, from equivariant maps at each level of hierarchy."
PNG
media_image1.png
315
1246
media_image1.png
Greyscale
Figure 1
Examiner notes:
Wang Figure 1 show that U~, K~, H~ acting on the set of elements P × Q × R at different level of hierachy. So each of Wang 's element has a form of (p,q,r) ∈ P x Q x R., and Wang expressly show that P,Q,R structures at different level of the hierarchy.
Wang recites from equivariant maps at each level hierarchy.
generating a transformation i.e. from equivariant maps (1)
However, Wang teaches generating a transformation at different level of the hierarchy, Wang did not explicitly teach each mode of the feature vectors represent each level of the hierarchy
Hanselmann teaches:
Hanselmann, paragraph [0020], “In a further advantageous example embodiment of the present invention, the numerical codes include vectors that have separate components for the levels of the tree in each case. …Each component assigned to a level then indicates a direction in which branching took place on the path from the root of the tree to the nodes in the transition to the respective level.”
Examiner notes:
Hanselmann recites a hierarchical tree using numerical code that includes vectors that separate comments for the level of the hierarchical tree and each component is assigned to a respective level of the hierarchy.
Examiner is interpreting a "mode" based on/in light of the definition from paragraph [0014] as an individual index. Hanselmann shows an individual index can be understood as separate component of a vector.
Accordingly, because the claim’s mode is an individual index, an individual index or component corresponding to respective level of the hierarchy.
So, each mode of the feature vectors i.e. each level of the hierarchy (2)
From (1) and (2) therefore, generating a transformation of each mode of the feature vectors i.e. from equivariant maps at each level of hierarchy.
Limitation 1c - the transformation including a pooling operation, a transformation operation, and an unpooling operation
Wang teaches:
PNG
media_image1.png
315
1246
media_image1.png
Greyscale
Wang, Page 2, Figure 1, "Figure 1: Wreath product can express the symmetries of hierarchical structures: wreath product of three groups U~K~H acting on the set of elements P × Q × R, can be seen as independent copies of groups, H, K and U at different level of hierarchy acting on copies of P;Q and R. Intuitively, a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H, performs pooling over leaves under each inner node , applies equivariant map for each inner structure (i.e.,WU, WK, WH respectively), and broadcasting the output back to the leaves. A U~K~H-equivariant map can be constructed as the sum of these three contributions, from equivariant maps at each level of hierarchy."
Figure 1
Examiner notes:
the transformation i.e. a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H
a pooling operation i.e. pooling over leaves under each inner node
transformation operation i.e. applies equivariant maps for each inner structure (i.e.,WU, WK, WH respectively),
an unpooling operation i.e. broadcasting the output back to the leaves
Limitation 1d - the pooling operation aggregates and collapses the feature vectors so that a coarse-grained feature set having a collapsed index space is produced
Wang teaches:
Wang, Page 7, Section 4.3, "With equivariant maps for direct product of groups, efficient implementation of
W
K
×
H
using efficient implementation for individual blocks
W
K
, and
W
H
is non-trivial – e.g., consider 2D convolution. In contrast, it is possible to use a black-box implementation of the parameter-sharing layers for
W
K
,,and
W
H
to construct
W
K
~
H
…let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
×
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form ”
Wang, page 7, Equation (3)”
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
where the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures)”
Alloyed, page 7, Section 4.3, Example 5: “Consider a coarse pixelization of an image into small patches. Eq. (3) gives the following recipe for a layer equivariant to independent translations within each patch as well as global translation of the coarse image: 1) apply convolution to each patch independently; 2) pool over each patch, apply convolution to the coarse image”
Wang, page 6, Section 4.2.2, Theorem 4.1, “Equation (2),
W
K
~
H
≔
W
H
⊗
1
Q
1
Q
⊤
+
I
P
⊗
W
K
where
1
Q
= [1,...,1]⊺
Examiner note:
Wang, Equation (3) recites that Pooling operation is
m
a
t
x
1
Q
where
m
a
t
(
x
)
∈
R
P
×
Q
is a matrix has (P x Q) dimension and Wang, Equation (2) recite
1
Q
is matrix that has (Q x 1) dimension. So, the result of multiplication of 2 matrix (P x Q) (Q x 1) = (P x 1). Which means dimension Q has collapsed.
the pooling operation aggregates and collapses the feature vectors i.e. the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures), and collpased it form (P x Q) to (P x 1)
that a coarse-grained feature set i.e. pool over each patch, apply convolution to the coarse image
a coarse-grained feature set having a collapsed index space is produced i.e. pool over each patch so that a coarse pixelization of an image have dimensions collapse from (P x Q) to (P x 1)
Limitation 1e - the transformation operation transforms the coarse-grained feature set into a transformed feature set that preserves the collapsed index space
Wang teaches:
Wang, Page 7, Section 4.3, " Wang, Page 7, Section 4.3, "With equivariant maps for direct product of groups, efficient implementation of
W
K
×
H
using efficient implementation for individual blocks
W
K
, and
W
H
is non-trivial – e.g., consider 2D convolution. In contrast, it is possible to use a black-box implementation of the parameter-sharing layers for
W
K
,,and
W
H
to construct
W
K
~
H
…let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form”
Wang, page 7, Equation (3)”
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
where the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures), and after application of the H-equivariant map
W
H
to the pooled value.
