In previous blog posts I have already talked about Logic Tensor Networks in general, their relation to Conceptual Spaces, and several additional membership functions that are in line with the Conceptual Spaces framework. As I already mentioned before, I want to apply them in a “proof of concept” scenario. Today I’m going to sketch this scenario in more detail.

# Category: PhD

## A hybrid way for obtaining the dimensions of a conceptual space (Part 2)

Last time, I gave a rough outline of a hybrid approach for obtaining the dimensions of a conceptual space that uses both multidimensional scaling (MDS) and artificial neural networks (ANNs) [1]. Today, I will show our first results (which we will present next week at the AIC workshop in Palermo).

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## A hybrid way for obtaining the dimensions of a conceptual space (Part 1)

In earlier blog posts, I have already talked about two ways of obtaining the dimensions of a conceptual space: Neural networks such as InfoGAN on the one hand and multidimensional scaling (MDS) on the other hand. Over the past few months, in a collaboration with Elektra Kypridemou, I have worked on a way of combining these two approaches. Today, I would like to give a quick overview of our recent proposal [1].

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## Extending Logic Tensor Networks (Part 2)

A while ago, I introduced Logic Tensor Networks (LTNs) and argued that they are nicely applicable in a conceptual spaces scenario. In one of my recent posts, I described how to ensure that an LTN can only learn convex concepts. Today, I will take this one step further by introducing additional ways of defining the membership function of an LTN.

## Some progress with InfoGAN

I’ve recently shared my first (and unfortunately relatively disappointing) results of applying InfoGAN [1] to simple shapes. Over the past weeks, I’ve continued to work on this, and my results are starting to look more promising. Today, I’m going to share the current state of my research.