4 ms·

>> This is not a very surprising result, because it is known NNs generalize fairly well and at these levels you mostly only have blobs and edges that do not loo

>> This is not a very surprising result, because it is known NNs generalize fairly well and at these levels you mostly only have blobs and edges that do not look much different from artificial ones. ANNs generalise atrociously badly, hence the need to train with ever bigger data to cover every nook and cranny of the instance space of each class of interest. Incidentally, when people say that ANNs "generalise" they mean many different things, for example that they "genealise on the test set" which is usually only observed when the tests set is known in advance (and so it has been used in tuning hyperparameters and the like) or even, incredibly that they "generalise on the training set" (i.e. the validation partitions in cross-validation). Conversely, there is a glut of novel terminology like "out-of-sample" or "out-of-distribution" to describe generalisation beyond the test set, but this kind of generalisation is typically held up as a weakness of ANN, because they're genreally really bad at it. In any case, strong evidence of robust generalisation on out-of-sample data from few examples and with no or little pre-training, in ANNs, would be a surprise, indeed.

urthor 5y ago
Exactly this. The difference between interpolation and extrapolation is almost the most important concept in all of machine learning practice. It's infinitesimally rare (from what I've seen so far) that a practical machine learning model can perform high quality extrapolation, for many different metrics of quality. There's almost always far, far too many confounding variable.
- Isinlor 5y ago
  Depends on how you define interpolation and extrapolation. In high dimensional spaces basically everything is extrapolation including in pixel space and embedding space. > The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample x whenever this sample falls inside or on the boundary of the given dataset's convex hull. Extrapolation occurs when x falls outside of that convex hull. One fundamental (mis)conception is that state-of-the-art algorithms work so well because of their ability to correctly interpolate training data. A second (mis)conception is that interpolation happens throughout tasks and datasets, in fact, many intuitions and theories rely on that assumption. We empirically and theoretically argue against those two points and demonstrate that on any high-dimensional (>100) dataset, interpolation almost surely never happens. Those results challenge the validity of our current interpolation/extrapolation definition as an indicator of generalization performances. https://arxiv.org/abs/2110.09485 https://arxiv.org/abs/2110.09485 Also: > The location of decision boundaries inside the convex hull of training set can be investigated in relation to the training samples. However, our analysis shows that in standard image classification datasets, all testing images are considerably outside that convex hull, in the pixel space, in the wavelet space, and in the internal representations learned by deep networks. Therefore, the performance of a trained model partially depends on how its decision boundaries are extended outside the convex hull of its training data. https://arxiv.org/abs/2101.09849 https://arxiv.org/abs/2101.09849
  - karpierz 5y ago
    I think that the parent comment is referring to extrapolation in the semantic space (ex: use brown cats as training data and see if the ML algorithm can recognize albino cats). Edit: or take photos of brown cats indoors from the front and see if the model recognizes albino cats from the side outside.
    - Isinlor 5y ago
      You still have to deal with the precise definition of interpolation vs. extrapolation. And it does not matter what space you are using as long as you operate under the convex hull definition of interpolation vs. extrapolation you will need exponentially more samples as intrinsic dimensionality of the space increases. This means that even under the manifold hypothesis, as long as intrinsic dimensionality is reasonably high i.e. in low hundreds, models will be doing extrapolation.
      - urthor 5y ago