Wang, page 6, Section 4.2.2, Theorem 4.1 “
W
H
∈ RP×P is H-equivariant”
Alloyed, page 7, Section 4.3, Example 5: “Consider a coarse pixelization of an image into small patches. Eq. (3) gives the following recipe for a layer equivariant to independent translations within each patch as well as global translation of the coarse image: 1) apply convolution to each patch independently; 2) pool over each patch, apply convolution to the coarse image”
Examiner notes:
the transformation operation transforms the coarse-grained feature set i.e. after application of the H-equivariant map
W
H
to the pooled value, in which the pool value is the outcome of the first multiplication mat(x)1Q taught in 1d or after pool over each patch, apply convolution to the coarse image
a transformed feature set that preserves the collapsed index space i.e. Theorem 4.1 recites pooled value have P x 1 dimension from 1d remain P x 1 dimension because
W
H
∈ RP×P is H-equivariant.
Limitation 1f - wherein the unpooling operation generates a final feature set in the original hierarchical index space by reverting pooling from the transformed feature set
Wang teaches:
Wang, page 7, Equation (3)” Wang, Page 7, Section 4.3, "With equivariant maps for direct product of groups, efficient implementation of
W
K
×
H
using efficient implementation for individual blocks
W
K
, and
W
H
is non-trivial – e.g., consider 2D convolution. In contrast, it is possible to use a black-box implementation of the parameter-sharing layers for
W
K
,,and
W
H
to construct
W
K
~
H
…let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
where the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures), and after application of the H-equivariant map
W
H
to the pooled value, the result is broadcasted back using right multiplication by
1
Q
⊤
”
Wang, page 7, Example 5, “and broadcast back to individual pixels in each patch.”
Wang, page 6, Section 4.2.2, Theorem 4.1, “Equation (2),
W
K
~
H
≔
W
H
⊗
1
Q
1
Q
⊤
+
I
P
⊗
W
K
where
1
Q
= [1,...,1]⊺
Examiner note:
The result after H-equivariant map
W
H
have dimension P x 1, and Equation (2) recites
1
Q
⊤
have dimension 1 x Q. So multiplication of 2 matrix (P x 1)(1 x Q) = P x Q, which is the original hierarchical dimension of the input.
the unpooling operation generates a final feature set / reverting pooling from the transformed feature set i.e. the result is broadcasted back using right multiplication by
1
Q
⊤
the original hierarchical index space i.e. (P x 1)(1 x Q) = P x Q, which is the original hierarchical dimension before pooling
Limitation 1g - transforming the feature vectors without any pooling or unpooling to produce an additional set of transformed feature vectors
Wang teaches:
Wang, Page 7, Section 4.3, Equation (3) “let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
×
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
The second term simply transforms each inner structure using
W
K
”
Wang, Page 6, Section 4.2.2, Theorem 4.1, " WK ∈ RQxQ”
Examiner note:
first term of equation (3),
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
which is pooling
m
a
t
x
1
Q
taught in limitation 1d, transformation
W
H
taught in limitation 1e and unpooling
1
Q
⊤
taught in limitation 1f
Equation 3 recite
m
a
t
x
∈
R
P
×
Q
, Theorem 4.1 recite WK ∈ RQxQ,
Second term of equation (3),
m
a
t
x
W
K
simply transforms each inner structure using
W
K
, without pooling
m
a
t
x
1
Q
and unpooling
1
Q
⊤
Second term
m
a
t
x
W
K
is multiplication of 2 matrix (P x Q)(Q x Q) = P x Q, which is the original hierarchical dimension of the input.
transforming the feature vectors without any pooling or unpooling to produce an additional set of transformed feature vectors i.e. second term
m
a
t
x
W
K
Limitation 1h - generating a summation that preserves the original hierarchical index space by summing the final feature set and the additional set of transformed feature vectors.
