Kenji Kawaguchi

Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen et al.

Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions. However, existing models, including recurrent neural networks (RNNs), transformers, and neural operators, face challenges such as long-time integration, long-range dependencies, chaotic dynamics, and extrapolation, to name a few. To this end, this paper introduces state-space models implemented in Mamba for accurate and efficient dynamical system operator learning. Mamba addresses the limitations of existing architectures by dynamically capturing long-range dependencies and enhancing computational efficiency through reparameterization techniques. To extensively test Mamba and compare against another 11 baselines, we introduce several strict extrapolation testbeds that go beyond the standard interpolation benchmarks. We demonstrate Mamba's superior performance in both interpolation and challenging extrapolation tasks. Mamba consistently ranks among the top models while maintaining the lowest computational cost and exceptional extrapolation capabilities. Moreover, we demonstrate the good performance of Mamba for a real-world application in quantitative systems pharmacology for assessing the efficacy of drugs in tumor growth under limited data scenarios. Taken together, our findings highlight Mamba's potential as a powerful tool for advancing scientific machine learning in dynamical systems modeling. (The code will be available at https://github.com/zheyuanhu01/State_Space_Model_Neural_Operator upon acceptance.)

Zhiyuan Liu, Sihang Li, Yanchen Luo et al.

Language Models (LMs) have demonstrated impressive molecule understanding ability on various 1D text-related tasks. However, they inherently lack 2D graph perception - a critical ability of human professionals in comprehending molecules' topological structures. To bridge this gap, we propose MolCA: Molecular Graph-Language Modeling with Cross-Modal Projector and Uni-Modal Adapter. MolCA enables an LM (e.g., Galactica) to understand both text- and graph-based molecular contents via the cross-modal projector. Specifically, the cross-modal projector is implemented as a Q-Former to connect a graph encoder's representation space and an LM's text space. Further, MolCA employs a uni-modal adapter (i.e., LoRA) for the LM's efficient adaptation to downstream tasks. Unlike previous studies that couple an LM with a graph encoder via cross-modal contrastive learning, MolCA retains the LM's ability of open-ended text generation and augments it with 2D graph information. To showcase its effectiveness, we extensively benchmark MolCA on tasks of molecule captioning, IUPAC name prediction, and molecule-text retrieval, on which MolCA significantly outperforms the baselines. Our codes and checkpoints can be found at https://github.com/acharkq/MolCA.

Zheyuan Hu, Khemraj Shukla, George Em Karniadakis et al.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Yuzhen Mao, Zhun Deng, Huaxiu Yao et al.

As machine learning has been deployed ubiquitously across applications in modern data science, algorithmic fairness has become a great concern. Among them, imposing fairness constraints during learning, i.e. in-processing fair training, has been a popular type of training method because they don't require accessing sensitive attributes during test time in contrast to post-processing methods. While this has been extensively studied in classical machine learning models, their impact on deep neural networks remains unclear. Recent research has shown that adding fairness constraints to the objective function leads to severe over-fitting to fairness criteria in large models, and how to solve this challenge is an important open question. To tackle this, we leverage the wisdom and power of pre-training and fine-tuning and develop a simple but novel framework to train fair neural networks in an efficient and inexpensive way -- last-layer fine-tuning alone can effectively promote fairness in deep neural networks. This framework offers valuable insights into representation learning for training fair neural networks.

Sihang Li, Zhiyuan Liu, Yanchen Luo et al.

Language Models (LMs) have greatly influenced diverse domains. However, their inherent limitation in comprehending 3D molecular structures has considerably constrained their potential in the biomolecular domain. To bridge this gap, we focus on 3D molecule-text interpretation, and propose 3D-MoLM: 3D-Molecular Language Modeling. Specifically, 3D-MoLM enables an LM to interpret and analyze 3D molecules by equipping the LM with a 3D molecular encoder. This integration is achieved by a 3D molecule-text projector, bridging the 3D molecular encoder's representation space and the LM's input space. Moreover, to enhance 3D-MoLM's ability of cross-modal molecular understanding and instruction following, we meticulously curated a 3D molecule-centric instruction tuning dataset -- 3D-MoIT. Through 3D molecule-text alignment and 3D molecule-centric instruction tuning, 3D-MoLM establishes an integration of 3D molecular encoder and LM. It significantly surpasses existing baselines on downstream tasks, including molecule-text retrieval, molecule captioning, and more challenging open-text molecular QA tasks, especially focusing on 3D-dependent properties. We release our codes and datasets at https://github.com/lsh0520/3D-MoLM.

