Offline reinforcement learning (RL) aims to train agents from pre-collected datasets.

ModernCNNscanreachhundreds of millions of parameters and billions of operations, which makes it difficult to deploy. To alleviate aforementioned problem, various methods have been proposed to increase the efficiency of CNNs.

In this work, we find that better model usage can make a huge difference.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on these models. However, existing error bounds require restrictive assumptions. In this paper, we employ the Gaussian process distribution and continuity arguments to derive a novel uniform error bound under weaker assumptions. Furthermore, we demonstrate how this distribution can be used to derive probabilistic Lipschitz constants and analyze the asymptotic behavior of our bound. Finally, we derive safety conditions for the control of unknown dynamical systems based on Gaussian process models and evaluate them in simulations of a robotic manipulator.

While the ImageNet dataset has been driving computer vision research over the past decade, significant label noise and ambiguity have made top-1 accuracy an insufficient measure of further progress. To address this, new label-sets and evaluation protocols have been proposed for ImageNet showing that state-of-the-art models already achieve over 95% accuracy and shifting the focus on investigating why the remaining errors persist.Recent work in this direction employed a panel of experts to manually categorize all remaining classification errors for two selected models. However, this process is time-consuming, prone to inconsistencies, and requires trained experts, making it unsuitable for regular model evaluation thus limiting its utility. To overcome these limitations, we propose the first automated error classification framework, a valuable tool to study how modeling choices affect error distributions. We use our framework to comprehensively evaluate the error distribution of over 900 models. Perhaps surprisingly, we find that across model architectures, scales, and pre-training corpora, top-1 accuracy is a strong predictor for the of all error types.

It is a popular belief that model-based Reinforcement Learning (RL) is more sample efficient than model-free RL, but in practice, it is not always true due to overweighed model errors. In complex and noisy settings, model-based RL tends to have trouble using the model if it does not know when to trust the model. In this work, we find that better model usage can make a huge difference. We show theoretically that if the use of model-generated data is restricted to state-action pairs where the model error is small, the performance gap between model and real rollouts can be reduced. It motivates us to use model rollouts only when the model is confident about its predictions. We propose Masked Model-based Actor-Critic (M2AC), a novel policy optimization algorithm that maximizes a model-based lower-bound of the true value function. M2AC implements a masking mechanism based on the model's uncertainty estimation to decide whether the model should be used or not. Consequently, the new algorithm tends to give robust policy improvements. Experiments on continuous control benchmarks demonstrate that M2AC has strong performance even when using long model rollouts in very noisy environments, and significantly outperforms previous state-of-the-art methods.

We investigate transformer prediction of long Collatz steps, a complex arithmetic function that maps odd integers to their distant successors in the Collatz sequence ( $u_{n+1}=u_n/2$ if $u_n$ is even, $u_{n+1}=(3u_n+1)/2$ if $u_n$ is odd). Model accuracy varies with the base used to encode input and output. It can be as high as $99.7\%$ for bases $24$ and $32$, and as low as $37$ and $25\%$ for bases $11$ and $3$. Yet, all models, no matter the base, follow a common learning pattern. As training proceeds, they learn a sequence of classes of inputs that share the same residual modulo $2^p$. Models achieve near-perfect accuracy on these classes, and less than $1\%$ for all other inputs. This maps to a mathematical property of Collatz sequences: the length of the loops involved in the computation of a long Collatz step can be deduced from the binary representation of its input. The learning pattern reflects the model learning to predict inputs associated with increasing loop lengths. An analysis of failure cases reveals that almost all model errors follow predictable patterns. Hallucination, a common feature of large language models, almost never happens. In over $90\%$ of failures, the model performs the correct calculation, but wrongly estimates loop lengths. Our observations give a full account of the algorithms learned by the models. They suggest that the difficulty of learning such complex arithmetic function lies in figuring the control structure of the computation -- the length of the loops. We believe that the approach outlined here, using mathematical problems as tools for understanding, explaining, and perhaps improving language models, can be applied to a broad range of problems and bear fruitful results.