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Theory · Learning Theory

Casper Gyurik, Riccardo Molteni, Vedran Dunjko

In recent times, there have been major developments in two distinct yet connected domains of quantum information. On the one hand, substantial progress has been made in so-called randomized measurement protocols. Here, a number of properties of unknown quantum states can be deduced from surprisingly few measurement outcomes, using schemes such as classical shadows. On the other hand, significant progress has been made in quantum machine learning. For example, exponential advantages have been proven when the data consists of quantum states and quantum algorithms can coherently measure multiple copies of input states. In this work, we aim to understand the implications and limitations of combining randomized measurement protocols with quantum machine learning, although the implications are broader. Specifically, we investigate quantum machine learning algorithms that, when dealing with quantum data, can either process it entirely using quantum methods or measure the input data through a fixed measurement scheme and utilize the resulting classical information. We prove limitations for the general class of quantum machine learning algorithms that use fixed measurement schemes on the input quantum states.Our results have several implications. From the perspective of randomized measurement procedures, we show limitations of measure-first protocols in the average case, improving on the state-of-the-art which only focuses on worst-case scenarios. Additionally, previous lower bounds were only known for physically unrealizable states. We improve upon this by employing quantum pseudorandom functions to prove that a learning separation also exists when dealing with physically realizable states, which may be encountered in experiments. From a machine learning perspective, our results are crucial for defining a physically meaningful task that shows fully quantum machine learning processing is not only more efficient but also necessary for solving certain problems. The tasks at hand are also realistic, as the algorithms and proven separations hold when working with efficiently preparable states and remain robust in the presence of measurement and preparation errors.

Applications · Chemistry, Physics, and Earth Sciences

Jiao Huang, Qianli Xing, Jinglong Ji, Bo Yang

Graph neural networks have recently demonstrated remarkable performance in predicting material properties. Crystalline material data is manually encoded into graph representations.Existing methods incorporate different attributes into constructing representations to satisfy the constraints arising from symmetries of material structure.However, existing methods for obtaining graph representations are specific to certain constraints, which are ineffective when facing new constraints.In this work, we propose a code generation framework with multiple large language model agents to obtain representations named Rep-CodeGen with three iterative stages simulating an evolutionary algorithm. To the best of our knowledge, Rep-CodeGen is the first framework for automatically generating code to obtain representations that can be used when facing new constraints. Furthermore, a type of representation from generated codes by our framework satisfies six constraints, with codes satisfying three constraints as bases. Extensive experiments on two real-world material datasets show that a property prediction method based on such a graph representation achieves state-of-the-art performance in material property prediction tasks.

Applications · Chemistry, Physics, and Earth Sciences

Guancheng Wan, Zijie Huang, Wanjia Zhao, Xiao Luo, Yizhou Sun, Wei Wang

Coupled dynamical systems govern essential phenomena across physics, biology, and engineering, where components interact through complex dependencies. While Graph Ordinary Differential Equations (GraphODE) offer a powerful framework to model these systems, their **generalization** capabilities degrade severely under limited observational training data due to two fundamental flaws: (i) the entanglement of static attributes and dynamic states in the initialization process, and (ii) the reliance on context-specific coupling patterns during training, which hinders performance in unseen scenarios. In this paper, we propose a Generalizable GraphODE with disentanglement and regularization (GREAT) to address these challenges. Through systematic analysis via the Structural Causal Model, we identify backdoor paths that undermine generalization and design two key modules to mitigate their effects. The *Dynamic-Static Equilibrium Decoupler (DyStaED)* disentangles static and dynamic states via orthogonal subspace projections, ensuring robust initialization. Furthermore, the *Causal Mediation for Coupled Dynamics (CMCD)* employs variational inference to estimate latent causal factors, reducing spurious correlations and enhancing universal coupling dynamics. Extensive experiments across diverse dynamical systems demonstrate that ours outperforms state-of-the-art methods within both in-distribution and out-of-distribution.

