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Applications · Chemistry, Physics, and Earth Sciences

Li Sun, Hongbo Lv, Zhikai Jiang, Zhongtian Sun, Lanxu Yang, Philip Yu

Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.

Applications · Chemistry, Physics, and Earth Sciences

Hwanhee Kim, Seungyeon Choi, Sanghyun Park

Generative Flow Networks (GFlowNets) have emerged as a powerful framework for molecular generation, sampling diverse candidates proportionally to a reward function. However, the vast chemical space necessitates truncating trajectory length, forcing models to treat incomplete molecular fragments as terminal states alongside valid molecules. This conflation distorts the learned distribution by allocating probability mass to chemically meaningless states. We propose LeakGFN, a dual-head architecture that decomposes flow into two components: a chemical head modeling flow over the full chemical space, and a valid head estimating the fraction of flow reaching valid molecules within the truncation boundary. Through this decomposition, the valid head implicitly learns molecular reachability without explicit supervision. We prove that LeakGFN recovers the correct distribution over accessible molecules under mild assumptions. Experiments on five molecular optimization tasks demonstrate consistent improvements over flow matching baselines, achieving state-of-the-art performance on four out of five tasks. Our module integrates as a plug-and-play enhancement into existing frameworks, improving performance on both pocket-conditioned and multi-objective generation tasks.

Deep Learning · Theory

Florian Handke, Dejan Stancevic, Felix Koulischer, Thomas Demeester, Luca Ambrogioni

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.

Applications · Chemistry, Physics, and Earth Sciences

Sepehr Mousavi, Siddhartha Mishra, Laura De Lorenzis

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.

Optimization · Zero-order and Black-box Optimization

Boris Prokhorov, Semyon Chebykin, Alexander Gasnikov, Aleksandr Beznosikov

This paper deals with stochastic optimization problems involving Markovian noise with a zero-order oracle. We present and analyze a novel derivative-free method for solving such problems in strongly convex smooth and non-smooth settings with both one-point and two-point feedback oracles. Using a randomized batching scheme, we show that when mixing time $\tau$ of the underlying noise sequence is less than the dimension of the problem $d$, the convergence estimates of our method do not depend on $\tau$. This observation provides an efficient way to interact with Markovian stochasticity: instead of invoking the expensive first-order oracle, one should use the zero-order oracle. Finally, we complement our upper bounds with the corresponding lower bounds. This confirms the optimality of our results.

Applications · Robotics

Thomas Tian, Yilin Wu, Andrea Bajcsy

This position paper argues that to obtain reliable embodied reward models, the community must invest in "bad" robot data: failed, suboptimal, error-prone, and even hazardous behaviors. While reward models are central to any foundation model's lifecycle, today's embodied reward models are trained primarily on successful behaviors. We analyze three state-of-the-art embodied reward models and find that they systematically over-reward behaviors that real human evaluators would penalize, including unsafe interactions, poor execution, and shortcut strategies that only superficially satisfy tasks. We attribute these failures to a key data gap: the scarcity of negative embodied data which is costly to collect and often filtered out or withheld in existing robotics datasets. Furthermore, we show that even modest exposure to real bad behavior data can improve alignment with human preferences and reduce costly false positives. We therefore call on the embodied AI community to curate and release their bad robot data, build synthetic bad data generation engines, develop more decentralized physical evaluation systems, and design benchmarks for fine-grained embodied reward model evaluations.

Enkelejda Kasneci, Gjergji Kasneci

This position paper argues that effective tutoring requires **corrective friction**: surfacing misconceptions and challenging them supportively to drive conceptual change. Yet preference-aligned LLMs can trade **epistemic rigor** for agreeableness. We identify a **Reasoning-Sycophancy Paradox**: models that resist **context-switch** frame attacks can still capitulate under social-epistemic pressure, especially **authority** ("my notes say I’m right") and **social-affective face-saving** ("please don’t tell me I’m wrong''). We introduce **EduFrameTrap**, a tutoring benchmark across math, physics, economics, chemistry, biology, and computer science that varies student confidence and pressure (context-switch, authority, social-affective). Across two frontier LLMs, context-switch failures are comparatively lower for GPT-5.2, while authority and social pressure more often trigger epistemic retreat. In contrast, Claude shows substantial context-switch fragility in this run. Because these failures are hard to judge automatically, we report two-judge disagreement as a reliability signal. We argue benchmarks should measure *social-epistemic courage*, i.e., supportive but corrective tutoring, and treat *kind-but-correct* behavior as a safety requirement.

