Molecular Structure Elucidation

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Period ending 2026-09-21

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A weekly snapshot of new work published in Molecular Structure Elucidation.

Period ending 2026-09-14

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A weekly snapshot of new work published in Molecular Structure Elucidation.

Period ending 2026-09-07

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A weekly snapshot of new work published in Molecular Structure Elucidation.

53 papers

Latest in Molecular Structure Elucidation

Sep 14, 2026cs.IT

Receiver-Surface Hit Patterns via Legendre Approximation for Molecular Signal Detection

Detecting whether a transmitter is actively communicating with a receiver is a fundamental problem in molecular communications. A spherical receiver may measure not only the number and arrival times of absorbed molecules, but also their absorption locations on the receiver surface. These locations contain a directional signature that is lost in count-only detection. In this letter, we develop a molecular signal detector based on a Legendre polynomial expansion of the receiver-surface hit density and extend it to a Legendre-based Viterbi sequence detector. By exploiting the surface-level directional signature of molecular arrivals, the proposed detectors provide geometry-aware, efficient, and better-performing alternatives to count-only detection.
Yasin Bastug, Erencem Ozbey, H. Birkan Yilmaz
Sep 13, 2026cs.LG

Robust small-molecule identification from incomplete, degraded, and inconsistent spectra using multimodal mixed-condition training

Reliable small-molecule identification often requires complementary evidence from multiple spectroscopic measurements. In practice, however, spectra may be unavailable, degraded by measurement-related variations, or even incorrectly associated with a sample, thereby hindering accurate molecular identification. Herein, we propose a multimodal mixed-condition training strategy that accommodates missing, degraded, and mismatched measurements for small-molecule structure identification. The strategy incorporates chemical and spectroscopic knowledge through predefined missing-input configurations, modality-specific spectral perturbations, and chemically informed spectrum replacements. Models were trained on 635,441 samples comprising mass spectrometry (MS), infrared (IR), and nuclear magnetic resonance (NMR) simulated spectra from the Multimodal Spectroscopic Dataset (MSSD). They were then systematically evaluated on 79,462 held-out samples across 30 views designed to represent variations in spectra. A controlled comparison of complete-input and mixed-condition training under concatenation and mixture-of-experts (MoE) fusion showed that the training strategy was the principal source of improvement. For MoE, mixed-condition training increased the mean reciprocal rank (MRR) by 6.08% (from 0.9203 to 0.9763) and the top-1 molecular identification rate by 7.67% (from 89.50% to 96.36%). Notably, under single-modality inputs, IR MRR increased 2.15-fold (from 0.4337 to 0.9307), while MS MRR increased 2.31-fold (from 0.3711 to 0.8575). With the proposed strategy, complete-input performance remained high, while sample-level mismatch detection also improved. Together, these results highlight the potential of multimodal mixed-condition training for practical molecular identification by explicitly addressing incomplete, degraded, and mismatched measurements encountered in real-world analysis.
Bowen Gao, Lei Zhu, Yiying Wang +1
Sep 9, 2026cs.LG

An Explainable Machine Learning Framework for Predicting Blood-Brain Barrier Permeability Using Molecular Descriptors

Blood-brain barrier (BBB) permeability is a critical determinant in the development of central nervous system therapeutics because it directly influences the ability of drug candidates to reach their target sites within the brain. In this study, an explainable machine learning framework was developed to predict BBB permeability using molecular descriptors generated from the MoleculeNet BBBP dataset with the RDKit cheminformatics toolkit. Fifteen physicochemical descriptors extracted from 2,039 compounds were used to train four supervised machine learning algorithms, including Logistic Regression, Support Vector Machine (SVM), Random Forest, and Extreme Gradient Boosting (XGBoost). Hyperparameter optimization was performed using GridSearchCV, while model interpretability was investigated using SHapley Additive exPlanations (SHAP). Among the evaluated models, the optimized XGBoost classifier achieved the best predictive performance, with an accuracy of 88.97%, a precision of 88.92%, a recall of 97.76%, an F1-score of 93.13%, and a ROC-AUC of 0.9282. Stratified five-fold cross-validation further demonstrated the robustness of the proposed model, yielding a mean ROC-AUC of 0.8982 +/- 0.0130. Feature importance and SHAP analyses consistently identified TPSA, HBD, and LogP as the most influential molecular descriptors governing BBB permeability prediction. Overall, the proposed framework provides an accurate, interpretable, and computationally efficient approach for BBB permeability prediction and may serve as a valuable tool for the early-stage screening of CNS drug candidates.
Fatemeh Mahmoudi
Sep 8, 2026physics.chem-ph

