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Questions tagged [topologies]

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Binary decision boundary requiring 2 hidden layers in neural network with limited neurons

I just started learning about neural networks and was wondering what a neural network with 2 hidden layers is able to express over a neural network with just 1 hidden layer (where number of neurons ...
Regina Dea's user avatar
3 votes
0 answers
87 views

There is no topology on the space of random variables s.t. a.s. convergent seqs are the converging seqs?

The post When do we find convergence in distribution to independent variables? prompted me to review convergence in distribution. As I read on, I encountered a property about almost sure convergence ...
Galen's user avatar
  • 8,754
4 votes
2 answers
267 views

In "A Topology Layer for Machine Learning," are the topological priors learned by the network or imposed by humans?

In this paper by Gabrielsson, Nelson, et al. the authors "present a differentiable topology layer that can, among other things, construct a loss on the output of a deep generative network to ...
kdbanman's user avatar
  • 857
3 votes
0 answers
53 views

Reference request: Network/graph topology inference

I am a mathematician looking for a survey/book on methods for inference of graph/network topology (structure). Specifically, the kind of problem I am looking to study is as follows: Given a graph $...
Rodrigo Zepeda's user avatar
4 votes
1 answer
174 views

Topological rather than metric based machine learning theory?

The first notion of continuity in a math class is usually the one based on metric spaces. In particular, the $\epsilon,\delta$ definition of continuity. But in topology, a more general notion of ...
user56834's user avatar
  • 2,819
2 votes
0 answers
41 views

How to identify manifolds for an optimisation problem

I don't have much experience in topology, but I am interested to know if: • Given a particular problem and associated cost function, how would one deduce what kind of manifold this problem lies on. ...
tisPrimeTime's user avatar
7 votes
2 answers
2k views

2 hidden layers are more powerful than 1

When searching for information on choosing the number of hidden layers in a neural network, I have come across the following table mutiple times, including in this answer: | Number of Hidden Layers ...
user76284's user avatar
  • 983
0 votes
1 answer
117 views

Optimising neural network to prevent overfitting

I'm looking for some advice on a general approach to optimise the training of a neural network. My primary concern is to avoid over-fitting to the training data and maintain as much generality as ...
tommyzer00's user avatar
2 votes
0 answers
407 views

Neural networks, mapping features to polar coordinates to deal with uncertain inputs

Let's say you've got a neural network which takes in a vector of real numbers as input. Additionally, let's say you're uncertain about the values of some components of the vector, and your level of ...
wlad's user avatar
  • 1,450
3 votes
1 answer
137 views

Visualizing model trajectories for Neural Networks using function approximator

Erhan et al. in their 2010 paper discusses how pre-training improves deep networks: http://www.jmlr.org/papers/volume11/erhan10a/erhan10a.pdf#page=15 In there, they compare different neural network ...
The Wanderer's user avatar
2 votes
1 answer
318 views

Deep learning with global connections/correlations

Deep learning for 1D/2D inputs usually assume some sort of local connections, whether it is using local filters, or recurrent connections etc. What if for our problem we think a connection between ...
highBandWidth's user avatar
9 votes
2 answers
410 views

Cases where TDA outperforms public benchmarks?

Precise Question What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data? Context When new ML algorithms are developed, it seems ...
user avatar
15 votes
2 answers
3k views

Graphical intuition of statistics on a manifold

On this post, you can read the statement: Models are usually represented by points $\theta$ on a finite dimensional manifold. On Differential Geometry and Statistics by Michael K Murray and ...
Antoni Parellada's user avatar
1 vote
1 answer
97 views

Difference between FFNN and NAR

What is the difference between feed forward neural network and non-linear autoregressive neural network. Do they have same structure. What is the difference in their equation
user6460588's user avatar
3 votes
0 answers
37 views

Analysis techiques for logical topologies

I'm working in the area of analysis of logical computer systems (e.g https://goo.gl/images/KyLCCo). Specifically in the field of anomaly detection of these systems. I was thinking about the field of ...
Jonathan Dunne's user avatar
4 votes
0 answers
131 views

Topology of Confidence Intervals

I hope this is the right site to post this. The example I have in my mind is a GLMM model, where we infer random effects, and a random effect caterpillar plot (with confidence intervals): Now, ...
Alex R.'s user avatar
  • 14k
10 votes
1 answer
325 views

Topologies for which the ensemble of probability distributions is complete

I have been struggling quite a bit with reconciling my intuitive understanding of probability distributions with the weird properties that almost all topologies on probability distributions possess. ...
Guillaume Dehaene's user avatar
1 vote
0 answers
52 views

ART neural network disambiguation

I have an assignment to implement the adaptive resonance theory (ART) type network (as part of a bigger project). I have red a lot of Internet resources on the topic and I think I've got the essence ...
irpbc's user avatar
  • 111
7 votes
1 answer
213 views

Laplacian-Beltrami approximation based on an empirical sample

Given a probability measure $\nu$ on a subset $M \subseteq \mathbb{R}^N$ we construct the corresponding operator $$L^tf(x)=f(x)\int_{M} e^{-\frac{||x-y||^2}{4t}}d\nu(y)-\int_{M}f(y)e^{-\frac{||x-y||^...
hearse's user avatar
  • 2,545
4 votes
2 answers
2k views

Where can I get real data of big network topology? [closed]

I want to model how traffic will flow on real networks (not just the internet, also, say, Intel's internal LAN). Is there a place I can get real network topologies data I can use?
Elazar Leibovich's user avatar
75 votes
3 answers
106k views

What's the difference between feed-forward and recurrent neural networks?

What is the difference between a feed-forward and recurrent neural network? Why would you use one over the other? Do other network topologies exist?
Shane's user avatar
  • 12.5k