Would you expect some part of the net to be left blank, because “a large neural net has a lot of spare neurons”?
If the lottery ticket hypothesis is true, yes.
The lottery ticket hypothesis is that some parts of the network start off doing something somewhat close to useful, and get trained towards usefulness. And some parts start off sufficiently un-useful that they just get trained to get out of the way.
Which fits with neural net distillation being a thing. (Ie training a big network, and then condensing it into a smaller network gives better performance than directly training a small network.
but gradient descent doesn’t care, it reaches in and adjusts every weight.
Here is an extreme example. Suppose the current parameters were implementing a computer chip, on which was running a holomorphically encrypted piece of code.
Holomorphic encryption itself is unlikely to form, but it serves at least as an existance proof for computational structures that can’t be adjusted with local optimization.
Basically the problem with gradient descent is that it’s local. And when the same neurons are doing things that the neural net does want, and things that the neural net doesn’t want (but doesn’t dis-want either) then its possible for the network to be trapped in a local optimum. Any small change to get rid of the bad behavior would also get rid of the good behavior.
Also, any bad behavior that only very rarely effects the output will produce very small gradients. Neural nets are trained for finite time. It’s possible that gradient descent just hasn’t got around to removing the bad behavior even if it would do so eventually.
Can you concoct even a vague or toy model of how what you propose could possibly be a local optimum?
You can make any algorithm that does better than chance into a local optimum on a sufficiently large neural net. Holomorphicly encrypt that algorithm, Any small change and the whole thing collapses into nonsense. Well actually, this involves discrete bits. But suppose the neurons have strong regularization to stop the values getting too large (past + or − 1) , and they also have uniform [0,1] noise added to them, so each neuron can store 1 bit and any attempt to adjust parameters immediately risks errors.
Looking at the article you linked. One simplification is that neural networks tend towards the max-entropy way to solve the problem. If there are multiple solutions, the solutions with more free parameters are more likely.
And there are few ways to predict next tokens, but lots of different kinds of paperclips the AI could want.
Some interesting points there. The lottery ticket hypothesis does make it more plausible that side computations could persist longer if they come to exist outside the main computation.
Regarding the homomorphic encryption thing: yes, it does seem that it might be impossible to make small adjustments to the homomorphically encrypted computation without wrecking it. Technically I don’t think that would be a local minimum since I’d expect the net would start memorizing the failure cases, but I suppose that the homomorphic computation combined with memorizations might be a local optimum particularly if the input and output are encrypted outside the network itself.
So I concede the point on the possible persistence of an underlying goal if it were to come to exist, though not on it coming to exist in the first place.
And there are few ways to predict next tokens, but lots of different kinds of paperclips the AI could want.
For most computations, there are many more ways for that computation to occur than there are ways for that computation to occur while also including anything resembling actual goals about the real world. Now, if the computation you are carrying out is such that it needs to determine how to achieve goals regarding the real world anyway (e.g. agentic mask), it only takes a small increase in complexity to have that computation apply outside the normal context. So, that’s the mask takeover possibility again. Even so, no matter how small the increase in complexity, that extra step isn’t likely to be reinforced in training, unless it can do self-modification or control the training environment.
if the computation you are carrying out is such that it needs to determine how to achieve goals regarding the real world anyway (e.g. agentic mask)
As well as agentic masks, there are uses for within network goal directed steps. (Ie like an optimizing compiler. A list of hashed followed by unhashed values isn’t particularly agenty. But the network needs to solve an optimization problem to reverse the hashes. Something it can use the goal directed reasoning section to do.
Neither of those would (immediately) lead to real world goals, because they aren’t targeted at real world state (an optimizing compiler is trying to output a fast program—it isn’t trying to create a world state such that the fast program exists). That being said, an optimizing compiler could open a path to potentially dangerous self-improvement, where it preserves/amplifies any agency there might actually be in its own code.
If the lottery ticket hypothesis is true, yes.
The lottery ticket hypothesis is that some parts of the network start off doing something somewhat close to useful, and get trained towards usefulness. And some parts start off sufficiently un-useful that they just get trained to get out of the way.
Which fits with neural net distillation being a thing. (Ie training a big network, and then condensing it into a smaller network gives better performance than directly training a small network.
Here is an extreme example. Suppose the current parameters were implementing a computer chip, on which was running a holomorphically encrypted piece of code.
Holomorphic encryption itself is unlikely to form, but it serves at least as an existance proof for computational structures that can’t be adjusted with local optimization.
Basically the problem with gradient descent is that it’s local. And when the same neurons are doing things that the neural net does want, and things that the neural net doesn’t want (but doesn’t dis-want either) then its possible for the network to be trapped in a local optimum. Any small change to get rid of the bad behavior would also get rid of the good behavior.
Also, any bad behavior that only very rarely effects the output will produce very small gradients. Neural nets are trained for finite time. It’s possible that gradient descent just hasn’t got around to removing the bad behavior even if it would do so eventually.
You can make any algorithm that does better than chance into a local optimum on a sufficiently large neural net. Holomorphicly encrypt that algorithm, Any small change and the whole thing collapses into nonsense. Well actually, this involves discrete bits. But suppose the neurons have strong regularization to stop the values getting too large (past + or − 1) , and they also have uniform [0,1] noise added to them, so each neuron can store 1 bit and any attempt to adjust parameters immediately risks errors.
Looking at the article you linked. One simplification is that neural networks tend towards the max-entropy way to solve the problem. If there are multiple solutions, the solutions with more free parameters are more likely.
And there are few ways to predict next tokens, but lots of different kinds of paperclips the AI could want.
Some interesting points there. The lottery ticket hypothesis does make it more plausible that side computations could persist longer if they come to exist outside the main computation.
Regarding the homomorphic encryption thing: yes, it does seem that it might be impossible to make small adjustments to the homomorphically encrypted computation without wrecking it. Technically I don’t think that would be a local minimum since I’d expect the net would start memorizing the failure cases, but I suppose that the homomorphic computation combined with memorizations might be a local optimum particularly if the input and output are encrypted outside the network itself.
So I concede the point on the possible persistence of an underlying goal if it were to come to exist, though not on it coming to exist in the first place.
For most computations, there are many more ways for that computation to occur than there are ways for that computation to occur while also including anything resembling actual goals about the real world. Now, if the computation you are carrying out is such that it needs to determine how to achieve goals regarding the real world anyway (e.g. agentic mask), it only takes a small increase in complexity to have that computation apply outside the normal context. So, that’s the mask takeover possibility again. Even so, no matter how small the increase in complexity, that extra step isn’t likely to be reinforced in training, unless it can do self-modification or control the training environment.
As well as agentic masks, there are uses for within network goal directed steps. (Ie like an optimizing compiler. A list of hashed followed by unhashed values isn’t particularly agenty. But the network needs to solve an optimization problem to reverse the hashes. Something it can use the goal directed reasoning section to do.
Neither of those would (immediately) lead to real world goals, because they aren’t targeted at real world state (an optimizing compiler is trying to output a fast program—it isn’t trying to create a world state such that the fast program exists). That being said, an optimizing compiler could open a path to potentially dangerous self-improvement, where it preserves/amplifies any agency there might actually be in its own code.