Daily Papers

Understanding the chemical structure from a graphical representation of a molecule is a challenging image caption task that would greatly benefit molecule-centric scientific discovery. Variations in molecular images and caption subtasks pose a significant challenge in both image representation learning and task modeling. Yet, existing methods only focus on a specific caption task that translates a molecular image into its graph structure, i.e., OCSR. In this paper, we propose the Optical Chemical Structure Understanding (OCSU) task, which extends OCSR to molecular image caption from motif level to molecule level and abstract level. We present two approaches for that, including an OCSR-based method and an end-to-end OCSR-free method. The proposed Double-Check achieves SOTA OCSR performance on real-world patent and journal article scenarios via attentive feature enhancement for local ambiguous atoms. Cascading with SMILES-based molecule understanding methods, it can leverage the power of existing task-specific models for OCSU. While Mol-VL is an end-to-end optimized VLM-based model. An OCSU dataset, Vis-CheBI20, is built based on the widely used CheBI20 dataset for training and evaluation. Extensive experimental results on Vis-CheBI20 demonstrate the effectiveness of the proposed approaches. Improving OCSR capability can lead to a better OCSU performance for OCSR-based approach, and the SOTA performance of Mol-VL demonstrates the great potential of end-to-end approach.

This report is a primarily survey on the chemical nature of some exotic species containing the positively charged muon and the muonic Helium, i.e., the negatively charged muon plus helium nucleus, as exotic isotopes of hydrogen, using the newly developed multi-component quantum theory of atoms in molecules (MC-QTAIM) analysis, employing ab initio non-Born-Oppenhiemer wavefunctions. Accordingly, the "atoms in molecules" analysis performed on various asymmetric exotic isotopomers of hydrogen molecule, recently detected experimentally [Science 331, 448 (2011)], demonstrates that both the exotic isotopes are capable of forming atoms in molecules and retaining the identity of hydrogen atom. Various derived properties of atomic basins containing muonic helium cast no doubt that apart from its short life time, it is a heavier isotope of hydrogen while the properties of basins containing the positively charged muon are more remote from those of the orthodox hydrogen basins, capable of appreciable donation of electrons as well as large charge polarization; however, with some tolerance, they may be categorized also as hydrogen basins though with a smaller electronegativity. All in all, present study also clearly demonstrates that the MC-QTAIM analysis is an efficient approach to decipher the chemical nature of species containing exotic constituents, hard to be elucidated by experimental and/or alternative theoretical schemes.

The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact ell_1 recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms H_c, {He_c}^+ and {Li_c}^{2+} confined by an impenetrable spherical box. Novel expressions for entropic uncertainty relation and Shannon entropies S_r and S_p are proposed to ensure their physical dimensionless characteristic. The electronic ground state energy and the quantities S_r, S_p and S_t are calculated for the hydrogenic-like atoms to different confinement radii by using a variational method. The global behavior of these quantities and different conjectures are analyzed. The results are compared, when available, with those previously published.

We explain how the so-called Einstein locality is to be understood in the Schr\"odinger picture of quantum mechanics. This notion is perfectly compatible with the Bell non-locality exhibited by entangled states. Contrary to some beliefs that quantum mechanics is incomplete, it is, in fact, its overcompleteness as exemplified by different pictures of quantum physics, that points to the same underlying reality.

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our representation satisfies all structural, geometric, efficiency, and generalizability constraints. Afterward, we provide a general algorithm to encode any atomistic system. Finally, we report performance comparable to state-of-the-art methods on numerous tasks. We open-source all code and datasets. The code and data are available at https://github.com/rahulkhorana/PolyatomicComplexes.

Field evaporation from ionic or covalently bonded materials often leads to the emission of molecular ions. The metastability of these molecular ions, particularly under the influence of the intense electrostatic field (1010 Vm-1), makes them prone to dissociation with or without an exchange of energy amongst them. These processes can affect the analytical performance of atom probe tomography (APT). For instance, neutral species formed through dissociation may not be detected at all or with a time of flight no longer related to their mass, causing their loss from the analysis. Here, we evaluated the changes in the measured composition of FeO, Fe2O3 and Fe3O4 across a wide range of analysis conditions. Possible dissociation reactions are predicted by density-functional theory (DFT) calculations considering the spin states of the molecules. The energetically favoured reactions are traced on to the multi-hit ion correlation histograms, to confirm their existence within experiments, using an automated Python-based routine. The detected reactions are carefully analysed to reflect upon the influence of these neutrals from dissociation reactions on the performance of APT for analysing iron oxides.

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.

Current artificial intelligence systems exhibit a fundamental architectural limitation: they resolve ambiguity prematurely. This premature semantic collapse--collapsing multiple valid interpretations into single outputs--stems from classical identity assumptions in neural architectures. We propose Non-Resolution Reasoning (NRR), a framework treating ambiguity retention as a valid reasoning mode. NRR introduces three principles: (1) Non-Identity (A neq A)--the same symbol refers to different entities across contexts; (2) Approximate Identity (A approx A)--entities share partial structural overlap without being identical; (3) Non-Resolution--conflicting interpretations coexist without forced convergence. We formalize these through Multi-Vector Embeddings for context-dependent representation, Non-Collapsing Attention for parallel interpretation retention, and Contextual Identity Tracking (CIT) for maintaining A neq A across inference. We illustrate NRR through case studies in paradox handling, creative generation, and context-dependent reasoning. Functional verification in a synthetic two-turn disambiguation task shows NRR-lite maintains high entropy (H = 0.91 bits, near-maximum 1.0) at ambiguous turns while standard architectures collapse early (H = 0.15 bits), preserving interpretive flexibility until context arrives. NRR challenges the assumption that meaning must collapse to be useful. The question is not whether AI should resolve ambiguity, but when, how, and under whose control.

Graph Neural Networks (GNNs) have been widely adopted for drug discovery with molecular graphs. Nevertheless, current GNNs are mainly good at leveraging short-range interactions (SRI) but struggle to capture long-range interactions (LRI), both of which are crucial for determining molecular properties. To tackle this issue, we propose a method that implicitly projects all original atoms into a few Neural Atoms, which abstracts the collective information of atomic groups within a molecule. Specifically, we explicitly exchange the information among neural atoms and project them back to the atoms' representations as an enhancement. With this mechanism, neural atoms establish the communication channels among distant nodes, effectively reducing the interaction scope of arbitrary node pairs into a single hop. To provide an inspection of our method from a physical perspective, we reveal its connection with the traditional LRI calculation method, Ewald Summation. We conduct extensive experiments on three long-range graph benchmarks, covering both graph-level and link-level tasks on molecular graphs. We empirically justify that our method can be equipped with an arbitrary GNN and help to capture LRI.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.

Photoionized nebulae comprise basically HII regions and planetary nebulae, and their abundances give important clues on the nucleosynthesis and chemical evolution of their host galaxies. There is presently a large amount of data on these objects, especially for the elements He and N, which are strongly affected by the evolution of intermediate mass stars, as well as O, Ne, S, and Ar, which are essentially synthesized in stars with larger masses. The abundances of these elements in several systems in the Local Group are discussed on the basis of distance-independent correlations.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But no resources exist to evaluate how well Large Language Models can use explicit reasoning to resolve ambiguity in language. We propose to use ambiguous definite descriptions for this purpose and create and publish the first benchmark dataset consisting of such phrases. Our method includes all information required to resolve the ambiguity in the prompt, which means a model does not require anything but reasoning to do well. We find this to be a challenging task for recent LLMs. Code and data available at: https://github.com/sfschouten/exploiting-ambiguity

Wigner's Friend-type paradoxes challenge the assumption that events are absolute -- that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer-independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely the Local Friendliness Theorem, we introduce the Causal Friendliness Paradox, a time-ordered analogue of it. In this framework, we replace the usual locality assumption with Axiological Time Symmetry (ATS), and show that, when combined with the assumptions of Absoluteness of Observed Events (AOE), No Retrocausality (NRC), and Screening via Pseudo Events (SPE), we obtain a causal inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.

We introduce Orb-v3, the next generation of the Orb family of universal interatomic potentials. Models in this family expand the performance-speed-memory Pareto frontier, offering near SoTA performance across a range of evaluations with a >10x reduction in latency and > 8x reduction in memory. Our experiments systematically traverse this frontier, charting the trade-off induced by roto-equivariance, conservatism and graph sparsity. Contrary to recent literature, we find that non-equivariant, non-conservative architectures can accurately model physical properties, including those which require higher-order derivatives of the potential energy surface. This model release is guided by the principle that the most valuable foundation models for atomic simulation will excel on all fronts: accuracy, latency and system size scalability. The reward for doing so is a new era of computational chemistry driven by high-throughput and mesoscale all-atom simulations.

Ambiguity is an intrinsic feature of natural language. Managing ambiguity is a key part of human language understanding, allowing us to anticipate misunderstanding as communicators and revise our interpretations as listeners. As language models (LMs) are increasingly employed as dialogue interfaces and writing aids, handling ambiguous language is critical to their success. We characterize ambiguity in a sentence by its effect on entailment relations with another sentence, and collect AmbiEnt, a linguist-annotated benchmark of 1,645 examples with diverse kinds of ambiguity. We design a suite of tests based on AmbiEnt, presenting the first evaluation of pretrained LMs to recognize ambiguity and disentangle possible meanings. We find that the task remains extremely challenging, including for the recent GPT-4, whose generated disambiguations are considered correct only 32% of the time in human evaluation, compared to 90% for disambiguations in our dataset. Finally, to illustrate the value of ambiguity-sensitive tools, we show that a multilabel NLI model can flag political claims in the wild that are misleading due to ambiguity. We encourage the field to rediscover the importance of ambiguity for NLP.