Fixed-Dimensional Latent Flow for Generating Variable-Size 3D Molecules

Molecular size is coupled to composition, structure, and function, yet most 3D molecular generators require a predefined atom count. We introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage framework that samples a fixed-dimensional latent vector using flow matching and uses an autoregressive Transformer to determine molecular size, atom types, coordinates, and chemical attributes. Canonical atom ordering and rigid-pose alignment enable Transformers without equivariant layers, while decoded attributes guide bond reconstruction. On PCQM4Mv2, unconditional generation yields 87.9% unique, novel molecules passing sanitization and PoseBusters checks, exceeding baselines with lower end-to-end training and sampling time and higher end-to-end throughput. Across ten target HOMO-LUMO gaps, internal ranking retains 30% of screened candidates and increases the density functional theory-verified hit rate within 0.1 eV from 25.0% to 52.4%, while largely preserving novelty and diversity. These results demonstrate fixed-dimensional latent generation with autoregressive decoding as a practical approach to molecular design without prespecifying size.
Weichi Yao, Cameron Gruich, Bryan R. Goldsmith +1
Aug 30, 2026cs.LG

Structural Hierarchy and Geometry in Molecular Representation Learning

Molecular self-supervised learning uses chemical structures to guide which molecular embeddings should be similar. We study whether explicitly encoding a molecule's Bemis-Murcko scaffold and using it to supervise the molecular embedding changes what the model learns. We further test whether this effect depends on the embedding geometry by comparing Euclidean and Lorentz contrastive objectives. Across two augmentation strengths, scaffold-supervised models consistently organize molecules according to both identical and structurally related scaffolds. The resulting embeddings also improve molecular property prediction on several tasks, while the exact gains depend on the predicted property. The effect of scaffold supervision on molecular organization is stronger under Lorentz objectives, but neither geometry provides a consistent overall advantage. These results show that explicitly teaching the relation between a molecule and its structural core can reliably shape the organization of molecular embedding space, while the extent of usefulness of this organization remains task dependent.
David Sulu, Lorenzo Di Fruscia, Jana M. Weber
Aug 13, 2026cs.LG

Simulation-to-real transfer learning for infrared spectroscopic chemical sensing and analysis from molecules to complex samples

Infrared (IR) spectroscopy is widely used for chemical sensing, but extracting reliable chemical information from spectra remains challenging. Conventional interpretation is labor-intensive, relies on prior knowledge and reference spectra, and is difficult to scale, whereas most machine-learning methods are tailored to individual tasks or datasets, require large labeled training sets, and transfer poorly across analytical objectives and experimental datasets. Here we introduce UltraIR, a foundation model for IR spectroscopy with more than 100 million parameters that enables simulation-to-real transfer learning for chemical sensing and analysis from molecules to complex samples. UltraIR is pretrained on approximately 60 million simulated IR spectra using spectral reconstruction, molecular fingerprint similarity alignment, and functional-group prediction, then adapted to downstream objectives with task-specific labels or targets. Across functional-group prediction, molecular structure elucidation, physicochemical property prediction, mixture-component identification and quantification, bacterial classification, medicinal-herb geographic origin traceability and constituent quantification, microplastics classification, and soil property prediction, UltraIR outperforms conventional machine-learning and task-specific deep-learning baselines. It performs strongly with limited labeled experimental spectra and in zero-shot inference for the same analytical task across Fourier-transform infrared spectrometers and laboratories, providing a route to adaptable, data-efficient chemical sensing from complex real-world samples.
Yusen Tan, Yixuan Chen, Zheng Fang +8
Aug 8, 2026cs.AI