Wang teaches:
Wang, Page 7, Section 4.3, Equation (3),
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
Examiner note:
first term of equation (3)
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
is the final set that has been pooling
m
a
t
x
1
Q
taught in limitation 1d, transformation
W
H
taught in limitation 1e and unpooling
1
Q
⊤
taught in limitation 1f
The second term is
m
a
t
x
W
K
is the additional set of transformed feature vectors without pooling or unpooling
Equation (3) show that they are getting sum to each other
generating a summation that preserves the original hierarchical index space by summing the final feature set and the additional set of transformed feature vectors. i.e the summation between first term which have (P x Q) dimension and second term which have (P x Q) dimension, the result will be (P x Q) which is the original hierarchical dimension of input.
It would have been obvious to a person having ordinary skill in the art at a time before the effective filing date of claim invention to have further modified the Wang disclosures and teachings by determined transformation of each mode of feature vector in an original index space, and each mode of the feature vector represent each level in the hierarchical structure, method can be perform on a computer taught or suggested by Hanselmann. Such a person would have been motivated to do so with a reasonable expectation of success to allow transformation of feature vector and perform it on each level of hierarchical structure (Hanselmann, par [0020]) using a computer Hanselmann, par [0039])
Regarding claim 2,
(preamble) - The computer-implemented method of claim 1 (preamble)
Limiation 2a - generating a transformation of the feature vectors to include the generated summation that preserves the original hierarchical index space
The combination Wang and Hanselmann teach:
Wang, Page 7, Section 4.3, Equation (3),
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
Examiner note:
first term of equation (3)
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
is the final set that has been pooling
m
a
t
x
1
Q
, transformation
W
H
and unpooling
1
Q
⊤
as established with respect to claim 1
The second term is
m
a
t
x
W
K
is the additional set of transformed feature vectors without pooling or unpooling
Equation (3) show that they are getting sum to each other
generating a transformation of the feature vectors to include the generated summation that preserves the original hierarchical index space. i.e. the summation between first term which have (P x Q) dimension and second term which have (P x Q) dimension, the result will be (P x Q) which is the original hierarchical dimension of input.
Limiation 2b - generating one or more other transformations of the feature vectors that preserve the original hierarchical space
The combination Wang and Hanselmann teach:
Alloyed, page 3, section 3.2, “An Equivariant MLP is a stack of equivariant feed-forward layers, where the composition of equivariant layers is also equivariant.”
Alloyed, page 3, section 3.2, “we assume the same action on the input and output.”
Examiner note:
generating one or more other transformations of the feature vectors that preserve the original hierarchical space i.e. a stack of equivariant feed-forward layers that have same action on the input and output, which means output have the original hierarchical dimension as the input signal.
Limitation 2c - sequentially composing a sequence of transformations that includes the generated transformation of the feature vectors, so that generated one or more other transformations of the feature vectors, so that an output from a given transformation in the sequence is provided as an input to a next transformation in the sequence.
The combination Wang and Hanselmann teaches:
Alloyed, page 3, section 3.2, “For a feed-forward layer
ϕ
∶ x ↦ σ(Wx), where σ is a point-wise non-linearity and W ∈ RN×N”
Alloyed, page 3, section 3.2, “An Equivariant MLP is a stack of equivariant feed-forward layers, where the composition of equivariant layers is also equivariant.”
Alloyed, page 3, section 3.2, “we assume the same action on the input and output.”
Examiner note:
sequentially composing a sequence of transformations that includes the generated transformation of the feature vectors i.e. stack of equivariant feed-forward layers, where the composition of equivariant layers is also equivariant.”
generated one or more other transformations of the feature vectors i.e. taught in 2b
an output from a given transformation in the sequence is provided as an input to a next transformation in the sequence. i.e. the stack of equivariant feed-forward layers are composed, and the data process sequentially, that means the output of this layer will be used as an input for next layer.
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 3,
(preamble) - The computer-implemented method of claim 1
Limitation 3a - processing the feature vectors by using a hierarchical mode-wise pooling (HMP) network that includes a stack of multiple HMP layers intercalated with constructs of a deep neural network, each HMP layer being a given transformation of the feature vectors
The combination Wang and Hanselmann teache:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels… using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
H
+
Π
⊤
[
W
3
*
Π
X
]
multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Wang, page 9, Section 5.2, “The architecture of WREATH PRODUCT NET. is a stack of equivariant layer Eq. (4) plus ReLU nonlinearity and residual connections.”