        I think we've just jumped from my "stochastic software engineering tip of the day" to a postgraduate level examination of validation and test set decision boundaries vs dataset boundaries. The thing is also, any individual hyper-dimensional case can be outside of the training set's convex hull itself and be correctly classified. However, you would still have to quantify what the relationship of the dimensions with the highest feature importance were to said space. Which is why the second paper is so fascinating. From the perspective of issues product/engineering teams face in the field, I'd definitely maintain that fire alarms should start sounding once you see any sort of extrapolation and you should dive deeper. Unfortunately the maturity level of this space is still at the point where peer review of data-set transformations before deploying to production and committing Jupyter Notebooks to GitHub is a heated in-office discussion. The majority of the commercial world is a long way from that kind of best practice.
  - YeGoblynQueenne 5y ago
    The problem with the second paper is that having a "test set" is meaningless when you can access that test set during training - "you" as in the researcher, who develops a system. This is especially so for machine vision datasets like the ones in the paper that have been "done to death". Basically anyone who has access to the test set of a popular benchmark and wants to get their paper published will do everything that can be done to ensure their system does well on the test set. That is a big flaw in machine learning research in general, but that's for another conversation, I guess. My point above is that if neural nets could generalise well, they wouldn't need so much data. In a sense, even if trained neural net models can generalise to instances outside the dense region of instance space circumscribed by their training set that is not that important, if that region has to be gigantic for this generalisation to be possbile in the first place. For one thing, at that point it becomes difficult to separate what is "training" and what is "test", especially so when test sets are four times the size of training sets as in typical practice.
momenti 5y ago
> ANNs generalise atrociously badly This statement is meaningless without controlling for model complexity and data type. For their simplicity, ANNs generalize well on a wide variety of data. GPT-3 yields almost human-level generalization ability for some tasks. I also clarified that the generalization is probably not far. There is not much complex "realism" to be found in low-to-mid-level features; they're almost mathematical in their simplicity, similar to basis functions.
- YeGoblynQueenne 5y ago
  >> GPT-3 yields almost human-level generalization ability for some tasks. That's an extravagant claim. There's no machine learning or other system, or algorithm, or technique, that can approach the ability of humans to "generalise" in any task, no matter how you want to define "generalisation". The models built by ANNs in particular are shallow and over-specialised and have none of the depth or complexity of whatever "models" of the world and the entities in the world that humans build in our heads. Evaluations that show "superhuman" ability are poorly designed. Machine learning research is following benchmarks and metrics that mean nothing and show nothing, beyond the ability to beat said benchmarks with said metrics, which is then blithely taken to mean "progress" towards the approximation of human intelligence. This then leads to hyperbole like in your comment.
  - momenti 5y ago
    > no matter how you want to define "generalisation" ... and how you want to define "task". For some prompts/"tasks", GPT-3 does generate impressive (more than trivial) outputs that cannot be found on the internet and that are indistinguishable from what a human would respond, so it generalizes in that sense. Maybe human ingenuity and generalization is also just slightly perturbed interpolation? It is very difficult to produce something truly novel, so we are also rather tightly limited by prior experience. Who knows? Also, who cares if submarines swim? Anyhow, it seems 50% of the internet is bikeshedding about definitions.
    - YeGoblynQueenne 5y ago

