Title: Emergence of shared sensory-motor graphical language from visual input. Abstract: The framework of Language Games studies the emergence of languages in populations of agents. Recent contributions relying on deep learning methods focused on agents communicating via an idealized communication channel, where utterances produced by a speaker are directly perceived by a listener. This comes in contrast with human communication, which instead relies on a sensory-motor channel, where motor commands produced by the speaker (e.g. vocal or gestural articulators) result in sensory effects perceived by the listener (e.g. audio or visual). Here, we investigate if agents can evolve a shared language when they are equipped with a continuous sensory-motor system to produce and perceive signs, e.g. drawings. To this end, we introduce the Graphical Referential Game (GREG) where a speaker must produce a graphical utterance to name a visual referent object consisting of combinations of MNIST digits while a listener has to select the corresponding object among distractor referents, given the produced message. The utterances are drawing images produced using dynamical motor primitives combined with a sketching library. To tackle GREG we present CURVES: a multimodal contrastive deep learning mechanism that represents the energy (alignment) between named referents and utterances generated through gradient ascent on the learned energy landscape. We, then, present a set of experiments and metrics based on a systematic compositional dataset to evaluate the resulting language. We show that our method allows the emergence of a shared, graphical language with compositional properties