Examiner note:
processing the feature vectors by using a hierarchical mode-wise pooling (HMP) i.e. Wang use WREATH PRODUCT NET architecture is a stack of equivariant layer Eq. (4), in which
Π
and
Π
⊤
performs the pooling and broadcasting
includes a stack of multiple HMP layers intercalated with constructs of a deep neural network i.e stack of equivariant layer plus ReLU nonlinearity which is non-linear activation function in deep neural network and residual connections in skip connection in deep neural network
each HMP layer being a given transformation of the feature vectors i.e. Wang equivariant layer Eq. (4) is wreath-product equivariant linear layer. So each layer in the stack perform a transformation of input feature vector X to get the output feature vector
ϕ
X
Limitation 3b – (i) the summation that preserves the original hierarchical index space or (ii) another summation that preserves the original hierarchical index space and is generated by summing another final feature set and another additional set of transformed feature vectors.
The combination Wang and Hanselmann teach::
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels… using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
H
+
Π
⊤
[
W
3
*
Π
X
]
multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Wang, page 9, Section 5.2, “The architecture of WREATH PRODUCT NET. is a stack of equivariant layer Eq. (4) plus ReLU nonlinearity and residual connections.”
Examiner note:
Equation (4) using the pool-broadcast interpretation given in Eq. (3), so the output of Equation (4) will have the original hierarchical dimension
(i) the summation that preserves the original hierarchical index space i.e. Equation 4 have the summation between no pooling or unpooling feature vector
X
W
H
and pooling, transformation, unpooling feature vector
Π
⊤
[
W
3
*
Π
X
]
or (ii) another summation that preserves the original hierarchical index space and is generated by summing another final feature set and another additional set of transformed feature vectors. i.e. Eq. (4) is a stack of equivariant that has ReLU non-linearity and residual connection, so it provides another layer that have corresponding summation.
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 4,
(preamble) - The computer-implemented method of claim 1
Limitation 4a - The feature vectors are
X
:
=
x
λ
:
λ
∈
Λ
,
x
λ
∈
R
D
, wherein the original hierarchical index space is
Λ
,
The combination Wang and Hanselmann teach::
Wang, Page 7, Section 4.3, "let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
×
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form”
Wang, Page 7, Section 4.3, “Throughout, we are assuming a single input-output channel, relying on the idea that having multiple channels simply corresponds to replicating the linear map for each input-output channel combination.”
Wang, Page 6, Section 4.2.2., “vectorization of the input follows the hierachy”
Wang, page 9, Section 5.1, “
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels.
Examiner note:
Examiner is interpreting
λ
an index identifying a feature vector within the original hierarchical index space (i.e. a hierarchical position e.g. (p x q))
Examiner is interpreting
x
λ
as an individual feature vector (i.e. the input signal at position
λ
)
Examiner is interpreting “
D
” as an individual feature dimension (i.e. the number of input channels C).
the original hierarchical index space
Λ
i.e. original hierarchical position e.g. (P x Q))
Therefore, the feature vectors are
X
:
=
x
λ
:
λ
∈
Λ
,
x
λ
∈
R
D
i.e.
X
:
=
x
(
p
,
q
)
:
(
p
,
q
)
∈
(
P
×
Q
)
,
x
(
p
,
q
)
∈
R
C
Limitation 4b - the computer-implemented method further comprises computing
f
X
=
L
0
X
+
Σ
m
∈
M
T
m
X
is a transformation of the feature vectors
X
preserving the original hierarchical index space
Λ
, wherein
L
0
X
is a transformation of the feature vectors
X
without pooling, wherein a mode is denoted by m, wherein M is a set of modes of interest, and wherein
T
m
X
is a mode-wise transformation for the mode m.
The combination Wang and Hanselmann teach:
Wang, page 7, Equation (3)”
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
where the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures), and after application of the H-equivariant map
W
H
to the pooled value, the result is broadcasted back using right multiplication by
1
Q
⊤
. The second term simply transforms each inner structure using
W
K
PNG
media_image1.png
315
1246
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Greyscale
Wang, Page 2, Figure 1, Wreath product can express the symmetries of hierarchical structures: wreath product of three groups U~K~H acting on the set of elements P × Q × R, can be seen as independent copies of groups, H, K and U at different level of hierarchy acting on copies of P;Q and R. Intuitively, a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H, performs pooling over leaves under each inner node , applies equivariant map for each inner structure (i.e.,WU, WK, WH respectively), and broadcasting the output back to the leaves. A U~K~H-equivariant map can be constructed as the sum of these three contributions, from equivariant maps at each level of hierarchy.
Examiner note:
a transformation of the feature vectors
X
preserving the original hierarchical index space
f
X
i.e. equivariant map
W
K
~
H
x
has the original hierarchical dimension before transformation, as established with respect to claim 1
L
0
X
is a transformation of the feature vectors
X
without pooling i.e. the second term simply transforms each inner structure using
W
K
without pooling or unpooling, as established with respect to claim 1
T
m
X
is a mode-wise transformation for the mode m. i.e.
