Hacker News Reader

> Focusing on mathematical abstracta completely misses the problem...

I don’t think it does.

We’ve been studying these networks for a long time now, and “common sense” interpretations are largely “completely bs” when examined closely.

These investigations have a tangible impact on how to prune and design networks.

High level hand waving about measuring the measuring device may seem profound, but I fail to see any meaningful application.

You can reconstruct 3D images from a few samples; see neural radiance fields. The observer is irrelevant.

My comment here wasnt aimed at the problem of understanding and improving DNNs; rather, of generalisation and 'comprehension' proper.

3d image reconstruction is trivially possible, with the right data and with the right assumptions encoded into the right algorithm.

My target of attack here is the equivocation that 'compression is comprehension'.

In my view comprehension isnt about 'generalization via compressed archetypes' as in ordinary NNs.

And it isnt about 3d reconstruction given the relevant modification to data and approach.

Rather generalization is abduction. It is the ability to, via a single instance, form law-like provisional universalising models which explain your environment. This process will lead to a 'compressed', 'representation', but nothing like the sense in which compression is here used.

It is this that intuitively is naively assumed of these systems. They do not, and cannot, abduct. Abduction isnt a statistical process; involving at the very least, counterfactual reasoning and hypothetical action.

This is the problem that such equivocations miss (ie. that c = c).

And in my view this is an engineering challenge; not something to be specified for a universal computer.

The relevant capacities missing arent better means of compression.

> In my view comprehension isnt about 'generalization via compressed archetypes' as in ordinary NNs...

How is this helpful?

Be specific.

The point being made is that inductions can be made by a compressed representation of the data.

No one is claiming this is a key insight to AGI; you’re just taking the word “comprehension” and arbitrarily assigning it some personal meaning.

This is why mathematicial descriptions are useful; you’re personal view of what “comprehension” means isn’t relevant here.

The article doesn’t discuss comprehension.

That is something you’ve, as far as I can tell, meaninglessly brought into this discussion.

How are your insights helpful for improving DNNs?

Be specific.

Sorry but I have to chime in here. His thoughts seem insightful and relevant to discussion. You are calling his contributions 'meaningless' and condescendingly telling him twice to 'be specific'. That's not how things are meant to be discussed around here and not how you get an answer out of someone.

Yip. I couldn't move myself to type the obvious: a person replying to my comment doesn't determine whether I am "on topic".

I’m comfortable, reading his comment history, that a blunt request to explain how the the comments are relevant to the OP (and the failure to articulate them when bluntly requested to do so) I indicates that what seems “insightful” is in fact, not falsifiable and therefore nothing more than armchair philosophy.

I’m not into that, so if it terminates the discussion then so be it.

There was nothing meaningful to discuss.

Isn't the observer model explicitly built into NeRF architectures?

It is; ive just skim read a paper.

Though, One trivial way to do it, with NNs in any case, is just to project forward from a range of observer models and guess the observer parameters from them.

This is still the wrong sense of generalisation. What cant be guessed is why a person took consecutive pictures at given angles/etc.

Such information is necessary to resolve deep ambiguities in cases where your observer model will fail.

Eg., yesterday i looked out my window and thought i saw two people; it was actually one with a shadow+bag.

I moved my eyes/head/body in such away so as to fit a variety of models and i was able to 'read the scene' in the end.

That is comprehension.

And there's no reason we couldn't have a deep learning system where the input data (images) included time-stamps and movement vectors, and it could be good both at easy image classification, and at choosing particular "head movements" like those you performed, to help resolve ambiguous cases.

Further food for thought: these ambiguous cases seem (do you agree?) to be very rare.

Ambiguity is the norm, it isn't rare. Almost all visual input, ie., light, is ambiguous. We (animals) use the history of our prior geometrical-light experiences (ie., walking around) to use environmental cues to resolve ambiguity.

That billions (, trillions) of images are needed to aproximate what we can do for a single instance, i think is a good guide to the magnitude of the problem.

Google the "amnes room" -- that "illusion" is how we are always seeing.

> Ambiguity is the norm

Right. But as you say, usually our priors are good enough. The cases where we stop, double-take, and deliberately look from another angle are rare.

