Is it correct to use "we" if there is only one author?
It's the "royal 'we'"
The Mathematics of Artificial Intelligence (2022)
31–40 of 61 posts
Re: The Mathematics of Artificial Intelligence (2022)
#32After a cursory glance, my feeling is that "The Mathematics of Neuronal Networks" would be a better title? In recent years, the term "Artificial Intelligence" is often used instead of "Neuronal Networks". I wouldn't be surprised if this will change again. If there is evidence that it will not and Neuronal Networks are for some reason the optimal medium for intelligence, I would love to read about it.
I like to explain that AI > ML > NN. Now, NNs are the ones getting results at computer vision and natural language, and more. I think most people would say that other ML approaches are computational statistics. The goalpost for AI keeps moving. If you are truly interested in the math of AI I think PAC Bayes learning is more appropriate and your book is Understanding Machine Learning [1] (not an easy read). A more gen…
Seconding this. "Learning From Data" is one of the best intros to machine learning theory I've seen through the years!
Re: The Mathematics of Artificial Intelligence (2022)
#33Does anybody know of textbooks, or articles, material etc. that focus on the /consequences/ of the mathematics of ANNs? For example: why in this problem using more layers is more or less efficient than using bigger layers, or branching evolutions of the outcomes as opposed to intensive computation of a single flow etc. A reasoned summary of the tricks, in a way ("this works because of that").
Some of the questions of depth vs breadth are explained intuitively in this Bengio Lecun paper from 2007.
Re: The Mathematics of Artificial Intelligence (2022)
#34Is it correct to use "we" if there is only one author?
Using the "royal we" is standard in mathematics. If you ever see someone do this in ordinary writing you can bump up your odds that they're a mathematician. Another giveaway is using "modulo" to mean "except for".
Re: The Mathematics of Artificial Intelligence (2022)
#35After a cursory glance, my feeling is that "The Mathematics of Neuronal Networks" would be a better title? In recent years, the term "Artificial Intelligence" is often used instead of "Neuronal Networks". I wouldn't be surprised if this will change again. If there is evidence that it will not and Neuronal Networks are for some reason the optimal medium for intelligence, I would love to read about it.
I like to explain that AI > ML > NN. Now, NNs are the ones getting results at computer vision and natural language, and more. I think most people would say that other ML approaches are computational statistics. The goalpost for AI keeps moving. If you are truly interested in the math of AI I think PAC Bayes learning is more appropriate and your book is Understanding Machine Learning [1] (not an easy read). A more gen…
NN > ML. The proof is that nematode or fly, I dont remember, with its simple NN fully mapped, and still remaining a mystery how it works. ML, which is just a matrix multiplication at its core, is a laughably simplistic model of NN.
Re: The Mathematics of Artificial Intelligence (2022)
#36Thanks, this is great.
Poorly thought out morning spitball coming. One of the reasons approximation theorems are so unsatisfying is that they are always of the form "for function class X there exists an architecture A of complexity O(N) such that blah". And then this is compared favorably with some other function class whose dimension is O(N). But there's something tricky about this: you leave the architecture unspecified. You are comparing a single space of functions with an enormous number of spaces, one for each architecture with the specified complexity, and then saying "well if I pick the right architecture I win". Doesn't seem like a fair comparison.
Re: The Mathematics of Artificial Intelligence (2022)
#37Shouldn't "the mathematics of artificial intelligence" be subsumed by computational statistics? It may be that only very general and weak statements are possible about "deep" NN's, but then that's merely a fact about the territory we're dealing with. Why should this be regarded as a "new" field?
Re: The Mathematics of Artificial Intelligence (2022)
#38After a cursory glance, my feeling is that "The Mathematics of Neuronal Networks" would be a better title? In recent years, the term "Artificial Intelligence" is often used instead of "Neuronal Networks". I wouldn't be surprised if this will change again. If there is evidence that it will not and Neuronal Networks are for some reason the optimal medium for intelligence, I would love to read about it.
> Neuronal Networks are for some reason the optimal medium for intelligence No, that's not the same 'intelligence' ("General Intelligence") as the "I" side in Artificial Intelligence. The term 'intelligence' applied to Artificial Neural Networks makes sense, as such: to reach a procedural solution it takes an engineer; the engineer is said to have reached the solution because "intelligent"; ANNs are (semi-)automated…
ANNs dont have the key component of intelligence - ability to learn. If our brains worked like ANNs, they'd be wired once at the brains factory, they'd produce the same output given the same input, and learning anything new would need a complete rewiring at the factory, possibly erasing other learnings (often unpredictably).
Even if ANNs could update themselves on the fly, in a reasonably incremental manner, they'd just imitate insect-level reactions. Intelligence would need those ANNs to have a virtual reality, run thought experiments there and learn from that.
Re: The Mathematics of Artificial Intelligence (2022)
#39Let L(uy,y) = fy denote a parametric partial differential equation with y being a parameter from a high-dimensional parameter space Y ⊆ Rp and uy the associated solution in a Hilbert space H. After a high-fidelity discretization... These AI folks are clearly very clever, but they don't actually believe that's got anything to do with how human thinking works, right?
Whenever I see "Hilbert space" remarks in a paper that doesn't concern abstract math, I roll my eyes and imagine a chef who starts his youtube video with "Today we are going to cook a salad. For better precision, we are going to use knifes of triangular shape, three dimensional plates of circular shape, and the 100% dihydrogen of oxyde solution." All this only to obfuscate the fact that the entire recipe is just chopping a few carrots.
Re: The Mathematics of Artificial Intelligence (2022)
#40Earlier quoted context omitted.
I like to explain that AI > ML > NN. Now, NNs are the ones getting results at computer vision and natural language, and more. I think most people would say that other ML approaches are computational statistics. The goalpost for AI keeps moving. If you are truly interested in the math of AI I think PAC Bayes learning is more appropriate and your book is Understanding Machine Learning [1] (not an easy read). A more gen…
NN > ML. The proof is that nematode or fly, I dont remember, with its simple NN fully mapped, and still remaining a mystery how it works. ML, which is just a matrix multiplication at its core, is a laughably simplistic model of NN.
GP means artificial neural network, not an actual nervous system.
Machine learning contains ANNs as a sub-discipline. Other non-ANN topics in ML include ensembled trees, Gaussian processes, and sampling theory.