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
a transformation using pool, transformation, unpooling for each mode as established with respect to claim 1
a mode is denoted by m i.e., each level of the hierarchy as established with respect to claim 1
Wang figure 1 recites that U~K~H-equivariant map can be constructed as the sum of these three contributions, from equivariant maps at each level of hierarchy. So, M i.e. the set of hierarchy of levels. And
Σ
m
∈
M
T
m
X
i.e. the sum of equivariant maps.
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 5,
(preamble) - The computer-implemented method of claim 4 (preamble)
Limitation 5a - further comprising computing the mode-wise transformation for the mode m by computing
T
m
X
≔
P
m
*
(
L
m
P
m
X
)
,wherein
P
m
is the pooling operation, wherein
L
m
is the transformation operation, wherein
P
m
*
is the unpooling operation
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels… using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
1
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Examiner note:
P
m
is the pooling operation i.e.
Π
X
performs pooling.
L
m
is the transformation operation i.e. convolution kernel
W
3
with C’ is the output channels
P
m
*
is the unpooling operation i.e.
Π
⊤
performs unpooling
Limitation 5b - the coarse-grained feature set resulting from the pooling operation is
Z
≔
z
τ
:
τ
∈
Λ
m
,
z
τ
∈
R
D
, wherein
Λ
m
is a space of aggregation types and is computed by
Λ
m
≔
τ
m
λ
:
λ
∈
Λ
,
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels. In addition to 3D coordinates, these channels may include RGB values, normal vectors or any other auxiliary information…Let
Π
∈
{
0,1
}
D
3
×
N
with one non-zero per column identify the voxel membership.…using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
1
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Examiner notes:
the coarse-grained feature set resulting from the pooling operation is
Z
i.e.
Π
X
performs the pooling form points within voxels
Examiner is interpreting
z
τ
as a pool feature vector (i.e. a pooled voxel feature after pooling operation)
Examiner is interpreting
τ
as a type of aggregation types (i.e. a voxel index)
Λ
m
i.e. a set of voxel indices
Examiner is interpreting
D
as an individual feature dimension (i.e. the number of input channels C)
τ
m
λ
i.e. a set of voxels membership of index
λ
Limitation 5c - wherein the transformed feature set is
Z
~
≔
z
~
t
:
τ
∈
Λ
m
,
z
~
t
∈
R
D
~
, wherein
D
~
is a value specified by a user
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels. In addition to 3D coordinates, these channels may include RGB values, normal vectors or any other auxiliary information. Consider a voxelization of the point cloud with a resolution D voxels per dimension, and consider the hierarchy of translation symmetry across voxels and permutation symmetry within each voxel. Let
Π
∈
{
0,1
}
D
3
×
N
with one non-zero per column identify the voxel membership.…using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
1
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Wang, page 17, Part C, Section C.1, “The number channel is fixed 64”
Examiner note:
transformed feature set
Z
~
i.e.
W
3
*
Π
X
still have the same voxel/coarse index space/dimension as
Π
X
Examiner is interpreting
z
~
t
as a transformed feature with type
τ
(i.e. transformed voxel feature)
Examiner is interpreting
τ
as a type of aggregation types (i.e. a voxel index)
Λ
m
i.e. a set of voxel indices
D
~
i.e. C’ output channels, which fixed at 64 that can be specified by a user.
Limitation 5d - wherein the final feature set is
Y
:
=
y
λ
:
λ
∈
Λ
,
y
λ
∈
R
D
~
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels. In addition to 3D coordinates, these channels may include RGB values, normal vectors or any other auxiliary information. Consider a voxelization of the point cloud with a resolution D voxels per dimension, and consider the hierarchy of translation symmetry across voxels and permutation symmetry within each voxel. Let
Π
∈
{
0,1
}
D
3
×
N
with one non-zero per column identify the voxel membership.…using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
1
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Examiner note:
final feature set
Y
i.e.
Π
⊤
[
W
3
*
Π
X
]
performs the broadcasting to points within voxels
Examiner is interpreting
y
λ
as a transformed feature vector with type
τ
(i.e. transformed voxel feature)
Examiner is interpreting
τ
as a type of aggregation type (i.e. a voxel index)
D
~
i.e. C’ output channels, which are fixed at 64 that can be specified by a user.
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 6,
(preamble) - The computer-implemented method of claim 5
Limitation 6a - wherein the pooling operation is selected from the group consisting of mean pooling, sum pooling, and max pooling
ϕ
m
a
g
g
The combination Wang and Hanselmann teach:
Wang, page 5.1, Section 5.1, “In the equation above pooling operation can replace summation (implicit in matrix multiplication) with any other commutative operation; …we use mean-pooling for the experiments.”