> long time

4 decades is not a long time. It is a minuscule amount of time in the grand scheme of things.

It might be the case, like with quantum mechanics, that NN theory is just fundamentally weird (e.g. because the space is so multidimensional), and it's hard for us to understand it no matter how long we study it.

>Compression is a necessary but not sufficient condition for 'comprehension'.

Actually, algorithmic information theory shows that maximum compression necessarily entails maximum comprehension, because the only way to maximally compress something is to exactly understand the process producing it.

Relative to a device to perform the understanding.

A string X maximally compresses datsets Y iff X is a 'comprehending' of Y.

'OK'... but what produces and evaluates X? ie., comprehension.

This is the problem with defining these terms mathematically; you state the problem in basically useless ways.

Yes, you can specify what eqn produces the mass of the higgs boson. Thats basically no guide to building the LHC.

The production of such understanding is not abstract. Comprehension isnt a relation between two binary strings; it is an action taken in an environment with a goal.

>Relative to a device to perform the understanding.

It uses Kolmogorov complexity, which is defined as the length of a shortest computer program in a predetermined programming language that produces the object as output. Note that this measure is relative to a programming language, not a program, and the exact choice of language doesn't matter too much. Compression means creating a smaller program that produces the same output, and to produce the same output with less code necessarily requires more understanding.

As a concrete example, imagine the output is [1,2,fizz,4,buzz,fizz,7,8,fizz,buzz,11,fizz,13,14,fizzbuzz..1000). The longest program to output this would just hard-code it in the source code (much as a very inexperienced programmer might solve the problem, or a large neural net). Someone with a better understanding would write a program using iteration and the modulus operator, which would be shorter.

But what if we drop the word comprehension, and we just go with “functional approximation X -> Y, computed from a finite dataset, which minimizes a predictive risk “?

It’s unclear why compression is necessary there, except as a practical benefit.

Yeap, it gets into a philosophical debate of what comprehension.

One could argue it's not about compression in bits but compression to primitives that makes sense to the human mind. But then the definition becomes to fuzzy because it naturally invites the question "Who's mind?"

The parent commenter is not disagreeing with information theory (and what you're saying is shown in the article anyway).

They're making a practical distinction that you generally don't have access to the actual thing in an empirical format for which compression will achieve true learning. Instead you have access to training data which represents, let's say, a projection of the actual thing in a smaller space with fewer dimensions.

Like trying to learn from images instead of the 3d world. Humans learn to distinguish between objects in a 3-dimensional space using sight and interaction. This learning generalizably transfers to recognition in 2 dimensions. We don't generally equip models with robotic interfaces to train in 3d before benchmarking them on ImageNet.

>Like trying to learn from images instead of the 3d world. Humans learn to distinguish between objects in a 3-dimensional space using sight and interaction. This learning generalizably transfers to recognition in 2 dimensions.

If we use human "comprehension" as a reference point, then the relevant point of comparison should be the understanding a human can develop given the same inputs.

Sure. But again, practically speaking, that isn't the reality of how we learn. The commenter wasn't refuting Kolmogorov complexity. They're just saying it's an extremely limited way of viewing the problem. Useful sure, but insufficient.

Sure, but how do you measure that? How do we figure out how much understanding a human can develop from only ever seeing 2d pictures, without any movement or interaction with a 3d world?

Most ML problems are things humans are quite good at and have a lot of context to draw from.

> We don't generally equip models with robotic interfaces to train in 3d before benchmarking them on ImageNet.

Don't they train models using 3D rendering and simulations ? We have relatively realistic simulations for various scenarios - having a learned model that could make inferences based on those complex simulations sounds like a win.

Compression is applied to data collected in the past while comprehension or intelligence also require adapting well to the future. Thus a pure compressor would optimize for a static distribution while an intelligent agent will probably be sub-optimal because it also needs to learn and adapt to the future.

I will nitpick and say that models don't compress data but extract useful information. Compression lossly or lossless is for data reconstruction. Machine learning models retain information that generalises

https://arxiv.org/abs/1906.05849

Isn't lossy compression pretty much the same thing as extracting some amount of useful information?

No, because lossy compression has the goal of preserving elements for replay. At the extreme you could turn a movie into subtitles, but not a costume from the movie alone. The costume might contain more information from the movie, but you can meaningfully recreate the movie from a single costume.

