7 ms·

Theories of Error Back-Propagation in the Brain

160 points by nopinsight 7y ago

londons_explore 7y ago
"Were guessing plausible ways the brain might work in ways similar to the machine learning world, but have no data to back it up"
- GChevalier 7y ago
  > "The relationship of spike-time-dependent plasticity to other models requires further clarifying work" - I got something for that, in fact I think I discovered that backpropagation engenders STDP: https://github.com/guillaume-chevalier/Spiking-Neural-Network-SNN-with-PyTorch-where-Backpropagation-engenders-STDP https://github.com/guillaume-chevalier/Spiking-Neural-Networ...
- ahartmetz 7y ago
  Backpropagation feels like a pretty gross hack to me anyway. It is a powerful component that still needs a large amount of additional hand-engineering to do more than recognize shapes it has seen before. And it's quite mathematical, which seems kind of difficult to implement in a brain. Edit: The article and code try to show how backpropagation might work given neuron behavior. I'll leave discussing the quality of the model to biologists.
  - marmaduke 7y ago
    > And it's quite mathematical, which seems kind of difficult to implement in a brain. Another commenter pointed out that you don't need perfect backprop, some random backprijections are sufficient.
subroutine 7y ago
As a neurobiologist, this interests me. I'm leaving this comment because I don't have time to read the article rn, but what to come back and see what HN thinks about it. Briefly, and naive to the content of the article, here is my concern. Consider this network architecture... You have 3000 input neurons that each makes ~10 synaptic connections with many downstream neurons, but let's focus on just one of those downstream neurons. This downstream neuron thus has 30k synaptic connections along its dendrite. At some time t its cell body (specifically the axon hillock area) receives enough graded electrical potential from some number of those synapses to fire an 'action potential' (a single electrical impulse). Some of those inputs contributed bursts of weak inputs, some may have contributed several strong inputs, some of the inputs were from synapses on very distal regions of the dendrite (therefore the graded signal was significantly weakened by the time it reached the cell body) some were from synapses very near the cell body. But they all integrate at the cell body, at which point, it doesn't matter where they came from - they've arrived is all that matters now - and together their strength is enough to evoke an action potential. Let's say this action potential impulse resulted in an error of some sort, somewhere downstream in the network. If you're playing by the rules of supervised learning with backprop, the synapses that evoked the signal producing the error-impulse should be made weaker. How? In biological NNs this is the impossible question. Signals that could target individual synapses do not propagate up axons through cell bodies up dendrites and back to synapses (you do have slow signaling that is for homeostatic scaling, but this is thought to simply scale network input up or down across all synapses). This means you will need another group of neurons to send error signals back. Maybe these recurrent projections exist, and say they did, these recurrent projections would need to (1) form a 3rd party connection at every synapse and (2) know which synapses were to blame for the error. Those don't seem like trivial phenomena from a neurophysiology perspective. I've read theories on local molecular tags or peptide synthesis, but they all seemed very much hand-wavy. Anything that has gained traction on those hypotheses hasn't stood up to scrutiny. The simplest theory to me, is that cortical networks on the size of human brains don't explicitly 'forget'. That is, they only learn. When you