Wang
Examiner note:
the pooling operation is selected from the group consisting of mean pooling, sum pooling, and max pooling
ϕ
m
a
g
g
i.e. the pooling operation can replace summation or use the mean-pooling
Limitation 6b - such that
z
τ
≔
ϕ
m
a
g
g
x
λ
:
λ
m
=
τ
wherein
λ
m
is an aggregation type of
λ
The combination Wang and Hanselmann teach:
Wang, Page 7, Section 4.3, "let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
×
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form … pools over columns (inner structures),”
Examiner note:
As established with respect to claim 1 in the claim chain. Wang recites the input signal that have hierarchical structure P x Q, where P is outer structure and outer structure. Wang also recites s (P x Q) matrix, and perform pooling over columns which is Q (inner structure)
As established with respect to claim 4 in the claim chain. Wang recites
λ
can be represented as a hierarchical position e.g. (p x q), and
x
λ
can be represented as the input signal at position
λ
As established with respect to claim 5 in the claim chain. Wang recites
z
τ
can be represented as a pooled voxel feature after pooling operation,
τ
can be represented as a voxel index
Because of Wang pool operation pool over column Q (inner structure), so (p,q) after pooling over q, p remains and q is collapse Thus, the aggregation types
λ
m
only have p left i.e.
λ
m
=
p
=
τ
. The pooling operation also produces the pooled voxel feature
z
τ
=
z
p
:
=
ϕ
m
a
g
g
(
x
p
,
q
:
λ
m
=
p
)
Limitation 6c -
λ
m
≔
λ
m
'
:
m
'
∉
s
u
b
m
, and wherein sub(m) is a substructure associated with the mode m, the substructure being the mode m and the descendants of the mode m.
The combination Wang and Hanselmann teach:
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315
1246
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Greyscale
Wang, Page 2, Figure 1, "Figure 1: Wreath product can express the symmetries of hierarchical structures: wreath product of three groups U~K~H acting on the set of elements P × Q × R, can be seen as independent copies of groups, H, K and U at different level of hierarchy acting on copies of P;Q and R. Intuitively, a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H, performs pooling over leaves under each inner node
PNG
media_image2.png
261
941
media_image2.png
Greyscale
Wang, Page 7, Section 4.2.3, “With more than two levels, the symmetry group involves more than one wreath product, which means that the equivariant map for the hierarchy is given by a recursive application of Theorem 4.1.
Examiner note:
Examiner is interpreting
m
'
as mode form the mode hierarchy that does not include belong to sub(m)
Examiner is interpreting
λ
m
'
as an individual index of mode m’
As established with respect to claim 1 in the claim chain, mode m corresponding to level of hierarchical in Wang.
Wang, figure 1, recites a multi-level hierarchy with {P, Q, R}, where Q below P and R is below Q. If mode m is at Q, then R corresponds to be a descendant mode of m. Then substructure associated with the mode m is sub(m) = {Q, R}
Wang also recites that after pooling over leaves under each inner node. The inner q, r, only the outer p remain which mean {p,q,r} after pooling only p remain.
The only aggregation type p
∉
s
u
b
m
Regarding claim 8,
(preamble) - The computer-implemented method of claim 1
Limitation - wherein the unpooling operation is implemented by broadcasting such that
y
λ
:
=
z
'
[
λ
]
m
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels. In addition to 3D coordinates, these channels may include RGB values, normal vectors or any other auxiliary information. Consider a voxelization of the point cloud with a resolution D voxels per dimension, and consider the hierarchy of translation symmetry across voxels and permutation symmetry within each voxel. Let
Π
∈
{
0,1
}
D
3
×
N
with one non-zero per column identify the voxel membership.…using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
H
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Examiner note:
Examiner is interpreting
λ
an index identifying a feature vector within the original hierarchical index space (i.e. an individual point index in the input point cloud that which has original hierarchical position (p,q)).
Examiner is interpreting
m
as mode (i.e. each level of the hierarchy as established with respect to claim 1)
Examiner is interpreting
λ
m
as the aggregation type associated with
λ
(i.e. the voxel identifier of
λ
)
Examiner is interpreting
z
'
[
λ
]
m
as the transformed pool feature that associated with aggregation type
λ
m
(i.e. transformed pooled voxel feature in
W
3
*
Π
X
]
)
Wang recites
λ
=
(
p
,
q
)
, after pooling (p,q), p only remains. So
λ
m
=
p
. The transformation operation produces transformed pooled voxel feature
z
'
p
. Wang’s broadcasting operation
Π
⊤
creates
y
(
p
,
q
)
=
z
'
p
and because
λ
m
=
p
. Therefore,
y
λ
=
z
'
[
λ
]
m
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 9,
(preamble) - The computer-implemented method of claim 1
Limitation - wherein a mode is denoted by m, and wherein the pooling operation further aggregates and collapses the feature vectors across indices of an aggregation type, which includes elements of a mode hierarchy except for the mode m in the mode hierarchy and descendants of the mode m in the mode hierarchy.
