In-context learning is an emergent paradigm in large language models (LLMs) that enables them to generalize to new tasks and domains by simply prompting these models with a few exemplars without explicit parameter updates. Many attempts have been made to understand in-context learning in LLMs as a function of model scale, pretraining data, and other factors. In this work, we propose a new mechanism to probe and understand in-context learning from the lens of decision boundaries for in-context binary classification. Decision boundaries are straightforward to visualize and provide important information about the qualitative behavior of the inductive biases of standard classifiers. To our surprise, we find that the decision boundaries learned by current LLMs in simple binary classification tasks are often irregularly non-smooth, regardless of task linearity. This paper investigates the factors influencing these decision boundaries and explores methods to enhance their generalizability. We assess various approaches, including training-free and fine-tuning methods for LLMs, the impact of model architecture, and the effectiveness of active prompting techniques for smoothing decision boundaries in a data-efficient manner. Our findings provide a deeper understanding of in-context learning dynamics and offer practical improvements for enhancing robustness and generalizability of in-context learning.

Despite recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains under-explored. Learning problems in physical systems are often characterized as discovering operators that map between function spaces based on a few instances of function pairs. This task frequently presents a severely ill-posed PDE inverse problem. In this work, we propose a novel neural operator architecture based on the attention mechanism, which we coin Nonlocal Attention Operator (NAO), and explore its capability towards developing a foundation physical model. In particular, we show that the attention mechanism is equivalent to a double integral operator that enables nonlocal interactions among spatial tokens, with a data-dependent kernel characterizing the inverse mapping from data to the hidden parameter field of the underlying operator. As such, the attention mechanism extracts global prior information from training data generated by multiple systems, and suggests the exploratory space in the form of a nonlinear kernel map. Consequently, NAO can address ill-posedness and rank deficiency in inverse PDE problems by encoding regularization and achieving generalizability. Lastly, we empirically demonstrate the advantages of NAO over baseline neural models in terms of the generalizability to unseen data resolutions and system states. Our work not only suggests a novel neural operator architecture for learning an interpretable foundation model of physical systems, but also offers a new perspective towards understanding the attention mechanism.

The neural network memorization problem is to study the expressive power of neural networks to interpolate a finite dataset. Although memorization is widely believed to have a close relationship with the strong generalizability of deep learning when using overparameterized models, to the best of our knowledge, there exists no theoretical study on the generalizability of memorization neural networks. In this paper, we give the first theoretical analysis of this topic.

Motion time series collected from low-power, always-on mobile and wearable devices such as smartphones and smartwatches offer significant insights into human behavioral patterns, with wide applications in healthcare, automation, IoT, and AR/XR. However, given security and privacy concerns, building large-scale motion time series datasets remains difficult, hindering the development of pre-trained models for human activity analysis. Typically, existing models are trained and tested on the same dataset, leading to poor generalizability across variations in device location, device mounting orientation, and human activity type. In this paper, we introduce UniMTS, the first unified pre-training procedure for motion time series that generalizes across diverse device latent factors and activities. Specifically, we employ a contrastive learning framework that aligns motion time series with text descriptions enriched by large language models.

Depth refinement aims to infer high-resolution depth with fine-grained edges and details, refining low-resolution results of depth estimation models. The prevailing methods adopt tile-based manners by merging numerous patches, which lacks efficiency and produces inconsistency. Besides, prior arts suffer from fuzzy depth boundaries and limited generalizability.