Generative Models: Principles, Architectures, and Applications

Generative AI has emerged as one of the most transformative forces in modern artificial intelligence, reshaping how we create, imagine, and interact with digital content. From photorealistic images to coherent text, from immersive videos to novel molecular structures, generative models now power applications that were once confined to science fiction. This book is designed to guide readers through the foundational principles, mathematical underpinnings, and practical architectures that underpin this revolution.
Jun Lu
Aug 5, 2026physics.chem-ph

Physics-Based Molecular Fingerprints from Spectral Graph Theory Provide Efficient Geometry-Aware Measures of Chemical Similarity

Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships. Despite the known importance of 3D structure to determine chemical and physical properties, the most widely used molecular fingerprints encode only two-dimensional connectivity. Such representations fail to distinguish similar but distinct stereoisomers and conformers. Alternative 3D methods are typically defined pairwise, making their application to large chemical spaces prohibitive, while deep learning embeddings are expressive but uninterpretable and limited by their training data diversity. Here, we introduce novel physics-inspired molecular fingerprints based on principles from spectral graph theory. We represent molecules as a complete graph in 3D space, with edge weights encoding heuristic physical interactions. Eigenvalue decomposition of the resulting graph Laplacian matrix results in a computationally efficient fixed-length chemical fingerprint that encodes 3D structure while obeying necessary physical symmetries of permutation and E(3) invariance. Spectral fingerprints differentiate between unique molecular structures with identical 2D connectivity, overcoming a limitation of 2D descriptors, while maintaining the low computational cost needed for efficient screening of vast chemical spaces. We evaluate our fingerprints with community detection algorithms and observe strong performance against representative baselines across datasets from organic, inorganic, biological, reticular, and reaction chemistry. Nearest-neighbor property estimation and applicability domain analyses reveal the utility of our molecular representation in machine learning and cheminformatics. We anticipate that spectral fingerprints will serve as generalizable, interpretable, and efficient measures of chemical similarity that incorporate 3D information at minimal cost.
Jacob W. Toney, Ayleen Y. Farnood, Samir Darouich +1
Aug 4, 2026cs.CV

MinerU.Chem: A High-Precision System for Optical Chemical Structure and Reaction Recognition

In organic chemistry papers and patents, molecular structures, reaction schemes, and experimental conditions are often presented as molecular structure depictions, reaction diagrams, and complex tables or figures. Such information is difficult for general-purpose document parsing systems to directly convert into machine-readable data. This limits data production for organic chemistry knowledge base construction and for AI for Chemistry tasks such as reaction prediction, retrosynthesis, condition recommendation, molecular property prediction, and drug molecule design. This report introduces MinerU-Chem, a document parsing system for organic chemistry literature integrated into the MinerU online platform. Built on top of MinerU's general document parsing pipeline, MinerU-Chem adds five chemistry-specific modules: chemistry relevance filtering, molecular structure detection, molecule identifier extraction, molecular structure recognition, and reaction scheme parsing. Together, these modules convert organic-chemistry-related image regions in documents into a Molecule Summary List and a Reaction Summary List. For molecular structure recognition, MinerU-Chem uses CARBON (Complex Atomic Representation and Bonding Object Notation) as its core representation. CARBON enables recognition results to preserve both the visual layout of the original image and complex chemical semantics, while supporting the export of standard downstream formats such as MolFile and SMILES. On the SMILES-evaluable subset of MolRecBench-Wild (N=2,392), MinerU-Chem's molecular structure recognition module achieves a SMILES exact-match accuracy of 93.02%, outperforming the best evaluated comparison system, GPT-5.6-Sol (74.87%), by 18.15 percentage points. The system has been integrated into the MinerU online platform and is available at https://mineru.net/OpenSourceTools/Extractor .
Haote Yang, Jiang Wu, Jingchao Wang +42
Jul 30, 2026cs.AI

SpecCal: Ambiguity-Aware Candidate Calibration for Infrared Spectrum-Based Molecular Structure Reconstruction