The AMS-02 experiment recently published time-dependent fluxes of deuterons (D) from May 2011 to April 2021, divided into 33 periods of four Bartels rotations each. These temporal structures are associated with solar modulation. In this study, three modified force-field approximation are employed to examine the long-term behavior of cosmic-ray (CR) isotopes such as D, ^3He, and ^4He, as well as the ratios D/^3He and ^3He/^4He. The solar modulation potential is rigidity-dependent for these modified force-field approximation models. Due to the unknown local interstellar spectrum (LIS) for these isotopes, we utilize the Non-LIS method for solar modulation. By fitting to the AMS-02 time-dependent fluxes, we derive the solar modulation parameters. Our findings prove the assumption in literature that all isotopes can be fitted using the same solar modulation parameters and it shown that the modified FFA models are validated parametrization for solar modulation. Based on these, we forecast the daily fluxes of D, ^3He and ^4He from 2011 to 2020.

Deep generative models have recently achieved superior performance in 3D molecule generation. Most of them first generate atoms and then add chemical bonds based on the generated atoms in a post-processing manner. However, there might be no corresponding bond solution for the temporally generated atoms as their locations are generated without considering potential bonds. We define this problem as the atom-bond inconsistency problem and claim it is the main reason for current approaches to generating unrealistic 3D molecules. To overcome this problem, we propose a new diffusion model called MolDiff which can generate atoms and bonds simultaneously while still maintaining their consistency by explicitly modeling the dependence between their relationships. We evaluated the generation ability of our proposed model and the quality of the generated molecules using criteria related to both geometry and chemical properties. The empirical studies showed that our model outperforms previous approaches, achieving a three-fold improvement in success rate and generating molecules with significantly better quality.

Polarization analysis in x-ray spectroscopy provides an orientation dependent sensitivity to local bonding environments. For a cluster of atoms, polarization sensitivity is most often discussed through the lens of point group symmetries. However, this is a discrete, qualitative method of classifying clusters, and it does little to indicate the degree of spectral anisotropy. Here we adopt a random forest model for quantitative prediction of spectral anisotropy. Its input relies on simplified local geometric and chemical information that can be obtained from any crystal structure file. The model is trained on over 10,000 experimentally realized transition metal structures from the Materials Project, with the target being VtC-XES calculated using the real space Green's function code FEFF. We find that the model can strongly predict the degree of spectral anisotropy, with the primary factors being derived from the spatial moments of ligands in a cluster.

Contrastively trained encoders have recently been proven to invert the data-generating process: they encode each input, e.g., an image, into the true latent vector that generated the image (Zimmermann et al., 2021). However, real-world observations often have inherent ambiguities. For instance, images may be blurred or only show a 2D view of a 3D object, so multiple latents could have generated them. This makes the true posterior for the latent vector probabilistic with heteroscedastic uncertainty. In this setup, we extend the common InfoNCE objective and encoders to predict latent distributions instead of points. We prove that these distributions recover the correct posteriors of the data-generating process, including its level of aleatoric uncertainty, up to a rotation of the latent space. In addition to providing calibrated uncertainty estimates, these posteriors allow the computation of credible intervals in image retrieval. They comprise images with the same latent as a given query, subject to its uncertainty. Code is available at https://github.com/mkirchhof/Probabilistic_Contrastive_Learning

The overwhelming majority of molecules remains unexplored. This is mostly due to the sheer number of them, which prohibits any enumeration of chemical space, the set of all such molecules. In practice, only subsets of chemical space are considered, but those subsets exhibit substantial bias, prohibiting data-driven characterization of chemical space itself. In this work, we provide a method produce unbiased representative random samples of chemical space without enumeration of constituent molecules and to estimate the number of molecules in any custom chemical space. The approach is applicable to molecules which can be represented as graph and runs efficiently even for molecules of 30 atoms. We use it to estimate the representativeness of current databases with respect to their underlying chemical space and to establish a necessary criterion for a lower bound of database sizes to be representative of an underlying chemical space.

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs has been trained from scratch because learning additional data typically requires to train again on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs) which combine structural properties and element information from the periodic table. These eeACSFs are a key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pre-trained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.

Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers. Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH2. This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians and a robust stochastic optimization routine. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.

We report on the trapping of single rubidium atoms in large arrays of optical tweezers comprising up to 2088 sites in a cryogenic environment at 6 K. Our approach relies on the use of microscope objectives that are in-vacuum but at room temperature, in combination with windowless thermal shields into which the objectives are protruding to ensure a cryogenic environment for the trapped atoms. To achieve enough optical power for efficient trapping, we combine two lasers at slightly different wavelengths. We discuss the performance and limitations of our design. Finally, we demonstrate atom-by-atom rearrangement of an 828-atom target array using moving optical tweezers controlled by a field-programmable gate array.

The binding energies of the five bound rotational levels J=0-4 in the highest vibrational level v=14 in the X^1Sigma_g^+ ground electronic state of H_2 were measured in a three-step ultraviolet-laser experiment. Two-photon UV-photolysis of H_2S produced population in these high-lying bound states, that were subsequently interrogated at high precision via Doppler-free spectroscopy of the F^1Sigma_g^+ - X^1Sigma_g^+ system. A third UV-laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on non-adiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The s-wave scattering length of the H + H system is derived from the binding energy of the last bound J=0 level via a direct semi-empirical approach, yielding a value of a_s = 0.2724(5) a_0, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the malpha^4 relativity contribution to a_s was found to be significant. In a similar manner a value for the p-wave scattering volume is determined via the J=1 binding energy yielding a_p = -134.0000(6) a_0^3. The binding energy of the last bound state in H_2, the (v=14, J=4) level, is determined at 0.023(4) cm^{-1}, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed.

Despite the frequent challenges posed by ambiguity when representing meaning via natural language, it is often ignored or deliberately removed in tasks mapping language to formally-designed representations, which generally assume a one-to-one mapping between linguistic and formal representations. We attempt to address this shortcoming by introducing AmP, a framework, dataset, and challenge for translating ambiguous natural language to formal representations like logic and code. We define templates and generate data for five well-documented linguistic ambiguities. Using AmP, we investigate how several few-shot text-to-code systems handle ambiguity, introducing three new metrics. We find that large pre-trained models perform poorly at capturing the distribution of possible meanings without deliberate instruction. However, models are able to capture the distribution well when ambiguity is attested in their inputs. These results motivate a call for including ambiguity explicitly in datasets and promote considering the distribution of possible outputs when evaluating systems. Data and code: https://github.com/esteng/ambiguous_parsing

The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets, and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

In recent years, diffusion-based models have demonstrated exceptional performance in searching for simultaneously stable, unique, and novel (S.U.N.) crystalline materials. However, most of these models don't have the ability to change the number of atoms in the crystal during the generation process, which limits the variability of model sampling trajectories. In this paper, we demonstrate the severity of this restriction and introduce a simple yet powerful technique, mirage infusion, which enables diffusion models to change the state of the atoms that make up the crystal from existent to non-existent (mirage) and vice versa. We show that this technique improves model quality by up to times2.5 compared to the same model without this modification. The resulting model, Mirage Atom Diffusion (MiAD), is an equivariant joint diffusion model for de novo crystal generation that is capable of altering the number of atoms during the generation process. MiAD achieves an 8.2% S.U.N. rate on the MP-20 dataset, which substantially exceeds existing state-of-the-art approaches. The source code can be found at https://github.com/andrey-okhotin/miad.git{github.com/andrey-okhotin/miad}.

Different entities with the same name can be difficult to distinguish. Handling confusing entity mentions is a crucial skill for language models (LMs). For example, given the question "Where was Michael Jordan educated?" and a set of documents discussing different people named Michael Jordan, can LMs distinguish entity mentions to generate a cohesive answer to the question? To test this ability, we introduce a new benchmark, AmbigDocs. By leveraging Wikipedia's disambiguation pages, we identify a set of documents, belonging to different entities who share an ambiguous name. From these documents, we generate questions containing an ambiguous name and their corresponding sets of answers. Our analysis reveals that current state-of-the-art models often yield ambiguous answers or incorrectly merge information belonging to different entities. We establish an ontology categorizing four types of incomplete answers and automatic evaluation metrics to identify such categories. We lay the foundation for future work on reasoning across multiple documents with ambiguous entities.

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.

Machine learning force fields (MLFFs) have revolutionized molecular simulations by providing quantum mechanical accuracy at the speed of molecular mechanical computations. However, a fundamental reliance of these models on fixed-cutoff architectures limits their applicability to macromolecular systems where long-range interactions dominate. We demonstrate that this locality constraint causes force prediction errors to scale monotonically with system size, revealing a critical architectural bottleneck. To overcome this, we establish the systematically designed MolLR25 ({Mol}ecules with {L}ong-{R}ange effect) benchmark up to 1200 atoms, generated using high-fidelity DFT, and introduce E2Former-LSR, an equivariant transformer that explicitly integrates long-range attention blocks. E2Former-LSR exhibits stable error scaling, achieves superior fidelity in capturing non-covalent decay, and maintains precision on complex protein conformations. Crucially, its efficient design provides up to 30% speedup compared to purely local models. This work validates the necessity of non-local architectures for generalizable MLFFs, enabling high-fidelity molecular dynamics for large-scale chemical and biological systems.

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105 585-593 (2003), Annu. Rev. Phys. Chem. 58 113-142 (2007)], emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models, and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential triangle G=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in phosphorylation-dephosphorylation cycle respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by "dissociation constants", which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule which can not be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein which can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon.