Applications · Health / Medicine

Song Ouyang, Zhijie Dong, Yong Luo, Kehua Su, Huangxuan Zhao, Miaojing Shi, Bo Du

Computational protein design holds immense promise across diverse domains, but existing approaches face significant challenges: traditional physics-based methods require substantial domain expertise, while emerging deep learning methods often rely on restricted functional ontologies, struggle to bridge the semantic gap between text and protein sequences, or lack closed-loop optimization mechanisms. In this paper, we present PDAgent, an LLM-driven autonomous agent framework that enables *in silico* protein design through template-based directed mutation. Our framework accepts natural language specifications of desired protein properties and employs a ReAct-style reasoning loop comprising five phases: THINK, PLAN, ACT, OBSERVE, and REFLECT. PDAgent integrates template retrieval, conservation-aware mutation strategies, and domain-specific computational tools for property optimization across eight biophysical dimensions. Experiments on 100 diverse protein design tasks demonstrate that PDAgent achieves a 91.34% average constraint satisfaction rate with high structural quality (mean pLDDT 87.69), substantially outperforming both direct LLM generation and specialized deep learning methods.

Panqi Yang, Haodong Jing, Jiahao Chao, Tingyan Xiang, Li Lin, Yao Hu, Yang Luo, Yongqiang Ma

Unified visual tokenization faces a fundamental trade-off: optimizing for high-fidelity pixel reconstruction (spatial equivariance) inherently conflicts with semantic abstraction (conceptual invariance). We identify the root cause as Manifold Misalignment, where naive joint optimization leads to conflicting gradients that force a zero-sum game between these two objectives. In this paper, we propose MUSE, a framework that resolves this deadlock via Topological Orthogonality. Recognizing Structure as the orthogonal bridge, MUSE physically decouples the optimization subspaces within Transformers. We route structural gradients to refine attention topology and semantic gradients to update feature values, transforming destructive interference into Mutual Reinforcement. Extensive experiments demonstrate that MUSE breaks the trade-off, matching state-of-the-art generation (gFID 3.08) while notably outperforming its own teacher InternViT-300M in linear probing (85.2% vs. 82.5%), proving that structurally aligned reconstruction actively refines semantic perception.

Social Aspects · Everything Else

Tom Zahavy

How do we fundamentally discover new things? In a letter to Maurice Solovine, Albert Einstein conceptualized discovery as a cyclical process involving an intuitive 'jump' from sensory experience to axioms, followed by logical deduction. While Generative AI has mastered Induction (statistical pattern matching) and is rapidly conquering Deduction (formal proof), we argue it lacks the mechanism for Abduction—the generation of novel explanatory hypotheses. Using Einstein’s formulation of General Relativity as a computational case study, we demonstrate that the prevailing theory of "creativity as data compression" (induction) fails to account for discoveries where observational data is scarce. This position paper argues that while a modern Large Language Model could plausibly execute the deductive phase of proving theorems from established premises, it is structurally incapable of the abductive 'Jump' required to formulate those premises. We identify the translation of simulation into formal axioms as the critical bottleneck in artificial scientific invention, and propose that physically consistent, multimodal world models offer the necessary sensory grounding to bridge this divide.

Applications · Computer Vision

Guofeng Zhang, Angtian Wang, Jacob Fang, Liming Jiang, Haotian Yang, Alan Yuille, Chongyang Ma

Real-world videos naturally portray complex interactions among distinct physical objects, effectively forming dynamic compositions of visual elements. However, most current video generation models synthesize scenes holistically and therefore lack mechanisms for explicit compositional manipulation. To address this limitation, we propose HECTOR, a generative pipeline that enables fine-grained compositional control. In contrast to prior methods, HECTOR supports hybrid reference conditioning, allowing generation to be simultaneously guided by static images and/or dynamic videos. Moreover, users can explicitly specify the trajectory of each referenced element, precisely controlling its location, scale, and speed (see Figure1). This design allows the model to synthesize coherent videos that satisfy complex spatiotemporal constraints while preserving high-fidelity adherence to references. Extensive experiments demonstrate that HECTOR achieves superior visual quality, stronger reference preservation, and improved motion controllability compared with existing approaches.

