This takes me back. 1990, building Boltzman machines and Perceptrons
from arrays of void pointers to "neurons" in plain C. What did we use
"AI" for back then? To guess the next note in a MIDI melody, and to
recognise the shape of a scored note, minim, crotchet, quaver on a 5 x
9 dot grid. 85% accuracy was "good enough" then.
Thanks for these links. You're right, I think computer-vision "sight
reading" is now a fairly done deal. Very impressive progress in the
past 30 years.
For small values of "music"? Really, no. But tbh, neither have more
advanced "AI" composition experiments I've encountered over the years,
Markov models, linear predictive coding, genetic/evolutionary algs,
rule based systems, and now modern diffusion and transormers... they
all lack the "spirit of jazz" [0]
My understanding is that the Harmonium (Smolensky) was the first restricted Boltzmann machine, but maximized “harmony” instead of minimizing “energy.” When Smolensky, Hinton and Rummelhart collaborated, they instead called it “goodness of fit.”
The harmonium paper [1] is a really nice read. Hinton obviously became the superstar and Smolensky wrote long books about linguistics.
It's more accurate to say that businesspeople consider research a waste in our quarter-by-quarter investment climate, since it generally doesn't lead to immediate gains.
And our current leadership considers research a threat, since science rarely supports conspiracy theorists or historical revisionism.
I mistook the title for "A Tiny Boltzmann Brain"! [0]
My own natural mind immediately solved the conundrum. Surely this was a case where a very small model was given randomly generated weights and then tested to see if it actually did something useful!
After all, the smaller the model, the more likely simple random generation can produce something interesting, relative to its size.
I stand corrected, but not discouraged!
I propose a new class of model, the "Unbiased-Architecture Instant Boltzmann Model" (UA-IBM).
One day we will have quantum computers large enough to simply set up the whole dataset as a classical constraint on a model defined with N serialized values, representing all the parameters and architecture settings. Then let a quantum system with N qubits take one inference step over all the classical samples, with all possible parameters and architectures in quantum superposition, and then reduce the result to return the best (or near best) model's parametesr and architecture in classical form.
Anyone have a few qubits laying around that want to give this a shot? (The irony that everything is quantum and yet so slippery we can hardly put any of it to work yet.
(Sci-fi story premise: the totally possible case of an alien species that evolved one-off quantum sensor, which evolved into a whole quantum sensory system, then a nervous system, and subsequently full quantum intelligence out of the gate. What kind of society and technological trajectory would they have? Hopefully they are in close orbit around a black hole, so the impact of their explosive progress has not threatened us yet. And then one day, they escape their gravity well, and ...)
My understanding, which is far from certain, is that problems like this (try a large combination of solutions, cooperate between superpositions to identify the best, then set up the quantum outputs so when they are classically sampled, the best answer is the most likely sample obtained) are solved in four stages:
1. N^2 potential solutions encoded in superposition across N qubuts.
2. Each superposition goes through the quantum version of a normal inference pass, using each superpositions weights to iteratively process all the classical data, then calculates performance. (This is all done without any classical sampling.)
3. Cross-superposition communication that results in agreement on the desired version. This is the weakest part of my knowledge. I know that is an operation type that exists, but I don't know how circuits implement it. But the number of bits being operated on is small, just a performance measure. (This is also done without any classical sampling.)
4. Then the output is sampled to get classical values. This requires N * log2(N) circuit complexity, where N is the number of bits defining the chosen solution, i.e. parameters and architectural settings. This can be a lot of hardware, obviously, perhaps more than the rest of the hardware, given N will be very large.
Don't take anything I say here for granted. I have designed parts of such a circuit, using ideal quantum gates in theory, but not all of it. I am not an expert, but I believe that every step here is well understood by others.
The downside relative to other approaches: It does a complete search of the entire solutions space directly, so the result comes from reducing N^2 superpositions across N qubits, where for interesting models the N can be very large (billions of parameters x parameter bit width), to get N qubits. No efficiencies are obtained from gradient information or any other heuristic. This is the brute force method. So an upper bound of hardware requirements.
