General ML · supervised learning

Self-supervised learning (SSL) aims to learn meaningful representations from unlabeled data. Orthogonal Low-rank Embedding (OLE) shows promise for SSL by enhancing intra-class similarity in a low-rank subspace and promoting inter-class dissimilarity in a high-rank subspace, making it particularly suitable for multi-view learning tasks. However, directly applying OLE to SSL poses significant challenges: (1) the virtually infinite number of "classes" in SSL makes achieving the OLE objective impractical, leading to representational collapse; and (2) low-rank constraints may fail to distinguish between positively and negatively correlated features, further undermining learning. To address these issues, we propose SSOLE (Self-Supervised Orthogonal Low-rank Embedding), a novel framework that integrates OLE principles into SSL by (1) decoupling the low-rank and high-rank enforcement to align with SSL objectives; and (2) applying low-rank constraints to feature deviations from their mean, ensuring better alignment of positive pairs by accounting for the signs of cosine similarities. Our theoretical analysis and empirical results demonstrate that these adaptations are crucial to SSOLE’s effectiveness. Moreover, SSOLE achieves competitive performance across SSL benchmarks without relying on large batch sizes, memory banks, or dual-encoder architectures, making it an efficient and scalable solution for self-supervised tasks. Code is available at https://github.com/husthuaan/ssole.

Solving partial differential equations (PDEs) is a fundamental problem in engineering and science. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is costly to obtain. Active learning (AL) could help surrogate models reach the same accuracy with smaller training sets by querying classical solvers with more informative initial conditions and PDE parameters. While AL is more common in other domains, it has yet to be studied extensively for neural PDE solvers. To bridge this gap, we introduce AL4PDE, a modular and extensible active learning benchmark. It provides multiple parametric PDEs and state-of-the-art surrogate models for the solver-in-the-loop setting, enabling the evaluation of existing and the development of new AL methods for PDE solving. We use the benchmark to evaluate batch active learning algorithms such as uncertainty- and feature-based methods. We show that AL reduces the average error by up to 71\% compared to random sampling and significantly reduces worst-case errors. Moreover, AL generates similar datasets across repeated runs, with consistent distributions over the PDE parameters and initial conditions. The acquired datasets are reusable, providing benefits for surrogate models not involved in the data generation.

In many science and engineering settings, system dynamics are characterized by governing partial differential equations (PDEs), and a major challenge is to solve inverse problems (IPs) where unknown PDE parameters are inferred based on observational data gathered under limited budget. Due to the high costs of setting up and running experiments, experimental design (ED) is often done with the help of PDE simulations to optimize for the most informative design parameters (e.g., sensor placements) to solve such IPs, prior to actual data collection. This process of optimizing design parameters is especially critical when the budget and other practical constraints make it infeasible to adjust the design parameters between trials during the experiments. However, existing experimental design (ED) methods tend to require sequential and frequent design parameter adjustments between trials. Furthermore, they also have significant computational bottlenecks due to the need for complex numerical simulations for PDEs, and do not exploit the advantages provided by physics informed neural networks (PINNs) in solving IPs for PDE-governed systems, such as its meshless solutions, differentiability, and amortized training. This work presents Physics-Informed Experimental Design (PIED), the first ED framework that makes use of PINNs in a fully differentiable architecture to perform continuous optimization of design parameters for IPs for one-shot deployments. PIED overcomes existing methods' computational bottlenecks through parallelized computation and meta-learning of PINN parameter initialization, and proposes novel methods to effectively take into account PINN training dynamics in optimizing the ED parameters. Through experiments based on noisy simulated data and even real world experimental data, we empirically show that given limited observation budget, PIED significantly outperforms existing ED methods in solving IPs, including for challenging settings where the inverse parameters are unknown functions rather than just finite-dimensional.

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings between past and future states, overlooking the fluid dynamics, or only modeling the velocity field, neglecting the coupling of multiple physical quantities. In this paper, we propose a new physics-informed learning approach that incorporates coupled physical quantities into the prediction process to assist with forecasting. Central to our method lies in the discretization of physical equations, which are directly integrated into the model architecture and loss function. This integration enables the model to provide robust, long-term future predictions. By incorporating physical equations, our model demonstrates temporal extrapolation and spatial generalization capabilities. Experimental results show that our approach achieves the state-of-the-art performance in spatiotemporal prediction across both numerical simulations and real-world extreme-precipitation nowcasting benchmarks.