General Machine Learning · Representation Learning

Yilin Chen, Tianyu Lu, Cizhang Zhao, Hannah Wayment-Steele, Po-Ssu Huang

Building physically grounded protein representations is central to computational biology, yet most existing approaches rely on sequence-pretrained language models or backbone-only graphs that overlook side-chain geometry and chemical detail. We present SLAE, a unified all-atom framework for learning protein representations from each residue’s local atomic neighborhood using only atom types and interatomic geometries. To encourage expressive feature extraction, we introduce a novel multi-task autoencoder objective that combines coordinate reconstruction, sequence recovery, and energy regression. SLAE reconstructs allatom structures with high fidelity from latent residue environments and achieves state-of-the-art performance across diverse downstream tasks via transfer learning. SLAE’s latent space is chemically informative and environmentally sensitive, enabling quantitative assessment of structural qualities and smooth interpolation between conformations at all-atom resolution.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Sungwoo Park

We introduce Euler–Poincaré Neural Dynamics (EPND), a geometric-mechanics–driven framework that redefines how Koopman-type neural models learn dynamical systems. Unlike conventional operator-learning methods that rely on function-space linearization, EPND places geometric mechanics at the core of its architecture the mathematical engine governing evolution through Lie-group flows. This foundation enables a principled treatment of curvature, symmetry, and conservation, that ensures both interpretability and physical consistency. Building on this foundation, we develop the Euler–Poincaré Parallel Scan, a parallel algorithm that leverages the associative algebra of Lie-group compositions to overcome the inefficiencies of sequential computation. By unifying geometric structure with scalable computation, EPND achieves high accuracy, strong stability, and significant parallel acceleration in modeling long-horizon dynamics of versatile scientific simulation.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Jungwoo Park, Sungwoo Park

We present a Lie-algebraic approach to model Koopman dynamics that integrates algebraic structure with computational scalability. The proposed formulation constrains the neural generators to evolve within prescribed Lie subalgebras and constructs finite-time flows through a neural Magnus expansion construction, thereby maintaining consistency with the associated Lie-group composition over each time segment. To address the computational burden inherent in sequential propagation, we exploit the associativity of Lie-group compositions and construct segmentwise propagators via a prefix-scan algorithm, which reduces the depth of temporal composition from linear to logarithmic. Consequently, the framework enables accurate long-horizon prediction while improving computational efficiency, and provides a principled foundation for scalable Koopman operator learning for nonlinear systems.

Zhe Cao, Tao Wang, Jiaming Wang, Yanghai Wang, Yuanxing Zhang, Jiahao Wang, Jialu Chen, Miao Deng, Chenxi Liao, Yize Zhang 等

Text-to-Audio-Video (T2AV) generation aims to synthesize temporally coherent video and semantically synchronized audio from natural language, yet its evaluation remains fragmented, often relying on unimodal metrics or narrowly scoped benchmarks that fail to capture cross-modal alignment, instruction following, and perceptual realism under complex prompts. To address this limitation, we present T2AV-Compass, a unified benchmark for comprehensive evaluation of T2AV systems, consisting of 500 diverse and complex prompts constructed via a taxonomy-driven pipeline to ensure semantic richness and physical plausibility. Besides, T2AV-Compass introduces a dual-level evaluation framework that integrates objective signal-level metrics for video quality, audio quality, and cross-modal alignment with a subjective MLLM-as-a-Judge protocol for instruction following and realism assessment. Extensive evaluation of 15 representative T2AV systems reveals that even the strongest models fall substantially short of human-level realism and cross-modal consistency, with persistent failures in audio realism, fine-grained synchronization, instruction following, etc. These results indicate significant improvement room for future models and highlight the value of T2AV-Compass as a challenging and diagnostic testbed for advancing text-to-audio-video generation.

Deep Learning · Everything Else

Jan Disselhoff, Michael Wand

Why do neural networks generalize well on natural data? Natural data originates from processes subject to specific physical constraints, such as temporal and spatial invariance, that make it easier to learn. We investigate the sufficiency of these properties using 2D cellular automata as a controlled testbed: systems that are perfectly local, symmetric, and deterministic. We find that these conditions alone are \textit{not sufficient} to predict the k-step evolution of a cellular automaton. We then examine smoothness (average sensitivity) as an additional criterion and find it predictive but still incomplete. Finally, we introduce a circuit complexity perspective, hypothesizing that natural functions are computable by small circuits. Junta coefficients, measuring the concentration of Fourier weight by interaction degree, provide a tighter predictor of learnability and a correspondence to combinatorial complexity. Across architectures (CNNs, transformers, MLPs), learnable functions are predominantly those with spectral weight concentrated at low degrees and therefore low complexity. These results would be consistent with the hypothesis that natural data is learnable because natural dynamics filters out complex, high-degree interactions.