Applications · Chemistry, Physics, and Earth Sciences

Jan Pauls, Max Zimmer, Berkant Turan, Sassan Saatchi, Philippe CIAIS, Sebastian Pokutta, Fabian Gieseke

With the rise in global greenhouse gas emissions, accurate large-scale tree canopy height maps are essential for understanding forest structure, estimating above-ground biomass, and monitoring ecological disruptions. To this end, we present a novel approach to generate large-scale, high-resolution canopy height maps over time. Our model accurately predicts canopy height over multiple years given Sentinel 2 time series satellite data. Using GEDI LiDAR data as the ground truth for training the model, we present the first 10 m resolution temporal canopy height map of the European continent for the period 2019–2022. As part of this product, we also offer a detailed canopy height map for 2020, providing more precise estimates than previous studies. Our pipeline and the resulting temporal height map are publicly available, enabling comprehensive large-scale monitoring of forests and, hence, facilitating future research and ecological analyses. For an interactive viewer, see https://europetreemap.projects.earthengine.app/view/europeheight.

Applications · Chemistry, Physics, and Earth Sciences

Shi Yin, Xinyang Pan, fengyan wang, Lixin He

We propose a framework to combine strong non-linear expressiveness with strict SO(3)-equivariance in prediction of the electronic-structure Hamiltonian, by exploring the mathematical relationships between SO(3)-invariant and SO(3)-equivariant quantities and their representations. The proposed framework, called **TraceGrad**, first constructs theoretical SO(3)-invariant **trace** quantities derived from the Hamiltonian targets, and use these invariant quantities as supervisory labels to guide the learning of high-quality SO(3)-invariant features. Given that SO(3)-invariance is preserved under non-linear operations, the learning of invariant features can extensively utilize non-linear mappings, thereby fully capturing the non-linear patterns inherent in physical systems. Building on this, we propose a **grad**ient-based mechanism to induce SO(3)-equivariant encodings of various degrees from the learned SO(3)-invariant features. This mechanism can incorporate powerful non-linear expressive capabilities into SO(3)-equivariant features with correspondence of physical dimensions to the regression targets, while theoretically preserving equivariant properties, establishing a strong foundation for predicting electronic-structure Hamiltonian. Experimental results on eight challenging benchmark databases demonstrate that our method achieves state-of-the-art performance in Hamiltonian prediction.

General Machine Learning · Sequential, Network, and Time Series Modeling

Andrea Testa, Søren Hauberg, Tamim Asfour, Leonel Rozo

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system’s behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.

Optimization · Convex

Ekaterina Borodich, Alexander Gasnikov, Dmitry Kovalev

We revisit the smooth convex-concave bilinearly-coupled saddle-point problem of the form $\min_x\max_y f(x) + \langle y,\mathbf{B} x\rangle - g(y)$. In the highly specific case where function $f(x)$ is strongly convex and function $g(y)$ is affine, or both functions are affine, there exist lower bounds on the number of gradient evaluations and matrix-vector multiplications required to solve the problem, as well as matching optimal algorithms. A notable aspect of these algorithms is that they are able to attain linear convergence, i.e., the number of iterations required to solve the problem is proportional to $\log(1/\epsilon)$. However, the class of bilinearly-coupled saddle-point problems for which linear convergence is possible is much wider and can involve general smooth non-strongly convex functions $f(x)$ and $g(y)$. Therefore, *we develop the first lower complexity bounds and matching optimal linearly converging algorithms for this problem class*. Our lower complexity bounds are much more general, but they cover and unify the existing results in the literature. On the other hand, our algorithm implements the separation of complexities, which, for the first time, enables the simultaneous achievement of both optimal gradient evaluation and matrix-vector multiplication complexities, resulting in the best theoretical performance to date.

