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# System prepended metadata

title: Disentengled representation using Mix-Up Loss
tags: [projects, ' disentenglement']

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tags: projects, disentenglement
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# Disentengled representation using Mix-Up Loss




Given object-centric representations $X \rightarrow \{f_0, \dots, f_i\}, Y \rightarrow \{g_0, \dots, g_i\},$ and $X+Y \rightarrow \{h_0, \dots, h_i\}$, we augment the contrastive loss with a term that learns dissimilar representations between pairs $(X, X+Y)$ and $(Y, X+Y)$.

$$\begin{aligned}
\mathcal{L}(\theta) = \mathbb{E}_{X, Y} \Big[
    &- \log \max_i \psi(h_i, f_i) + \log \sum_i \psi(h_i, h_i^-) \\
    &- \log \max_i \psi(h_i, g_i) + \log \sum_i \psi(h_i, h_i^-)\\
    &+ \log \sum_i \psi(h_i, f_i) \psi(h_i,g_i)\Big]
\end{aligned}$$

> [name=Florin][color=red]
> 1. I don't get what the max term is doing here, given that the loss is now on object representations: $-\log \max_i \psi(h_i,f_i)$.
> 2. Are there any other contrastive losses on object representations? I only know of [Kipf's (eqs:6,5)](https://arxiv.org/pdf/1911.12247.pdf) which is a bit more intuitive -- minimize distance between same object representations at different time steps and the other way around for negative examples.

> [name=Andrei][color=green]
> 1. X and X+Y probably don't share all the slots / factors, thus we select only the pair that is the most similar.



Benchmarks and code bases we could use:

1. Same [setup as in Lowe's](https://arxiv.org/pdf/2011.10287.pdf).
    - There's no code
    - But we can use their starting point, which is DeepSets + Slot Attention (and there's code for Slot Attention)
2. Use the p[rediction model setup from Ke](https://arxiv.org/pdf/2107.00848.pdf).
    - Maybe also the RL part
    - Advantage: there's a code base and several baselines we could dig into
3. Extend this to object centric latent space mumbo-jumbo.
4. There's also the code base of Brendel's group: https://brendel-group.github.io/cl-ica/