Inferring molecular structures from infrared (IR) spectra is a fundamental yet challenging problem. A key difficulty is that an IR spectrum provides limited structural information: different molecules may share similar functional groups and local vibrational patterns, leading to highly similar spectral responses. Thus, even when an observed spectrum has a unique underlying structure, reconstructing it from the spectrum remains ambiguous. Existing IR-to-molecule models usually generate a ranked set of candidate molecules, but this set is largely determined by the model's learned generation preference and may not fully capture the structures that best satisfy the observed spectral constraints. To address this limitation, we propose SpecCal, a training-free candidate calibration framework for IR-to-molecule prediction. SpecCal operates on the candidate outputs of existing base models and improves the prediction set by re-ranking current candidates while introducing additional structurally plausible alternatives guided by spectral consistency. The framework is plug-and-play and model-agnostic, requiring no parameter updates for integration with diverse base models. Experiments on multiple benchmarks show that SpecCal consistently improves top-k reconstruction at both SMILES and scaffold levels across different base models. Further analyses demonstrate that calibrating candidate sets under spectral ambiguity provides a practical way to improve molecular reconstruction from IR spectra. The code is available at: https://anonymous.4open.science/r/SpecCal-B18A.
Yixuan Chen, Bo Liu, Yusen Tan +3
Jul 28, 2026cs.LG

Data Fusion and Contrastive Alignment for Unconstrained IR Molecular Structure Elucidation

Automated molecular structure elucidation from infrared (IR) spectroscopy data has seen significant advancements in recent years, but its broad applicability is limited by a reliance on pre-determined chemical formulas provided as auxiliary model inputs. This limits model predictions to isomer identification rather than full molecular structure prediction. Although transformer models have been shown to identify molecular isomers with high accuracy, their reliability for unconstrained structure elucidation is comparatively low and poorly understood. In this work, we propose and evaluate key modifications to the traditional encoder-decoder transformer. To better address the vast chemical space of the unconstrained problem, we implement a novel Mixture-of-Experts (MoE) decoder module that utilizes non-additive aggregation via linear-order statistics and the Choquet integral. We further modify the transformer to utilize these non-additive operators when aggregating spectral representations as well. Together with an auxiliary contrastive alignment loss term, these enhancements improve Top-K prediction accuracy by over 10 percentage points compared to baseline IR-only models. Through sub-structure fragment analysis of molecular predictions, we further confirm that infrared spectra encode the vast majority of relevant chemical information, implying that the higher performance of isomer-ranking models is largely due to underrepresented or overlapping absorption bands for molecules in the explored chemical space. Ultimately, by demonstrating the efficacy of automated molecular structure elucidation from measured IR spectra, this work serves to significantly broaden the utility of AI in analytical chemistry.
Ethan J. Mick, Campbell A. Sweet, Matthias J. Young +1
Jul 26, 2026cs.LG

MS-GPT: Rethinking MS/MS De Novo Structure Elucidation as Spectrum-Induced Posterior Querying of a Molecule-Language Model

Molecular structure elucidation from tandem mass spectra (MS/MS) is a central inverse problem in analytical chemistry. Most existing approaches to MS/MS identification remain tied to reference libraries or predefined candidate sets, whereas de novo methods aim to generate structures directly from spectra. A common de novo route predicts a molecular fingerprint from the spectrum and then decodes structures from it, enabling decoder pretraining on large molecule-only corpora. However, this paradigm creates a training-inference mismatch: the decoder is trained on oracle fingerprints computed from molecules, but at inference it is queried with a noisy spectrum-induced fingerprint posterior that is typically collapsed to a single thresholded fingerprint. We introduce MS-GPT, which recasts fingerprint-mediated de novo elucidation as spectrum-induced posterior querying of a conditional molecule-language model. MS-GPT conditions a molecule-language model on fingerprints and formulas, then converts the spectrum-induced posterior into a band of fingerprint queries near the oracle-fingerprint manifold through active-bit density calibration. Candidates sampled across this band are pooled and ranked by generation-frequency consensus. A lightweight LoRA adapter further mitigates domain-specific posterior bias while preserving the pretrained molecular prior. On NPLIB1 and MassSpecGym, MS-GPT sets a new state of the art, reaching Top-1/Top-10 exact-match accuracy of 29.8%/41.1% and 23.9%/28.7%, respectively. Candidate-pool scaling shows that efficient autoregressive molecular generation continues to improve recall with a little additional inference cost. The source code and model checkpoints are available at https://github.com/VIKI623/MS-GPT.
Xin Zhao, Yumin Liu, Zhuo Li +5
Jul 23, 2026physics.chem-ph

