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The Illustrated Stable Diffusion

jalammar.github.io

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Re: The Illustrated Stable Diffusion

#121

Post by brundolf »

netruk44 wrote: post #9
Waterluvian wrote: post #5

Closer. But I still get lost when words like “tensor” are used. “structured lists of numbers” really doesn’t seem to explain it usefully. This reminds me that explaining seemingly complex things in simple terms is one of the most valuable and rarest skills in engineering. Most people just can’t. And often because they no-longer remember what’s not general knowledge. You end up with a recursive Feynmannian “now explai…

If it helps you to understand at all, assuming you have a CS background, any time you see the word "tensor" you can replace it with "array" and you'll be 95% of the way to understanding it. Or "matrix" if you have a mathematical background. Whereas CS arrays tend to be 1 dimensional, and sometimes 2 dimensional, tensors can be as many dimensions as you need. A 256x256 photo with RGB channels would be stored as a [256…

This is something that infuriates me about formal mathematics (and CS, for that matter): they don't just use the words people already know! They have to make up new words, sometimes even entirely new symbols, that often just mean the same thing as something else. And then the literature becomes entirely inaccessible unless you've learned this secret code. The bottleneck becomes translation, instead of understanding.

Re: The Illustrated Stable Diffusion

#122

Post by dr_dshiv »

TuringTest wrote: post #101
dr_dshiv wrote: post #99

Earlier quoted context omitted.

Or imagine a spreadsheet with 14 columns, amiright?

Technically true, but you're leaving out any possible visual insights if you do that.

I don’t know. I feel that, for most people, it is the most visual way to see in many dimensions. That is, it’s an insight—rather than having to imagine a 5-d cube or whatever, it’s just a spreadsheet, no big deal.

Re: The Illustrated Stable Diffusion

#123

Post by TuringTest »

pmoriarty wrote: post #111
TuringTest wrote: post #110

Earlier quoted context omitted.

Yes, but by boxing each sub-space, you can think of the pile of boxes as a dimension separate from the Z axis. It's like painting a house in isometric style. You draw each floor above the one below it, and put a "perpendicular" slanted axis to represent the third dimension in 2D. You could put a 'slanted' fourth axis in a 3D origin of coordinates, but I find it easier to think of the lower corner of each box as the o…

"You could put a 'slanted' fourth axis in a 3D origin of coordinates" Even with that the same problem occurs: "slanted" is a 3D relationship, so at best it's an analogy. It's like "translating" the color red to some shade of gray to a person who can only see in black and white. Or trying to describe through written words what music is like to someone who can't hear. These are all analogies which might allow us to rea…

> Even with that the same problem occurs: "slanted" is a 3D relationship, so at best it's an analogy.

Yeah, but it's the same analogy you use to represent 3D figures on a 2D plane, where slanted is a 2D relationship; and we are very well versed on it and know how it works as a projection of a 3D reality.

> These are all analogies which might allow us to reason and get interesting/useful results when we use such analogies... but we should not under the illusion that we really know what those things for which we have no senses are like.

Is this some reflections about Plato's cave? You don't need much insight to understand the basis of moving over an extra dimension - if you can understand what it's like to move over parallel planes from a 2D view, you can understand the same by moving over superposed volumes from a 3D view. A hyper-sphere can be visualized as a linear collection of increasingly small spheres glued together, in the same way that you can view a sphere as a linear collection of increasingly small circles over an axis orthogonal to its center.

> Also, there are probably all sorts of interesting/useful connections, relationships or conclusions that a being who really could sense 4D objects would find obvious or easy to make that we may never arrive at because our way of thinking of them is so limited in comparison.

Yeah, and some people are really bad at 3D visualization so they have no hope to arrive at conclusions that are trivial to an architect or engineer. That doesn't prevent higher-dimension visualization techniques from being useful for the insights that it can provide, even if they can't give omniscience. For all the other insights, we have formal methods and logic reasoning, which is how 4D space was originated to begin with.