Applications · Chemistry, Physics, and Earth Sciences

Viacheslav Meshchaninov, Pavel Strashnov, Andrey Shevtsov, Fedor Nikolaev, Nikita Ivanisenko, Olga Kardymon, Dmitry Vetrov

Protein *sequence* design has seen significant advances through discrete diffusion and autoregressive approaches, yet the potential of continuous diffusion remains underexplored. Here, we present *DiMA*, a latent diffusion framework that operates on protein language model representations. Through systematic exploration of architectural choices and diffusion components, we develop a robust methodology that generalizes across multiple protein encoders ranging from 8M to 3B parameters. We demonstrate that our framework achieves consistently high performance across sequence-only (ESM-2, ESMc), dual-decodable (CHEAP), and multimodal (SaProt) representations using the same architecture and training approach. We conduct extensive evaluation of existing methods alongside *DiMA* using multiple metrics across two protein modalities, covering quality, diversity, novelty, and distribution matching of generated proteins. *DiMA* consistently produces novel, high-quality and diverse protein sequences and achieves strong results compared to baselines such as autoregressive, discrete diffusion and flow matching language models. The model demonstrates versatile functionality, supporting conditional generation tasks including protein family-generation, motif scaffolding and infilling, and fold-specific sequence design, despite being trained solely on sequence data. This work provides a universal continuous diffusion framework for protein sequence generation, offering both architectural insights and practical applicability across various protein design scenarios. Code is released at [GitHub](https://github.com/MeshchaninovViacheslav/DiMA).

Applications · Chemistry, Physics, and Earth Sciences

Yeyun Chen

Predicting the solvation free energy of molecules using graph neural networks holds significant potential for advancing drug discovery and the design of novel materials. While previous methods have demonstrated success on independent and identically distributed (IID) datasets, their performance in out-of-distribution (OOD) scenarios remains largely unexplored. We propose a novel Relational Invariant Learning framework (RILOOD) to enhance OOD generalization in solvation free energy prediction. RILOOD comprises three key components: (i) a mixup-based conditional modeling module that integrates diverse environments, (ii) a novel multi-granularity refinement strategy that extends beyond core substructures to enable context-aware representation learning for capturing multi-level interactions, and (iii) an invariant learning mechanism that identifies robust patterns generalizable to unseen environments. Extensive experiments demonstrate that RILOOD significantly outperforms state-of-the-art methods across various distribution shifts, highlighting its effectiveness in improving solvation free energy prediction under diverse conditions.

Applications · Health / Medicine

Wei Qu, Jiawei Guan, Rui Ma, kezhai, weikun wu, haobo Wang

We introduce Pallatom, an innovative protein generation model capable of producing protein structures with all-atom coordinates. Pallatom directly learns and models the joint distribution $P(\textit{structure}, \textit{seq})$ by focusing on $P(\textit{all-atom})$, effectively addressing the interdependence between sequence and structure in protein generation. To achieve this, we propose a novel network architecture specifically designed for all-atom protein generation. Our model employs a dual-track framework that tokenizes proteins into token-level and atomic-level representations, integrating them through a multi-layer decoding process with "traversing" representations and recycling mechanism. We also introduce the $\texttt{atom14}$ representation method, which unifies the description of unknown side-chain coordinates, ensuring high fidelity between the generated all-atom conformation and its physical structure. Experimental results demonstrate that Pallatom excels in key metrics of protein design, including designability, diversity, and novelty, showing significant improvements across the board. Our model not only enhances the accuracy of protein generation but also exhibits excellent sampling efficiency, paving the way for future applications in larger and more complex systems.