Recent neural network-based wave functions have achieved state-of-the-art accuracies in modeling ab-initio ground-state potential energy surface. However, these networks can only solve different spatial arrangements of the same set of atoms. To overcome this limitation, we present Graph-learned orbital embeddings (Globe), a neural network-based reparametrization method that can adapt neural wave functions to different molecules. Globe learns representations of local electronic structures that generalize across molecules via spatial message passing by connecting molecular orbitals to covalent bonds. Further, we propose a size-consistent wave function Ansatz, the Molecular orbital network (Moon), tailored to jointly solve Schr\"odinger equations of different molecules. In our experiments, we find Moon converging in 4.5 times fewer steps to similar accuracy as previous methods or to lower energies given the same time. Further, our analysis shows that Moon's energy estimate scales additively with increased system sizes, unlike previous work where we observe divergence. In both computational chemistry and machine learning, we are the first to demonstrate that a single wave function can solve the Schr\"odinger equation of molecules with different atoms jointly.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

Discovering novel high-entropy alloys (HEAs) with desirable properties is challenging due to the vast compositional space and complex phase formation mechanisms. Efficient exploration of this space requires a strategic approach that integrates heterogeneous knowledge sources. Here, we propose a framework that systematically combines knowledge extracted from computational material datasets with domain knowledge distilled from scientific literature using large language models (LLMs). A central feature of this approach is the explicit consideration of element substitutability, identifying chemically similar elements that can be interchanged to potentially stabilize desired HEAs. Dempster-Shafer theory, a mathematical framework for reasoning under uncertainty, is employed to model and combine substitutabilities based on aggregated evidence from multiple sources. The framework predicts the phase stability of candidate HEA compositions and is systematically evaluated on both quaternary alloy systems, demonstrating superior performance compared to baseline machine learning models and methods reliant on single-source evidence in cross-validation experiments. By leveraging multi-source knowledge, the framework retains robust predictive power even when key elements are absent from the training data, underscoring its potential for knowledge transfer and extrapolation. Furthermore, the enhanced interpretability of the methodology offers insights into the fundamental factors governing HEA formation. Overall, this work provides a promising strategy for accelerating HEA discovery by integrating computational and textual knowledge sources, enabling efficient exploration of vast compositional spaces with improved generalization and interpretability.

The advent of material databases provides an unprecedented opportunity to uncover predictive descriptors for emergent material properties from vast data space. However, common reliance on high-throughput ab initio data necessarily inherits limitations of such data: mismatch with experiments. On the other hand, experimental decisions are often guided by an expert's intuition honed from experiences that are rarely articulated. We propose using machine learning to "bottle" such operational intuition into quantifiable descriptors using expertly curated measurement-based data. We introduce "Materials Expert-Artificial Intelligence" (ME-AI) to encapsulate and articulate this human intuition. As a first step towards such a program, we focus on the topological semimetal (TSM) among square-net materials as the property inspired by the expert-identified descriptor based on structural information: the tolerance factor. We start by curating a dataset encompassing 12 primary features of 879 square-net materials, using experimental data whenever possible. We then use Dirichlet-based Gaussian process regression using a specialized kernel to reveal composite descriptors for square-net topological semimetals. The ME-AI learned descriptors independently reproduce expert intuition and expand upon it. Specifically, new descriptors point to hypervalency as a critical chemical feature predicting TSM within square-net compounds. Our success with a carefully defined problem points to the "machine bottling human insight" approach as promising for machine learning-aided material discovery.

This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of subsets and the logic of partitions since subsets and partitions are category-theoretic dual concepts. In more basic terms, it starts with the duality between the elements (Its) of subsets and the distinctions (Dits, i.e., ordered pairs of elements in different blocks) of a partition. Mathematically, the Its & Dits duality is fully developed in category theory as the reverse-the-arrows duality. The quantitative versions of subsets and partitions are developed as probability theory and information theory (based on logical entropy). Classical physics was based on a view of reality as definite all the way down. In contrast, quantum physics embodies (objective) indefiniteness. And finally, there are the two fundamental dual mechanisms at work in biology, the selectionist mechanism and the generative mechanism, two mechanisms that embody the fundamental duality.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

In this work, we explore two classes of density dependent relativistic mean-field models, their predictions of proton fractions at high densities and neutron star structure. We have used a metamodelling approach to these relativistic density functionals. We have generated a large ensemble of models with these classes and then applied constraints from theoretical and experimental nuclear physics and astrophysical observations. We find that both models produce similar equations of state and neutron star mass-radius sequences. But, their underlying compositions, denoted by the proton fraction in this case, are vastly different. This reinstates previous findings that information on composition gets masqueraded in beta-equilibrium. Additional observations of non-equilibrium phenomena are necessary to pin it down.

A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the clusters. It is shown that thermal diffusion emerges in the collective description as a significant factor even if it is negligible when transport of the original molecular species is considered. Analytical expressions for the effective diffusion and thermal diffusion coefficients at temperature, pressure, and chemical composition gradients have been derived. The theory has been applied to a technology of H2S conversion in a centrifugal plasma-chemical reactor and has made it possible to account for sulfur clusters in numerical process modeling.

The origin of a chemical reaction between two reactant atoms is associated to the activation energy, with the assumption that, high-energy collisions between these atoms, are the ones that overcome the activation energy. Here, we (i) show that a stronger attractive van der Waals (vdW) and electron-ion Coulomb interactions between two polarized atoms are responsible to initiate a chemical reaction, either before or after the collision. We derive this stronger vdW attraction formula exactly using the quasi one-dimensional Drude model within the ionization energy theory and the energy-level spacing renormalization group method. Along the way, we (ii) expose the precise physical mechanism responsible for the existence of a stronger vdW interaction for both long and short distances, and also show how to technically avoid the electron-electron Coulomb repulsion between polarized electrons from these two reactant atoms. Finally, we properly and correctly associate the existence of this stronger attraction to Ramachandran's 'normal limits' (distance shorter than what is allowed by the standard vdW bond) between chemically nonbonded atoms.

Mott insulators with large and active (or multiflavor) local Hilbert spaces widely occur in quantum materials and ultracold atomic systems, and are dubbed "multiflavor Mott insulators". For these multiflavored Mott insulating materials, the spin-only description with the quadratic spin interactions is often insufficient to capture the major physical processes. In the situation with active orbitals, the Kugel-Khomskii superexchange model was then proposed. We briefly review this historical model and discuss the modern developments beyond the original spin-orbital context. These include and are not restricted to the 4d/5d transition metal compounds with the spin-orbit-entangled J=3/2 quadruplets, the rare-earth magnets with two weakly-separated crystal field doublets, breathing magnets and/or the cluster and molecular magnets, et al. We explain the microscopic origin of the emergent Kugel-Khomskii physics in each realization with some emphasis on the J=3/2 quadruplets, and refer the candidate multiflavor Mott insulators as "J=3/2 Mott insulators". For the ultracold atoms, we review the multiflavor Mott insulator realization with the ultracold alkaline and alkaline-earth atoms on the optical lattices. Despite a large local Hilbert space from the atomic hyperfine spin states, the system could naturally realize a large symmetry group such as the Sp(N) and SU(N) symmetries. These ultracold atomic systems lie in the large-N regime of these symmetry groups and are characterized by strong quantum fluctuations. The Kugel-Khomskii physics and the exotic quantum ground states with the "baryon-like" physics can appear in various limits. We conclude with our vision and outlook on this subject.

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the kappa=pm1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10^{-8} Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schr\"odinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood as key operational resources for quantum computation, communication, and simulation. Although traditionally investigated in distinct settings, recent theoretical and experimental advances have revealed deep conceptual, mathematical, and operational connections between them. This review presents a unified perspective on these developments based on sheaf-theoretic and graph-theoretic frameworks, which provide theory-independent characterizations of statistical correlations. These approaches clarify the structural relationship between contextuality and nonlocality, facilitate the formulation of experimentally testable inequalities, and guide implementations in realistic physical platforms, with particular emphasis on photonic systems. By bridging abstract theoretical structures and concrete experimental realizations, this review sheds light on the nonclassical foundations of quantum correlations and their emerging role in quantum technologies.

Metallic alloys often form phases - known as solid solutions - in which chemical elements are spread out on the same crystal lattice in an almost random manner. The tendency of certain chemical motifs to be more common than others is known as chemical short-range order (SRO) and it has received substantial consideration in alloys with multiple chemical elements present in large concentrations due to their extreme configurational complexity (e.g., high-entropy alloys). Short-range order renders solid solutions "slightly less random than completely random", which is a physically intuitive picture, but not easily quantifiable due to the sheer number of possible chemical motifs and their subtle spatial distribution on the lattice. Here we present a multiscale method to predict and quantify the SRO state of an alloy with atomic resolution, incorporating machine learning techniques to bridge the gap between electronic-structure calculations and the characteristic length scale of SRO. The result is an approach capable of predicting SRO length scale in agreement with experimental measurements while comprehensively correlating SRO with fundamental quantities such as local lattice distortions. This work advances the quantitative understanding of solid-solution phases, paving the way for SRO rigorous incorporation into predictive mechanical and thermodynamic models.

Machine learning-based interatomic potentials and force fields depend critically on accurate atomic structures, yet such data are scarce due to the limited availability of experimentally resolved crystals. Although atomic-resolution electron microscopy offers a potential source of structural data, converting these images into simulation-ready formats remains labor-intensive and error-prone, creating a bottleneck for model training and validation. We introduce AutoMat, an end-to-end, agent-assisted pipeline that automatically transforms scanning transmission electron microscopy (STEM) images into atomic crystal structures and predicts their physical properties. AutoMat combines pattern-adaptive denoising, physics-guided template retrieval, symmetry-aware atomic reconstruction, fast relaxation and property prediction via MatterSim, and coordinated orchestration across all stages. We propose the first dedicated STEM2Mat-Bench for this task and evaluate performance using lattice RMSD, formation energy MAE, and structure-matching success rate. By orchestrating external tool calls, AutoMat enables a text-only LLM to outperform vision-language models in this domain, achieving closed-loop reasoning throughout the pipeline. In large-scale experiments over 450 structure samples, AutoMat substantially outperforms existing multimodal large language models and tools. These results validate both AutoMat and STEM2Mat-Bench, marking a key step toward bridging microscopy and atomistic simulation in materials science.The code and dataset are publicly available at https://github.com/yyt-2378/AutoMat and https://huggingface.co/datasets/yaotianvector/STEM2Mat.