The combination Wang and Hanselmann teach:
Wang, Page 2, Figure 1, "Figure 1: Wreath product can express the symmetries of hierarchical structures: wreath product of three groups U~K~H acting on the set of elements P × Q × R, can be seen as independent copies of groups, H, K and U at different level of hierarchy acting on copies of P;Q and R. Intuitively, a linear map WU~K~H : RPQR → RPQR equivariant to U~K~H, performs pooling over leaves under each inner node , applies equivariant map for each inner structure (i.e.,WU, WK, WH respectively), and broadcasting the output back to the leaves. A U~K~H-equivariant map can be constructed as the sum of these three
PNG
media_image1.png
315
1246
media_image1.png
Greyscale
contributions, from equivariant maps at each level of hierarchy."
Examiner note:
As established with respect to claim 1 in the claim chain, mode m corresponding to level of hierarchical in Wang.
Wang, figure 1, recites a multi-level hierarchy with {P, Q, R}, where Q below P and R is below Q. If mode m is at Q, then R corresponds to be a descendant mode of m. So the collapse feature vector is Q, R and the remaining is P
Therefore. an aggregation type which includes elements of a mode hierarchy (i.e. P), not include the mode m in the mode hierarchy (i.e. Q) and descendants of the mode m in the mode hierarchy (i.e. R)
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 10,
(preamble) - The computer-implemented method of claim 1
Limitation - the generating the transformation of each mode includes computing a sequential composition of the pooling operation, the transformation operation, and the unpooling operation.
The combination Wang and Hanselmann teach:
Wang, page 7, Equation (3)” Wang, Page 7, Section 4.3, "With equivariant maps for direct product of groups, efficient implementation of
W
K
×
H
using efficient implementation for individual blocks
W
K
, and
W
H
is non-trivial – e.g., consider 2D convolution. In contrast, it is possible to use a black-box implementation of the parameter-sharing layers for
W
K
,,and
W
H
to construct
W
K
~
H
…let
x
∈
R
P
×
Q
be the input signal, and
m
a
t
(
x
)
∈
R
P
Q
denote its matrix form; for example in a set of sets, each column is an inner set in this matrix form
W
K
~
H
x
≔
v
e
c
{
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
+
m
a
t
x
W
K
}
where the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures), and after application of the H-equivariant map
W
H
to the pooled value, the result is broadcasted back using right multiplication by
1
Q
⊤
”
Examiner note:
the pooling operation i.e. the first multiplication
m
a
t
x
1
Q
pools over columns (inner structures)
the transformation operation i.e. application of the H-equivariant map
W
H
to the pooled value,
W
H
m
a
t
x
1
Q
the unpooling operation i.e. the result is broadcasted back using right multiplication by
1
Q
⊤
,
[
W
H
m
a
t
x
1
Q
]
1
Q
⊤
Wang equation (3) show that pooling operation, transformation operation and unpooling operation are perform sequentially
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 11,
(preamble) - The computer-implemented method of claim 1
Limitation - the transforming the feature vectors without any pooling or unpooling includes transforming the feature vectors for an entirety of the indices.
The combination Wang and Hanselmann teach:
Wang, page 9, Section 5.1, Equation (4)”
x
∈
R
N
×
C
be the input point cloud, where N is the number of points and C is the number of input channels… using the pool-broadcast interpretation given in Eq. (3), results in the following wreath-product equivariant linear layer
ϕ
X
=
X
W
1
+
Π
⊤
[
W
3
*
Π
X
]
where
W
1
∈
R
C
×
C
'
.
, denotes the convolution operation,
W
3
∈
R
K
3
×
C
×
C
'
.
. is the convolution kernel, with kernel width K, and C’ output channels. Here, multiplication with
Π
and
Π
⊤
performs the pooling and broadcasting from/to points within voxels, respectively. “
Examiner note:
the transforming the feature vectors without any pooling or unpooling i.e
X
W
1
does not have the pooling
Π
or broadcasting
Π
⊤
includes transforming the feature vectors for an entirety of the indices. i.e.
X
W
1
include feature vectors for all N input points
The reasons of obviousness have been noted in the rejection of Claim 1 above and applicable herein.
