there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix. you should probably review your linear algebra textbook (hint: scaling is extremely important).
i don't understand who is having trouble reading the dialogue here you or i;
> there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix... (hint: scaling is extremely important)
...
> SVD is the decomposition of a matrix into two rotation matrices and a scaling matrix, by definition:
yes that's exactly what i was implying when i said SVD more than just rotation, scaling is also important.
my point, which is my same original point, is that if you think learning about rotation/euler matrices is going to prepare you in any way, shape, or form for ML (vis-a-vis SVD/PCA or RoPE or anything else) you're in for a very rude awakening.
PCA is an orthogonal transformation of the covariance matrix, so like all orthogonal transformations, it’s _literally a rotation_ in N-dimensional space.
SVD is more complex but ultimately it’s just another useful decomposition of a matrix.
I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
Whether or not that helps you with ML depends more on what you’re doing in ML. FAANG doesn’t have a monopoly on ML or on interesting work in ML.
> PCA is an orthogonal transformation of the covariance matrix
Yes you're now the second person the literally repeat the same thing I've already stated extremely clearly and succinctly: PCA is not just rotation (hint: you also need to understand covariance).
> I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
I've already literally drawn the analogy/metaphor that I've drawn: if you think 2d/3d rotation matrices as they are used in graphics is any kind of introduction to the matrices in ML (modeling linear transformations or otherwise) then you're probably the type of person that believes that cash registers any kind of introduction to finance.
My point is not that hard to understand. Graphics in no way, way, shape, or form prepares you for ML. I don't understand why this is so controversial.
Have you done any serious graphics programming? Even at the OpenGL 1.x level? What you’re saying just doesn’t make sense.
Just because you’re rotating and translating things in 3-space doesn’t negate that you have a stack of transforms that relate a point in world space to one on screen space and you want to be able to project from one to the other.
Nor does it make it any easier when you need to think about how to stack transforms to achieve effects like rendering a mirror.
I honed a lot of useful practical skill with linear algebra trying to get graphics to do what I wanted. And I say this as someone who’s spent the bulk of my career using linear algebra in the context of quantum mechanics, physical simulation, and ML-adjacent areas.
> negate that you have a stack of transforms that relate a point in world space to one on screen space and you want to be able to project from one to the other.
no it doesn't "negate", it's all completely orthogonal (pun) or irrelevant. like for real just please take a look at
> tell me which operators you’re imagining have any resemblance with typical graphics linear algebra
FWIW, since it seems like you’re unaware: most of those are used in graphics in general, and have been used since long before Torch existed. Convolution’s extremely common. Pooling is just a type of image resampling to graphics people. Non-linear activations are just response functions that graphics people use for colors for example, also volume rendering. Normalization, linear, distance, vision, and shuffle layers are all absolutely standard common operations in graphics, on everything from images to meshes to volumes to matrices.
BTW, most of those Torch layers aren’t “linear algebra” per se, they are just convenient building blocks for neural networks, many of which are also convenient building blocks for graphics… and for similar reasons.
Was your point implicitly limited to rotations or a raster pipeline’s model-view-projection matrix? That certainly does not amount to all “graphics”, right?
> Graphics in no way, way, shape, or form prepares you for ML. I don't understand why this is so controversial.
This isn’t really controversial, it’s just not particularly true as stated. Graphics is much more than 3d rotation matrices, and doing real modern graphics involves all kinds of linear algebra, with immense amounts of overlap between the linear algebra that ML and computer vision use.
Perhaps missing from this conversation is any thoughtful consideration to the history of today’s ML and the cross pollination between the fields we call graphics, vision, and ML. The implicit assumption you seem to be making that they are distinct fields without a shared history and co-development and without a shared foundation is not a good assumption.
I personally know enough ex-graphics people that transitioned to ML and were well prepared by graphics and are wildly successful in ML that it makes your claim sound somewhat ignorant of what’s happened and is happening in both graphics and ML from my perspective, for what it’s worth.
https://en.wikipedia.org/wiki/Singular_value_decomposition
> there is absolutely no sense in which the SVD/PCA decomposition is just a rotation matrix... (hint: scaling is extremely important)
...