Graph-Theoretic Neural Network Fragmentation with Covariant Direct Molecular Force Learning: Enabling Coupled-Cluster Accuracy AIMD for Fluxional Systems

Accurate ab initio molecular dynamics (AIMD) simulations of complex, fluxional chemical systems are severely limited by the high computational scaling of correlated electronic structure methods. To overcome this bottleneck, we present a robust, graph-theoretic molecular fragmentation framework integrated with machine learning to directly model post-Hartree-Fock nuclear forces at coupled cluster accuracy. Bypassing the limitations of automatic differentiation on learned energy surfaces that may struggle with link-atom Jacobians, our approach directly predicts nuclear force vectors. By projecting these vectors onto fragment-fixed principal axes of inertia, we establish co-variant descriptors that naturally preserve rotational, translational, and permutational invariance. The methodology achieves exceptional high parameter efficiency through a vector-valued training protocol that reduces trainable parameters by over an order of magnitude, while an unsupervised mini-batch k-means space tessellation algorithm constructs highly representative training databases using only 10% to 20% of reference configurations. We rigorously validated this framework on the highly fluxional solvated Zundel cation H_{13}O_6^+ ). Our fully machine-learning-predicted AIMD trajectories successfully reproduced complex dynamical signatures and key structural characteristics, including radial distribution functions and the velocity autocorrelation power spectrum. Ultimately, this scalable, systematically improvable framework bridges the gap between high-level correlated wavefunction theories and long-timescale reactive sampling, laying the foundation for advanced, LLM-inspired transfer learning in modern chemical dynamics simulations.
Xiao Zhu, Srinivasan S. Iyengar
Jul 23, 2026cs.CE

Chemical Chain-of-Thought Functions as a Hallucination-Prone Molecular Scratchpad

Chemical reasoning language models are expected to derive molecular answers through faithful chain-of-thought (CoT). However, across four reasoning model families and twelve chemistry tasks, hallucination is widespread and largely decoupled from answer correctness: correct answers often coexist with fabricated structural claims absent from the relevant molecules. Yet this does not make the reasoning trace computationally irrelevant. Attribution analyses suggest a shared scratchpad function expressed in model-specific forms: Chem-R and ether-0 rely on fragmented SMILES drafts, whereas ChemDFM-R emphasizes scaffold, positional, and naming cues. Notably, perturbing Chem-R's SMILES sketches degrades generation, showing that structural drafts can be causally load-bearing even when verbal structural claims are largely inert. Together, these results show that chemical CoT is neither a faithful explanation nor merely a post-hoc rationalization, but a hallucination-prone molecular scratchpad. This finding cautions against treating CoT as direct evidence of faithful reasoning and motivates process-level supervision beyond answer-only evaluation.
Jiatong Li, Yuxuan Ren, Weida Wang +2
Jul 22, 2026physics.chem-ph

Hypothesis-and-Refinement Learning of Organic Structures from Multimodal Spectroscopic Data

