TY - CONF AB - We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task. AU - Sahoo, Subham AU - Lampert, Christoph AU - Martius, Georg S ID - 6012 T2 - Proceedings of the 35th International Conference on Machine Learning TI - Learning equations for extrapolation and control VL - 80 ER - TY - DATA AB - This package contains data for the publication "Nonlinear decoding of a complex movie from the mammalian retina" by Deny S. et al, PLOS Comput Biol (2018). The data consists of (i) 91 spike sorted, isolated rat retinal ganglion cells that pass stability and quality criteria, recorded on the multi-electrode array, in response to the presentation of the complex movie with many randomly moving dark discs. The responses are represented as 648000 x 91 binary matrix, where the first index indicates the timebin of duration 12.5 ms, and the second index the neural identity. The matrix entry is 0/1 if the neuron didn't/did spike in the particular time bin. (ii) README file and a graphical illustration of the structure of the experiment, specifying how the 648000 timebins are split into epochs where 1, 2, 4, or 10 discs were displayed, and which stimulus segments are exact repeats or unique ball trajectories. (iii) a 648000 x 400 matrix of luminance traces for each of the 20 x 20 positions ("sites") in the movie frame, with time that is locked to the recorded raster. The luminance traces are produced as described in the manuscript by filtering the raw disc movie with a small gaussian spatial kernel. AU - Deny, Stephane AU - Marre, Olivier AU - Botella-Soler, Vicente AU - Martius, Georg S AU - Tkacik, Gasper ID - 5584 KW - retina KW - decoding KW - regression KW - neural networks KW - complex stimulus TI - Nonlinear decoding of a complex movie from the mammalian retina ER - TY - CONF AB - We present an approach that enables robots to self-organize their sensorimotor behavior from scratch without providing specific information about neither the robot nor its environment. This is achieved by a simple neural control law that increases the consistency between external sensor dynamics and internal neural dynamics of the utterly simple controller. In this way, the embodiment and the agent-environment coupling are the only source of individual development. We show how an anthropomorphic tendon driven arm-shoulder system develops different behaviors depending on that coupling. For instance: Given a bottle half-filled with water, the arm starts to shake it, driven by the physical response of the water. When attaching a brush, the arm can be manipulated into wiping a table, and when connected to a revolvable wheel it finds out how to rotate it. Thus, the robot may be said to discover the affordances of the world. When allowing two (simulated) humanoid robots to interact physically, they engage into a joint behavior development leading to, for instance, spontaneous cooperation. More social effects are observed if the robots can visually perceive each other. Although, as an observer, it is tempting to attribute an apparent intentionality, there is nothing of the kind put in. As a conclusion, we argue that emergent behavior may be much less rooted in explicit intentions, internal motivations, or specific reward systems than is commonly believed. AU - Der, Ralf AU - Martius, Georg S ID - 652 SN - 978-150905069-7 TI - Dynamical self consistency leads to behavioral development and emergent social interactions in robots ER - TY - JOUR AB - With the accelerated development of robot technologies, control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of specific objectives for the task at hand. While very successful in many applications, self-organized control schemes seem to be favored in large complex systems with unknown dynamics or which are difficult to model. Reasons are the expected scalability, robustness, and resilience of self-organizing systems. The paper presents a self-learning neurocontroller based on extrinsic differential plasticity introduced recently, applying it to an anthropomorphic musculoskeletal robot arm with attached objects of unknown physical dynamics. The central finding of the paper is the following effect: by the mere feedback through the internal dynamics of the object, the robot is learning to relate each of the objects with a very specific sensorimotor pattern. Specifically, an attached pendulum pilots the arm into a circular motion, a half-filled bottle produces axis oriented shaking behavior, a wheel is getting rotated, and wiping patterns emerge automatically in a table-plus-brush setting. By these object-specific dynamical patterns, the robot may be said to recognize the object's identity, or in other words, it discovers dynamical affordances of objects. Furthermore, when including hand coordinates obtained from a camera, a dedicated hand-eye coordination self-organizes spontaneously. These phenomena are discussed from a specific dynamical system perspective. Central is the dedicated working regime at the border to instability with its potentially infinite reservoir of (limit cycle) attractors "waiting" to be excited. Besides converging toward one of these attractors, variate behavior is also arising from a self-induced attractor morphing driven by the learning rule. We claim that experimental investigations with this anthropomorphic, self-learning robot not only generate interesting and potentially useful behaviors, but may also help to better understand what subjective human muscle feelings are, how they can be rooted in sensorimotor patterns, and how these concepts may feed back on robotics. AU - Der, Ralf AU - Martius, Georg S ID - 658 IS - MAR JF - Frontiers in Neurorobotics SN - 16625218 TI - Self organized behavior generation for musculoskeletal robots VL - 11 ER - TY - CONF AB - In classical machine learning, regression is treated as a black box process of identifying a suitable function from a hypothesis set without attempting to gain insight into the mechanism connecting inputs and outputs. In the natural sciences, however, finding an interpretable function for a phenomenon is the prime goal as it allows to understand and generalize results. This paper proposes a novel type of function learning network, called equation learner (EQL), that can learn analytical expressions and is able to extrapolate to unseen