> SVD is the decomposition of a matrix into two rotation matrices and a scaling matrix, by definition:
yes that's exactly what i was implying when i said SVD more than just rotation, scaling is also important.
my point, which is my same original point, is that if you think learning about rotation/euler matrices is going to prepare you in any way, shape, or form for ML (vis-a-vis SVD/PCA or RoPE or anything else) you're in for a very rude awakening.
> I've been in ML for ~5 years in multiple FAANGs and I have never seen a rotation matrix.
Presumably you've used SVD, but you've never seen a rotation matrix. So something is cooked.
Maybe corollary: that FAANG job wasn't that interesting.
SVD is more complex but ultimately it’s just another useful decomposition of a matrix.
I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
Whether or not that helps you with ML depends more on what you’re doing in ML. FAANG doesn’t have a monopoly on ML or on interesting work in ML.
Yes you're now the second person the literally repeat the same thing I've already stated extremely clearly and succinctly: PCA is not just rotation (hint: you also need to understand covariance).
> I’m not sure why you’re both negative and dismissive. Transformation matrices in graphics are a good and approachable way to get used to linear transformations, which turn out to be useful pretty much everywhere.
I've already literally drawn the analogy/metaphor that I've drawn: if you think 2d/3d rotation matrices as they are used in graphics is any kind of introduction to the matrices in ML (modeling linear transformations or otherwise) then you're probably the type of person that believes that cash registers any kind of introduction to finance.
My point is not that hard to understand. Graphics in no way, way, shape, or form prepares you for ML. I don't understand why this is so controversial.
Have you done any serious graphics programming? Even at the OpenGL 1.x level? What you’re saying just doesn’t make sense.
Just because you’re rotating and translating things in 3-space doesn’t negate that you have a stack of transforms that relate a point in world space to one on screen space and you want to be able to project from one to the other.
Nor does it make it any easier when you need to think about how to stack transforms to achieve effects like rendering a mirror.
I honed a lot of useful practical skill with linear algebra trying to get graphics to do what I wanted. And I say this as someone who’s spent the bulk of my career using linear algebra in the context of quantum mechanics, physical simulation, and ML-adjacent areas.
no it doesn't "negate", it's all completely orthogonal (pun) or irrelevant. like for real just please take a look at
https://docs.pytorch.org/docs/2.12/nn.html
and tell me which operators you're imagining have any resemblance with typical graphics linear algebra.
like when you people make such claims do you really have anything concrete in mind or just hype?
FWIW, since it seems like you’re unaware: most of those are used in graphics in general, and have been used since long before Torch existed. Convolution’s extremely common. Pooling is just a type of image resampling to graphics people. Non-linear activations are just response functions that graphics people use for colors for example, also volume rendering. Normalization, linear, distance, vision, and shuffle layers are all absolutely standard common operations in graphics, on everything from images to meshes to volumes to matrices.
BTW, most of those Torch layers aren’t “linear algebra” per se, they are just convenient building blocks for neural networks, many of which are also convenient building blocks for graphics… and for similar reasons.
Was your point implicitly limited to rotations or a raster pipeline’s model-view-projection matrix? That certainly does not amount to all “graphics”, right?
> Graphics in no way, way, shape, or form prepares you for ML. I don't understand why this is so controversial.
This isn’t really controversial, it’s just not particularly true as stated. Graphics is much more than 3d rotation matrices, and doing real modern graphics involves all kinds of linear algebra, with immense amounts of overlap between the linear algebra that ML and computer vision use.
Perhaps missing from this conversation is any thoughtful consideration to the history of today’s ML and the cross pollination between the fields we call graphics, vision, and ML. The implicit assumption you seem to be making that they are distinct fields without a shared history and co-development and without a shared foundation is not a good assumption.
I personally know enough ex-graphics people that transitioned to ML and were well prepared by graphics and are wildly successful in ML that it makes your claim sound somewhat ignorant of what’s happened and is happening in both graphics and ML from my perspective, for what it’s worth.
If anyone needs a review it's not cognoboffin.
You led with the claim you have never seen a rotation matrix in ML. I am having doubts about whether you have the ability to recognise one.
I suspect new hires get a free pass as long as they can talk a storm about backpropagation these days.