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Backpropagation is a leaky abstraction in the sense that every algorithm/physics-principle/mathematical-theorem is a leaky abstraction. Take 'sort.' If you use

by fizixer 10y ago

Backpropagation is a leaky abstraction in the sense that every algorithm/physics-principle/mathematical-theorem is a leaky abstraction. Take 'sort.' If you use a sort API for large N in a performance-critical section of your code without knowing if the implementation of that sort is an insertion-sort or a quicksort, "you would be nervous." Hence you are dealing with a leaky abstraction, per this article. I would much rather respond to the students who ask about why they need to know the details, by saying "because you registered for this class." Essentially the question "if you’re never going to write backward passes once the class is over, why practice writing them?" is another way of asking "why reinvent the wheel?". And the best answer is "because learning is all about reinventing the wheel". The "code reuse as much as possible" mantra applies to when you're "using" a technique to do something else, not when you're "learning" the technique itself. They might as well register for Calculus and ask "why learn integrals and derivatives when mathematica can do them for you", or take an Aerodynamics class and ask "why learn fluid mechanics and dynamics, heck newton's laws, when an airplane can run on autopilot." I doubt "because calculus is a leaky abstraction" or "because fluid dynamics is a leaky abstraction" is a good answer to that.

thecity2 10y ago
"because fluid dynamics is a leaky abstraction" No pun intended!
skybrian 10y ago
I think you're sweeping an important distinction under the rug. If every major language provides an O(n log n) sort function, is it still a leaky abstraction? I'd say no. You can use it without worrying much about the details. But it sounds like the situation with back-propagation is different, since the internal details of the algorithm affect whether you get a usable answer at all. A borderline case might be something like a SQL database, where in theory, creating an index shouldn't change query results, but in practice, the performance can change so much that it effectively does. Unlike with back-propagation, you can tune database performance without worrying about queries returning different results (assuming they don't time out). So it's still a useful guarantee.
- nullc 10y ago
  > You can use it without worrying much about the details. I invite you to start sorting data which is often already sorted (or often all identical) and tell me you didn't need to worry about the details.
- sirclueless 10y ago
  Speaking from experience, I've had to worry about what implementation of sort is being used in many languages, from Java to C++, even Go and Python. There are a lot of details to get right: how are elements compared? Is the sort stable? Is it efficient for small N? Is it efficient for nearly-sorted arrays? Is it efficient when almost all the elements compare equal? Is it guaranteed O(n log n) or average? If average, is there an input that reliably triggers n^2 behavior making it a DDoS vector? Anything is a leaky abstraction when you care enough.
  - im3w1l 10y ago
    Those properties should ideally be part of the documentation so that the abstraction stops leaking.
    - 4ad 10y ago
      One could argue that if these details are necessary for correct/performant operation, then it is a leaky abstraction.
      - im3w1l 10y ago
        To me a leaky abstraction is an abstraction that does not expose all the relevant details. So if those details are written on the spec sheet of the black box then there is no leak. If the box is only labelled with O(nlog n) without specifying constants then there is a leak.
  - ezanmoto 10y ago
    I feel that if you care that much about the internals of the abstraction then you don't necessarily want an abstraction anymore, but rather the concrete thing that is being abstracted over. I think abstraction is an admirable quality that has numerous advantages, but if you need guarantees on the properties of what's under the abstraction then an abstraction is probably not what's needed at that point.