Recent advances in diffusion models have shown remarkable potential in the conditional generation of novel molecules. These models can be guided in two ways: (i) explicitly, through additional features representing the condition, or (ii) implicitly, using a property predictor. However, training property predictors or conditional diffusion models requires an abundance of labeled data and is inherently challenging in real-world applications. We propose a novel approach that attenuates the limitations of acquiring large labeled datasets by leveraging domain knowledge from quantum chemistry as a non-differentiable oracle to guide an unconditional diffusion model. Instead of relying on neural networks, the oracle provides accurate guidance in the form of estimated gradients, allowing the diffusion process to sample from a conditional distribution specified by quantum chemistry. We show that this results in more precise conditional generation of novel and stable molecular structures. Our experiments demonstrate that our method: (1) significantly reduces atomic forces, enhancing the validity of generated molecules when used for stability optimization; (2) is compatible with both explicit and implicit guidance in diffusion models, enabling joint optimization of molecular properties and stability; and (3) generalizes effectively to molecular optimization tasks beyond stability optimization.

Powder X-ray diffraction (XRD) is a foundational technique for characterizing crystalline materials. However, the reliable interpretation of XRD patterns, particularly in multiphase systems, remains a manual and expertise-demanding task. As a characterization method that only provides structural information, multiple reference phases can often be fit to a single pattern, leading to potential misinterpretation when alternative solutions are overlooked. To ease humans' efforts and address the challenge, we introduce Dara (Data-driven Automated Rietveld Analysis), a framework designed to automate the robust identification and refinement of multiple phases from powder XRD data. Dara performs an exhaustive tree search over all plausible phase combinations within a given chemical space and validates each hypothesis using a robust Rietveld refinement routine (BGMN). Key features include structural database filtering, automatic clustering of isostructural phases during tree expansion, peak-matching-based scoring to identify promising phases for refinement. When ambiguity exists, Dara generates multiple hypothesis which can then be decided between by human experts or with further characteriztion tools. By enhancing the reliability and accuracy of phase identification, Dara enables scalable analysis of realistic complex XRD patterns and provides a foundation for integration into multimodal characterization workflows, moving toward fully self-driving materials discovery.

Large Language Models (LLMs) have recently demonstrated strong capabilities in translating natural language into database queries, especially when dealing with complex graph-structured data. However, real-world queries often contain inherent ambiguities, and the interconnected nature of graph structures can amplify these challenges, leading to unintended or incorrect query results. To systematically evaluate LLMs on this front, we propose a taxonomy of graph-query ambiguities, comprising three primary types: Attribute Ambiguity, Relationship Ambiguity, and Attribute-Relationship Ambiguity, each subdivided into Same-Entity and Cross-Entity scenarios. We introduce AmbiGraph-Eval, a novel benchmark of real-world ambiguous queries paired with expert-verified graph query answers. Evaluating 9 representative LLMs shows that even top models struggle with ambiguous graph queries. Our findings reveal a critical gap in ambiguity handling and motivate future work on specialized resolution techniques.

Building generalist models has recently demonstrated remarkable capabilities in diverse scientific domains. Within the realm of molecular learning, several studies have explored unifying diverse tasks across diverse domains. However, negative conflicts and interference between molecules and knowledge from different domain may have a worse impact in threefold. First, conflicting molecular representations can lead to optimization difficulties for the models. Second, mixing and scaling up training data across diverse tasks is inherently challenging. Third, the computational cost of refined pretraining is prohibitively high. To address these limitations, this paper presents Omni-Mol, a scalable and unified LLM-based framework for direct instruction tuning. Omni-Mol builds on three key components to tackles conflicts: (1) a unified encoding mechanism for any task input; (2) an active-learning-driven data selection strategy that significantly reduces dataset size; (3) a novel design of the adaptive gradient stabilization module and anchor-and-reconcile MoE framework that ensures stable convergence. Experimentally, Omni-Mol achieves state-of-the-art performance across 15 molecular tasks, demonstrates the presence of scaling laws in the molecular domain, and is supported by extensive ablation studies and analyses validating the effectiveness of its design. The code and weights of the powerful AI-driven chemistry generalist are open-sourced at: https://anonymous.4open.science/r/Omni-Mol-8EDB.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

Scale variation is a fundamental challenge in computer vision. Objects of the same class can have different sizes, and their perceived size is further affected by the distance from the camera. These variations are local to the objects, i.e., different object sizes may change differently within the same image. To effectively handle scale variations, we present a deep equilibrium canonicalizer (DEC) to improve the local scale equivariance of a model. DEC can be easily incorporated into existing network architectures and can be adapted to a pre-trained model. Notably, we show that on the competitive ImageNet benchmark, DEC improves both model performance and local scale consistency across four popular pre-trained deep-nets, e.g., ViT, DeiT, Swin, and BEiT. Our code is available at https://github.com/ashiq24/local-scale-equivariance.

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term "explanation" in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors' claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label "understandable AI" to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following Kuorikoski & Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent's success in using the system, in drawing correct inferences from it.

Ultracold gases of highly magnetic lanthanide atoms have enabled the realisation of dipolar quantum droplets and supersolids. However, future studies could be limited by the achievable atom numbers and hindered by high three-body loss rates. Here we study density-dependent atom loss in an ultracold gas of {}^{166}Er for magnetic fields below 4 G, identifying six previously unreported, strongly temperature-dependent features. We find that their positions and widths show a linear temperature dependence up to at least 15,muK. In addition, we observe a weak, polarisation-dependent shift of the loss features with the intensity of the light used to optically trap the atoms. This detailed knowledge of the loss landscape allows us to optimise the production of dipolar BECs with more than 2 times 10^5 atoms and points towards optimal strategies for the study of large-atom-number dipolar gases in the droplet and supersolid regimes.

In interactions between users and language model agents, user utterances frequently exhibit ellipsis (omission of words or phrases) or imprecision (lack of exactness) to prioritize efficiency. This can lead to varying interpretations of the same input based on different assumptions or background knowledge. It is thus crucial for agents to adeptly handle the inherent ambiguity in queries to ensure reliability. However, even state-of-the-art large language models (LLMs) still face challenges in such scenarios, primarily due to the following hurdles: (1) LLMs are not explicitly trained to deal with ambiguous utterances; (2) the degree of ambiguity perceived by the LLMs may vary depending on the possessed knowledge. To address these issues, we propose Alignment with Perceived Ambiguity (APA), a novel pipeline that aligns LLMs to manage ambiguous queries by leveraging their own assessment of ambiguity (i.e., perceived ambiguity). Experimental results on question-answering datasets demonstrate that APA empowers LLMs to explicitly detect and manage ambiguous queries while retaining the ability to answer clear questions. Furthermore, our finding proves that APA excels beyond training with gold-standard labels, especially in out-of-distribution scenarios.

Accurate and scalable machine-learned inter-atomic potentials (MLIPs) are essential for molecular simulations ranging from drug discovery to new material design. Current state-of-the-art models enforce roto-translational symmetries through equivariant neural network architectures, a hard-wired inductive bias that can often lead to reduced flexibility, computational efficiency, and scalability. In this work, we introduce TransIP: Transformer-based Inter-Atomic Potentials, a novel training paradigm for interatomic potentials achieving symmetry compliance without explicit architectural constraints. Our approach guides a generic non-equivariant Transformer-based model to learn SO(3)-equivariance by optimizing its representations in the embedding space. Trained on the recent Open Molecules (OMol25) collection, a large and diverse molecular dataset built specifically for MLIPs and covering different types of molecules (including small organics, biomolecular fragments, and electrolyte-like species), TransIP attains comparable performance in machine-learning force fields versus state-of-the-art equivariant baselines. Further, compared to a data augmentation baseline, TransIP achieves 40% to 60% improvement in performance across varying OMol25 dataset sizes. More broadly, our work shows that learned equivariance can be a powerful and efficient alternative to equivariant or augmentation-based MLIP models.

Diffusion models are the standard toolkit for generative modelling of 3D atomic systems. However, for different types of atomic systems - such as molecules and materials - the generative processes are usually highly specific to the target system despite the underlying physics being the same. We introduce the All-atom Diffusion Transformer (ADiT), a unified latent diffusion framework for jointly generating both periodic materials and non-periodic molecular systems using the same model: (1) An autoencoder maps a unified, all-atom representations of molecules and materials to a shared latent embedding space; and (2) A diffusion model is trained to generate new latent embeddings that the autoencoder can decode to sample new molecules or materials. Experiments on QM9 and MP20 datasets demonstrate that jointly trained ADiT generates realistic and valid molecules as well as materials, exceeding state-of-the-art results from molecule and crystal-specific models. ADiT uses standard Transformers for both the autoencoder and diffusion model, resulting in significant speedups during training and inference compared to equivariant diffusion models. Scaling ADiT up to half a billion parameters predictably improves performance, representing a step towards broadly generalizable foundation models for generative chemistry. Open source code: https://github.com/facebookresearch/all-atom-diffusion-transformer

Crystalline materials are a fundamental component in next-generation technologies, yet modeling their distribution presents unique computational challenges. Of the plausible arrangements of atoms in a periodic lattice only a vanishingly small percentage are thermodynamically stable, which is a key indicator of the materials that can be experimentally realized. Two fundamental tasks in this area are to (a) predict the stable crystal structure of a known composition of elements and (b) propose novel compositions along with their stable structures. We present FlowMM, a pair of generative models that achieve state-of-the-art performance on both tasks while being more efficient and more flexible than competing methods. We generalize Riemannian Flow Matching to suit the symmetries inherent to crystals: translation, rotation, permutation, and periodic boundary conditions. Our framework enables the freedom to choose the flow base distributions, drastically simplifying the problem of learning crystal structures compared with diffusion models. In addition to standard benchmarks, we validate FlowMM's generated structures with quantum chemistry calculations, demonstrating that it is about 3x more efficient, in terms of integration steps, at finding stable materials compared to previous open methods.

