Search for: All records

Despite the 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 underexplored. 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 refer to as the Nonlocal Attention Operator (NAO), and explore its capability in 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. We empirically demonstrate the advantages of NAO over baseline neural models in terms of generalizability to unseen data resolutions and system states. Our work not only suggests a novel neural operator architecture for learning interpretable foundation models of physical systems, but also offers a new perspective towards understanding the attention mechanism. Our code and data accompanying this paper are available at https://github.com/fishmoon1234/NAO. 

Identifying the subset of events that influence events of interest from continuous time datasets is of great interest in various applications. Existing methods however often fail to produce accurate and interpretable results in a time-efficient manner. In this paper, we propose a neural model – Influence-Aware Attention for Multivariate Temporal Point Processes (IAA-MTPPs) – which leverages the powerful attention mechanism in transformers to capture temporal dynamics between event types, which is different from existing instance-to-instance attentions, using variational inference while maintaining interpretability. Given event sequences and a prior influence matrix, IAA-MTPP efficiently learns an approximate posterior by an Attention-to-Influence mechanism, and subsequently models the conditional likelihood of the sequences given a sampled influence through an Influence-to-Attention formulation. Both steps are completed efficiently inside a B-block multi-head self-attention layer, thus our end-to-end training with parallelizable transformer architecture enables faster training compared to sequential models such as RNNs. We demonstrate strong empirical performance compared to existing baselines on multiple synthetic and real benchmarks, including qualitative analysis for an application in decentralized finance. 

Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved promising performance in terms of accuracy and efficiency. However, most methods make strong assumptions of homoscedastic noise, i.e., exogenous noises have equal variances across variables, observations, or even both. The noises in real data usually violate both assumptions due to the biases introduced by different data collection processes. To address the heteroscedastic noise issue, we introduce relaxed implementable sufficient conditions and prove the identifiability of a general class of SEM subject to those conditions. Based on the identifiable general SEM, we propose a novel formulation for DAG learning which accounts for the noise variance variation across variables and observations. We then propose an effective two-phase iterative DAG learning algorithm to address the increasing optimization difficulties and learn a causal DAG from data with heteroscedastic variables noise under varying variance. We show significant empirical gains of the proposed approaches over state-of-the-art methods on both synthetic data and real data. 

Streams of irregularly occurring events are commonly modeled as a marked temporal point process. Many real-world datasets such as e-commerce transactions and electronic health records often involve events where multiple event types co-occur, e.g. multiple items purchased or multiple diseases diagnosed simultaneously. In this paper, we tackle multi-label prediction in such a problem setting, and propose a novel Transformer-based Conditional Mixture of Bernoulli Network (TCMBN) that leverages neural density estimation to capture complex temporal dependence as well as probabilistic dependence between concurrent event types. We also propose potentially incorporating domain knowledge in the objective by regularizing the predicted probability. To represent probabilistic dependence of concurrent event types graphically, we design a two-step approach that first learns the mixture of Bernoulli network and then solves a least-squares semi-definite constrained program to numerically approximate the sparse precision matrix from a learned covariance matrix. This approach proves to be effective for event prediction while also providing an interpretable and possibly non-stationary structure for insights into event co-occurrence. We demonstrate the superior performance of our approach compared to existing baselines on multiple synthetic and real benchmarks.