Re: The Illustrated Stable Diffusion

#124

Post by TuringTest »

dr_dshiv wrote: post #122
TuringTest wrote: post #101

Earlier quoted context omitted.

Technically true, but you're leaving out any possible visual insights if you do that.

I don’t know. I feel that, for most people, it is the most visual way to see in many dimensions. That is, it’s an insight—rather than having to imagine a 5-d cube or whatever, it’s just a spreadsheet, no big deal.

Yes, but they see it as a data dump, without perceiving any spacial connections between the vectors represented by each row. The point of spatial reasoning is using our minds inner eye to visualize those connections intuitively, and the tabular data dump has nothing of it.

Re: The Illustrated Stable Diffusion

#125

Post by dr_dshiv »

TuringTest wrote: post #124
dr_dshiv wrote: post #122

Earlier quoted context omitted.

I don’t know. I feel that, for most people, it is the most visual way to see in many dimensions. That is, it’s an insight—rather than having to imagine a 5-d cube or whatever, it’s just a spreadsheet, no big deal.

Yes, but they see it as a data dump, without perceiving any spacial connections between the vectors represented by each row. The point of spatial reasoning is using our minds inner eye to visualize those connections intuitively, and the tabular data dump has nothing of it.

But I’d argue a 5d cube has even less use, as a mental model. Most people don’t know that each additional column is another dimension. People can imagine the sense of distance between varying points/entries in a table easier than a 5d cube, for instance. (Actually, that’s an empirical question)

Re: The Illustrated Stable Diffusion

#126

Post by paulgrant999 »

OkayPhysicist wrote: post #60
zestyping wrote: post #54

Earlier quoted context omitted.

> we use tensor because it allows for any number of dimensions "Vector" implies one dimension and "matrix" strongly implies two. But an array can have any number of dimensions, so "array" is the best word. We don't need the word "tensor"; when the context is programming, "tensor" is only confusing and doesn't really add any useful meaning.

Tensor does imply a set of operations that are expected. Multiplying two arrays together is an ambiguous operation; multiplying two tensors together is well-defined. And really, the context is math, not programming. The programming side of DL is approximately trivial, the interesting bits are all represented as mathematical operations on a set of tensors.

No post body was provided.

Re: The Illustrated Stable Diffusion

#127

Post by paulgrant999 »

pdntspa wrote: post #66
Waterluvian wrote: post #5

Closer. But I still get lost when words like “tensor” are used. “structured lists of numbers” really doesn’t seem to explain it usefully. This reminds me that explaining seemingly complex things in simple terms is one of the most valuable and rarest skills in engineering. Most people just can’t. And often because they no-longer remember what’s not general knowledge. You end up with a recursive Feynmannian “now explai…

I got lost at the word 'tensor' too, but then I just googled it and skilled up... But simply put, a 'tensor' is a 3+-dimensional array of floats. Or a stack of matrices.

No post body was provided.

Re: The Illustrated Stable Diffusion

#128

Post by Breza »

brundolf wrote: post #121
netruk44 wrote: post #9

Earlier quoted context omitted.

If it helps you to understand at all, assuming you have a CS background, any time you see the word "tensor" you can replace it with "array" and you'll be 95% of the way to understanding it. Or "matrix" if you have a mathematical background. Whereas CS arrays tend to be 1 dimensional, and sometimes 2 dimensional, tensors can be as many dimensions as you need. A 256x256 photo with RGB channels would be stored as a [256…

This is something that infuriates me about formal mathematics (and CS, for that matter): they don't just use the words people already know! They have to make up new words, sometimes even entirely new symbols, that often just mean the same thing as something else. And then the literature becomes entirely inaccessible unless you've learned this secret code. The bottleneck becomes translation, instead of understanding.

I agree with you. Fields like graph theory and set theory are fun once you wrap your head around the symbols, but I remember having a lot of trouble with both as a teenager.
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