urthor 5y ago

Exactly this. The difference between interpolation and extrapolation is almost the most important concept in all of machine learning practice. It's infinitesimally rare (from what I've seen so far) that a practical machine learning model can perform high quality extrapolation, for many different metrics of quality. There's almost always far, far too many confounding variable.

Isinlor 5y ago
Depends on how you define interpolation and extrapolation. In high dimensional spaces basically everything is extrapolation including in pixel space and embedding space. > The notion of interpolation and extrapolation is fundamental in various fields from deep learning to function approximation. Interpolation occurs for a sample x whenever this sample falls inside or on the boundary of the given dataset's convex hull. Extrapolation occurs when x falls outside of that convex hull. One fundamental (mis)conception is that state-of-the-art algorithms work so well because of their ability to correctly interpolate training data. A second (mis)conception is that interpolation happens throughout tasks and datasets, in fact, many intuitions and theories rely on that assumption. We empirically and theoretically argue against those two points and demonstrate that on any high-dimensional (>100) dataset, interpolation almost surely never happens. Those results challenge the validity of our current interpolation/extrapolation definition as an indicator of generalization performances. https://arxiv.org/abs/2110.09485 https://arxiv.org/abs/2110.09485 Also: > The location of decision boundaries inside the convex hull of training set can be investigated in relation to the training samples. However, our analysis shows that in standard image classification datasets, all testing images are considerably outside that convex hull, in the pixel space, in the wavelet space, and in the internal representations learned by deep networks. Therefore, the performance of a trained model partially depends on how its decision boundaries are extended outside the convex hull of its training data. https://arxiv.org/abs/2101.09849 https://arxiv.org/abs/2101.09849
- karpierz 5y ago
  I think that the parent comment is referring to extrapolation in the semantic space (ex: use brown cats as training data and see if the ML algorithm can recognize albino cats). Edit: or take photos of brown cats indoors from the front and see if the model recognizes albino cats from the side outside.
  - Isinlor 5y ago
    You still have to deal with the precise definition of interpolation vs. extrapolation. And it does not matter what space you are using as long as you operate under the convex hull definition of interpolation vs. extrapolation you will need exponentially more samples as intrinsic dimensionality of the space increases. This means that even under the manifold hypothesis, as long as intrinsic dimensionality is reasonably high i.e. in low hundreds, models will be doing extrapolation.
    - urthor 5y ago
      I think we've just jumped from my "stochastic software engineering tip of the day" to a postgraduate level examination of validation and test set decision boundaries vs dataset boundaries. The thing is also, any individual hyper-dimensional case can be outside of the training set's convex hull itself and be correctly classified. However, you would still have to quantify what the relationship of the dimensions with the highest feature importance were to said space. Which is why the second paper is so fascinating. From the perspective of issues product/engineering teams face in the field, I'd definitely maintain that fire alarms should start sounding once you see any sort of extrapolation and you should dive deeper. Unfortunately the maturity level of this space is still at the point where peer review of data-set transformations before deploying to production and committing Jupyter Notebooks to GitHub is a heated in-office discussion. The majority of the commercial world is a long way from that kind of best practice.
- YeGoblynQueenne 5y ago
  The problem with the second paper is that having a "test set" is meaningless when you can access that test set during training - "you" as in the researcher, who develops a system. This is especially so for machine vision datasets like the ones in the paper that have been "done to death". Basically anyone who has access to the test set of a popular benchmark and wants to get their paper published will do everything that can be done to ensure their system does well on the test set. That is a big flaw in machine learning research in general, but that's for another conversation, I guess. My point above is that if neural nets could generalise well, they wouldn't need so much data. In a sense, even if trained neural net models can generalise to instances outside the dense region of instance space circumscribed by their training set that is not that important, if that region has to be gigantic for this generalisation to be possbile in the first place. For one thing, at that point it becomes difficult to separate what is "training" and what is "test", especially so when test sets are four times the size of training sets as in typical practice.

momenti 5y ago

> ANNs generalise atrociously badly This statement is meaningless without controlling for model complexity and data type. For their simplicity, ANNs generalize well on a wide variety of data. GPT-3 yields almost human-level generalization ability for some tasks. I also clarified that the generalization is probably not far. There is not much complex "realism" to be found in low-to-mid-level features; they're almost mathematical in their simplicity, similar to basis functions.

YeGoblynQueenne 5y ago
>> GPT-3 yields almost human-level generalization ability for some tasks. That's an extravagant claim. There's no machine learning or other system, or algorithm, or technique, that can approach the ability of humans to "generalise" in any task, no matter how you want to define "generalisation". The models built by ANNs in particular are shallow and over-specialised and have none of the depth or complexity of whatever "models" of the world and the entities in the world that humans build in our heads. Evaluations that show "superhuman" ability are poorly designed. Machine learning research is following benchmarks and metrics that mean nothing and show nothing, beyond the ability to beat said benchmarks with said metrics, which is then blithely taken to mean "progress" towards the approximation of human intelligence. This then leads to hyperbole like in your comment.
- momenti 5y ago
  > no matter how you want to define "generalisation" ... and how you want to define "task". For some prompts/"tasks", GPT-3 does generate impressive (more than trivial) outputs that cannot be found on the internet and that are indistinguishable from what a human would respond, so it generalizes in that sense. Maybe human ingenuity and generalization is also just slightly perturbed interpolation? It is very difficult to produce something truly novel, so we are also rather tightly limited by prior experience. Who knows? Also, who cares if submarines swim? Anyhow, it seems 50% of the internet is bikeshedding about definitions.
  - YeGoblynQueenne 5y ago