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It seems they are trying to answer "WHAT do NN's learn?", and "How do NN's WORK?", as much as their title question of "How do NN's learn?". Here's an excerpt f

It seems they are trying to answer "WHAT do NN's learn?", and "How do NN's WORK?", as much as their title question of "How do NN's learn?". Here's an excerpt from the article: "The researchers found that a formula used in statistical analysis provides a streamlined mathematical description of how neural networks, such as GPT-2, a precursor to ChatGPT, learn relevant patterns in data, known as features. This formula also explains how neural networks use these relevant patterns to make predictions." The trite answer to "HOW do NN's learn?" is obviously gradient descent - error minimization, with the features being learnt being those that best support error minimization by the higher layers, effectively learning some basis set of features that can be composed into more complex higher level patterns. The more interesting question perhaps is WHAT (not HOW) do NN's learn, and there doesn't seem to be any single answer to that - it depends on the network architecture. What a CNN learns is not the same as what an LLM such GPT-2 (which they claim to address) learns. What an LLM learns is tied to the question of how does a trained LLM actually work, and this is very much a research question - the field of mechanistic interpretability (induction head circuits, and so forth). I guess you could combine this with the question of HOW does an LLM learn if you are looking for a higher level transformer-specific answer, and not just the generic error minimization answer: how does a transformer learn those circuits? Other types of NN may be better understood, but anyone claiming to fully know how an LLM works is deluding themselves. Companies like Anthropic don't themselves fully know, and in fact have mechanistic interpretability as a potential roadblock to further scaling since they have committed to scaling safely, and want to understand the inner workings of the model in order both to control it and provide guarantees that a larger model has not learnt to do anything dangerous.

tarsinge 3y ago
In short we do know how NNs learn and work, but not what NNs learn. The corollary being we don't understand where do the emergent properties come from?
- wredue 3y ago
  If you start a non with the same weight and do the same gradients, it’ll “learn” the same things. The “emergent” properties are going to be impacted by randomness of your starting point as well as ordering of your training.
  - HarHarVeryFunny 3y ago
    No - emergent properties are primarily a function of scaling up NN size and training data. I don't think they are much dependent on the training process.
    - wredue 3y ago
      Of course they are? If you train in a different order, start with different weights, or change the gradient delta amount, different things will emerge out of an otherwise exactly the same NN. You can see this out of videos where people train a NN to do something multiple times and each time, the NN picks up on something slightly different. Slight variances in what is fed as inputs during training can cause actually high variation in what is picked up on. I’m getting decently annoyed with HNs constant pretending that this is all just “magic”.
      - HarHarVeryFunny 3y ago
        You're talking about something a bit different - dependence on how the NN is initialized, etc. When people talk about "emergent properties" of LLMs, this is not what they are talking about - they are talking about specific capabilities that the net has that were not anticipated. For example, LLMs can translate between different languages, but were not trained to do this - this would be considered as an emergent property. Nobody is saying this is magic - it's just something that is (with our current level of knowledge) impossible to predict will happen. If you scale a model up, and/or give it more training data, then it'll usually get better at what it could already do, but it may also develop some new (emergent) capabilities that no-one had anticipated.
        3y ago
- HarHarVeryFunny 3y ago
  It depends on the type of NN, and also what level of explanation you are looking for. At the basic level we do of course know how NN's learn, and what any architecture is doing (what each piece is doing), since we designed them! In the case of LLMs like ChatGPT, while we understand the architecture, and how it works at that level (attention via key matching, etc), what is missing is how the architecture is actually being utilized by the trained model. For example, it turns out that consecutive pairs of attention heads sometimes learn to coordinate and can look words (tokens) up in the context and copy them to the output - this isn't something you could really have predicted just by looking at the architecture. The companies like Anthropic developing these have discovered a few such insights into how they are actually working, but not too many! Yes, we don't really understand where emergent capabilities are coming from, at least not to extent of being able to predict them ahead of time ("if we feed it this amount of data, of this type, it'll learn to do X"). New emergent capabilities arise, from time to time, as models are scaled up, but no one can predict exactly what their next-gen model is going to be capable of.
  - nyrikki 3y ago
    >Yes, we don't really understand where emergent capabilities are coming from, at least not to extent of being able to predict them ahead of time ("if we feed it this amount of data, of this type, it'll learn to do X"). New emergent capabilities arise, from time to time, as models are scaled up, but no one can predict exactly what their next-gen model is going to be capable of. While finite precision, finite width transformers aren't TC, I don't see why the same property of the game of life, where one cannot predict the end state from the starting state wouldn't hold. As we know transformers are at least as powerful as TC^0 which contains AC^0, which is as powerful as first order logic, it is undecidable and thus may be similar to HALT, were we will never be able to accurately predict when emergence happens so approximation may be the best we do unless there are constraints through something like the parallelism tradeoff that allows for it. If you consider PCP[O(log n),O(1)] = NP, or that only O(log n) bits are required for NP, the results of this paper seems more plausible. https://arxiv.org/abs/2304.15004 https://arxiv.org/abs/2304.15004 I have yet to see any peer review that makes that continuous view invalid. As you pointed out, we understand the underlying systems, but I think we should be surprised if someone does find a good approximation reduction. But in my experience that also indicates an extreme limit in what can be modeled. Then again all FFNs are effectively DAGs and I.I.D. does force a gaussian distribution of inputs. But unless you are learning something that is Markovian and Ergotic undecidablity seems like a high probability.
- omniscient_oce 3y ago
  I'm not an expert by any means but there are some papers exploring this using category theory.