We combine a regularized variant of the strongly constrained and appropriately normed semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] with the latest generation semi-classical London dispersion correction. The resulting density functional approximation r2SCAN-D4 has the speed of generalized gradient approximations while approaching the accuracy of hybrid functionals for general chemical applications. We demonstrate its numerical robustness in real-life settings and benchmark molecular geometries, general main group and organo-metallic thermochemistry, as well as non-covalent interactions in supramolecular complexes and molecular crystals. Main group and transition metal bond lengths have errors of just 0.8%, which is competitive with hybrid functionals for main group molecules and outperforms them for transition metal complexes. The weighted mean absolute deviation (WTMAD2) on the large GMTKN55 database of chemical properties is exceptionally small at 7.5 kcal/mol. This also holds for metal organic reactions with an MAD of 3.3 kcal/mol. The versatile applicability to organic and metal-organic systems transfers to condensed systems, where lattice energies of molecular crystals are within chemical accuracy (errors <1 kcal/mol).

Solar photospheric abundances and CI-chondrite compositions are reviewed and updated to obtain representative solar system abundances of the elements and their isotopes. The new photospheric abundances obtained here lead to higher solar metallicity. Full 3D NLTE photospheric analyses are only available for 11 elements. A quality index for analyses is introduced. For several elements, uncertainties remain large. Protosolar mass fractions are H (X = 0.7060), He (Y = 0.2753), and for metals Li to U (Z = 0.0187). The protosolar (C+N)/H agrees within 13% with the ratio for the solar core from the Borexino experiment. Elemental abundances in CI-chondrites were screened by analytical methods, sample sizes, and evaluated using concentration frequency distributions. Aqueously mobile elements (e.g., alkalis, alkaline earths, etc.) often deviate from normal distributions indicating mobilization and/or sequestration into carbonates, phosphates, and sulfates. Revised CI-chondrite abundances of non-volatile elements are similar to earlier estimates. The moderately volatile elements F and Sb are higher than before, as are C, Br and I, whereas the CI-abundances of Hg and N are now significantly lower. The solar system nuclide distribution curves of s-process elements agree within 4% with s-process predictions of Galactic chemical evolution models. P-process nuclide distributions are assessed. No obvious correlation of CI-chondritic to solar elemental abundance ratios with condensation temperatures is observed, nor is there one for ratios of CI-chondrites/solar wind abundances.

The study demonstrates the capabilities of a vector-based approach for calculating stoichiometric coefficients in chemical equations, using black powder as an illustrative example. A method is proposed for selecting and constraining intermediate interactions between reactants, as well as for identifying final products. It is shown that even a small number of components can lead to a large number of final and intermediate products. Through concrete calculations, a correlation is established between the number of possible chemical equations and the number of reactants. A methodology is proposed for computing all possible chemical equations within a reaction system for arbitrary component ratios, enabling the derivation of all feasible chemical reactions. Additionally, a method is developed for calculating the chemical composition for a fixed set of reactants, allowing for the evaluation of the set of products resulting from all possible chemical interactions given a specified initial composition.

We propose a new score-based approach to generate 3D molecules represented as atomic densities on regular grids. First, we train a denoising neural network that learns to map from a smooth distribution of noisy molecules to the distribution of real molecules. Then, we follow the neural empirical Bayes framework [Saremi and Hyvarinen, 2019] and generate molecules in two steps: (i) sample noisy density grids from a smooth distribution via underdamped Langevin Markov chain Monte Carlo, and (ii) recover the ``clean'' molecule by denoising the noisy grid with a single step. Our method, VoxMol, generates molecules in a fundamentally different way than the current state of the art (i.e., diffusion models applied to atom point clouds). It differs in terms of the data representation, the noise model, the network architecture and the generative modeling algorithm. VoxMol achieves comparable results to state of the art on unconditional 3D molecule generation while being simpler to train and faster to generate molecules.

We propose a formal reconstruction of quantum mechanics grounded not in external mathematical abstractions, but in the structured dynamics of subjective experience. The Qualia Abstraction Language (QAL) models physical systems as evolving streams of introspective units, structured sequences of modality, shape, and functional effect, rather than as state vectors in Hilbert space. This approach reimagines core quantum concepts: superposition becomes a form of structured ambiguity; collapse is reframed as an introspective contraction; and entanglement is modeled as semantic resonance across streams of qualia. Drawing on insights from nominalist philosophy and oversight theoretic limits in AI, we argue that the observer paradox in quantum mechanics reflects not an ontological lacuna, but a linguistic one: the absence of a formal vocabulary for modeling first person structure. QAL introduces such a vocabulary, providing a morphodynamic framework that embeds the observer within the system and replaces abstract projection with endogenous transformation. We analyze the alignment of QAL with endophysical approaches, contrast it with standard interpretations of quantum theory, and explore its implications for a post Platonist, introspectively grounded physics.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wavefunction. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.

Ambiguous words or underspecified references require interlocutors to resolve them, often by relying on shared context and commonsense knowledge. Therefore, we systematically investigate whether Large Language Models (LLMs) can leverage commonsense to resolve referential ambiguity in multi-turn conversations and analyze their behavior when ambiguity persists. Further, we study how requests for simplified language affect this capacity. Using a novel multilingual evaluation dataset, we test DeepSeek v3, GPT-4o, Qwen3-32B, GPT-4o-mini, and Llama-3.1-8B via LLM-as-Judge and human annotations. Our findings indicate that current LLMs struggle to resolve ambiguity effectively: they tend to commit to a single interpretation or cover all possible references, rather than hedging or seeking clarification. This limitation becomes more pronounced under simplification prompts, which drastically reduce the use of commonsense reasoning and diverse response strategies. Fine-tuning Llama-3.1-8B with Direct Preference Optimization substantially improves ambiguity resolution across all request types. These results underscore the need for advanced fine-tuning to improve LLMs' handling of ambiguity and to ensure robust performance across diverse communication styles.

Generative models for structure-based drug design are often limited to a specific modality, restricting their broader applicability. To address this challenge, we introduce FuncBind, a framework based on computer vision to generate target-conditioned, all-atom molecules across atomic systems. FuncBind uses neural fields to represent molecules as continuous atomic densities and employs score-based generative models with modern architectures adapted from the computer vision literature. This modality-agnostic representation allows a single unified model to be trained on diverse atomic systems, from small to large molecules, and handle variable atom/residue counts, including non-canonical amino acids. FuncBind achieves competitive in silico performance in generating small molecules, macrocyclic peptides, and antibody complementarity-determining region loops, conditioned on target structures. FuncBind also generated in vitro novel antibody binders via de novo redesign of the complementarity-determining region H3 loop of two chosen co-crystal structures. As a final contribution, we introduce a new dataset and benchmark for structure-conditioned macrocyclic peptide generation. The code is available at https://github.com/prescient-design/funcbind.

Ambiguous questions are a challenge for Question Answering models, as they require answers that cover multiple interpretations of the original query. To this end, these models are required to generate long-form answers that often combine conflicting pieces of information. Although recent advances in the field have shown strong capabilities in generating fluent responses, certain research questions remain unanswered. Does model/data scaling improve the answers' quality? Do automated metrics align with human judgment? To what extent do these models ground their answers in evidence? In this study, we aim to thoroughly investigate these aspects, and provide valuable insights into the limitations of the current approaches. To aid in reproducibility and further extension of our work, we open-source our code at https://github.com/din0s/ambig_lfqa.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with DFT calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set of new efficient and powerful SO(2)-equivariant operations and performing all off-diagonal feature updates and message passing within SO(2) local frames, thereby eliminating the need of SO(3) tensor products. Moreover, a continuous SO(2) tensor product is performed within the SO(2) local frame at each node to fuse node features, mimicking the symmetric contraction operation. Extensive experiments on the large QH9 and MD17 datasets demonstrate that our model achieves superior performance across a wide range of molecular structures and trajectories, highlighting its strong generalization capability. The proposed SO(2) operations on SO(2) local frames offer a promising direction for scalable and symmetry-aware learning of electronic structures. Our code will be released as part of the AIRS library https://github.com/divelab/AIRS.

Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed recently for predicting the limited number of features for these states, or estimating the expectation values of operators, without the need for full state reconstruction. These ideas go under the general name of shadow tomography. Here we provide an experimental demonstration of property estimation based on classical shadows proposed in [H.-Y. Huang, R. Kueng, J. Preskill. Nat. Phys. https://doi.org/10.1038/s41567-020-0932-7 (2020)] and study its performance in the quantum optical experiment with high-dimensional spatial states of photons. We show on experimental data how this procedure outperforms conventional state reconstruction in fidelity estimation from a limited number of measurements.

The discovery of novel materials and functional molecules can help to solve some of society's most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering -- generally denoted as inverse design -- was based massively on human intuition and high-throughput virtual screening. The last few years have seen the emergence of significant interest in computer-inspired designs based on evolutionary or deep learning methods. The major challenge here is that the standard strings molecular representation SMILES shows substantial weaknesses in that task because large fractions of strings do not correspond to valid molecules. Here, we solve this problem at a fundamental level and introduce SELFIES (SELF-referencIng Embedded Strings), a string-based representation of molecules which is 100\% robust. Every SELFIES string corresponds to a valid molecule, and SELFIES can represent every molecule. SELFIES can be directly applied in arbitrary machine learning models without the adaptation of the models; each of the generated molecule candidates is valid. In our experiments, the model's internal memory stores two orders of magnitude more diverse molecules than a similar test with SMILES. Furthermore, as all molecules are valid, it allows for explanation and interpretation of the internal working of the generative models.

Orbital-free density functional theory (OF-DFT) holds the promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of the electron density only. We here set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU; and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of the nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths; and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.

Isotopic substitution in molecular systems can affect fundamental molecular properties including the energy position and spacing of electronic, vibrational and rotational levels, thus modifying the dynamics associated to their coherent superposition. In extreme ultraviolet spectroscopy, the photoelectron leaving the molecule after the absorption of a single photon can trigger an ultrafast nuclear motion in the cation, which can lead, eventually, to molecular fragmentation. This dynamics depends on the mass of the constituents of the cation, thus showing, in general, a significant isotopic dependence. In time-resolved attosecond photoelectron interferometry, the absorption of the extreme ultraviolet photon is accompanied by the exchange of an additional quantum of energy (typically in the infrared spectral range) with the photoelectron-photoion system, offering the opportunity to investigate in time the influence of isotopic substitution on the characteristics of the photoionisation dynamics. Here we show that attosecond photoelectron interferometry is sensitive to isotopic substitution by investigating the two-color photoionisation spectra measured in a mixture of methane (CH_4) and deuteromethane (CD_4). The isotopic dependence manifests itself in the modification of the amplitude and contrast of the oscillations of the photoelectron peaks generated in the two-color field with the two isotopologues. The observed effects are interpreted considering the differences in the time evolution of the nuclear autocorrelation functions in the two molecules.

