We introduce a dataset of concept learning tasks that helps uncover implicit biases in large language models. Using in-context concept learning experiments, we found that language models may have a bias toward upward monotonicity in quantifiers; such bias is less apparent when the model is tested by direct prompting without concept learning components. This demonstrates that in-context concept learning can be an effective way to discover hidden biases in language models.

Molecular dynamics (MD) is a powerful tool for exploring the behavior of atomistic systems, but its reliance on sequential numerical integration limits simulation efficiency. We present a novel neural network architecture, MDtrajNet, and a pre-trained foundational model, MDtrajNet-1, that directly generates MD trajectories across chemical space, bypassing force calculations and integration. This approach accelerates simulations by up to two orders of magnitude compared to traditional MD, even those enhanced by machine-learning interatomic potentials. MDtrajNet combines equivariant neural networks with a transformer-based architecture to achieve strong accuracy and transferability in predicting long-time trajectories. Remarkably, the errors of the trajectories generated by MDtrajNet-1 for various known and unseen molecular systems are close to those of the conventional ab initio MD. The architecture's flexible design supports diverse application scenarios, including different statistical ensembles, boundary conditions, and interaction types. By overcoming the intrinsic speed barrier of conventional MD, MDtrajNet opens new frontiers in efficient and scalable atomistic simulations.

New findings in natural language processing (NLP) demonstrate that the strong memorization capability contributes a lot to the success of Large Language Models (LLM). This inspires us to explicitly bring an independent memory mechanism into CTR ranking model to learn and memorize cross features' representations. In this paper, we propose multi-Hash Codebook NETwork (HCNet) as the memory mechanism for efficiently learning and memorizing representations of cross features in CTR tasks. HCNet uses a multi-hash codebook as the main memory place and the whole memory procedure consists of three phases: multi-hash addressing, memory restoring, and feature shrinking. We also propose a new CTR model named MemoNet which combines HCNet with a DNN backbone. Extensive experimental results on three public datasets and online test show that MemoNet reaches superior performance over state-of-the-art approaches. Besides, MemoNet shows scaling law of large language model in NLP, which means we can enlarge the size of the codebook in HCNet to sustainably obtain performance gains. Our work demonstrates the importance and feasibility of learning and memorizing representations of cross features, which sheds light on a new promising research direction.

Koopman decomposition is a non-linear generalization of eigen decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its variants provide approximations to the Koopman operator, and have been applied extensively in many fluid dynamic problems. Despite being endowed with a richer dictionary of nonlinear observables, nonlinear variants of the DMD, such as extended/kernel dynamic mode decomposition (EDMD/KDMD) are seldom applied to large-scale problems primarily due to the difficulty of discerning the Koopman invariant subspace from thousands of resulting Koopman triplets: eigenvalues, eigenvectors, and modes. To address this issue, we revisit the formulation of EDMD and KDMD, and propose an algorithm based on multi-task feature learning to extract the most informative Koopman invariant subspace by removing redundant and spurious Koopman triplets. These algorithms can be viewed as sparsity promoting extensions of EDMD/KDMD and are presented in an open-source package. Further, we extend KDMD to a continuous-time setting and show a relationship between the present algorithm, sparsity-promoting DMD and an empirical criterion from the viewpoint of non-convex optimization. The effectiveness of our algorithm is demonstrated on examples ranging from simple dynamical systems to two-dimensional cylinder wake flows at different Reynolds numbers and a three-dimensional turbulent ship air-wake flow. The latter two problems are designed such that very strong transients are present in the flow evolution, thus requiring accurate representation of decaying modes.