call someone Bob, and they correct you saying their name is Mike, your neural nets don't erase Bob and replace it with Mike. They remember the old name, the new name, the embarrassing situation, all of it. Biological neural nets don't need to explicitly forget because forgetting is (unfortunately?) a byproduct of being a biological entity. Also, neurons have finite resources (they are essentially zero-sum), so you simply will not see infinite run-up of synaptic strengths (which you might in some artificial NN without setting certain hyperparameters). Together, this suggests that recency is a fairly dominant factor when it comes to associative learning (and what gets forgotten) in biological NN.
- raindeer3 7y ago
  How is your concern with the lack of symmetric backwards connections related to the last paragraph about the brain not forgetting? The backward pass is used to both strengthen and weaken weights so in bp the forgetting and learning happens at the same time.
  - subroutine 7y ago
    Hebbian plasticity in biological NN assumes strengthening happens during the forward pass (the only pass). It is a local phenomena at individual synapses that detect a coincidence (2 inputs occur simultaneously or nearly) and is mediated by calcium influx. NMDA receptors will pass calcium but only if two things happen: (1) they are currently bound to glutamate neurotransmitter (input from their own upstream axon), and (2) magnesium is not blocking their calcium channel (Mg will be ejected briefly from the Ca channel if the neuron is depolarized - meaning currently receiving input from elsewhere). If you are receiving sensory input from both my voice and my face, some set of neurons are detecting this coincidence and strengthening that connection so the next time you hear my voice, it becomes easier to picture my face from all the different faces you have seen. Here is a good article explaining not just in theory how LTP (long term potentiation) works in neurons but why a particular protocol always works irl (I can attest to the validity of these statements based on first hand experience): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3843869/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3843869/ To summarize, the most reliable way to induce LTP is to "take control of the postsynaptic membrane with intracellular Cs+ to block K+ channels, which allows the experimenter to hold the cell at a constant membrane potential and induce a minimal ‘pairing’ protocol to induce LTP: depolarizing the cell to 0 mV while stimulating synapses." Holding the cell at 0 mV ensures Mg is always ejected, so any upstream stimulation will always be seen as a coincidence.
    - raindeer3 7y ago
      Yes, but also in hebbian learning you must have some weakening of weights, otherwise the weights would just grow indefinitely? One example I guess is Oja's rule. The difference to bp is just how to select what weights to strengthen and what to weaken based on what information. Forgetting and learning must always happen one way or the other. Or am I not getting your point?
marmaduke 7y ago
The problem with the brain, is that you find what you go looking for.
GChevalier 7y ago
> "The relationship of spike-time-dependent plasticity to other models requires further clarifying work" - I got something for that, in fact I think I discovered that backpropagation engenders STDP: https://github.com/guillaume-chevalier/Spiking-Neural-Network-SNN-with-PyTorch-where-Backpropagation-engenders-STDP https://github.com/guillaume-chevalier/Spiking-Neural-Networ...
- marmaduke 7y ago
  It was interesting to read how you did a spiking eural network in PyTorch, but it seems your neurons' states are coupled continuously in time, whereas in the brain, it would be the opposite, ie. the spike timing carries information and not the state values. > backprop engenders STDP This is backwards I think, but definitely an interesting association to make