3D molecule generation is crucial for drug discovery and material science, requiring models to process complex multi-modalities, including atom types, chemical bonds, and 3D coordinates. A key challenge is integrating these modalities of different shapes while maintaining SE(3) equivariance for 3D coordinates. To achieve this, existing approaches typically maintain separate latent spaces for invariant and equivariant modalities, reducing efficiency in both training and sampling. In this work, we propose Unified Variational Auto-Encoder for 3D Molecular Latent Diffusion Modeling (UAE-3D), a multi-modal VAE that compresses 3D molecules into latent sequences from a unified latent space, while maintaining near-zero reconstruction error. This unified latent space eliminates the complexities of handling multi-modality and equivariance when performing latent diffusion modeling. We demonstrate this by employing the Diffusion Transformer--a general-purpose diffusion model without any molecular inductive bias--for latent generation. Extensive experiments on GEOM-Drugs and QM9 datasets demonstrate that our method significantly establishes new benchmarks in both de novo and conditional 3D molecule generation, achieving leading efficiency and quality.

This article presents a review about the main CERN n\_TOF contributions to the field of neutron-capture experiments of interest for s-process nucleosynthesis studies over the last 25 years, with special focus on the measurement of radioactive isotopes. A few recent capture experiments on stable isotopes of astrophysical interest are also discussed. Results on s-process branching nuclei are appropriate to illustrate how advances in detection systems and upgrades in the facility have enabled increasingly challenging experiments and, as a consequence, have led to a better understanding and modeling of the s-process mechanism of nucleosynthesis. New endeavors combining radioactive-ion beams from ISOLDE for the production of radioisotopically pure samples for activation experiments at the new NEAR facility at n\_TOF are briefly discussed. On the basis of these new exciting results, also current limitations of state-of-the-art TOF and activation techniques will be depicted, thereby showing the pressing need for further upgrades and enhancements on both facilities and detection systems. A brief account of the potential technique based on inverse kinematics for direct neutron-capture measurements is also presented.

We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are evaluated by elementary techniques, and connections with the Schr\"{o}dinger and Dirac equations are established. Historical developments and key transitions from classical to quantum theory are discussed to clarify the structure and significance of the old quantum mechanics.

Recent advances in Large Language Models (LLMs) and Reinforcement Learning (RL) have led to strong performance in open-domain question answering (QA). However, existing models still struggle with questions that admit multiple valid answers. Standard QA benchmarks, which typically assume a single gold answer, overlook this reality and thus produce inappropriate training signals. Existing attempts to handle ambiguity often rely on costly manual annotation, which is difficult to scale to multi-hop datasets such as HotpotQA and MuSiQue. In this paper, we present A^2Search, an annotation-free, end-to-end training framework to recognize and handle ambiguity. At its core is an automated pipeline that detects ambiguous questions and gathers alternative answers via trajectory sampling and evidence verification. The model is then optimized with RL using a carefully designed AnsF1 reward, which naturally accommodates multiple answers. Experiments on eight open-domain QA benchmarks demonstrate that A^2Search achieves new state-of-the-art performance. With only a single rollout, A^2Search-7B yields an average AnsF1@1 score of 48.4% across four multi-hop benchmarks, outperforming all strong baselines, including the substantially larger ReSearch-32B (46.2%). Extensive analyses further show that A^2Search resolves ambiguity and generalizes across benchmarks, highlighting that embracing ambiguity is essential for building more reliable QA systems. Our code, data, and model weights can be found at https://github.com/zfj1998/A2Search

HeH^+ was the first heteronuclear molecule to form in the metal-free Universe after the Big Bang. The molecule gained significant attention following its first circumstellar detection in the young and dense planetary nebula NGC 7027. We target some hydride ions associated with the noble gases (HeH^+, ArH^+, and NeH^+) to investigate their formation in harsh environments like the nova outburst region. We use a photoionization modeling (based on previously published best-fit physical parameters) of the moderately fast ONe type nova, QU Vulpeculae 1984, and the CO type novae, RS Ophiuchi and V1716 Scorpii. Our steady-state modeling reveals a convincing amount of HeH^+, especially in the dense clump of RS Ophiuchi and V1716 Scorpii. The calculated upper limit on the surface brightness of HeH^+ transitions suggests that the James Webb Space Telescope (JWST) could detect some of them, particularly in sources like RS Ophiuchi and V1716 Scorpii, which have similar physical and chemical conditions and evolution. It must be clearly noted that the sources studied are used as templates, and not as targets for observations. The detection of these lines could be useful for determining the physical conditions in similar types of systems and for validating our predictions based on new electron-impact ro-vibrational collisional data at temperatures of up to 20,000 K.

Diffusion large language models (dLLMs) represent a significant advancement in text generation, offering parallel token decoding capabilities. However, existing open-source implementations suffer from quality-speed trade-offs that impede their practical deployment. Conservative sampling strategies typically decode only the most confident token per step to ensure quality (i.e., greedy decoding), at the cost of inference efficiency due to repeated redundant refinement iterations--a phenomenon we term delayed decoding. Through systematic analysis of dLLM decoding dynamics, we characterize this delayed decoding behavior and propose a training-free adaptive parallel decoding strategy, named LocalLeap, to address these inefficiencies. LocalLeap is built on two fundamental empirical principles: local determinism propagation centered on high-confidence anchors and progressive spatial consistency decay. By applying these principles, LocalLeap identifies anchors and performs localized relaxed parallel decoding within bounded neighborhoods, achieving substantial inference step reduction through early commitment of already-determined tokens without compromising output quality. Comprehensive evaluation on various benchmarks demonstrates that LocalLeap achieves 6.94times throughput improvements and reduces decoding steps to just 14.2\% of the original requirement, achieving these gains with negligible performance impact. The source codes are available at: https://github.com/friedrichor/LocalLeap.

Identifying the chemical structure from a graphical representation, or image, of a molecule is a challenging pattern recognition task that would greatly benefit drug development. Yet, existing methods for chemical structure recognition do not typically generalize well, and show diminished effectiveness when confronted with domains where data is sparse, or costly to generate, such as hand-drawn molecule images. To address this limitation, we propose a new chemical structure recognition tool that delivers state-of-the-art performance and can adapt to new domains with a limited number of data samples and supervision. Unlike previous approaches, our method provides atom-level localization, and can therefore segment the image into the different atoms and bonds. Our model is the first model to perform OCSR with atom-level entity detection with only SMILES supervision. Through rigorous and extensive benchmarking, we demonstrate the preeminence of our chemical structure recognition approach in terms of data efficiency, accuracy, and atom-level entity prediction.

This paper explores the intersection of identity, individuality, and reality through competing frameworks, including classical metaphysics, quantum mechanics, and computational theories. Traditional metaphysical notions of fixed identity are challenged by advancements in cloning, teletransportation, and digital replication, which reveal the fluid and relational nature of individuality. Quantum mechanics further complicates these notions, emphasizing the indistinguishability and contextuality of fundamental particles. Computational approaches, such as the Ruliad and Constructor Theory, offer expansive views of emergent realities but often lack practical constraints for observer relevance. Algorithmic idealism is introduced as a unifying framework, proposing that reality is an emergent construct governed by computational rules prioritizing coherence, sufficiency, and observer-dependent experiences. By redefining identity as an informational construct and reality as a process shaped by algorithmic transitions, algorithmic idealism resolves foundational paradoxes and offers a superior lens for understanding existence in an increasingly digital and interconnected world. The framework bridges gaps between competing theories, providing a coherent and pragmatic model for addressing ethical, metaphysical, and technological challenges.

Obtaining the desired effect of drugs is highly dependent on their molecular geometries. Thus, the current prevailing paradigm focuses on 3D point-cloud atom representations, utilizing graph neural network (GNN) parametrizations, with rotational symmetries baked in via E(3) invariant layers. We prove that such models must necessarily disregard chirality, a geometric property of the molecules that cannot be superimposed on their mirror image by rotation and translation. Chirality plays a key role in determining drug safety and potency. To address this glaring issue, we introduce a novel field-based representation, proposing reference rotations that replace rotational symmetry constraints. The proposed model captures all molecular geometries including chirality, while still achieving highly competitive performance with E(3)-based methods across standard benchmarking metrics.

An amplitude analysis of B^-rightarrow D^- D^0 K_S^0 decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 9,fb^{-1}, collected with the LHCb detector at center-of-mass energies of 7, 8, and 13,Tekern -0.1em V. A resonant structure of spin-parity 0^+ is observed in the D^0 K_S^0 invariant-mass spectrum with a significance of 5.3,sigma. The mass and width of the state, modeled with a Breit-Wigner lineshape, are determined to be 2883pm11pm6,Mekern -0.1em V!/c^2 and 87_{-47}^{+22}pm6,Mekern -0.1em V respectively, where the first uncertainties are statistical and the second systematic. These properties and the quark content are consistent with those of the open-charm tetraquark state T_{cs 0}^{*}(2870)^0 observed previously in the D^+ K^- final state of the B^-rightarrow D^- D^+ K^- decay. This result confirms the existence of the T_{cs 0}^{*}(2870)^0 state in a new decay mode. The T_{cs1}^{*}(2900)^0 state, reported in the B^-rightarrow D^- D^+ K^- decay, is also searched for in the D^0 K_S^0 invariant-mass spectrum of the B^- rightarrow D^- D^0 K_S^0 decay, without finding evidence for it.

