instruction:
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.
question:
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.
answer:
We present local ensembles, a method for detecting extrapolation in trained models, which approximates the variance of an ensemble using local-second order information.

question:
We extend the Consensus Network framework to Transductive Consensus Network (TCN), a semi-supervised multi-modal classification framework, and identify its two mechanisms: consensus and classification. By putting forward three variants as ablation studies, we show both mechanisms should be functioning together. Overall, TCNs outperform or align with the best benchmark algorithms when only 20 to 200 labeled data points are available.
answer:
A semi-supervised multi-modal classification framework, TCN, that outperforms various benchmarks.

question:
We compare the model-free reinforcement learning with the model-based approaches through the lens of the expressive power of neural networks for policies, $Q$-functions, and dynamics. We show, theoretically and empirically, that even for one-dimensional continuous state space, there are many MDPs whose optimal $Q$-functions and policies are much more complex than the dynamics. We hypothesize many real-world MDPs also have a similar property. For these MDPs, model-based planning is a favorable algorithm, because the resulting policies can approximate the optimal policy significantly better than a neural network parameterization can, and model-free or model-based policy optimization rely on policy parameterization. Motivated by the theory, we apply a simple multi-step model-based bootstrapping planner (BOOTS) to bootstrap a weak $Q$-function into a stronger policy. Empirical results show that applying BOOTS on top of model-based or model-free policy optimization algorithms at the test time improves the performance on MuJoCo benchmark tasks.
answer:
We compare deep model-based and model-free RL algorithms by studying the approximability of $Q$-functions, policies, and dynamics by neural networks.