A Differentiable Physics Engine for Deep Learning in Robotics.

An important field in robotics is the optimization of controllers. Currently, robots are often treated as a black box in this optimization process, which is the reason why derivative-free optimization methods such as evolutionary algorithms or reinforcement learning are omnipresent. When gradient-based methods are used, models are kept small or rely on finite difference approximations for the Jacobian. This method quickly grows expensive with increasing numbers of parameters, such as found in deep learning. We propose the implementation of a modern physics engine, which can differentiate control parameters. This engine is implemented for both CPU and GPU. Firstly, this paper shows how such an engine speeds up the optimization process, even for small problems. Furthermore, it explains why this is an alternative approach to deep Q-learning, for using deep learning in robotics. Finally, we argue that this is a big step for deep learning in robotics, as it opens up new possibilities to optimize robots, both in hardware and software.

Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalization.

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is comparable to other state-of-the-art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here, we investigated the online learning approach by training an optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.

Embodiment of Learning in Electro-Optical Signal Processors.

Delay-coupled electro-optical systems have received much attention for their dynamical properties and their potential use in signal processing. In particular, it has recently been demonstrated, using the artificial intelligence algorithm known as reservoir computing, that photonic implementations of such systems solve complex tasks such as speech recognition. Here, we show how the backpropagation algorithm can be physically implemented on the same electro-optical delay-coupled architecture used for computation with only minor changes to the original design. We find that, compared to when the backpropagation algorithm is not used, the error rate of the resulting computing device, evaluated on three benchmark tasks, decreases considerably. This demonstrates that electro-optical analog computers can embody a large part of their own training process, allowing them to be applied to new, more difficult tasks.

Trainable hardware for dynamical computing using error backpropagation through physical media.

Neural networks are currently implemented on digital Von Neumann machines, which do not fully leverage their intrinsic parallelism. We demonstrate how to use a novel class of reconfigurable dynamical systems for analogue information processing, mitigating this problem. Our generic hardware platform for dynamic, analogue computing consists of a reciprocal linear dynamical system with nonlinear feedback. Thanks to reciprocity, a ubiquitous property of many physical phenomena like the propagation of light and sound, the error backpropagation-a crucial step for tuning such systems towards a specific task-can happen in hardware. This can potentially speed up the optimization process significantly, offering important benefits for the scalability of neuro-inspired hardware. In this paper, we show, using one experimentally validated and one conceptual example, that such systems may provide a straightforward mechanism for constructing highly scalable, fully dynamical analogue computers.

Memristor models for machine learning.

In the quest for alternatives to traditional complementary metal-oxide-semiconductor, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is being used today. In particular, large gains in area and power efficiency could be achieved by dedicated analog realizations of approximate computing engines. In this work we explore the use of memristor networks for analog approximate computation, based on a machine learning framework called reservoir computing. Most experimental investigations on the dynamics of memristors focus on their nonvolatile behavior. Hence, the volatility that is present in the developed technologies is usually unwanted and is not included in simulation models. In contrast, in reservoir computing, volatility is not only desirable but necessary. Therefore, in this work, we propose two different ways to incorporate it into memristor simulation models. The first is an extension of Strukov's model, and the second is an equivalent Wiener model approximation. We analyze and compare the dynamical properties of these models and discuss their implications for the memory and the nonlinear processing capacity of memristor networks. Our results indicate that device variability, increasingly causing problems in traditional computer design, is an asset in the context of reservoir computing. We conclude that although both models could lead to useful memristor-based reservoir computing systems, their computational performance will differ. Therefore, experimental modeling research is required for the development of accurate volatile memristor models.

Optoelectronic Systems Trained With Backpropagation Through Time.

Delay-coupled optoelectronic systems form promising candidates to act as powerful information processing devices. In this brief, we consider such a system that has been studied before in the context of reservoir computing (RC). Instead of viewing the system as a random dynamical system, we see it as a true machine-learning model, which can be fully optimized. We use a recently introduced extension of backpropagation through time, an optimization algorithm originally designed for recurrent neural networks, and use it to let the network perform a difficult phoneme recognition task. We show that full optimization of all system parameters of delay-coupled optoelectronics systems yields a significant improvement over the previously applied RC approach.