Retrieval-augmented language models are being increasingly tasked with subjective, contentious, and conflicting queries such as "is aspartame linked to cancer". To resolve these ambiguous queries, one must search through a large range of websites and consider "which, if any, of this evidence do I find convincing?". In this work, we study how LLMs answer this question. In particular, we construct ConflictingQA, a dataset that pairs controversial queries with a series of real-world evidence documents that contain different facts (e.g., quantitative results), argument styles (e.g., appeals to authority), and answers (Yes or No). We use this dataset to perform sensitivity and counterfactual analyses to explore which text features most affect LLM predictions. Overall, we find that current models rely heavily on the relevance of a website to the query, while largely ignoring stylistic features that humans find important such as whether a text contains scientific references or is written with a neutral tone. Taken together, these results highlight the importance of RAG corpus quality (e.g., the need to filter misinformation), and possibly even a shift in how LLMs are trained to better align with human judgements.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Visual clustering is a common perceptual task in scatterplots that supports diverse analytics tasks (e.g., cluster identification). However, even with the same scatterplot, the ways of perceiving clusters (i.e., conducting visual clustering) can differ due to the differences among individuals and ambiguous cluster boundaries. Although such perceptual variability casts doubt on the reliability of data analysis based on visual clustering, we lack a systematic way to efficiently assess this variability. In this research, we study perceptual variability in conducting visual clustering, which we call Cluster Ambiguity. To this end, we introduce CLAMS, a data-driven visual quality measure for automatically predicting cluster ambiguity in monochrome scatterplots. We first conduct a qualitative study to identify key factors that affect the visual separation of clusters (e.g., proximity or size difference between clusters). Based on study findings, we deploy a regression module that estimates the human-judged separability of two clusters. Then, CLAMS predicts cluster ambiguity by analyzing the aggregated results of all pairwise separability between clusters that are generated by the module. CLAMS outperforms widely-used clustering techniques in predicting ground truth cluster ambiguity. Meanwhile, CLAMS exhibits performance on par with human annotators. We conclude our work by presenting two applications for optimizing and benchmarking data mining techniques using CLAMS. The interactive demo of CLAMS is available at clusterambiguity.dev.

The structure of amorphous materials has been debated since the 1930's as a binary question: amorphous materials are either Zachariasen continuous random networks (Z-CRNs) or Z-CRNs containing crystallites. It was recently demonstrated, however, that amorphous diamond can be synthesized in either form. Here we address the question of the structure of single-atom-thick amorphous monolayers. We reanalyze the results of prior simulations for amorphous graphene and report kinetic Monte Carlo simulations based on alternative algorithms. We find that crystallite-containing Z-CRN is the favored structure of elemental amorphous graphene, as recently fabricated, whereas the most likely structure of binary monolayer amorphous BN is altogether different than either of the two long-debated options: it is a compositionally disordered "pseudo-CRN" comprising a mix of B-N and noncanonical B-B and N-N bonds and containing "pseudocrystallites", namely honeycomb regions made of noncanonical hexagons. Implications for other non-elemental 2D and bulk amorphous materials are discussed.

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fr\"ohlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fr\"ohlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties.

Machine learning potentials (MLPs) have become essential for large-scale atomistic simulations, enabling ab initio-level accuracy with computational efficiency. However, current MLPs struggle with uncertainty quantification, limiting their reliability for active learning, calibration, and out-of-distribution (OOD) detection. We address these challenges by developing Bayesian E(3) equivariant MLPs with iterative restratification of many-body message passing. Our approach introduces the joint energy-force negative log-likelihood (NLL_JEF) loss function, which explicitly models uncertainty in both energies and interatomic forces, yielding superior accuracy compared to conventional NLL losses. We systematically benchmark multiple Bayesian approaches, including deep ensembles with mean-variance estimation, stochastic weight averaging Gaussian, improved variational online Newton, and laplace approximation by evaluating their performance on uncertainty prediction, OOD detection, calibration, and active learning tasks. We further demonstrate that NLL_JEF facilitates efficient active learning by quantifying energy and force uncertainties. Using Bayesian active learning by disagreement (BALD), our framework outperforms random sampling and energy-uncertainty-based sampling. Our results demonstrate that Bayesian MLPs achieve competitive accuracy with state-of-the-art models while enabling uncertainty-guided active learning, OOD detection, and energy/forces calibration. This work establishes Bayesian equivariant neural networks as a powerful framework for developing uncertainty-aware MLPs for atomistic simulations at scale.

Accurate prediction of bond dissociation energies (BDEs) underpins mechanistic insight and the rational design of molecules and materials. We present a systematic, reproducible benchmark comparing quantum and classical machine learning models for BDE prediction using a chemically curated feature set encompassing atomic properties (atomic numbers, hybridization), bond characteristics (bond order, type), and local environmental descriptors. Our quantum framework, implemented in Qiskit Aer on six qubits, employs ZZFeatureMap encodings with variational ansatz (RealAmplitudes) across multiple architectures Variational Quantum Regressors (VQR), Quantum Support Vector Regressors (QSVR), Quantum Neural Networks (QNN), Quantum Convolutional Neural Networks (QCNN), and Quantum Random Forests (QRF). These are rigorously benchmarked against strong classical baselines, including Support Vector Regression (SVR), Random Forests (RF), and Multi-Layer Perceptrons (MLP). Comprehensive evaluation spanning absolute and relative error metrics, threshold accuracies, and error distributions shows that top-performing quantum models (QCNN, QRF) match the predictive accuracy and robustness of classical ensembles and deep networks, particularly within the chemically prevalent mid-range BDE regime. These findings establish a transparent baseline for quantum-enhanced molecular property prediction and outline a practical foundation for advancing quantum computational chemistry toward near chemical accuracy.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 33 percent reduction in both force and energy prediction errors relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.

Astrochemical models of interstellar clouds, the sites of stars, and planet formation require information about spin-state chemistry to allow quantitative comparison with spectroscopic observations. In particular, it is important to know if full scrambling or H abstraction (also known as proton hopping) takes place in ion-neutral reactions. The reaction of Cl+ and HCl+ with H2 and isotopologues has been studied at cryogenic temperatures between 20 and 180 K using a 22 pole radio frequency ion trap. Isotopic exchange processes are used to probe the reaction mechanism of the HCl+ + H2 reaction. The results are compared with previous measurements and theoretical predictions. The rate coefficients for the Cl+ + H2 and HCl+ + H2 reactions are found to be constant in the range of temperatures studied, except for the DCl+ + D2 reaction, where a weak negative temperature dependence is observed, and reactions with D2 are found to be significantly slower than the Langevin rate. No isotopic exchange reactions are observed to occur for the H2Cl+ ion. The analysis of the products of the HCl+ + H2 isotopic system clearly indicates that the reaction proceeds via simple hydrogen atom abstraction.

In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition.

The groundbreaking advance in materials and chemical research has been driven by the development of atomistic simulations. However, the broader applicability of the atomistic simulations remains restricted, as they inherently depend on energy models that are either inaccurate or computationally prohibitive. Machine learning interatomic potentials (MLIPs) have recently emerged as a promising class of energy models, but their deployment remains challenging due to the lack of systematic protocols for generating diverse training data. Here we automate the construction of training datasets to enable the development of general-purpose MLIPs, by introducing GAIA, an end-to-end framework to build a wide range of atomic arrangements. By employing systematic evaluation of metadynamics for effective structural exploration, GAIA overcomes the heuristic nature of conventional dataset generation. Using GAIA, we constructed Titan25, a benchmark-scale dataset, and trained MLIPs that closely match both static and dynamic density functional theory results. The models further reproduce experimental observations across reactive regimes, including detonation, coalescence, and catalytic activity. GAIA narrows the gap between experiment and simulation, and paves the way for the development of universal MLIPs that can reliably describe a wide spectrum of materials and chemical processes.

We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are directly about information, independently of the details of particular physical instantiations, it does not regard information as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. It does not suffer from the circularity at the foundations of existing information theory (namely that information and distinguishability are each defined in terms of the other). It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information).

Although quantum simulation can give insight into elusive or intractable physical phenomena, many quantum simulators are unavoidably limited in the models they mimic. Such is also the case for atom arrays interacting via Rydberg states - a platform potentially capable of simulating any kind of spin exchange model, albeit with currently unattainable experimental capabilities. Here, we propose a new route towards simulating generic spin exchange Hamiltonians in atom arrays, using Floquet engineering with both global and local control. To demonstrate the versatility and applicability of our approach, we numerically investigate the generation of several spin exchange models which have yet to be realized in atom arrays, using only previously-demonstrated experimental capabilities. Our proposed scheme can be readily explored in many existing setups, providing a path to investigate a large class of exotic quantum spin models.

Large language models (LLMs) are prone to hallucinations in question-answering (QA) tasks when faced with ambiguous questions. Users often assume that LLMs share their cognitive alignment, a mutual understanding of context, intent, and implicit details, leading them to omit critical information in the queries. However, LLMs generate responses based on assumptions that can misalign with user intent, which may be perceived as hallucinations if they misalign with the user's intent. Therefore, identifying those implicit assumptions is crucial to resolve ambiguities in QA. Prior work, such as AmbigQA, reduces ambiguity in queries via human-annotated clarifications, which is not feasible in real application. Meanwhile, ASQA compiles AmbigQA's short answers into long-form responses but inherits human biases and fails capture explicit logical distinctions that differentiates the answers. We introduce Conditional Ambiguous Question-Answering (CondAmbigQA), a benchmark with 200 ambiguous queries and condition-aware evaluation metrics. Our study pioneers the concept of ``conditions'' in ambiguous QA tasks, where conditions stand for contextual constraints or assumptions that resolve ambiguities. The retrieval-based annotation strategy uses retrieved Wikipedia fragments to identify possible interpretations for a given query as its conditions and annotate the answers through those conditions. Such a strategy minimizes human bias introduced by different knowledge levels among annotators. By fixing retrieval results, CondAmbigQA evaluates how RAG systems leverage conditions to resolve ambiguities. Experiments show that models considering conditions before answering improve performance by 20%, with an additional 5% gain when conditions are explicitly provided. These results underscore the value of conditional reasoning in QA, offering researchers tools to rigorously evaluate ambiguity resolution.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

Handling ambiguity and underspecification is an important challenge in natural language interfaces, particularly for tasks like text-to-SQL semantic parsing. We propose a modular approach that resolves ambiguity using natural language interpretations before mapping these to logical forms (e.g., SQL queries). Although LLMs excel at parsing unambiguous utterances, they show strong biases for ambiguous ones, typically predicting only preferred interpretations. We constructively exploit this bias to generate an initial set of preferred disambiguations and then apply a specialized infilling model to identify and generate missing interpretations. To train the infilling model, we introduce an annotation method that uses SQL execution to validate different meanings. Our approach improves interpretation coverage and generalizes across datasets with different annotation styles, database structures, and ambiguity types.