Zheyuan Hu, Zekun Shi, George Em Karniadakis et al.

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing Hutchinson Trace Estimation (HTE). Starting with the second-order high-dimensional PDEs ubiquitous in scientific computing, HTE transforms the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach alleviates the computational bottleneck via Taylor-mode automatic differentiation and significantly reduces memory consumption from the Hessian matrix to HVP. We further showcase HTE's convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variance among dimensions. We further extend HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Yiran Zhao, Wenxuan Zhang, Huiming Wang et al.

As an effective alternative to the direct fine-tuning on target tasks in specific languages, cross-lingual transfer addresses the challenges of limited training data by decoupling ''task ability'' and ''language ability'' by fine-tuning on the target task in the source language and another selected task in the target language, respectively. However, they fail to fully separate the task ability from the source language or the language ability from the chosen task. In this paper, we acknowledge the mutual reliance between task ability and language ability and direct our attention toward the gap between the target language and the source language on tasks. As the gap removes the impact of tasks, we assume that it remains consistent across tasks. Based on this assumption, we propose a new cross-lingual transfer method called $\texttt{AdaMergeX}$ that utilizes adaptive adapter merging. By introducing a reference task, we can determine that the divergence of adapters fine-tuned on the reference task in both languages follows the same distribution as the divergence of adapters fine-tuned on the target task in both languages. Hence, we can obtain target adapters by combining the other three adapters. Furthermore, we propose a structure-adaptive adapter merging method. Our empirical results demonstrate that our approach yields new and effective cross-lingual transfer, outperforming existing methods across all settings.

Do Xuan Long, Duong Ngoc Yen, Anh Tuan Luu et al.

We present Multi-expert Prompting, a novel enhancement of ExpertPrompting (Xu et al., 2023), designed to improve the large language model (LLM) generation. Specifically, it guides an LLM to fulfill an input instruction by simulating multiple experts, aggregating their responses, and selecting the best among individual and aggregated responses. This process is performed in a single chain of thoughts through our seven carefully designed subtasks derived from the Nominal Group Technique (Ven and Delbecq, 1974), a well-established decision-making framework. Our evaluations demonstrate that Multi-expert Prompting significantly outperforms ExpertPrompting and comparable baselines in enhancing the truthfulness, factuality, informativeness, and usefulness of responses while reducing toxicity and hurtfulness. It further achieves state-of-the-art truthfulness by outperforming the best baseline by 8.69% with ChatGPT. Multi-expert Prompting is efficient, explainable, and highly adaptable to diverse scenarios, eliminating the need for manual prompt construction.

Jin Song, Kenji Kawaguchi, Zhenya Yan

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network architectures, combined with their heavy reliance on large-scale data, often hinder effective training and result in poor extrapolation performance. In this paper, inspired by traditional numerical methods, we propose a novel physics guided multi-step neural operator (PMNO) architecture to address these challenges in long-horizon prediction of complex physical systems. Distinct from general operator learning methods, the PMNO framework replaces the single-step input with multi-step historical data in the forward pass and introduces an implicit time-stepping scheme based on the Backward Differentiation Formula (BDF) during backpropagation. This design not only strengthens the model's extrapolation capacity but also facilitates more efficient and stable training with fewer data samples, especially for long-term predictions. Meanwhile, a causal training strategy is employed to circumvent the need for multi-stage training and to ensure efficient end-to-end optimization. The neural operator architecture possesses resolution-invariant properties, enabling the trained model to perform fast extrapolation on arbitrary spatial resolutions. We demonstrate the superior predictive performance of PMNO predictor across a diverse range of physical systems, including 2D linear system, modeling over irregular domain, complex-valued wave dynamics, and reaction-diffusion processes. Depending on the specific problem setting, various neural operator architectures, including FNO, DeepONet, and their variants, can be seamlessly integrated into the PMNO framework.