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which relevant statistics (e.g., RMS and two-point correlations) can be derived. Here, we propose a graph-based latent diffusion model that enables direct sampling of states from their equilibrium distribution, given a mesh discretization of the system and its physical parameters. This allows for the efficient computation of flow statistics without running long and expensive numerical simulations. The graph-based structure enables operations on unstructured meshes, which is critical for representing complex geometries with spatially localized high gradients, while latent-space diffusion modeling with a multi-scale GNN allows for efficient learning and inference of entire distributions of solutions. A key finding of our work is that the proposed networks can accurately learn full distributions even when trained on incomplete data from relatively short simulations. We apply this method to a range of fluid dynamics tasks, such as predicting pressure distributions on 3D wing models in turbulent flow, demonstrating both accuracy and computational efficiency in challenging scenarios. The ability to directly sample accurate solutions, and capturing their diversity from short ground-truth simulations, is highly promising for complex scientific modeling tasks.

One of the most practical and challenging types of black-box adversarial attacks is the hard-label attack, where only the top-1 predicted label is available. One effective approach is to search for the optimal ray direction from the benign image that minimizes the $\ell_p$ norm distance to the adversarial region. The unique advantage of this approach is that it transforms the hard-label attack into a continuous optimization problem. The objective function value is the ray's radius, which can be obtained via binary search at a high query cost. Existing methods use a "sign trick" in gradient estimation to reduce the number of queries. In this paper, we theoretically analyze the quality of this gradient estimation and propose a novel prior-guided approach to improve ray search efficiency both theoretically and empirically. Specifically, we utilize the transfer-based priors from surrogate models, and our gradient estimators appropriately integrate them by approximating the projection of the true gradient onto the subspace spanned by these priors and random directions, in a query-efficient manner. We theoretically derive the expected cosine similarities between the obtained gradient estimators and the true gradient, and demonstrate the improvement achieved by incorporating priors. Extensive experiments on the ImageNet and CIFAR-10 datasets show that our approach significantly outperforms 11 state-of-the-art methods in terms of query efficiency.

Offline model-based optimization (MBO) aims to identify a design that maximizes a black-box function using only a fixed, pre-collected dataset of designs and their corresponding scores. This problem has garnered significant attention from both scientific and industrial domains. A common approach in offline MBO is to train a regression-based surrogate model by minimizing mean squared error (MSE) and then find the best design within this surrogate model by different optimizers (e.g., gradient ascent). However, a critical challenge is the risk of out-of-distribution errors, i.e., the surrogate model may typically overestimate the scores and mislead the optimizers into suboptimal regions. Prior works have attempted to address this issue in various ways, such as using regularization techniques and ensemble learning to enhance the robustness of the model, but it still remains. In this paper, we argue that regression models trained with MSE are not well-aligned with the primary goal of offline MBO, which is to \textit{select} promising designs rather than to predict their scores precisely. Notably, if a surrogate model can maintain the order of candidate designs based on their relative score relationships, it can produce the best designs even without precise predictions. To validate it, we conduct experiments to compare the relationship between the quality of the final designs and MSE, finding that the correlation is really very weak. In contrast, a metric that measures order-maintaining quality shows a significantly stronger correlation. Based on this observation, we propose learning a ranking-based model that leverages learning to rank techniques to prioritize promising designs based on their relative scores. We show that the generalization error on ranking loss can be well bounded. Empirical results across diverse tasks demonstrate the superior performance of our proposed ranking-based method than twenty existing methods. Our implementation is available at \url{https://github.com/lamda-bbo/Offline-RaM}.

Downsampling layers are crucial building blocks in CNN architectures, which help to increase the receptive field for learning high-level features and reduce the amount of memory/computation in the model. In this work, we study the generalization of the uniform downsampling layer for group equivariant architectures, e.g., $G$-CNNs. That is, we aim to downsample signals (feature maps) on general finite groups *with* anti-aliasing. This involves the following: **(a)** Given a finite group and a downsampling rate, we present an algorithm to form a suitable choice of subgroup. **(b)** Given a group and a subgroup, we study the notion of bandlimited-ness and propose how to perform anti-aliasing. Notably, our method generalizes the notion of downsampling based on classical sampling theory. When the signal is on a cyclic group, i.e., periodic, our method recovers the standard downsampling of an ideal low-pass filter followed by a subsampling operation. Finally, we conducted experiments on image classification tasks demonstrating that the proposed downsampling operation improves accuracy, better preserves equivariance, and reduces model size when incorporated into $G$-equivariant networks

Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast surrogate models with adjustable complexity reacting on time-varying inputs signals. By leveraging the VAE’s dimensionality reduction using a non-hierarchical prior, our method adaptively assigns stochastic noise, naturally complementing known NeuralODE training enhancements and enabling probabilistic time series modeling. We show that standard Latent ODEs struggle with dimensionality reduction in systems with time-varying inputs. Our approach mitigates this by continuously propagating variational parameters through time, establishing fixed information channels in latent space. This results in a flexible and robust method that can learn different system complexities, e.g. deep neural networks or linear matrices. Hereby, it enables efficient approximation of the Koopman operator without the need for predefining its dimensionality. As our method balances dimensionality reduction and reconstruction accuracy, we call it Balanced Neural ODE (B-NODE). We demonstrate the effectiveness of this methods on several academic and real-world test cases, e.g. a power plant or MuJoCo data.

Recent advancements in Large Language Models (LLMs) have led to a rapid growth of agentic systems capable of handling a wide range of complex tasks. However, current research largely relies on manual, task-specific design, limiting their adaptability to novel tasks. In this paper, we introduce a new research problem: Modularized LLM Agent Search (MoLAS). We propose a modular design space that abstracts existing LLM agent designs into four fundamental modules with uniform IO interface: Planning, Reasoning, Tool Use, and Memory. Building on this design space, we present a novel LLM agent search framework called AgentSquare, which introduces two core mechanisms, i.e., module evolution and recombination, to efficiently search for optimized LLM agents. To further accelerate the process, we design a performance predictor that uses in-context surrogate models to skip unpromising agent designs. Extensive experiments across six benchmarks, covering the diverse scenarios of web, embodied, tool use and game applications, show that AgentSquare substantially outperforms hand-crafted agents, achieving an average performance gain of 17.2% against best-known human designs. Moreover, AgentSquare can generate interpretable design insights, enabling a deeper understanding of agentic architecture and its impact on task performance. We believe that the modular design space and AgentSquare search framework offer a platform for fully exploiting the potential of prior successful designs and consolidate the collective efforts of research community. Code repo is available at https://github.com/tsinghua-fib-lab/AgentSquare.

The experimental discovery of neutrinoless double-beta decay (NLDBD) would answer one of the most important questions in physics: Why is there more matter than antimatter in our universe? To maximize the chances of discovery, NLDBD experiments must optimize their detector designs to minimize the probability of background events contaminating the detector. Given that this probability is inherently low, design optimization either requires extremely costly simulations to generate sufficient background counts or contending with significant variance. In this work, we formalize this dilemma as a Rare Event Design (RED) problem: identifying optimal design parameters when the design metric to be minimized is inherently small. We then designed the Rare Event Surrogate Model (RESuM) for physics detector design optimization under RED conditions. RESuM uses a pre-trained Conditional Neural Process (CNP) model to incorporate additional prior knowledge into a Multi-Fidelity Gaussian Process model. We applied RESuM to optimize neutron shielding designs for the LEGEND NLDBD experiment, identifying an optimal design that reduces the neutron background by $(66.5 \pm 3.5)$% while using only 3.3% of the computational resources compared to traditional methods. Given the prevalence of RED problems in other fields of physical sciences, especially in rare-event searches, the RESuM algorithm has broad potential for accelerating simulation-intensive applications.

Directed acyclic graphs (DAGs) serve as crucial data representations in domains such as hardware synthesis and compiler/program optimization for computing systems. DAG generative models facilitate the creation of synthetic DAGs, which can be used for benchmarking computing systems while preserving intellectual property. However, generating realistic DAGs is challenging due to their inherent directional and logical dependencies. This paper introduces LayerDAG, an autoregressive diffusion model, to address these challenges. LayerDAG decouples the strong node dependencies into manageable units that can be processed sequentially. By interpreting the partial order of nodes as a sequence of bipartite graphs, LayerDAG leverages autoregressive generation to model directional dependencies and employs diffusion models to capture logical dependencies within each bipartite graph. Comparative analyses demonstrate that LayerDAG outperforms existing DAG generative models in both expressiveness and generalization, particularly for generating large-scale DAGs with up to 400 nodes—a critical scenario for system benchmarking. Extensive experiments on both synthetic and real-world flow graphs from various computing platforms show that LayerDAG generates valid DAGs with superior statistical properties and benchmarking performance. The synthetic DAGs generated by LayerDAG enhance the training of ML-based surrogate models, resulting in improved accuracy in predicting performance metrics of real-world DAGs across diverse computing platforms.

