All Questions
Tagged with machine-learning reference-request
15
questions
3
votes
0
answers
109
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Short path problem on Cayley graphs as language translation task (from "Permutlandski" to "Cayleylandski"(s) :). Reference/suggestion request
Context: Algorithms to find short paths on Cayley graphs of (finite) groups are of some interest - see below.
There can be several approaches to that task. One of ideas coming to my mind - in some ...
- 24.4k
5
votes
1
answer
1k
views
Mathematics research relating to machine learning
What branch/branches of math are most relevant in enhancing machine learning (mostly in terms of practical use as opposed to theoretical/possible use)? Specifically, I want to know about math research ...
- 173
1
vote
0
answers
32
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Convergent gradient-type scheme for solving smooth nonconvex constrained optimization problem
Let $x_1,\ldots,x_n \in \mathbb R^d$ and $y_1,\ldots,y_n \in \{\pm 1\}$, and $\epsilon, h \gt 0$. Define $\theta(t) := Q((t-\epsilon)/h)$, where $Q(z) := \int_{z}^\infty \phi (z)\mathrm{d}z$ is the ...
- 6,824
2
votes
0
answers
37
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Stochastic gradient descent in 'stronger' settings
I am minimzing a function $F(x) = \mathbb E(f(x,\Xi))$ where $\Xi$ is some random value, by a stochastic gradient descent that generates a random number $\xi$ from the distribution of $\Xi$ at each ...
- 686
17
votes
3
answers
2k
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Theoretical results on neural networks
With this question I'd like to have a recollection of theoretical rigorous results on neural networks.
I'd like to have results that have been settled, as opposed to hypothesis. As an example, this ...
1
vote
0
answers
136
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Continuous decomposition of permutation-invariant set functions
The seminal machine learning paper Deep Sets (Zaheer et al., 2017) discusses representations of permutation-invariant functions on real tuples, or (multi)set functions.
Given a countable set $X$ and a ...
- 233
7
votes
2
answers
2k
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Mathematics of GANs (generative adversarial networks)
Generative Adversarial Networks were introduced in http://papers.nips.cc/paper/5423-generative-adversarial-nets and has more than 20000 citations.
The paper introduced key paradigm changes which ...
- 13.8k
2
votes
0
answers
49
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What are some beginner's references on algebraically structured (statistical) models, and their connection with group actions and Fourier transform?
I asked this question on Cross Validated a few days ago, but didn't really get a favorable response, so asking here to see if I get any.
I'm looking at the description of a short-term position in ...
- 223
2
votes
1
answer
212
views
Uniform Lipschitz function approximation by shallow neural networks
Fix $d\in \mathbb{N}$. Let $F_1$ be the set of all 1-Lipschitz functions mapping $[0, 1]^d$ to $\mathbb{R}$.
For $\varphi: \mathbb{R} \rightarrow \mathbb{R}$ and $m \in \mathbb{N}$, let $N_\varphi^m$ ...
- 1,095
11
votes
1
answer
798
views
Abstract mathematical concepts/tools appeared in machine learning research
I am interested in knowing about abstract mathematical concepts, tools or methods that have come up in theoretical machine learning. By "abstract" I mean something that is not immediately related to ...
1
vote
0
answers
99
views
Plethora of variant neural networks?
Since a decade ago when new life was breathed in to neural networks in the form of deep learning a plethora of different architectures have come about. Is there a reference that gives compendium of ...
- 13.8k
13
votes
2
answers
679
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Reference Request: Theoretical Mixing Times Research in Machine Learning / Artificial Intelligence (AI)
I'm doing a PhD in probability theory, focusing mostly on mixing times. It's a pure maths PhD, considering precise models and showing rigorous mixing results. I'm also interested in stuff like machine ...
- 560
0
votes
1
answer
108
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General results regarding linear separability?
I'm reading up on the theory behind support vector machines and would like a good reference with some general results about linear separability.
Specifically, questions like below:
Given two ...
- 101
57
votes
4
answers
14k
views
Group theory in machine learning
I'm a Machine Learning researcher who would like to research applications of group theory in ML.
There is a term "Partially Observed Groups" in machine learning theory which has been ...
- 587
94
votes
14
answers
14k
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Deep learning / Deep neural nets for mathematician
I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".
Most of the papers/books that are often quoted in papers/...