arikrak 10y ago
If someone wants to know a little calculus for a small area of engineering, do they really need to learn various manual techniques for calculating integrals? Why can't they use Mathematica? (What if they're just taking calculus as a requirement of CS or premed?) They're not planning on developing new integrations techniques. Does a pilot need to learn fluid dynamics like an airplane engineer? Maybe educational students should only require what's actually practical. That can include things that can be solved by computers if they teach ideas that have practical value.
- conistonwater 10y ago
  > If someone wants to know a little calculus for a small area of engineering, do they really need to learn various manual techniques for calculating integrals? Yes, but the logic goes the other way: if they are unable to use the technique manually, then one may conclude they do not understand the idea well enough to use it, whether or not Mathematica is available. The two, manual application and understanding/intuition, go hand in hand and can't be separated. My understanding is that this has even been studied more formally, there is a paper I remember reading by Kahneman and somebody else [1] about the development of intuition and the tension between heuristics-and-biases and naturalistic decision making. In short, don't trust people so much, if they say they understand something but are unable to actually do it, be a bit more skeptical. [1] Found it: https://www.ncbi.nlm.nih.gov/pubmed/19739881 https://www.ncbi.nlm.nih.gov/pubmed/19739881 On second thought, it's probably not as relevant as I remembered it.
posterboy 10y ago
> "because you registered for this class." The Authoritative Argument is not very convincing when your good authority over the course material being challenged. Maybe there is some irony or deeper truth, lost on me. Are you perhaps a leaky abstraction? edit: > The "code reuse as much as possible" mantra applies to when ... ... you are able to reasonably compromise, got it.
- KODeKarnage 10y ago
  > The Authoritative Argument is not very convincing Neither is a straw man argument. He wasn't making an argument from authority. He was essentially saying "because you are learning, not doing".
  - posterboy 10y ago
    >essentially No, implicitly and very subtly. The essence of the argument was the student in a voluntary class. The implications are manifold, but not stating the implications has a meaning on the meta level, that the students understanding is not expected, but the students expectation of an authoritative answer has to be satisfied anyway by stating the obvious to establish or retain authority.
sherjilozair 10y ago
I think Andrej is arguing over and above the reasons you cite. Not only should you learn backprop because of the same reason you learn to do 2+2, but you should learn backprop ALSO because it's a leaky abstraction. This is a non-trivial statement, because there are other things which are not leaky. For example, he's not arguing that deep learning practitioners should also learn assembly programming or go into how CUBLAS implements matrix multiplication. Although these things are nice to learn, you probably won't need them 99.9% of the times. Backprop knowledge, however, is much more crucial to design novel deep learning systems.
- annnnd 10y ago
  > Backprop knowledge, however, is much more crucial to design novel deep learning systems. I would argue that it's not just for that. You need to understand what is happening inside DNN if you want to construct it properly.
kazinator 10y ago
Performance is the same thing as correctness only in hard real time. A better analogy might be stable sort versus unstable. If you need a stable sort, and unstable one is wrong. (Not sure if that counts as an abstraction leak, though! It's just the semantics. Unstable sort doesn't leak that it is unstable; that's its behavior. If a sort is just documented as putting items in order, an actual implementation does leak information about whether or not it is stable.)