domains. It is implemented as an end-to-end differentiable feed-forward network and allows for efficient gradient based training. Due to sparsity regularization concise interpretable expressions can be obtained. Often the true underlying source expression is identified. AU - Martius, Georg S AU - Lampert, Christoph ID - 6841 T2 - 5th International Conference on Learning Representations, ICLR 2017 - Workshop Track Proceedings TI - Extrapolation and learning equations ER - TY - CONF AB - With the accelerated development of robot technologies, optimal control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of the history of sensor values, guided by the goals, intentions, objectives, learning schemes, and so forth. While very successful with classical robots, these methods run into severe difficulties when applied to soft robots, a new field of robotics with large interest for human-robot interaction. We claim that a novel controller paradigm opens new perspective for this field. This paper applies a recently developed neuro controller with differential extrinsic synaptic plasticity to a muscle-tendon driven arm-shoulder system from the Myorobotics toolkit. In the experiments, we observe a vast variety of self-organized behavior patterns: when left alone, the arm realizes pseudo-random sequences of different poses. By applying physical forces, the system can be entrained into definite motion patterns like wiping a table. Most interestingly, after attaching an object, the controller gets in a functional resonance with the object's internal dynamics, starting to shake spontaneously bottles half-filled with water or sensitively driving an attached pendulum into a circular mode. When attached to the crank of a wheel the neural system independently develops to rotate it. In this way, the robot discovers affordances of objects its body is interacting with. AU - Martius, Georg S AU - Hostettler, Raphael AU - Knoll, Alois AU - Der, Ralf ID - 1214 TI - Compliant control for soft robots: Emergent behavior of a tendon driven anthropomorphic arm VL - 2016-November ER - TY - CONF AB - With the accelerated development of robot technologies, optimal control becomes one of the central themes of research. In traditional approaches, the controller, by its internal functionality, finds appropriate actions on the basis of the history of sensor values, guided by the goals, intentions, objectives, learning schemes, and so forth. The idea is that the controller controls the world---the body plus its environment---as reliably as possible. This paper focuses on new lines of self-organization for developmental robotics. We apply the recently developed differential extrinsic synaptic plasticity to a muscle-tendon driven arm-shoulder system from the Myorobotics toolkit. In the experiments, we observe a vast variety of self-organized behavior patterns: when left alone, the arm realizes pseudo-random sequences of different poses. By applying physical forces, the system can be entrained into definite motion patterns like wiping a table. Most interestingly, after attaching an object, the controller gets in a functional resonance with the object's internal dynamics, starting to shake spontaneously bottles half-filled with water or sensitively driving an attached pendulum into a circular mode. When attached to the crank of a wheel the neural system independently discovers how to rotate it. In this way, the robot discovers affordances of objects its body is interacting with. AU - Martius, Georg S AU - Hostettler, Rafael AU - Knoll, Alois AU - Der, Ralf ID - 8094 SN - 9780262339360 T2 - Proceedings of the Artificial Life Conference 2016 TI - Self-organized control of an tendon driven arm by differential extrinsic plasticity VL - 28 ER - TY - JOUR AB - Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher-level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive rhythmic behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no systemspecific modifications of the DEP rule. They rather arise from the underlying mechanism of spontaneous symmetry breaking,which is due to the tight brain body environment coupling. The new synaptic rule is biologically plausible and would be an interesting target for neurobiological investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution. AU - Der, Ralf AU - Martius, Georg S ID - 1570 IS - 45 JF - PNAS TI - Novel plasticity rule can explain the development of sensorimotor intelligence VL - 112 ER - TY - CONF AU - Martius, Georg S AU - Olbrich, Eckehard ID - 12881 SN - 9780262330275 T2 - Proceedings of the 13th European Conference on Artificial Life TI - Quantifying self-organizing behavior of autonomous robots ER - TY - JOUR AB - Quantifying behaviors of robots which were generated autonomously from task-independent objective functions is an important prerequisite for objective comparisons of algorithms and movements of animals. The temporal sequence of such a behavior can be considered as a time series and hence complexity measures developed for time series are natural candidates for its quantification. The predictive information and the excess entropy are such complexity measures. They measure the amount of information the past contains about the future and thus quantify the nonrandom structure in the temporal sequence. However, when using these measures for systems with continuous states one has to deal with the fact that their values will depend on the resolution with which the systems states are observed. For deterministic systems both measures will diverge with increasing resolution. We therefore propose a new decomposition of the excess entropy in resolution dependent and resolution independent parts and discuss how they depend on the dimensionality of the dynamics, correlations and the noise level. For the practical estimation we propose to use estimates based on the correlation integral instead of the direct estimation of the mutual information based on next neighbor statistics because the latter allows less control of the scale dependencies. Using our algorithm we are able to show how autonomous learning generates behavior of increasing complexity with increasing learning duration. AU - Martius, Georg S AU - Olbrich, Eckehard ID - 1655 IS - 10 JF - Entropy TI - Quantifying emergent behavior of autonomous robots VL - 17 ER -