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> NNs are good for approximation / interpolation / extrapolation Extrapolation? I was under the impression that generalizability of NNs beyond the training dat

> NNs are good for approximation / interpolation / extrapolation Extrapolation? I was under the impression that generalizability of NNs beyond the training data was one of the major problems faced by NNs.

johnwatson11218 7y ago
When they don't generalize well it usually means you have over trained on your training data. When you take classes on this stuff they have whole sections that talk about trying to detect this and what to do about it e.g. regularization, better models, more training data etc.
- Cybiote 7y ago
  What you list remains insufficient to tackle the difficulty of extrapolation. Extrapolation of the kind we're able to do with Physics theories is difficult in the general case for all methods, not just deep learning. With even the relevant variables subject to change, things like distribution shift and non-stationarity are but the tip of the ice-berg. For neural networks, if you take something basic like sorting a list or multiplying two decimal numbers, the further you are from range the models were trained on, the worse they will do (yes, transformers too). Only exception I can think of are carefully trained Neural GPUs, which will quickly struggle to be 100% correct as you depart simple tasks. While consuming a great deal of computational resources. Program synthesis is the general area, with no approach clearly dominant in the same way deep learning has dominated machine learning.
- deleted 7y ago
  [deleted]
- YeGoblynQueenne 7y ago
  What is meant above by "generalisation" is generalisation on out-of-sample data, i.e. not the sample on which you train and test your model (whether you have access to the test set or not). If out-of-sample data has a different distribution than the sampled dataset, then you're SOL, regularisation or not. As a for instance, here's an interesting paper I found out about from HN that describes how image classifiers trained on one standard dataset (ImageNet etc) do much worse on other standard datasets and how it's even possible to identify the dataset a classifier was trained on: Unbiased look at dataset bias https://people.csail.mit.edu/torralba/publications/datasets_cvpr11.pdf https://people.csail.mit.edu/torralba/publications/datasets_...
  - tel 7y ago
    Not strictly true, regularization in various forms can help have expert knowledge apply to create better extrapolation. Parametric models could be thought of as a kind of regularization even.
velcroscientist 7y ago
You're correct. As long as your test set remains within the training distribution, you can expect the NN to be well behaved. However, its behavior is undefined for testing data out of training distribution. There is a lot of work on detecting out of distribution inputs, regularizing NNs to follow a simple prior, etc. but the core problem remains because NNs learn from data. Extrapolation is something that symbolic systems do well, and NNs do not.
- killjoywashere 7y ago
  Let's say I have an interesting problem, like classifying cancer from images. What are some classes of symbolic systems that can reason about types of cancer the system wasn't trained on? Even humans don't know what to do until they've seen it. And then, the grown up answer is "variance is infinite when N=1"

johnwatson11218 7y ago

When they don't generalize well it usually means you have over trained on your training data. When you take classes on this stuff they have whole sections that talk about trying to detect this and what to do about it e.g. regularization, better models, more training data etc.

Cybiote 7y ago
What you list remains insufficient to tackle the difficulty of extrapolation. Extrapolation of the kind we're able to do with Physics theories is difficult in the general case for all methods, not just deep learning. With even the relevant variables subject to change, things like distribution shift and non-stationarity are but the tip of the ice-berg. For neural networks, if you take something basic like sorting a list or multiplying two decimal numbers, the further you are from range the models were trained on, the worse they will do (yes, transformers too). Only exception I can think of are carefully trained Neural GPUs, which will quickly struggle to be 100% correct as you depart simple tasks. While consuming a great deal of computational resources. Program synthesis is the general area, with no approach clearly dominant in the same way deep learning has dominated machine learning.
deleted 7y ago
[deleted]
YeGoblynQueenne 7y ago
What is meant above by "generalisation" is generalisation on out-of-sample data, i.e. not the sample on which you train and test your model (whether you have access to the test set or not). If out-of-sample data has a different distribution than the sampled dataset, then you're SOL, regularisation or not. As a for instance, here's an interesting paper I found out about from HN that describes how image classifiers trained on one standard dataset (ImageNet etc) do much worse on other standard datasets and how it's even possible to identify the dataset a classifier was trained on: Unbiased look at dataset bias https://people.csail.mit.edu/torralba/publications/datasets_cvpr11.pdf https://people.csail.mit.edu/torralba/publications/datasets_...
- tel 7y ago
  Not strictly true, regularization in various forms can help have expert knowledge apply to create better extrapolation. Parametric models could be thought of as a kind of regularization even.

velcroscientist 7y ago

You're correct. As long as your test set remains within the training distribution, you can expect the NN to be well behaved. However, its behavior is undefined for testing data out of training distribution. There is a lot of work on detecting out of distribution inputs, regularizing NNs to follow a simple prior, etc. but the core problem remains because NNs learn from data. Extrapolation is something that symbolic systems do well, and NNs do not.

killjoywashere 7y ago
Let's say I have an interesting problem, like classifying cancer from images. What are some classes of symbolic systems that can reason about types of cancer the system wasn't trained on? Even humans don't know what to do until they've seen it. And then, the grown up answer is "variance is infinite when N=1"