by fizixer 10y ago

thecity2 10y ago

"because fluid dynamics is a leaky abstraction" No pun intended!

skybrian 10y ago

I think you're sweeping an important distinction under the rug. If every major language provides an O(n log n) sort function, is it still a leaky abstraction? I'd say no. You can use it without worrying much about the details. But it sounds like the situation with back-propagation is different, since the internal details of the algorithm affect whether you get a usable answer at all. A borderline case might be something like a SQL database, where in theory, creating an index shouldn't change query results, but in practice, the performance can change so much that it effectively does. Unlike with back-propagation, you can tune database performance without worrying about queries returning different results (assuming they don't time out). So it's still a useful guarantee.

nullc 10y ago
> You can use it without worrying much about the details. I invite you to start sorting data which is often already sorted (or often all identical) and tell me you didn't need to worry about the details.
sirclueless 10y ago
Speaking from experience, I've had to worry about what implementation of sort is being used in many languages, from Java to C++, even Go and Python. There are a lot of details to get right: how are elements compared? Is the sort stable? Is it efficient for small N? Is it efficient for nearly-sorted arrays? Is it efficient when almost all the elements compare equal? Is it guaranteed O(n log n) or average? If average, is there an input that reliably triggers n^2 behavior making it a DDoS vector? Anything is a leaky abstraction when you care enough.
- im3w1l 10y ago
  Those properties should ideally be part of the documentation so that the abstraction stops leaking.
  - 4ad 10y ago
    One could argue that if these details are necessary for correct/performant operation, then it is a leaky abstraction.
    - im3w1l 10y ago
      To me a leaky abstraction is an abstraction that does not expose all the relevant details. So if those details are written on the spec sheet of the black box then there is no leak. If the box is only labelled with O(nlog n) without specifying constants then there is a leak.
- ezanmoto 10y ago
  I feel that if you care that much about the internals of the abstraction then you don't necessarily want an abstraction anymore, but rather the concrete thing that is being abstracted over. I think abstraction is an admirable quality that has numerous advantages, but if you need guarantees on the properties of what's under the abstraction then an abstraction is probably not what's needed at that point.

arikrak 10y ago

If someone wants to know a little calculus for a small area of engineering, do they really need to learn various manual techniques for calculating integrals? Why can't they use Mathematica? (What if they're just taking calculus as a requirement of CS or premed?) They're not planning on developing new integrations techniques. Does a pilot need to learn fluid dynamics like an airplane engineer? Maybe educational students should only require what's actually practical. That can include things that can be solved by computers if they teach ideas that have practical value.

conistonwater 10y ago
> If someone wants to know a little calculus for a small area of engineering, do they really need to learn various manual techniques for calculating integrals? Yes, but the logic goes the other way: if they are unable to use the technique manually, then one may conclude they do not understand the idea well enough to use it, whether or not Mathematica is available. The two, manual application and understanding/intuition, go hand in hand and can't be separated. My understanding is that this has even been studied more formally, there is a paper I remember reading by Kahneman and somebody else [1] about the development of intuition and the tension between heuristics-and-biases and naturalistic decision making. In short, don't trust people so much, if they say they understand something but are unable to actually do it, be a bit more skeptical. [1] Found it: https://www.ncbi.nlm.nih.gov/pubmed/19739881 https://www.ncbi.nlm.nih.gov/pubmed/19739881 On second thought, it's probably not as relevant as I remembered it.

posterboy 10y ago

> "because you registered for this class." The Authoritative Argument is not very convincing when your good authority over the course material being challenged. Maybe there is some irony or deeper truth, lost on me. Are you perhaps a leaky abstraction? edit: > The "code reuse as much as possible" mantra applies to when ... ... you are able to reasonably compromise, got it.

KODeKarnage 10y ago
> The Authoritative Argument is not very convincing Neither is a straw man argument. He wasn't making an argument from authority. He was essentially saying "because you are learning, not doing".
- posterboy 10y ago
  >essentially No, implicitly and very subtly. The essence of the argument was the student in a voluntary class. The implications are manifold, but not stating the implications has a meaning on the meta level, that the students understanding is not expected, but the students expectation of an authoritative answer has to be satisfied anyway by stating the obvious to establish or retain authority.

sherjilozair 10y ago

I think Andrej is arguing over and above the reasons you cite. Not only should you learn backprop because of the same reason you learn to do 2+2, but you should learn backprop ALSO because it's a leaky abstraction. This is a non-trivial statement, because there are other things which are not leaky. For example, he's not arguing that deep learning practitioners should also learn assembly programming or go into how CUBLAS implements matrix multiplication. Although these things are nice to learn, you probably won't need them 99.9% of the times. Backprop knowledge, however, is much more crucial to design novel deep learning systems.

annnnd 10y ago
> Backprop knowledge, however, is much more crucial to design novel deep learning systems. I would argue that it's not just for that. You need to understand what is happening inside DNN if you want to construct it properly.

kazinator 10y ago

Performance is the same thing as correctness only in hard real time. A better analogy might be stable sort versus unstable. If you need a stable sort, and unstable one is wrong. (Not sure if that counts as an abstraction leak, though! It's just the semantics. Unstable sort doesn't leak that it is unstable; that's its behavior. If a sort is just documented as putting items in order, an actual implementation does leak information about whether or not it is stable.)