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Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter. Previous work has used Gaussian processes—a statistical framework that extends Bayesian nonparametric approaches to regression—to model human function learning. We build on this work, modeling the process of learning to learn functions as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters.more » « less

Intelligent biological systems are characterized by their embodiment in a complex environment and the intimate interplay between their nervous systems and the nonlinear mechanical properties of their bodies. This coordination, in which the dynamics of the motor system coevolved to reduce the computational burden on the brain, is referred to as "mechanical intelligence" or "morphological computation". In this work, we seek to develop machine learning analogs of this process, in which we jointly learn the morphology of complex nonlinear elastic solids along with a deep neural network to control it. By using a specialized differentiable simulator of elastic mechanics coupled to conventional deep learning architectureswhich we refer to as neuromechanical autoencoderswe are able to learn to perform morphological computation via gradient descent. Key to our approach is the use of mechanical metamaterialscellular solids, in particularas the morphological substrate. Just as deep neural networks provide flexible and massivelyparametric function approximators for perceptual and control tasks, cellular solid metamaterials are promising as a rich and learnable space for approximating a variety of actuation tasks. In this work we take advantage of these complementary computational concepts to codesign materials and neural network controls to achieve nonintuitive mechanical behavior. We demonstrate in simulation how it is possible to achieve translation, rotation, and shape matching, as well as a "digital MNIST" task. We additionally manufacture and evaluate one of the designs to verify its realworld behavior.more » « less

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in apply ing MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a highfidelity physical simulation, an intractable integral, or a slowlyconverging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low fidelity computation, leading to bias in the resulting target density. Multifidelity MCMC algorithms combine models of varying fidelities in order to obtain an ap proximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multifidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudomarginal MCMC approach for multifidelity inference that utilizes a cheaper, randomizedfidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the lowfidelity sequence of models. Finally, we discuss and evaluate the proposed multifidelity MCMC approach on several applications, including logGaussian Cox process modeling, Bayesian ODE system identification, PDEconstrained optimization, and Gaussian process parameter inference.more » « less

Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond the wellstudied techniques used in supervised learning. While supervised learning methods can generalize effectively without explicitly accounting for epistemic uncertainty, we describe why appropriate uncertainty handling can actually be essential in RL. We show that generalization to unseen test conditions from a limited number of training conditions induces a kind of implicit partial observability, effectively turning even fullyobserved MDPs into POMDPs. Informed by this observation, we recast the problem of generalization in RL as solving the induced partially observed Markov decision process, which we call the epistemic POMDP. We demonstrate the failure modes of algorithms that do not appropriately handle this partial observability, and suggest a simple ensemblebased technique for approximately solving the partially observed problem. Empirically, we demonstrate that our simple algorithm derived from the epistemic POMDP achieves significant gains in generalization over current methods on the Procgen benchmark suite.more » « less

null (Ed.)Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it may be beneficial to trade the cost of collecting an environmental measurement against the quality or "fidelity" of this measurement and how the measurement affects changepoint estimation. For instance, one might decide between inertial measurements or GPS to determine changepoints for motion. A Bayesian approach to changepoint detection is particularly appealing because we can represent our posterior uncertainty about changepoints and make active, costsensitive decisions about data fidelity to reduce this posterior uncertainty. Moreover, the total cost could be dramatically lowered through active fidelity switching, while remaining robust to changes in data distribution. We propose a multifidelity approach that makes costsensitive decisions about which data fidelity to collect based on maximizing information gain with respect to changepoints. We evaluate this framework on synthetic, video, and audio data and show that this informationbased approach results in accurate predictions while reducing total cost.more » « less

In design, fabrication, and control problems, we are often faced with the task of synthesis, in which we must generate an object or configuration that satisfies a set of constraints while maximizing one or more objective functions. The synthesis problem is typically characterized by a physical process in which many different realizations may achieve the goal. This manytoone map presents challenges to the supervised learning of feedforward synthesis, as the set of viable designs may have a complex structure. In addition, the nondifferentiable nature of many physical simulations prevents efficient direct optimization. We address both of these problems with a twostage neural network architecture that we may consider to be an autoencoder. We first learn the decoder: a differentiable surrogate that approximates the manytoone physical realization process. We then learn the encoder, which maps from goal to design, while using the fixed decoder to evaluate the quality of the realization. We evaluate the approach on two case studies: extruder path planning in additive manufacturing and constrained soft robot inverse kinematics. We compare our approach to direct optimization of the design using the learned surrogate, and to supervised learning of the synthesis problem. We find that our approach produces higher quality solutions than supervised learning, while being competitive in quality with direct optimization, at a greatly reduced computational cost.more » « less

null (Ed.)The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reversemode automatic differentiation (AD) to compute gradients of megadimensional objectives. The AD techniques underlying these tools were designed to compute exact gradients to numerical precision, but modern machine learning models are almost always trained with stochastic gradient descent. Why spend computation and memory on exact (minibatch) gradients only to use them for stochastic optimization? We develop a general framework and approach for randomized automatic differentiation (RAD), which can allow unbiased gradient estimates to be computed with reduced memory in return for variance. We examine limitations of the general approach, and argue that we must leverage problem specific structure to realize benefits. We develop RAD techniques for a variety of simple neural network architectures, and show that for a fixed memory budget, RAD converges in fewer iterations than using a small batch size for feedforward networks, and in a similar number for recurrent networks. We also show that RAD can be applied to scientific computing, and use it to develop a lowmemory stochastic gradient method for optimizing the control parameters of a linear reactiondiffusion PDE representing a fission reactor.more » « less

Many probabilistic modeling problems in machine learning use gradientbased optimization in which the objective takes the form of an expectation. These problems can be challenging when the parameters to be optimized determine the probability distribution under which the expectation is being taken, as the na\"ive Monte Carlo procedure is not differentiable. Reparameterization gradients make it possible to efficiently perform optimization of these Monte Carlo objectives by transforming the expectation to be differentiable, but the approach is typically limited to distributions with simple forms and tractable normalization constants. Here we describe how to differentiate samples from slice sampling to compute \textit{slice sampling reparameterization gradients}, enabling a richer class of Monte Carlo objective functions to be optimized. Slice sampling is a Markov chain Monte Carlo algorithm for simulating samples from probability distributions; it only requires a density function that can be evaluated pointwise up to a normalization constant, making it applicable to a variety of inference problems and unnormalized models. Our approach is based on the observation that when the slice endpoints are known, the sampling path is a deterministic and differentiable function of the pseudorandom variables, since the algorithm is rejectionfree. We evaluate the method on synthetic examples and apply it to a variety of applications with reparameterization of unnormalized probability distributions.more » « less