- codekansas 7y ago
  There's a cool package called Nengo from Chris Eliasmith's group at UWaterloo which hasn't received as much attention as I think it should: https://www.nengo.ai/nengo-dl/examples/tensorflow-models.html https://www.nengo.ai/nengo-dl/examples/tensorflow-models.htm...
- etiam 7y ago
  You may be interested to watch this talk: http://www.cs.nyu.edu/~yann/deep07/videos/mov010.avi http://www.cs.nyu.edu/~yann/deep07/videos/mov010.avi Slides: http://www.cs.toronto.edu/~hinton/backpropincortex2007.pdf http://www.cs.toronto.edu/~hinton/backpropincortex2007.pdf
mjpuser 7y ago
I have been on similar kicks for drawing similarities between the two, but it never pans out to anything useful. I.e how does this move the science forward? I can play devil's advocate (aka classic hacker news' commenter) and say what about inhibiting neurons? Tonic neurons? What about the ability for the brain to do recall after hearing a name once? Procedural memory? Does the relationship you point out help you understand any of these things?
rdlecler1 7y ago
It’s interesting that most AI models focus on learning, but in biology the heavy lifting was all done in the developmental evolution and neurogenesis. You’re not going to teach your dog relativity with back propagation—-yet we treat BP like it was going to solve all the problems in AI. Until we start focusing more on neural architecture I have no worries about AI taking over the world.
- TekMol 7y ago
  Well, at the moment we are not teaching dogs. We are trying to create dogs.
  - rdlecler1 7y ago
    That’s not what I see.
- creddit 7y ago
  This is a valuable observation. I think the question, though, comes down to which of these two things should be mastered first or if they should be done in parallel. In general, the explosion of successes in DL in the last few years has been driven by AD and backprop rising to the occasion to make novel architectures explorable for the first time.
- olooney 7y ago
  > You’re not going to teach your dog relativity with back propagation What do you mean? RNN's can be taught to do math using BP[1]. Heck, you can do a simple version yourself in less than an hour[2]. They can't do tensor calculus yet (AFAIK) but there doesn't seem be any reason why BP in particular would be the stumbling block; the difficulty is finding the right representation. > yet we treat BP like it was going to solve all the problems in AI Except for reinforcement learning which does not use BP to solve the Bellma equations[3], AlphaZero which uses minimax[4], AutoML based on non-gradient methods such as bayesian optimization[5], etc. Research into CNNs and RNNs for image, text, and voice processing does tend to focus on BP, but not inappropriately so considering that that approach continues to make rapid progress in those domains. > Until we start focusing more on neural architecture I have no worries about AI taking over the world. I can't tell if you're arguing for or against. Are you suggesting that we should focus more on "neural architecture" so that AI can take over the world? Or are you approving of the current narrow focus for reasons of safety? [1] https://arxiv.org/pdf/1809.08590.pdf https://arxiv.org/pdf/1809.08590.pdf [2] https://machinelearningmastery.com/learn-add-numbers-seq2seq-recurrent-neural-networks/ https://machinelearningmastery.com/learn-add-numbers-seq2seq... [3] https://towardsdatascience.com/introduction-to-various-reinforcement-learning-algorithms-i-q-learning-sarsa-dqn-ddpg-72a5e0cb6287 https://towardsdatascience.com/introduction-to-various-reinf... [4] https://www.depthfirstlearning.com/2018/AlphaGoZero https://www.depthfirstlearning.com/2018/AlphaGoZero [5] https://en.wikipedia.org/wiki/Bayesian_optimization https://en.wikipedia.org/wiki/Bayesian_optimization

