Planning in high-dimensional space remains a challenging problem, even with recent advances in algorithms and computational power. We are inspired by efference copy and sensory reafference theory from neuroscience.   Our aim is to allow agents to form mental models of their environments for planning.   The cerebellum is emulated with a two-stream, fully connected, predictor network. The network receives as inputs the efference as well as the features of the current state. Building on insights gained from knowledge distillation methods, we choose as our features the outputs of a pre-trained network,  yielding a compressed representation of the current state.   The representation is chosen such that it allows for fast search using classical graph search algorithms. We display the effectiveness of our approach on a viewpoint-matching task using a modified best-first search algorithm. As we manipulate an object in our hands, we can accurately predict how it looks after some action is performed. Through our visual sensory system, we receive high-dimensional information about the object. However, we do not hallucinate its full-dimensional representation as we estimate how it would look and feel after we act. But we feel that we understood what happened if there is an agreement between the experience of the event and our predicted experience. There has been much recent work on methods that take advantage of compact representations of states for search and exploration. One of the advantages of this approach is that finding a good representation allows for faster and more efficient planning. This holds in particular when the latent space is of a much lower dimensionality than the one where the states originally live in. Our central nervous system (CNS) sends a command (efferent) to our motor system, as well as sending a copy of the efferent to our cerebellum, which is our key organ for predicting the sensory outcome of actions when we initiate a movement and is responsible for fine motor control. The cerebellum then compares the result of the action (sensory reafference) with the intended consequences. If they differ, then the cerebellum makes changes to its internal structure such that it does a better job next time -i.e., in no uncertain terms, it learns. The cerebellum receives 40 times more information than it outputs, by a count of the number of axons. This gives us a sense of the scale of the compression ratio between the high dimensional input and low dimensional output. Thus, we constrain our attention to planning in a low-dimensional space, without necessarily reconstructing the high-dimensional one. We apply this insight for reducing the complexity of tasks such that planning in high dimensionality space can be done by classical AI methods in low dimensionality space . Our contributions are thus twofold: provide a link between efference theory and classical planning with a simple model and introduce a search method for applying the model to reduced state-space search. We validate our approach experimentally on visual data associated with categorical actions that connect the images, for example taking an object and rotating it. We create a simple manipulation task using the NORB dataset (LeCun et al., 2004) , where the agent is presented with a starting viewpoint of an object and the task is to produce a sequence of actions such that the agent ends up with the target viewpoint of the object. As the NORB data set can be embedded on a cylinder (Schüler et al., 2018) (Hadsell et al., 2006) or a sphere (Wang et al., 2018) , we can visualize the actions as traversing the embedded manifold. Pairing the EfferenceNet with a good but generic feature map allows us to perform an accurate search in the latent space of manipulating unseen objects. This remarkably simple method, inspired by the neurology of the cerebellum, reveals a promising line of future work. We validate our method by on a viewpoint-matching task derived from the NORB dataset. In the case of deterministic environments, EfferenceNets calculate features of the current state and action, which in turn define the next state. This opens up a future direction of research by combining EfferenceNets with successor features (Barreto et al., 2017) . Furthermore, the study of effective feature maps strikes us as an important factor in this line of work to consider. We utilize here Laplacian Eigenmaps and pre-trained deep networks. It is probably possible to improve the performance of the system by end-to-end training but we believe that it is more promising to work on generic multi-purpose representations. Possible further methods include Slow Feature Analysis (SFA) (Wiskott & Sejnowski, 2002) (Schüler et al., 2018) . SFA has been previously shown (Sprekeler, 2011) to solve a special case of LEMs while it allows for natural out-of-sample embeddings.
We present a neuroscience-inspired method based on neural networks for latent space search
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