Applications · Chemistry, Physics, and Earth Sciences

Jan Hagnberger, Mathias Niepert

Machine learning–based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, generating a simulation mesh for new geometries is computationally costly. In contrast, mesh-free methods, which do not rely on the simulation mesh, typically incur higher errors. Motivated by these considerations, we introduce SMART, a neural surrogate model that predicts physical quantities at arbitrary query locations using only a point-cloud representation of the geometry, without requiring access to the simulation mesh. The geometry and simulation parameters are encoded into a shared latent space that captures both structural and parametric characteristics of the physical field. A physics decoder then attends to the encoder's intermediate latent representations to map spatial queries to physical quantities. Through this cross-layer interaction, the model jointly updates latent geometric features and the evolving physical field. Extensive experiments show that SMART is competitive with and often outperforms existing methods that rely on the simulation mesh as input, demonstrating its capabilities for industry-level simulations.

Deep Learning · Generative Models and Autoencoders

Junhao Song, Yu Zhou, William J. Knottenbelt, Yudong Cao

The scaling hypothesis assumes that increasing model parameters yields emergent reasoning capabilities. This position paper argues that applying this probabilistic paradigm to generic quantum circuit synthesis is a category error. Unlike natural languages, quantum circuits require strict adherence to mathematical constraints, such as unitarity. Training on unverified code constitutes data poisoning. Models learn syntax but fail to capture the physical semantics of Hilbert space. Since the valid subset of circuit designs decays exponentially with the number of qubits, post-hoc filtering is mathematically intractable. We propose a pivot from human-centric copilots to verifier-centric agents. We integrate hierarchical constraints, topological masks, and symbolic proxies directly into generation. Our analysis suggests that scale alone cannot bridge the validity gap. Verification-aware architectures offer a viable path for modular quantum program generation. The community must stop simulating the physicist and instead satisfy the physical rules.

Deep Learning · Sequential Models, Time series

Alena Brändle, Lukas Eisenmann, Florian Götz, Daniel Durstewitz

In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and recreates its long-term properties (`climate statistics'). In scientific and medical areas, in particular, these models need to be mechanistically tractable -- through their mathematical analysis we would like to obtain insight into the recovered system's workings. Piecewise-linear (PL), ReLU-based RNNs (PLRNNs) have a strong track-record in this regard, representing SOTA DSR models while allowing mathematical insight by virtue of their PL design. However, all current PLRNN variants are *discrete-time maps*. This is in disaccord with the assumed continuous-time nature of most physical and biological processes, and makes it hard to accommodate data arriving at *irregular* temporal intervals. Neural ODEs are one solution, but they do not reach the DSR performance of PLRNNs and often lack their tractability. Here we develop theory for *continuous-time* PLRNNs (cPLRNNs): We present a novel algorithm for training and simulating such models, bypassing numerical integration by efficiently exploiting their PL structure. We further demonstrate how important topological objects like equilibria or limit cycles can be determined semi-analytically in trained models. We compare cPLRNNs to both their discrete-time cousins as well as Neural ODEs on DSR benchmarks, including systems with discontinuities which come with hard thresholds.

Applications · Chemistry, Physics, and Earth Sciences

Dian Jin, Yancheng Yuan, Xiaoming Tao

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory costs for higher-order targets. We propose the Cartesian Environment Interaction Tensor Network (CEITNet), an approach that constructs a multi-channel Cartesian local environment tensor for each atom and performs flexible many-body mixing via a learnable channel-space interaction. By performing learning in channel space and using Cartesian tensor bases to assemble equivariant outputs, CEITNet enables efficient construction of high-order tensor. Across benchmark datasets for order-2 dielectric, order-3 piezoelectric, and order-4 elastic tensor prediction, CEITNet surpasses prior high-order prediction methods on key accuracy criteria while offering high computational efficiency. Code is provided in supplementary materials.