Abstract
It has been shown that “visual numerosity emerges as a statistical property of images in ‘deep networks’ that learn a hierarchical generative model of the sensory input”, through unsupervised deep learning [1]. The original deep generative model was based on stochastic neurons and, more importantly, on input (image) reconstruction. Statistical analysis highlighted a correlation between the numerosity present in the input and the population activity of some neurons in the second hidden layer of the network, whereas population activity of neurons in the first hidden layer correlated with total area (i.e., number of pixels) of the objects in the image. Here we further investigate whether numerosity information can be isolated as a disentangled factor of variation of the visual input. We train in unsupervised and semi-supervised fashion a latent-space generative model that has been shown capable of disentangling relevant semantic features in a variety of complex datasets, and we test its generative performance under different conditions. We then propose an approach to the problem based on the assumption that, in order to let numerosity emerge as disentangled factor of variation, we need to cancel out the sources of variation at graphical level.
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- 1.
It is worth clarifying that for each component of the cost functions shown in all the equations, for all the three models considered, we apply a weighting hyper-parameter (thus, not only for the Information based reguliarized of the InfoGAN model), and we investigate empirically the effect of changing them.
- 2.
In our first setup to investigate this model we used, as second dataset, the labels themselves, feeding one line of the model with the labels and the other line with images. It must be noted however that this approach can be extended to a setup that does not use labels at all, however we leave this for future developments.
- 3.
Even when the Categorical dimensionality is somehow compatible with the numerosity being analized, for example with numerosity 5 and Categorical dimension 5, or Categorical dimension 10 to account for 8 quantities and 2 possible graphical expressions, w/b or b/w.
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Zanetti, A., Testolin, A., Zorzi, M., Wawrzynski, P. (2019). Numerosity Representation in InfoGAN: An Empirical Study. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2019. Lecture Notes in Computer Science(), vol 11507. Springer, Cham. https://doi.org/10.1007/978-3-030-20518-8_5
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DOI: https://doi.org/10.1007/978-3-030-20518-8_5
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