If I derive Kepler's laws from positions of planets, I have preserved elements of their motion for replay as well.

The laws alone don’t have enough information to replay their motion without each planets location, a foci, the orbital period, and an associated timestamp or equivalent information.

So, include that data and it’s lossy compression, exclude it and it’s not.

According to Wikipedia [data] compression "is the process of encoding information using fewer bits than the original representation" [1] while lossy compression is "the class of data encoding methods that uses inexact approximations and partial data discarding to represent the content" [2]

There is a difference between feature extraction and compression. The former selects the most unique and important elements from a set of data, while the latter attempts, in the case of lossy compression, to find a smaller approximation of the original data set.

For example imagine a data set of paintings. Feature extraction might simply identify what color paints were used in each painting. That alone might allow classification of paintings with respect to the painter, style or period. But this would not be an approximation of the original picture, unless you consider resizing a Jackson Pollock into an 8x1 pixel image to be compression.

[1] https://en.wikipedia.org/wiki/Data_compression [2] https://en.wikipedia.org/wiki/Lossy_compression

"The former selects the most unique and important elements from a set of data, while the latter attempts, in the case of lossy compression, to find a smaller approximation of the original data set."

The compressor finds a smaller approximation of the data by finding the most redundant data, and as a byproduct it also finds the most unique. At least from the description you gave there is no difference between the two.

"For example imagine a data set of paintings. Feature extraction might simply identify what color paints were used in each painting. That alone might allow classification of paintings with respect to the painter, style or period. But this would not be an approximation of the original picture, unless you consider resizing a Jackson Pollock into an 8x1 pixel image to be compression."

You can and we do use compressors to do exactly that. Take a painting (or a set) as reference and use it to compress other paintings and the greater the compression the more similar the styles are.

For an example see: https://www.sciencedirect.com/science/article/abs/pii/S00313...

EDIT: In fact one step in a compressor is feature extraction (usually called modelling) and the other is coding.

Is there a meaningful / well defined difference? One could say that lossy compression is extraction of useful information. You need to identify unnecessary information to know what to discard safely.

One is a subset of the other. Compression being the larger category.

A mean is a compression of a dataset and useful information.

My issue in my comment is that 'compression' corresponds to a massive class of technquies and there isnt a lot of content in the observation that useful information is compressive.

However there is some hypey people out there who think this observation has legs. Precisely the people who think intelligence is a mathematical problem, and not an engineering one -- which is my view.

ie., that a body isnt incidental to intelligence, but the heart of it.

Or: devices matter.

I tend to think about it the same way as you. Having an algorithm for multiplying two numbers is qualitatively different than having a lossy compression of a huge dataset of multiplication tables. The latter is what GPT3 has and it just doesn't scale.

Consider a generative adversarial network for faces. Photos have let's say some unique scars

A successful model could create faces with scars in them. But not the exact scar and face and background that they trained on without additional information. What you are looking for is mutual information between the images not compression

Yes you could use a very well trained GAN for face compression. But a GAN model itself would not be able to reconstruct its training input without being shown the images again

> Focusing on mathematical abstracta completely misses the problem.

That rather depends on what you think the problem is or ought to be. I'm not sure that the author or many readers agree with you. It seemed fairly clear to me that they are interested in how well they can generate outputs corresponding to novel inputs that do well on some utility function. And for that, the "mathematical abstracta" is rather important and useful. "Comprehension" might also be important and useful, but is itself neither necessary nor sufficient.

A self-driving car will hopefully try to avoid running over a two-headed person crossing a road, without needing to worry about whether a two-headed person is mythical vs a miscomprehension of a woman carrying a child.

Besides, the layer at which comprehension occurs is not fixed. Our measuring devices themselves take in ambiguous inputs and process them. Do you stop at the surface of the skin? The nerve impulses? Various layers within the brain and nervous system?

Your complaint is reasonable, yet is not really that different from saying that computers are pointless without any I/O capabilities -- it doesn't matter what they compute if it is unobservable and has no effect on the world. That is true, yet doesn't mean that the whole of computer science is "a bit of a misdirection".

Such a great comment, thank you