Applications · Everything Else

Yinyan Bu, Jiajie Yu, Kai Zheng, Xinyu Zhang, Piya Pal

We address the challenge of achieving angular super-resolution in multi-antenna radar systems that are widely used for localization, navigation, and automotive perception. A multi-antenna radar achieves very high resolution by computationally creating a large virtual sensing system using very few physical antennas. However, practical constraints imposed by hardware, noise, and a limited number of antennas can impede its performance. Conventional supervised learning models that rely on extensive pre-training with large datasets, often exhibit poor generalization in unseen environments. To overcome these limitations, we propose NEAR, an untrained implicit neural representation (INR) framework that predicts radar responses at unseen locations from sparse measurements, by leveraging latent harmonic structures inherent in radar wave propagation. We establish new theoretical results linking antenna array response to expressive power of INR architectures, and develop a novel physics-informed and latent geometry-aware regularizer. Our approach integrates classical signal representation with modern implicit neural learning, enabling high-resolution radar sensing that is both interpretable and generalizable. Extensive simulations and real-world experiments using radar platforms demonstrate NEAR's effectiveness and its ability to adapt to unseen environments.

Applications · Chemistry, Physics, and Earth Sciences

Mohit Pandey, Gopeshh Subbaraj, Artem Cherkasov, Martin Ester, Emmanuel Bengio

Generative Flow Networks (GFlowNets) have recently emerged as a suitable framework for generating diverse and high-quality molecular structures by learning from rewards treated as unnormalized distributions. Previous works in this framework often restrict exploration by using predefined molecular fragments as building blocks, limiting the chemical space that can be accessed. In this work, we introduce Atomic GFlowNets (A-GFNs), a foundational generative model leveraging individual atoms as building blocks to explore drug-like chemical space more comprehensively. We propose an unsupervised pre-training approach using drug-like molecule datasets, which teaches A-GFNs about inexpensive yet informative molecular descriptors such as drug-likeliness, topological polar surface area, and synthetic accessibility scores. These properties serve as proxy rewards, guiding A-GFNs towards regions of chemical space that exhibit desirable pharmacological properties. We further implement a goal-conditioned finetuning process, which adapts A-GFNs to optimize for specific target properties. In this work, we pretrain A-GFN on a subset of ZINC dataset, and by employing robust evaluation metrics we show the effectiveness of our approach when compared to other relevant baseline methods for a wide range of drug design tasks. The code is accessible at https://github.com/diamondspark/AGFN.

Applications · Chemistry, Physics, and Earth Sciences

Cheng-Yen Hsieh, Xinyou Wang, Daiheng Zhang, Dongyu Xue, Fei YE, Shujian Huang, Zaixiang Zheng, Quanquan Gu

Multimodal protein language models (PLMs) integrate sequence and token-based structural information, serving as a powerful foundation for protein modeling, generation, and design. However, the reliance on tokenizing 3D structures into discrete tokens causes substantial loss of fidelity about fine-grained structural details and correlations. In this paper, we systematically elucidate the design space of multimodal PLMs to overcome their limitations. We identify tokenization loss and inaccurate structure token predictions by the PLMs as major bottlenecks.To address these, our proposed design space covers improved generative modeling, structure-aware architectures and representation learning, and data exploration. Our advancements approach finer-grained supervision, demonstrating that token-based multimodal PLMs can achieve robust structural modeling.The effective design methods dramatically improve the structure generation diversity, and notably, folding abilities of our 650M model by reducing the RMSD from 5.52 to 2.36 on PDB testset, even outperforming 3B baselines and on par with the specialized folding models.Project page and code: https://bytedance.github.io/dplm/dplm-2.1.

Applications · Chemistry, Physics, and Earth Sciences

Krzysztof Kacprzyk, Julianna Piskorz, Mihaela van der Schaar

While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system's underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system's dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system's behavior, such as the trajectory's shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.