Regarding claim 12, it is rejected for similar reasons as claim 1
A computer system comprising: a processor set; a set of one or more computer-readable storage media; and program instructions, collectively stored in the set of one or more computer-readable storage media, for causing the processor set to perform the following computer operations to perform the steps recited in claim 1. (Hanselmann’s claim 30)
Regarding claim 13, it is rejected for similar reasons as claim 2
Regarding claim 14, it is rejected for similar reasons as claim 3
Regarding claim 15, it is rejected for similar reasons as claim 4
Regarding claim 16, it is rejected for similar reasons as claim 5
Regarding claim 17, it is rejected for similar reasons as claim 1
A computer program product comprising: a set of one or more computer-readable storage media; and program instructions, collectively stored in the set of one or more computer-readable storage media, for causing a processor set to perform the following computer operations: to perform the steps recited in claim 1 (Hanselmann’s claim 30)
Regarding claim 18, it is rejected for similar reasons as claim 2
Regarding claim 19, it is rejected for similar reasons as claim 3
Regarding claim 20, it is rejected for similar reasons as claim 4
Claims 7 is rejected under 35 U.S.C. 103 as being unpatentable over Wang et al (Equivariant Maps for Hierarchical Structures) in view of Hanselmann et al (US 20230032634 A1) as applied in claim 5, and further view of Ji et al (JointContrast: Skeleton-Based Interaction Recognition with New Representation and Contrastive Learning)
Regarding claim 7,
The combination Wang and Hanselmann teach:
The computer-implemented method of claim 5 (preamble)
The combination Wang and Hanselmann does not explicitly teach:
wherein the transformation operation is a linear mapping, such that
z
~
τ
~
=
Σ
τ
ϵ
N
m
τ
~
W
τ
~
τ
m
z
τ
, wherein each
W
τ
~
τ
m
∈
R
D
~
×
D
is learnable matrix and
N
m
τ
~
is a suitable neighbor of type
τ
~
Ji teaches:
wherein the transformation operation is a linear mapping, such that
z
~
τ
~
=
Σ
τ
ϵ
N
m
τ
~
W
τ
~
τ
m
z
τ
, wherein each
W
τ
~
τ
m
∈
R
D
~
×
D
is learnable matrix and
N
m
τ
~
is a suitable neighbor of type
τ
~
Ji, Page 4, Section 3, Part 3.1, “Define the neighboring set of
V
t
i
as
N
(
V
t
i
)
”
Ji, Page 4, Section 3, Equation (1), “The graph convolution is calculated in the form of:
Y
V
t
i
=
∑
V
t
i
∈
N
V
t
i
1
Z
t
i
V
t
i
X
(
V
t
j
)
W
(
1
V
t
j
)
where
X
(
V
t
j
)
denotes the feature representation of node
V
t
j
“
Ji, Page 6, Section 3, Equation (6), “the improved graph convolution can be expressed as:
Y
V
t
i
=
1
K
1
∑
k
=
0
K
1
-
1
D
k
-
1
ϕ
k
A
t
X
t
W
k
+
1
K
2
∑
k
'
=
0
K
2
-
1
D
k
'
'
ϕ
k
'
'
B
t
X
t
'
W
k
'
Ji, Page 6, Section 3, Part 3.2, “
W
k
'
∈
R
C
'
×
C
is a matrix of learnable parameters formed by superimposing the weight vectors of multiple output channels, where C and C’ represent the input and output feature dimensions, respectively.
Examiner note:
the transformation operation is a linear mapping i.e. equation (1) teaches that graph convolution
Y
V
t
i
is an output from features
X
(
V
t
j
)
z
τ
i.e.
X
(
V
t
j
)
denotes the feature representation of node
V
t
j
N
m
τ
~
is a suitable neighbor of type
τ
~
i.e. the neighboring set of
V
t
i
as
N
(
V
t
i
)
W
τ
~
τ
m
∈
R
D
~
×
D
is learnable matrix i.e.
W
k
'
∈
R
C
'
×
C
is a matrix of learnable parameters
It would have been obvious to a person having ordinary skill in the art at a time before the effective filing date of the application to have further modified the Wang and Hanselmann disclosures and teachings by performing transformation operation on each mode of feature vector and transform operation using a linear mapping that include a suitable neighbor, a learnable matrix taught and suggested by Ji. Such a person would have been motivated to do so with a reasonable expectation of success that equivariant map using and a linear map that include the neighboring set and a matrix of learnable parameters (Ji, equation (1) and (6))
Conclusion
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/HAO THIEN VONG/Examiner, Art Unit 2147
/VIKER A LAMARDO/Supervisory Patent Examiner, Art Unit 2147
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