Simple Hierarchical Planning with Diffusion

Diffusion-based generative methods have proven effective in modeling trajectories with offline datasets. However, they often face computational challenges and can falter in generalization, especially in capturing temporal abstractions for long-horizon tasks. To overcome this, we introduce the Hierarchical Diffuser, a simple, fast, yet surprisingly effective planning method combining the advantages of hierarchical and diffusion-based planning. Our model adopts a "jumpy" planning strategy at the higher level, which allows it to have a larger receptive field but at a lower computational cost -- a crucial factor for diffusion-based planning methods, as we have empirically verified. Additionally, the jumpy sub-goals guide our low-level planner, facilitating a fine-tuning stage and further improving our approach's effectiveness. We conducted empirical evaluations on standard offline reinforcement learning benchmarks, demonstrating our method's superior performance and efficiency in terms of training and planning speed compared to the non-hierarchical Diffuser as well as other hierarchical planning methods. Moreover, we explore our model's generalization capability, particularly on how our method improves generalization capabilities on compositional out-of-distribution tasks.

Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by blending seamlessly 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.

Prompt Optimization via Adversarial In-Context Learning

We propose a new method, Adversarial In-Context Learning (adv-ICL), to optimize prompt for in-context learning (ICL) by employing one LLM as a generator, another as a discriminator, and a third as a prompt modifier. As in traditional adversarial learning, adv-ICL is implemented as a two-player game between the generator and discriminator, where the generator tries to generate realistic enough output to fool the discriminator. In each round, given an input prefixed by task instructions and several exemplars, the generator produces an output. The discriminator is then tasked with classifying the generator input-output pair as model-generated or real data. Based on the discriminator loss, the prompt modifier proposes possible edits to the generator and discriminator prompts, and the edits that most improve the adversarial loss are selected. We show that adv-ICL results in significant improvements over state-of-the-art prompt optimization techniques for both open and closed-source models on 11 generation and classification tasks including summarization, arithmetic reasoning, machine translation, data-to-text generation, and the MMLU and big-bench hard benchmarks. In addition, because our method uses pre-trained models and updates only prompts rather than model parameters, it is computationally efficient, easy to extend to any LLM and task, and effective in low-resource settings.

Learning Unorthogonalized Matrices for Rotation Estimation

Estimating 3D rotations is a common procedure for 3D computer vision. The accuracy depends heavily on the rotation representation. One form of representation -- rotation matrices -- is popular due to its continuity, especially for pose estimation tasks. The learning process usually incorporates orthogonalization to ensure orthonormal matrices. Our work reveals, through gradient analysis, that common orthogonalization procedures based on the Gram-Schmidt process and singular value decomposition will slow down training efficiency. To this end, we advocate removing orthogonalization from the learning process and learning unorthogonalized `Pseudo' Rotation Matrices (PRoM). An optimization analysis shows that PRoM converges faster and to a better solution. By replacing the orthogonalization incorporated representation with our proposed PRoM in various rotation-related tasks, we achieve state-of-the-art results on large-scale benchmarks for human pose estimation.

Probabilistic Copyright Protection Can Fail for Text-to-Image Generative Models

The booming use of text-to-image generative models has raised concerns about their high risk of producing copyright-infringing content. While probabilistic copyright protection methods provide a probabilistic guarantee against such infringement, in this paper, we introduce Virtually Assured Amplification Attack (VA3), a novel online attack framework that exposes the vulnerabilities of these protection mechanisms. The proposed framework significantly amplifies the probability of generating infringing content on the sustained interactions with generative models and a lower-bounded success probability of each engagement. Our theoretical and experimental results demonstrate the effectiveness of our approach and highlight the potential risk of implementing probabilistic copyright protection in practical applications of text-to-image generative models. Code is available at https://github.com/South7X/VA3.

Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

While physics-informed neural networks (PINNs) have been proven effective for low-dimensional partial differential equations (PDEs), the computational cost remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling Monte Carlo methods for derivative approximation, eliminating the need for costly auto-differentiation. Despite its computational efficiency in high dimensions, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD). We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss and the PDE nonlinearity. We propose tailored bias correction techniques based on the order of PDE nonlinearity. The unbiased RS-PINN allows for a detailed examination of its pros and cons compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, HJB, viscous Burgers', Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

ChOiRe: Characterizing and Predicting Human Opinions with Chain of Opinion Reasoning

Aligning language models (LMs) with human opinion is challenging yet vital to enhance their grasp of human values, preferences, and beliefs. We present ChOiRe, a four-step solution framework to predict human opinion that differentiates between the user explicit personae (i.e. demographic or ideological attributes) that are manually declared and implicit personae inferred from user historical opinions. Specifically, it consists of (i) an LM analyzing the user explicit personae to filter out irrelevant attributes; (ii) the LM ranking the implicit persona opinions into a preferential list; (iii) Chain-of-Opinion (CoO) reasoning, where the LM sequentially analyzes the explicit personae and the most relevant implicit personae to perform opinion prediction; (iv) and where ChOiRe executes Step (iii) CoO multiple times with increasingly larger lists of implicit personae to overcome insufficient personae information to infer a final result. ChOiRe achieves new state-of-the-art effectiveness with limited inference calls, improving previous LLM-based techniques significantly by 3.22%.

Rethinking Tokenizer and Decoder in Masked Graph Modeling for Molecules

Masked graph modeling excels in the self-supervised representation learning of molecular graphs. Scrutinizing previous studies, we can reveal a common scheme consisting of three key components: (1) graph tokenizer, which breaks a molecular graph into smaller fragments (i.e., subgraphs) and converts them into tokens; (2) graph masking, which corrupts the graph with masks; (3) graph autoencoder, which first applies an encoder on the masked graph to generate the representations, and then employs a decoder on the representations to recover the tokens of the original graph. However, the previous MGM studies focus extensively on graph masking and encoder, while there is limited understanding of tokenizer and decoder. To bridge the gap, we first summarize popular molecule tokenizers at the granularity of node, edge, motif, and Graph Neural Networks (GNNs), and then examine their roles as the MGM's reconstruction targets. Further, we explore the potential of adopting an expressive decoder in MGM. Our results show that a subgraph-level tokenizer and a sufficiently expressive decoder with remask decoding have a large impact on the encoder's representation learning. Finally, we propose a novel MGM method SimSGT, featuring a Simple GNN-based Tokenizer (SGT) and an effective decoding strategy. We empirically validate that our method outperforms the existing molecule self-supervised learning methods. Our codes and checkpoints are available at https://github.com/syr-cn/SimSGT.

PICProp: Physics-Informed Confidence Propagation for Uncertainty Quantification

Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. Indicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on the selection of priors, and the posterior can be sampled only approximately, which leads to poor approximations because of the associated computational cost. This paper introduces and studies confidence interval (CI) estimation for deterministic partial differential equations as a novel problem. That is, to propagate confidence, in the form of CIs, from data locations to the entire domain with probabilistic guarantees. We propose a method, termed Physics-Informed Confidence Propagation (PICProp), based on bi-level optimization to compute a valid CI without making heavy assumptions. We provide a theorem regarding the validity of our method, and computational experiments, where the focus is on physics-informed learning.

MolCA: Molecular Graph-Language Modeling with Cross-Modal Projector and Uni-Modal Adapter

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.