tarsinge 3y ago

In short we do know how NNs learn and work, but not what NNs learn. The corollary being we don't understand where do the emergent properties come from?

wredue 3y ago
If you start a non with the same weight and do the same gradients, it’ll “learn” the same things. The “emergent” properties are going to be impacted by randomness of your starting point as well as ordering of your training.
- HarHarVeryFunny 3y ago
  No - emergent properties are primarily a function of scaling up NN size and training data. I don't think they are much dependent on the training process.
  - wredue 3y ago
    Of course they are? If you train in a different order, start with different weights, or change the gradient delta amount, different things will emerge out of an otherwise exactly the same NN. You can see this out of videos where people train a NN to do something multiple times and each time, the NN picks up on something slightly different. Slight variances in what is fed as inputs during training can cause actually high variation in what is picked up on. I’m getting decently annoyed with HNs constant pretending that this is all just “magic”.
    - HarHarVeryFunny 3y ago
      You're talking about something a bit different - dependence on how the NN is initialized, etc. When people talk about "emergent properties" of LLMs, this is not what they are talking about - they are talking about specific capabilities that the net has that were not anticipated. For example, LLMs can translate between different languages, but were not trained to do this - this would be considered as an emergent property. Nobody is saying this is magic - it's just something that is (with our current level of knowledge) impossible to predict will happen. If you scale a model up, and/or give it more training data, then it'll usually get better at what it could already do, but it may also develop some new (emergent) capabilities that no-one had anticipated.
      - 3y ago
HarHarVeryFunny 3y ago
It depends on the type of NN, and also what level of explanation you are looking for. At the basic level we do of course know how NN's learn, and what any architecture is doing (what each piece is doing), since we designed them! In the case of LLMs like ChatGPT, while we understand the architecture, and how it works at that level (attention via key matching, etc), what is missing is how the architecture is actually being utilized by the trained model. For example, it turns out that consecutive pairs of attention heads sometimes learn to coordinate and can look words (tokens) up in the context and copy them to the output - this isn't something you could really have predicted just by looking at the architecture. The companies like Anthropic developing these have discovered a few such insights into how they are actually working, but not too many! Yes, we don't really understand where emergent capabilities are coming from, at least not to extent of being able to predict them ahead of time ("if we feed it this amount of data, of this type, it'll learn to do X"). New emergent capabilities arise, from time to time, as models are scaled up, but no one can predict exactly what their next-gen model is going to be capable of.
- nyrikki 3y ago
  >Yes, we don't really understand where emergent capabilities are coming from, at least not to extent of being able to predict them ahead of time ("if we feed it this amount of data, of this type, it'll learn to do X"). New emergent capabilities arise, from time to time, as models are scaled up, but no one can predict exactly what their next-gen model is going to be capable of. While finite precision, finite width transformers aren't TC, I don't see why the same property of the game of life, where one cannot predict the end state from the starting state wouldn't hold. As we know transformers are at least as powerful as TC^0 which contains AC^0, which is as powerful as first order logic, it is undecidable and thus may be similar to HALT, were we will never be able to accurately predict when emergence happens so approximation may be the best we do unless there are constraints through something like the parallelism tradeoff that allows for it. If you consider PCP[O(log n),O(1)] = NP, or that only O(log n) bits are required for NP, the results of this paper seems more plausible. https://arxiv.org/abs/2304.15004 https://arxiv.org/abs/2304.15004 I have yet to see any peer review that makes that continuous view invalid. As you pointed out, we understand the underlying systems, but I think we should be surprised if someone does find a good approximation reduction. But in my experience that also indicates an extreme limit in what can be modeled. Then again all FFNs are effectively DAGs and I.I.D. does force a gaussian distribution of inputs. But unless you are learning something that is Markovian and Ergotic undecidablity seems like a high probability.
omniscient_oce 3y ago
I'm not an expert by any means but there are some papers exploring this using category theory.