In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

We present local ensembles, a method for detecting extrapolation at test time in a pre-trained model. We focus on underdetermination as a key component of extrapolation: we aim to detect when many possible predictions are consistent with the training data and model class. Our method uses local second-order information to approximate the variance of predictions across an ensemble of models from the same class. We compute this approximation by estimating the norm of the component of a test point's gradient that aligns with the low-curvature directions of the Hessian, and provide a tractable method for estimating this quantity. Experimentally, we show that our method is capable of detecting when a pre-trained model is extrapolating on test data, with applications to out-of-distribution detection, detecting spurious correlates, and active learning.
We present local ensembles, a method for detecting extrapolation in trained models, which approximates the variance of an ensemble using local-second order information.

We present a simple idea that allows to record a speaker in a given language and synthesize their voice in other languages that they may not even know. These techniques open a wide range of potential applications such as cross-language communication, language learning or automatic video dubbing. We call this general problem multi-language speaker-conditioned speech synthesis and we present a simple but strong baseline for it.

 Our model architecture is similar to the encoder-decoder Char2Wav model or Tacotron. The main difference is that, instead of conditioning on characters or phonemes that are specific to a given language, we condition on a shared phonetic representation that is universal to all languages. This cross-language phonetic representation of text allows to synthesize speech in any language while preserving the vocal characteristics of the original speaker. Furthermore, we show that fine-tuning the weights of our model allows us to extend our results to speakers outside of the training dataset.
We present a simple idea that allows to record a speaker in a given language and synthesize their voice in other languages that they may not even know.

Several state of the art convolutional networks rely on inter-connecting different layers to ease the flow of information and gradient between their input and output layers. These techniques have enabled practitioners to successfully train deep convolutional networks with hundreds of layers. Particularly, a novel way of interconnecting layers was introduced as the Dense Convolutional Network (DenseNet) and has achieved state of the art performance on relevant image recognition tasks. Despite their notable empirical success, their theoretical understanding is still limited. In this work, we address this problem by analyzing the effect of layer interconnection on the overall expressive power of a convolutional network. In particular, the  connections used in DenseNet are compared with other types of inter-layer connectivity. We carry out a tensor analysis on the expressive power inter-connections on convolutional arithmetic circuits (ConvACs) and relate our results to standard convolutional networks. The analysis leads to performance bounds and practical guidelines for design of ConvACs. The generalization of these results are discussed for other kinds of convolutional networks via generalized tensor decompositions.

We analyze the expressive power of the connections used in DenseNets via tensor decompositions.