Questions tagged [topologies]

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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 ...
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3 votes
0 answers
48 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 $...
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4 votes
1 answer
122 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 ...
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2 votes
0 answers
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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. ...
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6 votes
2 answers
1k 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 ...
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0 votes
1 answer
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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 ...
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2 votes
0 answers
390 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 ...
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3 votes
1 answer
99 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 ...
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1 vote
1 answer
305 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 ...
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6 votes
1 answer
316 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 ...
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13 votes
2 answers
2k 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 ...
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1 vote
1 answer
77 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
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3 votes
0 answers
36 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 ...
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4 votes
0 answers
107 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, ...
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9 votes
1 answer
300 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. ...
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1 vote
0 answers
50 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 ...
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7 votes
1 answer
207 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||^...
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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?
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71 votes
3 answers
94k 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?
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