Another disadvantage, is since the solution was not obtained by following a gradient, the best solution might not be robust. Meaning, it might be a kind of vertex between robust solutions that manages to do best on the designed data, but small changes of input samples from the design data might not generalize well. This is less likely to be a problem if smoothing/regularization information is taken into account account for determining each superpositions performance.
Poor quantum beings. They don't have access to a computation model that exceeds the speeds of their own thoughts and they are forever doomed to be waiting a long time for computations to happen
Just FYI: mouse-scrolling is much too sensitive for some reason (I'm assuming it swipes just fine in mobile contexts, have not checked that). The result is that it jumped from first to last "page" and back whenever I tried scrolling. Luckily keyboard input worked so I could still read the whole thing.
IIUC, we need gibbs sampling(to compute the weight updates) instead of using the gradient based forward and backward passes with today's NNetworks that we are used to. Any one understand why that is so?
Thought I'd weigh in here as well, I believe Gibbs sampling is being used as a way to approximate the expectation over the model distribution. This value is required to compute the gradient of the log likelihood but integrating the distribution is intractable.
This is done in a similar way as you may use MCMC to draw a representative sample from a VAE. In the deep learning formulation of a neural network the gradient is estimated over batches of the dataset rather than over an explicitly modeled probability distribution.
Not an expert, but I have a bit of formal training on Bayesian stuff which handles similar problems.
Usually Gibbs is used when there's no directly straight-forward gradient (or when you are interested in reproducing the distribution itself, rather than a point estimate), but you do have some marginal/conditional likelihoods which are simple to sample from.
Since each visible node depends on each hidden node and each hidden node effects all visible nodes, the gradient ends up being very messy, so its much simpler to use Gibbs sampling to adjust based on marginal likelihoods.
I might be mistaken, but I think this is partly because of the undirected structure of RBMs, so you can't build a computational graph in the same way as with feed-forward networks.
By "undirected structure" I assume you refer to the presence of cycles in the graph? I was taught to call such networks "recurrent" but it seems that that term has evolved to mean something slightly different. Anyway yeah, because of the cycles Gibbs sampling is key to the network's operation. One still employs gradient descent during training, but the procedure to calculate the gradient itself involves Gibbs sampling.
Edit: Actually was talking about the General Boltzmann Machine. For the Restricted Boltzmann Machine an approximation has been assumed which obviates the need for full Gibbs sampling during training. Then (quoting the article, emphasis mine) "after training, it can sample new data from the learned distribution using Gibbs sampling."
Readit News
Reading music off a lined page sounds like a fun project, particularly to do it from scratch like 3Blue1Brown's number NN example[1].
Mix with something like Chuck[2] and you can write a completely clientside application with today's tech.
[1] - https://www.3blue1brown.com/lessons/neural-networks
[2] - https://chuck.stanford.edu/
[0] https://i.pinimg.com/originals/e4/84/79/e484792971cc77ddff8f...
The harmonium paper [1] is a really nice read. Hinton obviously became the superstar and Smolensky wrote long books about linguistics.
Anyone know more about this history?
[1] https://stanford.edu/~jlmcc/papers/PDP/Volume%201/Chap6_PDP8...
Do check out his T2 Tile Project.
The value of grad students is often overlooked, they contribute so much and then later on advance the research even more.
Why does America look on research as a waste, when it has move everything so far?
https://en.wikipedia.org/wiki/List_of_sovereign_states_by_re...
And our current leadership considers research a threat, since science rarely supports conspiracy theorists or historical revisionism.
Cleaning up the abundance of typos, margin, and scroll issues now, thanks for pointing them out.
My own natural mind immediately solved the conundrum. Surely this was a case where a very small model was given randomly generated weights and then tested to see if it actually did something useful!
After all, the smaller the model, the more likely simple random generation can produce something interesting, relative to its size.