Determining molecular structures from spectroscopic data remains fundamentally challenging because the inverse problem is intrinsically underdetermined: individual spectra are sparse, low-dimensional, and encode only partial structural evidence relative to the vast space of possible molecules. We address this challenge by formulating automated structure elucidation as a scalable hypothesis-refinement paradigm that tightly integrates spectral evidence with large-scale molecular priors. To supply structure-resolving NMR signals for multimodal learning, we construct \textbf{QM9SPIN}, a DFT-derived dataset comprising diverse 1D and 2D spectra, including J-coupling, DEPT experiments, and explicit spin--spin interactions. On this foundation, we introduce \textbf{SpectroMol}, a spectrum-to-structure model that proposes chemically valid molecular hypotheses conditioned on multimodal spectral inputs. Complementarily, we develop \textbf{MS-Mol2Mol}, a high-resolution mass-constrained molecular generator that integrates molecular formula, exact mass, and degree of unsaturation within a conditional generative prior trained on 400 million molecules, ensuring global compositional consistency and chemically realistic refinement. The integrated system achieves 93.8% top-1 accuracy on the simulated benchmark, adapts effectively from simulated to experimental spectra with limited experimental fine-tuning, and further improves experimental predictions through mass-guided refinement, establishing a scalable route toward automated, data-driven organic structure elucidation.
Chengchun Liu, Zhiyuan Yan, Li Yuan +5
Jul 21, 2026cs.LG

DBMol: Design of High-Affinity, Target-Specific Small Molecules through Structure Prediction Models

Designing small molecule ligands that bind with high affinity to specific protein pockets is a fundamental goal in drug discovery, as small molecules constitute a major fraction of approved therapeutics. Recent breakthroughs in structure prediction, such as AlphaFold-3 and Boltz-2, enable accurate biomolecular interaction prediction and show promise as foundation models for downstream tasks, including binding affinity prediction. We propose to leverage these models and introduce DBMol, a new structure predictor-guided framework for de novo small molecule design. DBMol formulates an alternating optimization and projection process. In the optimization stage, DBMol starts from an initial molecule and uses gradient-based optimization to improve pocket-specific interactions and predicted binding affinity using a structure prediction model. In the projection stage, a flow-matching model maps the optimized molecular graph to discrete and chemically valid molecules. Experiments show that DBMol effectively optimizes the Boltz-2 affinity proxy and generates molecules with strong predicted affinity and specificity under Boltz-2 evaluation. To reduce self-confirmation bias, we further evaluate generated molecules using held-out metrics, including AF3-based evaluation. DBMol substantially improves pocket coverage while maintaining molecular diversity over unconditional generation, and is competitive under held-out metrics despite the absence of reference-ligand supervision. These results support the promise of structure prediction models as effective optimization signals for de novo molecular design.
Yiming Qin, Kai Yi, Miruna Cretu +3
Jul 16, 2026cs.SE

StructureClaw: Traceable LLM Agents and an Executable Benchmark for Structural Engineering Workflows

Addressing a structural-engineering request requires more than a single answer; it requires a chain of interdependent artifacts: interpreted requirements, a computable model, validation records, solver outputs, code-check records, and a final report. Evaluations centered on question answering or script generation rarely verify this complete evidence chain and may therefore reward fluent outputs even when the underlying engineering workflow is incomplete, internally inconsistent, or non-executable. To address this limitation, we present StructureClaw, an artifact-centered workbench in which LLM agents operate through governed engineering skills, typed tools, shared artifact state, and local analysis backends. We also introduce StructureClaw-Bench, an executable benchmark of 150 controlled scenarios spanning standard workflow execution, interactive robustness, and multimodal structural-model reconstruction. A scenario succeeds only when all required artifact- and execution-level assertions pass in a single run. Across ten agent-model configurations, each evaluated on the same 50 standard cases, the average Success Rate rises from 56.8% with the generic-skill baseline to 88.6% with the full automatic workflow. The interactive and multimodal evaluations identify two prominent remaining challenges: safe handling of invalid numerical inputs and fixture-consistent reconstruction of structural models. These findings show that artifact-centered evaluation can expose workflow-level failures that are difficult to identify from final responses alone, providing a more rigorous basis for evaluating and improving structural-engineering agents. The code and benchmark are available at https://github.com/structureclaw/structureclaw.
Sizhong Qin, Yi Gu, Yao Jiang +13
Jul 10, 2026physics.chem-ph

Inverse-IMPRESSION: A Graph-based Platform for Molecular Structure Elucidation from Experimental NMR Spectroscopic Properties