160 points by nopinsight 7y ago

"Were guessing plausible ways the brain might work in ways similar to the machine learning world, but have no data to back it up"

GChevalier 7y ago
> "The relationship of spike-time-dependent plasticity to other models requires further clarifying work" - I got something for that, in fact I think I discovered that backpropagation engenders STDP: https://github.com/guillaume-chevalier/Spiking-Neural-Network-SNN-with-PyTorch-where-Backpropagation-engenders-STDP https://github.com/guillaume-chevalier/Spiking-Neural-Networ...
ahartmetz 7y ago
Backpropagation feels like a pretty gross hack to me anyway. It is a powerful component that still needs a large amount of additional hand-engineering to do more than recognize shapes it has seen before. And it's quite mathematical, which seems kind of difficult to implement in a brain. Edit: The article and code try to show how backpropagation might work given neuron behavior. I'll leave discussing the quality of the model to biologists.
- marmaduke 7y ago
  > And it's quite mathematical, which seems kind of difficult to implement in a brain. Another commenter pointed out that you don't need perfect backprop, some random backprijections are sufficient.

subroutine 7y ago

As a neurobiologist, this interests me. I'm leaving this comment because I don't have time to read the article rn, but what to come back and see what HN thinks about it. Briefly, and naive to the content of the article, here is my concern. Consider this network architecture... You have 3000 input neurons that each makes ~10 synaptic connections with many downstream neurons, but let's focus on just one of those downstream neurons. This downstream neuron thus has 30k synaptic connections along its dendrite. At some time t its cell body (specifically the axon hillock area) receives enough graded electrical potential from some number of those synapses to fire an 'action potential' (a single electrical impulse). Some of those inputs contributed bursts of weak inputs, some may have contributed several strong inputs, some of the inputs were from synapses on very distal regions of the dendrite (therefore the graded signal was significantly weakened by the time it reached the cell body) some were from synapses very near the cell body. But they all integrate at the cell body, at which point, it doesn't matter where they came from - they've arrived is all that matters now - and together their strength is enough to evoke an action potential. Let's say this action potential impulse resulted in an error of some sort, somewhere downstream in the network. If you're playing by the rules of supervised learning with backprop, the synapses that evoked the signal producing the error-impulse should be made weaker. How? In biological NNs this is the impossible question. Signals that could target individual synapses do not propagate up axons through cell bodies up dendrites and back to synapses (you do have slow signaling that is for homeostatic scaling, but this is thought to simply scale network input up or down across all synapses). This means you will need another group of neurons to send error signals back. Maybe these recurrent projections exist, and say they did, these recurrent projections would need to (1) form a 3rd party connection at every synapse and (2) know which synapses were to blame for the error. Those don't seem like trivial phenomena from a neurophysiology perspective. I've read theories on local molecular tags or peptide synthesis, but they all seemed very much hand-wavy. Anything that has gained traction on those hypotheses hasn't stood up to scrutiny. The simplest theory to me, is that cortical networks on the size of human brains don't explicitly 'forget'. That is, they only learn. When you call someone Bob, and they correct you saying their name is Mike, your neural nets don't erase Bob and replace it with Mike. They remember the old name, the new name, the embarrassing situation, all of it. Biological neural nets don't need to explicitly forget because forgetting is (unfortunately?) a byproduct of being a biological entity. Also, neurons have finite resources (they are essentially zero-sum), so you simply will not see infinite run-up of synaptic strengths (which you might in some artificial NN without setting certain hyperparameters). Together, this suggests that recency is a fairly dominant factor when it comes to associative learning (and what gets forgotten) in biological NN.

raindeer3 7y ago
How is your concern with the lack of symmetric backwards connections related to the last paragraph about the brain not forgetting? The backward pass is used to both strengthen and weaken weights so in bp the forgetting and learning happens at the same time.
- subroutine 7y ago
  Hebbian plasticity in biological NN assumes strengthening happens during the forward pass (the only pass). It is a local phenomena at individual synapses that detect a coincidence (2 inputs occur simultaneously or nearly) and is mediated by calcium influx. NMDA receptors will pass calcium but only if two things happen: (1) they are currently bound to glutamate neurotransmitter (input from their own upstream axon), and (2) magnesium is not blocking their calcium channel (Mg will be ejected briefly from the Ca channel if the neuron is depolarized - meaning currently receiving input from elsewhere). If you are receiving sensory input from both my voice and my face, some set of neurons are detecting this coincidence and strengthening that connection so the next time you hear my voice, it becomes easier to picture my face from all the different faces you have seen. Here is a good article explaining not just in theory how LTP (long term potentiation) works in neurons but why a particular protocol always works irl (I can attest to the validity of these statements based on first hand experience): https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3843869/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3843869/ To summarize, the most reliable way to induce LTP is to "take control of the postsynaptic membrane with intracellular Cs+ to block K+ channels, which allows the experimenter to hold the cell at a constant membrane potential and induce a minimal ‘pairing’ protocol to induce LTP: depolarizing the cell to 0 mV while stimulating synapses." Holding the cell at 0 mV ensures Mg is always ejected, so any upstream stimulation will always be seen as a coincidence.
  - raindeer3 7y ago
    Yes, but also in hebbian learning you must have some weakening of weights, otherwise the weights would just grow indefinitely? One example I guess is Oja's rule. The difference to bp is just how to select what weights to strengthen and what to weaken based on what information. Forgetting and learning must always happen one way or the other. Or am I not getting your point?

marmaduke 7y ago

The problem with the brain, is that you find what you go looking for.