Self-supervised learning has recently gained growing interest in molecular modeling for scientific tasks such as AI-assisted drug discovery. Current studies consider leveraging both 2D and 3D molecular structures for representation learning. However, relying on straightforward alignment strategies that treat each modality separately, these methods fail to exploit the intrinsic correlation between 2D and 3D representations that reflect the underlying structural characteristics of molecules, and only perform coarse-grained molecule-level alignment. To derive fine-grained alignment and promote structural molecule understanding, we introduce an atomic-relation level "blend-then-predict" self-supervised learning approach, MoleBLEND, which first blends atom relations represented by different modalities into one unified relation matrix for joint encoding, then recovers modality-specific information for 2D and 3D structures individually. By treating atom relationships as anchors, MoleBLEND organically aligns and integrates visually dissimilar 2D and 3D modalities of the same molecule at fine-grained atomic level, painting a more comprehensive depiction of each molecule. Extensive experiments show that MoleBLEND achieves state-of-the-art performance across major 2D/3D molecular benchmarks. We further provide theoretical insights from the perspective of mutual-information maximization, demonstrating that our method unifies contrastive, generative (cross-modality prediction) and mask-then-predict (single-modality prediction) objectives into one single cohesive framework.

We have conducted an extensive towed-magnetic-sled survey during the period of June 14-28, 2023, over the seafloor about 85 km north of Manus Island, Papua New Guinea, centered around the calculated path of the bolide CNEOS 2014-01-08 (IM1). We found about 850 spherules of diameter 0.1-1.3 millimeters in our samples. The samples were analyzed by micro-XRF, Electron Probe Microanalyzer and ICP Mass spectrometry. Here we report major and trace element compositions of the samples and classify spherules based on that analysis. Spherules comprising 22% of the collection, appear to all reflect planetary igneous differentiation and are all different from previously described spherules. A subset of the differentiated-spherules show an excess of Be, La and U, by up to three orders of magnitude relative to the solar system standard of CI chondrites. Detailed mass spectrometry of 12 of these "BeLaU"-type spherules, the population of which may constitute up to ~10% of our entire collected sample, suggests that they are derived from material formed by planetary igneous fractionation. Their chemical composition is unlike any known solar system material. The "BeLaU"-type spherules reflect a highly differentiated, extremely evolved composition of an unknown source.

We explore the integration of Kolmogorov Networks (KANs) into molecular dynamics (MD) simulations to improve interatomic potentials. We propose that widely used potentials, such as the Lennard-Jones (LJ) potential, the embedded atom model (EAM), and artificial neural network (ANN) potentials, can be interpreted within the KAN framework. Specifically, we demonstrate that the descriptors for ANN potentials, typically constructed using polynomials, can be redefined using KAN's non-linear functions. By employing linear or cubic spline interpolations for these KAN functions, we show that the computational cost of evaluating ANN potentials and their derivatives is reduced.

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

We estimate ([M/H], [alpha/M]) for 48 million giants and dwarfs in low-dust extinction regions from the Gaia DR3 XP spectra by using tree-based machine-learning models trained on APOGEE DR17 and metal-poor star sample from Li et al. The root mean square error of our estimation is 0.0890 dex for [M/H] and 0.0436 dex for [alpha/M], when we evaluate our models on the test data that are not used in training the models. Because the training data is dominated by giants, our estimation is most reliable for giants. The high-[alpha/M] stars and low-[alpha/M] stars selected by our ([M/H], [alpha/M]) show different kinematical properties for giants and low-temperature dwarfs. We further investigate how our machine-learning models extract information on ([M/H], [alpha/M]). Intriguingly, we find that our models seem to extract information on [alpha/M] from Na D lines (589 nm) and Mg I line (516 nm). This result is understandable given the observed correlation between Na and Mg abundances in the literature. The catalog of ([M/H], [alpha/M]) as well as their associated uncertainties are publicly available online.

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange-correlation (XC) functionals (PBE, BLYP, TPSS, SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation -- particularly noncovalent interaction subsets -- HF-DFT is highly beneficial, particularly at low HF exchange percentages. For subsets with significant static correlation (i.e., where a Hartree-Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals -- consistent with Grimme's proposal of the PBE38 functional -- HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4). Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that of HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree-Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorically optimized empirical range-separated hybrids wB97X-V and wB97M-V.

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of ``slow thinking" into multimodal large language models (MLLMs). Contrary to existing methods that rely on direct or fast thinking, our key idea is to construct long chains of thought (CoT) consisting of atomic actions in a step-by-step manner, guiding MLLMs to perform complex reasoning. To this end, we design a novel AtomThink framework composed of three key modules: (i) a CoT annotation engine that automatically generates high-quality CoT annotations to address the lack of high-quality visual mathematical data; (ii) an atomic step fine-tuning strategy that jointly optimizes an MLLM and a policy reward model (PRM) for step-wise reasoning; and (iii) four different search strategies that can be applied with the PRM to complete reasoning. Additionally, we propose AtomMATH, a large-scale multimodal dataset of long CoTs, and an atomic capability evaluation metric for mathematical tasks. Extensive experimental results show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving approximately 50\% relative accuracy gains on MathVista and 120\% on MathVerse. To support the advancement of multimodal slow-thinking models, we will make our code and dataset publicly available on https://github.com/Quinn777/AtomThink.

We implement physics-informed neural networks (PINNs) to solve the time-independent Schr\"odinger equation for three canonical one-dimensional quantum potentials: an infinite square well, a finite square well, and a finite barrier. The PINN models incorporate trial wavefunctions that exactly satisfy boundary conditions (Dirichlet zeros at domain boundaries), and they optimize a loss functional combining the PDE residual with a normalization constraint. For the infinite well, the ground-state energy is known (E = pi^2 in dimensionless units) and held fixed in training, whereas for the finite well and barrier, the eigenenergy is treated as a trainable parameter. We use fully-connected neural networks with smooth activation functions to represent the wavefunction and demonstrate that PINNs can learn the ground-state eigenfunctions and eigenvalues for these quantum systems. The results show that the PINN-predicted wavefunctions closely match analytical solutions or expected behaviors, and the learned eigenenergies converge to known values. We present training logs and convergence of the energy parameter, as well as figures comparing the PINN solutions to exact results. The discussion addresses the performance of PINNs relative to traditional numerical methods, highlighting challenges such as convergence to the correct eigenvalue, sensitivity to initialization, and the difficulty of modeling discontinuous potentials. We also discuss the importance of the normalization term to resolve the scaling ambiguity of the wavefunction. Finally, we conclude that PINNs are a viable approach for quantum eigenvalue problems, and we outline future directions including extensions to higher-dimensional and time-dependent Schr\"odinger equations.

We respond to the recent paper by Makelov et al. (2023), which reviews subspace interchange intervention methods like distributed alignment search (DAS; Geiger et al. 2023) and claims that these methods potentially cause "interpretability illusions". We first review Makelov et al. (2023)'s technical notion of what an "interpretability illusion" is, and then we show that even intuitive and desirable explanations can qualify as illusions in this sense. As a result, their method of discovering "illusions" can reject explanations they consider "non-illusory". We then argue that the illusions Makelov et al. (2023) see in practice are artifacts of their training and evaluation paradigms. We close by emphasizing that, though we disagree with their core characterization, Makelov et al. (2023)'s examples and discussion have undoubtedly pushed the field of interpretability forward.

While Large Language Models (LLMs) demonstrate impressive capabilities, they still struggle with generating factually incorrect content (i.e., hallucinations). A promising approach to mitigate this issue is enabling models to express uncertainty when unsure. Previous research on uncertainty modeling has primarily focused on short-form QA, but realworld applications often require much longer responses. In this work, we introduce the task of Long-form Generation with Uncertainty(LoGU). We identify two key challenges: Uncertainty Suppression, where models hesitate to express uncertainty, and Uncertainty Misalignment, where models convey uncertainty inaccurately. To tackle these challenges, we propose a refinement-based data collection framework and a two-stage training pipeline. Our framework adopts a divide-and-conquer strategy, refining uncertainty based on atomic claims. The collected data are then used in training through supervised fine-tuning (SFT) and direct preference optimization (DPO) to enhance uncertainty expression. Extensive experiments on three long-form instruction following datasets show that our method significantly improves accuracy, reduces hallucinations, and maintains the comprehensiveness of responses.

Rigorousness and clarity are both essential for interpretations of DNNs to engender human trust. Path methods are commonly employed to generate rigorous attributions that satisfy three axioms. However, the meaning of attributions remains ambiguous due to distinct path choices. To address the ambiguity, we introduce Concentration Principle, which centrally allocates high attributions to indispensable features, thereby endowing aesthetic and sparsity. We then present SAMP, a model-agnostic interpreter, which efficiently searches the near-optimal path from a pre-defined set of manipulation paths. Moreover, we propose the infinitesimal constraint (IC) and momentum strategy (MS) to improve the rigorousness and optimality. Visualizations show that SAMP can precisely reveal DNNs by pinpointing salient image pixels. We also perform quantitative experiments and observe that our method significantly outperforms the counterparts. Code: https://github.com/zbr17/SAMP.