Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical works suggest that the Euclidean structure of space induces invariants in an agent's raw sensorimotor experience. We hypothesize that capturing these invariants is beneficial for sensorimotor prediction and that, under certain exploratory conditions, a motor representation capturing the structure of the external space should emerge as a byproduct of learning to predict future sensory experiences. We propose a simple sensorimotor predictive scheme, apply it to different agents and types of exploration, and evaluate the pertinence of these hypotheses. We show that a naive agent can capture the topology and metric regularity of its sensor's position in an egocentric spatial frame without any a priori knowledge, nor extraneous supervision.
Different flavors of Variational Auto-Encoders have been used to encode spatial factors of variation in a latent representation @cite_8 ; a work that more recently led to the definition of disentanglement of spatial factors as in an agent's experience @cite_0 .
@cite_0 @cite_8
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We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned with the underlying generative factors of variation of data emerge when optimising the modified ELBO bound in @math -VAE, as training progresses. From these insights, we propose a modification to the training regime of @math -VAE, that progressively increases the information capacity of the latent code during training. This modification facilitates the robust learning of disentangled representations in @math -VAE, without the previous trade-off in reconstruction accuracy. Variational autoencoders (VAEs) have received much attention recently as an end-to-end architecture for text generation with latent variables. In this paper, we investigate several multi-level structures to learn a VAE model to generate long, and coherent text. In particular, we use a hierarchy of stochastic layers between the encoder and decoder networks to generate more informative latent codes. We also investigate a multi-level decoder structure to learn a coherent long-term structure by generating intermediate sentence representations as high-level plan vectors. Empirical results demonstrate that a multi-level VAE model produces more coherent and less repetitive long text compared to the standard VAE models and can further mitigate the posterior-collapse issue. Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers. Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.