Applications · Chemistry, Physics, and Earth Sciences

Jan Ole Ernst, Aniket Chatterjee, Tim Franzmeyer, Axel Kuhn

Quantum control is concerned with the realisation of desired dynamics in quantum systems, serving as a linchpin for advancing quantum technologies and fundamental research. Analytic approaches and standard optimisation algorithms do not yield satisfactory solutions for more complex quantum systems, and especially not for real world quantum systems which are open and noisy. We devise a physics-constrained Reinforcement Learning (RL) algorithm that restricts the space of possible solutions.We incorporate priors about the desired time scales of the quantum state dynamics - as well as realistic control signal limitations - as constraints to the RL algorithm. These constraints improve solution quality and enhance computational scaleability. We evaluate our method on three broadly relevant quantum systems and incorporate real-world complications, arising from dissipation and control signal perturbations. We achieve both higher fidelities - which exceed 0.999 across all systems - and better robustness to time-dependent perturbations and experimental imperfections than previous methods. Lastly, we demonstrate that incorporating multi-step feedback can yield solutions robust even to strong perturbations. Our implementation can be found at: https://github.com/jan-o-e/RL4qcWpc.

Applications · Chemistry, Physics, and Earth Sciences

Jeet Mohapatra, Nima Dehmamy, Csaba Both, Subhro Das, Tommi Jaakkola

We introduce a novel approach for discovering effective degrees of freedom (DOF) in molecular dynamics simulations by mapping the DOF to approximate symmetries of the energy landscape. Unlike most existing methods, we do not require trajectory data but instead rely on knowledge of the forcefield (energy function) around the initial state. We present a scalable symmetry loss function compatible with existing force-field frameworks and a Hessian-based method efficient for smaller systems. Our approach enables systematic exploration of conformational space by connecting structural dynamics to energy landscape symmetries. We apply our method to two systems, Alanine dipeptide and Chignolin, recovering their known important conformations. Our approach can prove useful for efficient exploration in molecular simulations with potential applications in protein folding and drug discovery.

Reinforcement Learning · Deep RL

Yucen Wang, Rui Yu, Shenghua Wan, Le Gan, De-Chuan Zhan

Foundation Models (FMs) and World Models (WMs) offer complementary strengths in task generalization at different levels. In this work, we propose FOUNDER, a framework that integrates the generalizable knowledge embedded in FMs with the dynamic modeling capabilities of WMs to enable open-ended task solving in embodied environments in a reward-free manner. We learn a mapping function that grounds FM representations in the WM state space, effectively inferring the agent's physical states in the world simulator from external observations. This mapping enables the learning of a goal-conditioned policy through imagination during behavior learning, with the mapped task serving as the goal state. Our method leverages the predicted temporal distance to the goal state as an informative reward signal. FOUNDER demonstrates superior performance on various multi-task offline visual control benchmarks, excelling in capturing the deep-level semantics of tasks specified by text or videos, particularly in scenarios involving complex observations or domain gaps where prior methods struggle. The consistency of our learned reward function with the ground-truth reward is also empirically validated. Our project website is https://sites.google.com/view/founder-rl.

Applications · Chemistry, Physics, and Earth Sciences

Angxiao Yue, Zichong Wang, Hongteng Xu

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications.Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency.In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format.We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves on-par performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37$\times$ faster than RFDiffusion and 63$\times$ faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency.

Applications · Robotics

Xupeng Zhu, Fan Wang, Robin Walters, Jane Shi

Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose Spherical Diffusion Policy (SDP), an SE(3) equivariant diffusion policy that adapts trajectories according to 3D transformations of the scene. Such equivariance is achieved by embedding the states, actions, and the denoising process in spherical Fourier space. Additionally, we employ novel spherical FiLM layers to condition the action denoising process equivariantly on the scene embeddings. Lastly, we propose a spherical denoising temporal U-net that achieves spatiotemporal equivariance with computational efficiency. In the end, SDP is end-to-end SE(3) equivariant, allowing robust generalization across transformed 3D scenes. SDP demonstrates a large performance improvement over strong baselines in 20 simulation tasks and 5 physical robot tasks including single-arm and bi-manual embodiments. Code is available at https://github.com/amazon-science/Spherical_Diffusion_Policy.

Applications · Everything Else

Arturs Berzins, Andreas Radler, Eric Volkmann, Sebastian Sanokowski, Sepp Hochreiter, Johannes Brandstetter

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.