This paper considers the Lipschitz bandit problem, where the set of arms is continuous and the expected reward is a Lipschitz function over the arm space. This problem has been extensively studied. Prior algorithms need to store the reward information of all visited arms, leading to significant memory consumption. We address this issue by introducing an algorithm named Log-space Lipschitz bandits (Log-Li), which achieves an optimal (up to logarithmic factors) regret of $\widetilde{O}\left(T^{\frac{d_z+1}{d_z+2}}\right)$ while only uses $O\left(\log T\right)$ bits of memory. Additionally, we provide a complexity analysis for this problem, demonstrating that $\Omega\left(\log T\right)$ bits of space are necessary for any algorithm to achieve the optimal regret. We also conduct numerical simulations, and the results show that our new algorithm achieves regret comparable to the state-of-the-art while reducing memory usage by orders of magnitude.

Self-supervision is often used for pre-training to foster performance on a downstream task by constructing meaningful representations of samples. Self-supervised learning (SSL) generally involves generating different views of the same sample and thus requires data augmentations that are challenging to construct for tabular data. This constitutes one of the main challenges of self-supervision for structured data. In the present work, we propose a novel augmentation-free SSL method for tabular data. Our approach, T-JEPA, relies on a Joint Embedding Predictive Architecture (JEPA) and is akin to mask reconstruction in the latent space. It involves predicting the latent representation of one subset of features from the latent representation of a different subset within the same sample, thereby learning rich representations without augmentations. We use our method as a pre-training technique and train several deep classifiers on the obtained representation. Our experimental results demonstrate a substantial improvement in both classification and regression tasks, outperforming models trained directly on samples in their original data space. Moreover, T-JEPA enables some methods to consistently outperform or match the performance of traditional methods likes Gradient Boosted Decision Trees. To understand why, we extensively characterize the obtained representations and show that T-JEPA effectively identifies relevant features for downstream tasks without access to the labels. Additionally, we introduce regularization tokens, a novel regularization method critical for training of JEPA-based models on structured data.

Operator learning, which aims to approximate maps between infinite-dimensional function spaces, is an important area in scientific machine learning with applications across various physical domains. Here we introduce the Continuous Vision Transformer (CViT), a novel neural operator architecture that leverages advances in computer vision to address challenges in learning complex physical systems. CViT combines a vision transformer encoder, a novel grid-based coordinate embedding, and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. This design allows for flexible output representations and consistent evaluation at arbitrary resolutions. We demonstrate CViT's effectiveness across a diverse range of partial differential equation (PDE) systems, including fluid dynamics, climate modeling, and reaction-diffusion processes. Our comprehensive experiments show that CViT achieves state-of-the-art performance on multiple benchmarks, often surpassing larger foundation models, even without extensive pretraining and roll-out fine-tuning. Taken together, CViT exhibits robust handling of discontinuous solutions, multi-scale features, and intricate spatio-temporal dynamics. Our contributions can be viewed as a significant step towards adapting advanced computer vision architectures for building more flexible and accurate machine learning models in the physical sciences.

Learning disentangled representations of concepts and re-composing them in unseen ways is crucial for generalizing to out-of-domain situations. However, the underlying properties of concepts that enable such disentanglement and compositional generalization remain poorly understood. In this work, we propose the principle of interaction asymmetry which states: "Parts of the same concept have more complex interactions than parts of different concepts". We formalize this via block diagonality conditions on the $(n+1)$th order derivatives of the generator mapping concepts to observed data, where different orders of "complexity" correspond to different $n$. Using this formalism, we prove that interaction asymmetry enables both disentanglement and compositional generalization. Our results unify recent theoretical results for learning concepts of objects, which we show are recovered as special cases with $n=0$ or $1$. We provide results for up to $n=2$, thus extending these prior works to more flexible generator functions, and conjecture that the same proof strategies generalize to larger $n$. Practically, our theory suggests that, to disentangle concepts, an autoencoder should penalize its latent capacity and the interactions between concepts during decoding. We propose an implementation of these criteria using a flexible Transformer-based VAE, with a novel regularizer on the attention weights of the decoder. On synthetic image datasets consisting of objects, we provide evidence that this model can achieve comparable object disentanglement to existing models that use more explicit object-centric priors.

