Code accompanying the paper Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation The paper has been accepted at NeurIPS 2023 for an oral presentation.

We tackle the problems of latent variables identification and "out-of-support'' image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders used for object-centric representation learning (OCRL) and well suited for images that can be decomposed as a sum of object-specific images. We provide conditions under which exactly solving the reconstruction problem using an additive decoder is guaranteed to identify the blocks of latent variables up to permutation and block-wise invertible transformations. This guarantee relies only on very weak assumptions about the distribution of the latent factors, which might present statistical dependencies and have an almost arbitrarily shaped support. Our result provides a new setting where nonlinear independent component analysis (ICA) is possible and adds to our theoretical understanding of OCRL methods. We also show theoretically that additive decoders can generate novel images by recombining observed factors of variations in novel ways, an ability we refer to as Cartesian-product extrapolation. We show empirically that additivity is crucial for both identifiability and extrapolation on simulated data.

• python data/balls_dataset.py --latent_case supp_l_shape
• python data/balls_dataset.py --latent_case supp_extrapolate

• python scripts/scalar_disentanglement_exps.py --case train

• python scripts/scalar_disentanglement_exps.py --case eval

• python scripts/gen_draft_results.py --results_case violin_plot_2d

• python data/balls_dataset.py --latent_case latent_traversal_x_axis
• python data/balls_dataset.py --latent_case latent_traversal_y_axis
• python data/balls_dataset.py --latent_case supp_iid_no_occ
• python data/balls_dataset.py --latent_case supp_scm_linear

• python scripts/block_disentanglement_exps.py --case train

• python scripts/block_disentanglement_exps.py --case eval

• python scripts/gen_draft_results.py --results_case violin_plot_4d