I stand corrected, but not discouraged!
I propose a new class of model, the "Unbiased-Architecture Instant Boltzmann Model" (UA-IBM).
One day we will have quantum computers large enough to simply set up the whole dataset as a classical constraint on a model defined with N serialized values, representing all the parameters and architecture settings. Then let a quantum system with N qubits take one inference step over all the classical samples, with all possible parameters and architectures in quantum superposition, and then reduce the result to return the best (or near best) model's parametesr and architecture in classical form.
Anyone have a few qubits laying around that want to give this a shot? (The irony that everything is quantum and yet so slippery we can hardly put any of it to work yet.
(Sci-fi story premise: the totally possible case of an alien species that evolved one-off quantum sensor, which evolved into a whole quantum sensory system, then a nervous system, and subsequently full quantum intelligence out of the gate. What kind of society and technological trajectory would they have? Hopefully they are in close orbit around a black hole, so the impact of their explosive progress has not threatened us yet. And then one day, they escape their gravity well, and ...)
[0] https://en.wikipedia.org/wiki/Boltzmann_brain
1. N^2 potential solutions encoded in superposition across N qubuts.
2. Each superposition goes through the quantum version of a normal inference pass, using each superpositions weights to iteratively process all the classical data, then calculates performance. (This is all done without any classical sampling.)
3. Cross-superposition communication that results in agreement on the desired version. This is the weakest part of my knowledge. I know that is an operation type that exists, but I don't know how circuits implement it. But the number of bits being operated on is small, just a performance measure. (This is also done without any classical sampling.)
4. Then the output is sampled to get classical values. This requires N * log2(N) circuit complexity, where N is the number of bits defining the chosen solution, i.e. parameters and architectural settings. This can be a lot of hardware, obviously, perhaps more than the rest of the hardware, given N will be very large.
Don't take anything I say here for granted. I have designed parts of such a circuit, using ideal quantum gates in theory, but not all of it. I am not an expert, but I believe that every step here is well understood by others.
The downside relative to other approaches: It does a complete search of the entire solutions space directly, so the result comes from reducing N^2 superpositions across N qubits, where for interesting models the N can be very large (billions of parameters x parameter bit width), to get N qubits. No efficiencies are obtained from gradient information or any other heuristic. This is the brute force method. So an upper bound of hardware requirements.
Another disadvantage, is since the solution was not obtained by following a gradient, the best solution might not be robust. Meaning, it might be a kind of vertex between robust solutions that manages to do best on the designed data, but small changes of input samples from the design data might not generalize well. This is less likely to be a problem if smoothing/regularization information is taken into account account for determining each superpositions performance.
Just FYI: mouse-scrolling is much too sensitive for some reason (I'm assuming it swipes just fine in mobile contexts, have not checked that). The result is that it jumped from first to last "page" and back whenever I tried scrolling. Luckily keyboard input worked so I could still read the whole thing.
This is done in a similar way as you may use MCMC to draw a representative sample from a VAE. In the deep learning formulation of a neural network the gradient is estimated over batches of the dataset rather than over an explicitly modeled probability distribution.
Usually Gibbs is used when there's no directly straight-forward gradient (or when you are interested in reproducing the distribution itself, rather than a point estimate), but you do have some marginal/conditional likelihoods which are simple to sample from.
Since each visible node depends on each hidden node and each hidden node effects all visible nodes, the gradient ends up being very messy, so its much simpler to use Gibbs sampling to adjust based on marginal likelihoods.
Edit: Actually was talking about the General Boltzmann Machine. For the Restricted Boltzmann Machine an approximation has been assumed which obviates the need for full Gibbs sampling during training. Then (quoting the article, emphasis mine) "after training, it can sample new data from the learned distribution using Gibbs sampling."
It brings up a lot of memories! Shameless plug: I made a visualization of an RBM being trained years ago: https://www.youtube.com/watch?v=lKAy_NONg3g