PatrickHuembeli
commented
4 years ago We would like to thank Aishwarya Balwani for her comments and for reviewing our article. We address all her points below:
Introduction:
- We adapted the sentence. Thanks for the recommendation. It reads much nicer now.
- And we changed the sentence “Here, we embark on a journey” to “We invite the reader on a journey”
EBMs:
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We adapted several typos as suggested.
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About the probability and intelligent behaviour, we changed the paragraph to: As an initial strategic choice, we aim to use this random behaviour of the particles to our advantage and use it to model the probability distribution of some data that should be learned. The goal is to design probabilistic systems that harness randomness in their intelligent behaviour. As we will later see, compared to a deterministic physical system a probabilistic one will not only be able to learn and retrieve data patterns, it will as well be able to generate new data that resembles the learned data patterns.
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The paragraphs were adapted as mentioned. It indeed makes more sense like this.
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We added one sentence to the coarse-grained part to explain what we mean by this. Thanks for pointing this out. It was indeed a bit vague. It reads now: Typically only coarse-grained information can be accessed, signifying that in general one does not keep track of all the degrees of freedom but of macroscopic properties of the system.
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We added a reference for the total energy. And reformulated the paragraph around the fixed energy
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We agree that the term entropy should be explained and because we did not want to disturb the reading flow too much we added a footnote with more explanations.
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Like the reviewer suggested, we added a footnote that explains the notion of a bath and temperature a bit better.
Figure1:
- We are not sure what labels we should add to this figure. There are already labels, no? But as suggested we added the signs of the nodes and the figure is indeed easier to read.
- We also added a title.
Architecture:
- We agree that this sentence with +-bi was confusing. We added a footnote instead just to be very clear what this individual energy implies.
- We added a reference to auto-associative memories.
- We implemented the changes as suggested and made clear that Hopfield networks are a subset of RBMs and indicate clearly that visible is v and hidden is h.
Figure 2:
- We added a comment to the caption for the color scheme.
Sampling:
- We added parentheses
Training:
- This is correct. We replaced position with displacement to make it more clear.
Figure (Training an RBM):
- This is indeed a bit vague. We did not change the sentence, but we added an explanation of what we exactly mean. We think it is good to keep in mind what these most likely configurations mean: they are the data that is learned by the RBM.
Figure (Using an RBM to retrieve damaged images):
- This was an excellent idea. We added a different energy landscape for each image.
The following communications-focused peer review was solicited as part of the Distill review process.
The reviewer chose to waive anonymity. Distill offers reviewers a choice between anonymous review and offering reviews under their name. Non-anonymous review allows reviewers to get credit for the service they offer to the community.
Distill is grateful to Aishwarya Balwani for taking the time to review this article.
General Comments
"Introduction: “Inspiration takes many forms.” → Replace period with a semicolon? “Neuroscience has inspired… fundamental laws of nature” → At present there are two separate sentences here. It would be nice to join them and say something more like, “While neuroscience has inspired many of the mathematical models that form the bedrock of research in ML and AI, is it possible to dive deeper and draw inspiration from the fundamental laws of nature themselves?” “Here we embark on a...interacting physical properties” → I get the meaning, but the line reads a little awkwardly.
