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After we listen to a series of words, we can silently replay them in our mind. Does this mental replay involve a reactivation of our original perceptual dynamics? We recorded electrocorticographic (ECoG) activity across the lateral cerebral cortex as people heard and then mentally rehearsed spoken sentences. For each region, we tested whether silent rehearsal of sentences involved reactivation of sentence-specific representations established during perception or transformation to a distinct representation. In sensorimotor and premotor cortex, we observed reliable and temporally precise responses to speech; these patterns transformed to distinct sentence-specific representations during mental rehearsal. In contrast, we observed less reliable and less temporally precise responses in prefrontal and temporoparietal cortex; these higher-order representations, which were sensitive to sentence semantics, were shared across perception and rehearsal of the same sentence. The mental rehearsal of natural speech involves the transformation of stimulus-locked speech representations in sensorimotor and premotor cortex, combined with diffuse reactivation of higher-order semantic representations. 

Nonparametric estimation of multivariate functions is an important problem in statisti- cal machine learning with many applications, ranging from nonparametric regression to nonparametric graphical models. Several authors have proposed to estimate multivariate functions under the smoothing spline analysis of variance (SSANOVA) framework, which assumes that the multivariate function can be decomposed into the summation of main effects, two-way interaction effects, and higher order interaction effects. However, existing methods are not scalable to the dimension of the random variables and the order of inter- actions. We propose a LAyer-wiSE leaRning strategy (LASER) to estimate multivariate functions under the SSANOVA framework. The main idea is to approximate the multivari- ate function sequentially starting from a model with only the main effects. Conditioned on the support of the estimated main effects, we estimate the two-way interaction effects only when the corresponding main effects are estimated to be non-zero. This process is con- tinued until no more higher order interaction effects are identified. The proposed strategy provides a data-driven approach for estimating multivariate functions under the SSANOVA framework. Our proposal yields a sequence of estimators. To study the theoretical prop- erties of the sequence of estimators, we establish the notion of post-selection persistency. Extensive numerical studies are performed to evaluate the performance of LASER.