GChevalier 7y ago

> "The relationship of spike-time-dependent plasticity to other models requires further clarifying work" - I got something for that, in fact I think I discovered that backpropagation engenders STDP: https://github.com/guillaume-chevalier/Spiking-Neural-Network-SNN-with-PyTorch-where-Backpropagation-engenders-STDP https://github.com/guillaume-chevalier/Spiking-Neural-Networ...

marmaduke 7y ago
It was interesting to read how you did a spiking eural network in PyTorch, but it seems your neurons' states are coupled continuously in time, whereas in the brain, it would be the opposite, ie. the spike timing carries information and not the state values. > backprop engenders STDP This is backwards I think, but definitely an interesting association to make
codekansas 7y ago
There's a cool package called Nengo from Chris Eliasmith's group at UWaterloo which hasn't received as much attention as I think it should: https://www.nengo.ai/nengo-dl/examples/tensorflow-models.html https://www.nengo.ai/nengo-dl/examples/tensorflow-models.htm...
etiam 7y ago
You may be interested to watch this talk: http://www.cs.nyu.edu/~yann/deep07/videos/mov010.avi http://www.cs.nyu.edu/~yann/deep07/videos/mov010.avi Slides: http://www.cs.toronto.edu/~hinton/backpropincortex2007.pdf http://www.cs.toronto.edu/~hinton/backpropincortex2007.pdf

mjpuser 7y ago

I have been on similar kicks for drawing similarities between the two, but it never pans out to anything useful. I.e how does this move the science forward? I can play devil's advocate (aka classic hacker news' commenter) and say what about inhibiting neurons? Tonic neurons? What about the ability for the brain to do recall after hearing a name once? Procedural memory? Does the relationship you point out help you understand any of these things?

rdlecler1 7y ago

It’s interesting that most AI models focus on learning, but in biology the heavy lifting was all done in the developmental evolution and neurogenesis. You’re not going to teach your dog relativity with back propagation—-yet we treat BP like it was going to solve all the problems in AI. Until we start focusing more on neural architecture I have no worries about AI taking over the world.

TekMol 7y ago
Well, at the moment we are not teaching dogs. We are trying to create dogs.
- rdlecler1 7y ago
  That’s not what I see.
creddit 7y ago
This is a valuable observation. I think the question, though, comes down to which of these two things should be mastered first or if they should be done in parallel. In general, the explosion of successes in DL in the last few years has been driven by AD and backprop rising to the occasion to make novel architectures explorable for the first time.
olooney 7y ago
> You’re not going to teach your dog relativity with back propagation What do you mean? RNN's can be taught to do math using BP[1]. Heck, you can do a simple version yourself in less than an hour[2]. They can't do tensor calculus yet (AFAIK) but there doesn't seem be any reason why BP in particular would be the stumbling block; the difficulty is finding the right representation. > yet we treat BP like it was going to solve all the problems in AI Except for reinforcement learning which does not use BP to solve the Bellma equations[3], AlphaZero which uses minimax[4], AutoML based on non-gradient methods such as bayesian optimization[5], etc. Research into CNNs and RNNs for image, text, and voice processing does tend to focus on BP, but not inappropriately so considering that that approach continues to make rapid progress in those domains. > Until we start focusing more on neural architecture I have no worries about AI taking over the world. I can't tell if you're arguing for or against. Are you suggesting that we should focus more on "neural architecture" so that AI can take over the world? Or are you approving of the current narrow focus for reasons of safety? [1] https://arxiv.org/pdf/1809.08590.pdf https://arxiv.org/pdf/1809.08590.pdf [2] https://machinelearningmastery.com/learn-add-numbers-seq2seq-recurrent-neural-networks/ https://machinelearningmastery.com/learn-add-numbers-seq2seq... [3] https://towardsdatascience.com/introduction-to-various-reinforcement-learning-algorithms-i-q-learning-sarsa-dqn-ddpg-72a5e0cb6287 https://towardsdatascience.com/introduction-to-various-reinf... [4] https://www.depthfirstlearning.com/2018/AlphaGoZero https://www.depthfirstlearning.com/2018/AlphaGoZero [5] https://en.wikipedia.org/wiki/Bayesian_optimization https://en.wikipedia.org/wiki/Bayesian_optimization