EBMs: “Energy based models emerged in the ML literature of the 1980s” → Replace “of” with “in”? “...to replace discriminators in GANs” → Sentence construction is awkward given the previous part of the sentence. Perhaps replace the phrase with, “as potential replacements for discriminators in GANs”? “...we imagine being ambitious experimental...” → Replace “being” with “ourselves as” so that the sentence reads, “...we imagine ourselves as ambitious experimental...” Delete “artificial intelligence in the lab” “This is definitely ambitious...is challenging” Make the sentence, “This is definitely ambitious, as being able to fully engineer a large collection of particles is challenging” Reverse order from “typically they” to “they typically” “As an initial strategic choice...The goal is to design...in their intelligent behaviour” → Why is it a good idea to use random fluctuations? Is it just because we don’t know how to explain it? Does it help us computationally to generate intelligence in some manner? Would be useful for the reader to be given some intuition here why a probabilistic system makes sense in this situation. Maybe also say why designing a deterministic system isn’t a good idea? It’s also a little unclear what exactly is meant by “random fluctuations”. I would consider just saying “the random behaviour of these particles”. “...but also simple enough that they can be...” → Add “such” so that the sentence reads, “...but also simple enough such that they can be...” The sentence at present reads a little awkwardly, but I don’t know the best way to remedy it either :) I would consider breaking the paragraph “To understand the origin...trained and characterized” at the sentence, “Mathematically, a probabilistic system...” and combine the rest of the text in this paragraph with the next paragraph where the authors talk about the difficulty of keeping track of the system’s internal degrees of freedom. “Typically only coarse grained information can be accessed.” → Coarse grained information about what? What does coarse grained imply? Is it a sampling problem in some sense? What would fine grained mean? How are we at a disadvantage if we only have access to coarse grained info? After elaborating a little about what the authors mean by coarse grained and how it is different from the ideal case scenario, I would now consider breaking into a new paragraph when starting to talk about the energy function. “...which can even be theoretically...” Delete “even”. Also, would be nice to have a reference for total energy. It is unclear that the authors are defining total energy when they start the sentence by saying, “This is encapsulated...” I would instead say, “The total energy of a system is defined in terms of an energy function E(x), which assigns energy values to all its possible configurations.” I would then explain in the next line a n-body system can have so-and-so different configurations, if the xis can take discrete or continuous values, and give the spins example along with a couple of others, perhaps? “If the average energy is fixed...” → The jump to average energy feels very unnatural. How is it defined/calculated? Just stating that it is the mean of the energies of all the possible states of the system would be helpful. Also, what does it mean for to be fixed? Isn’t it always fixed?
“What probability distribution...” → What are we assigning a probability distribution to? I would assume it is to the energy values assigned to the different states, but making it a little explicit would be nice.
“It is reasonable to choose...” It is unclear how fixed energy implies no information. The authors also make the assumption that the readers know what entropy is. Stating that entropy is a measure of randomness of the system, adding a reference for the same, and defining it mathematically would be helpful. The authors immediately use the mathematical formula for entropy, but fail to mention explicitly that’s what it is.
Replace “giving” with “and is given as”
The introduction of temperature seems rather random - some context about why we’re talking about thermal equilibrium (perhaps as a footnote?) would be helpful.
“In the context of machine learning…energy based models” → Since this is where EBMs are defined, I would consider making that sentence bold, as opposed to only italicizing “energy based models”.
“The Boltzmann distribution is one example of how to connect energy with probability” → Seems a little out of place, given the previous sentence. Would consider moving it to a little before, to the part of the paragraph that states the Boltzmann distribution establishes a concrete relationship between energy and probability.
Figure 1: Could we label the axes in the interactive temperature + coupling figure? Also might help to have +/- signs below the dots to show which of x1, x2 are positive or negative. Title for the figure is missing!
Architectures: “...which take the values +/- bi” → I found this a little confusing, might be alright to not include it? I think the authors mean that the individual spin energies can be +/- bi, depending on whether sigmai is +/- 1 right? I feel like that comes through given the preceding sentence. A reference for auto-associative memory would be nice. “...a Boltzmann machine is equivalent to a Hopfield network when the interactions...” → I think replacing “is equivalent” with “simplifies” makes things a little less confusing - as stated now, I briefly wasn’t sure which of Boltzmann machines or Hopfield networks was the subset and which the superset. “Conventionally, the state of an RBM...” → While implied, it would be nice to state explicitly that v corresponds to the visible nodes and h to the hidden nodes in the following equation(s).
Figure 2: In the figure showing a Hopfield network, a Boltzmann machine, and an RBM, how are the red and gray hidden nodes different from each other? Is the difference the same as the black and white visible nodes? Stating so explicitly might be helpful.
Sampling: “For an Ising energy function, the change in energy delta E introduced by changing...” → Put “delta E” in parentheses
Training: “... where y is the position of the mass” → This is with the assumption that the mass is initially at 0, correct? Else y should correspond to the displacement in the spring rather than simply the position?
Figure (Training an RBM): Training an RBM figure → The authors encourage the readers to adjust the parameters so that a data pattern is learnt, which I think is cool - but where do the readers see what pattern’s been learnt? Unless the authors meant the probability distribution on the right, which isn’t exactly a data pattern, is it?
Figure (Using an RBM to retrieve damaged images): Using an RBM to retrieve damaged images figure → Would it be possible to make the figure a little more interactive? As of now, the energy curve is static and nothing changes when selecting the different image samples.
Future of Physics and ML: “There is a one-to one correspondence...” → Add hyphen after “to”"
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