Conformal prediction yields a prediction set with guaranteed $1-\alpha$ coverage of the true target under the i.i.d. assumption, which can fail and lead to a gap between $1-\alpha$ and the actual coverage. Prior studies bound the gap using total variation distance, which cannot identify the gap changes under distribution shift at different $\alpha$, thus serving as a weak indicator of prediction set validity. Besides, existing methods are mostly limited to covariate shifts, while general joint distribution shifts are more common in practice but less researched. In response, we first propose a Wasserstein distance-based upper bound of the coverage gap and analyze the bound using probability measure pushforwards between the shifted joint data and conformal score distributions, enabling a separation of the effect of covariate and concept shifts over the coverage gap. We exploit the separation to design algorithms based on importance weighting and regularized representation learning (WR-CP) to reduce the Wasserstein bound with a finite-sample error bound. WR-CP achieves a controllable balance between conformal prediction accuracy and efficiency. Experiments on six datasets prove that WR-CP can reduce coverage gaps to 3.2% across different confidence levels and outputs prediction sets 37% smaller than the worst-case approach on average.

Preferential Bayesian Optimization (PBO) is a sample-efficient method to learn latent user utilities from preferential feedback over a pair of designs. It relies on a statistical surrogate model for the latent function, usually a Gaussian process, and an acquisition strategy to select the next candidate pair to get user feedback on. Due to the non-conjugacy of the associated likelihood, every PBO step requires a significant amount of computations with various approximate inference techniques. This computational overhead is incompatible with the way humans interact with computers, hindering the use of PBO in real-world cases. Building on the recent advances of amortized BO, we propose to circumvent this issue by fully amortizing PBO, meta-learning both the surrogate and the acquisition function. Our method comprises a novel transformer neural process architecture, trained using reinforcement learning and tailored auxiliary losses. On a benchmark composed of synthetic and real-world datasets, our method is several orders of magnitude faster than the usual Gaussian process-based strategies and often outperforms them in accuracy.

Generalization in reinforcement learning (RL) remains a significant challenge, especially when agents encounter novel environments with unseen dynamics. Drawing inspiration from human compositional reasoning—where known components are reconfigured to handle new situations—we introduce World Modeling with Compositional Causal Components (WM3C). This novel framework enhances RL generalization by learning and leveraging compositional causal components. Unlike previous approaches focusing on invariant representation learning or meta-learning, WM3C identifies and utilizes causal dynamics among composable elements, facilitating robust adaptation to new tasks. Our approach integrates language as a compositional modality to decompose the latent space into meaningful components and provides theoretical guarantees for their unique identification under mild assumptions. Our practical implementation uses a masked autoencoder with mutual information constraints and adaptive sparsity regularization to capture high-level semantic information and effectively disentangle transition dynamics. Experiments on numerical simulations and real-world robotic manipulation tasks demonstrate that WM3C significantly outperforms existing methods in identifying latent processes, improving policy learning, and generalizing to unseen tasks.

Semi-supervised learning (SSL) effectively leverages unlabeled data and has been proven successful across various fields. Current safe SSL methods believe that unseen classes in unlabeled data harm the performance of SSL models. However, previous methods for assessing the impact of unseen classes on SSL model performance are flawed. They fix the size of the unlabeled dataset and adjust the proportion of unseen classes within the unlabeled data to assess the impact. This process contravenes the principle of controlling variables. Adjusting the proportion of unseen classes in unlabeled data alters the proportion of seen classes, meaning the decreased classification performance of seen classes may not be due to an increase in unseen class samples in the unlabeled data, but rather a decrease in seen class samples. Thus, the prior flawed assessment standard that "unseen classes in unlabeled data can damage SSL model performance" may not always hold true. This paper strictly adheres to the principle of controlling variables, maintaining the proportion of seen classes in unlabeled data while only changing the unseen classes across five critical dimensions, to investigate their impact on SSL models from global robustness and local robustness. Experiments demonstrate that unseen classes in unlabeled data do not necessarily impair the performance of SSL models; in fact, under certain conditions, unseen classes may even enhance them.