Toward unified hybrid simulation techniques for spiking neural networks.

In the field of neural network simulation techniques, the common conception is that spiking neural network simulators can be divided in two categories: time-step-based and event-driven methods. In this letter, we look at state-of-the art simulation techniques in both categories and show that a clear distinction between both methods is increasingly difficult to define. In an attempt to improve the weak points of each simulation method, ideas of the alternative method are, sometimes unknowingly, incorporated in the simulation engine. Clearly the ideal simulation method is a mix of both methods. We formulate the key properties of such an efficient and generally applicable hybrid approach.

Automated design of complex dynamic systems.

Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system's structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems.

MACOP modular architecture with control primitives.

Walking, catching a ball and reaching are all tasks in which humans and animals exhibit advanced motor skills. Findings in biological research concerning motor control suggest a modular control hierarchy which combines movement/motor primitives into complex and natural movements. Engineers inspire their research on these findings in the quest for adaptive and skillful control for robots. In this work we propose a modular architecture with control primitives (MACOP) which uses a set of controllers, where each controller becomes specialized in a subregion of its joint and task-space. Instead of having a single controller being used in this subregion [such as MOSAIC (modular selection and identification for control) on which MACOP is inspired], MACOP relates more to the idea of continuously mixing a limited set of primitive controllers. By enforcing a set of desired properties on the mixing mechanism, a mixture of primitives emerges unsupervised which successfully solves the control task. We evaluate MACOP on a numerical model of a robot arm by training it to generate desired trajectories. We investigate how the tracking performance is affected by the number of controllers in MACOP and examine how the individual controllers and their generated control primitives contribute to solving the task. Furthermore, we show how MACOP compensates for the dynamic effects caused by a fixed control rate and the inertia of the robot.

Recurrent kernel machines: computing with infinite echo state networks.

Echo state networks (ESNs) are large, random recurrent neural networks with a single trained linear readout layer. Despite the untrained nature of the recurrent weights, they are capable of performing universal computations on temporal input data, which makes them interesting for both theoretical research and practical applications. The key to their success lies in the fact that the network computes a broad set of nonlinear, spatiotemporal mappings of the input data, on which linear regression or classification can easily be performed. One could consider the reservoir as a spatiotemporal kernel, in which the mapping to a high-dimensional space is computed explicitly. In this letter, we build on this idea and extend the concept of ESNs to infinite-sized recurrent neural networks, which can be considered recursive kernels that subsequently can be used to create recursive support vector machines. We present the theoretical framework, provide several practical examples of recursive kernels, and apply them to typical temporal tasks.

Memory in linear recurrent neural networks in continuous time.

Reservoir Computing is a novel technique which employs recurrent neural networks while circumventing difficult training algorithms. A very recent trend in Reservoir Computing is the use of real physical dynamical systems as implementation platforms, rather than the customary digital emulations. Physical systems operate in continuous time, creating a fundamental difference with the classic discrete time definitions of Reservoir Computing. The specific goal of this paper is to study the memory properties of such systems, where we will limit ourselves to linear dynamics. We develop an analytical model which allows the calculation of the memory function for continuous time linear dynamical systems, which can be considered as networks of linear leaky integrator neurons. We then use this model to research memory properties for different types of reservoir. We start with random connection matrices with a shifted eigenvalue spectrum, which perform very poorly. Next, we transform two specific reservoir types, which are known to give good performance in discrete time, to the continuous time domain. Reservoirs based on uniform spreading of connection matrix eigenvalues on the unit disk in discrete time give much better memory properties than reservoirs with random connection matrices, where reservoirs based on orthogonal connection matrices in discrete time are very robust against noise and their memory properties can be tuned. The overall results found in this work yield important insights into how to design networks for continuous time.