Here, we present a platform built on our inverted Graph Transformer Network, IMPRESSION-G2, which can accurately and rapidly reconstruct molecular bonding directly from experimental nuclear magnetic resonance (NMR) spectroscopic information. It comprises three interconnected stages: a one-shot model that predicts bond connectivity between atoms; a structure-correction stage that corrects the predicted structures by removing uncertain bonds and iteratively reassigning them; noise-augmented multi-shot prediction, generating an ensemble of candidate structures, which are ranked to identify the best-fit structure. By integrating a range of 1^{1}H and 13^{13}C NMR data, including two-dimensional (2D) experiments such as COSY, HSQC, and HMBC, the inverse-IMPRESSION platform correctly identifies the structures of 77.8% of molecules with up to 30 heavy atoms (H, C, N, O and F) using simulated NMR data, and 10 of 19 (53%) molecules using experimental NMR data. The experimental structures solved have molecular weights of up to 480 Da and are representative of the complex structures in synthetic and natural products that routinely challenge chemists. The inverse-IMPRESSION framework thus provides the first effective approach for automated molecular structure elucidation using graph-based machine learning on experimental data.
Zheqi Jin, Grace Armitage, Richard Cox +3
Jul 7, 2026cs.LG

A Quiet Failure in Calibrated Virtual Screening: Marginal Conformal Prediction Under-Covers the Minority Class, and a Class-Conditional Fix Recovers It

Conformal prediction is being adopted in drug discovery to put an honest number on model reliability: pick an error rate alpha, and the method returns prediction sets containing the true label with probability at least 1 - alpha. We show this guarantee can be dangerous on imbalanced datasets. Across four datasets, standard (marginal) conformal prediction hits its global 90% coverage target while leaving the minority class badly exposed: realized minority coverage falls to 64.8% on blood-brain-barrier penetration and to 4.2% on clinical-trial toxicity, where the rare class is nearly abandoned. The failure is not tied to one model: a random forest, a graph network, and a frozen chemical language model all reproduce it (p < 0.001 in every case), with severity tracking baseline calibration on rare labels rather than architecture. A conservation identity explains the effect: the minority's shortfall equals the majority's surplus amplified by the imbalance ratio, predicting the measured gap to within one point and ordering severity across datasets. The failure survives realistic scaffold splits and a second conformal score, while aggregate accuracy and overall coverage stay reassuringly high, which is exactly why it is easy to miss. Class-conditional (Mondrian) conformal prediction closes the gap on every dataset, restoring minority coverage to target for a modest increase in prediction-set size. We localize the failures to generic molecular scaffolds - plain benzene and pyridine cores occurring in both classes - propose a one-number diagnostic, and show with a cost model that abstaining on affected compounds flips a screening campaign from net-negative to net-positive utility. Our contribution is demonstrating on real chemistry how severe and invisible this known conformal-theory gap becomes under imbalance, and laying out a practical protocol restoring per-class reliability.
Muhammadjon Tursunbadalov, Mustafojon Tursunbadalov
Jul 6, 2026cs.LG

MARLIN: De Novo Molecular Structure Elucidation from Tandem Mass Spectra without a Ground-Truth Formula

Untargeted tandem mass spectrometry (MS/MS) detects thousands of small molecules per biological sample, yet most go unidentified because they are absent from spectral libraries. These uncharacterized metabolites and natural products are precisely the compounds that matter for drug discovery, biomarker research, and exposomics. Computational de novo structure elucidation could close this gap, but almost all state-of-the-art methods assume the ground-truth molecular formula is known, an oracle that does not exist for genuinely novel compounds and is itself predicted with substantial error. We present MARLIN, a de novo method that elucidates structures directly from a spectrum with no molecular formula at any stage. A self-supervised encoder predicts a molecular fingerprint from the raw peaks, and a block-diffusion language model generates candidate structures conditioned only on the fingerprint and the instrument-measured precursor mass. A provably safe mass-shell constraint keeps every candidate consistent with the measured mass without fixing the atom inventory, and candidates are accepted by exact parts-per-million mass agreement. A symmetric noise objective absorbs encoder error, and a candidate-diversity mechanism keeps the candidates from collapsing to a single structure. On the NPLIB1 benchmark, MARLIN is the strongest method evaluated without a ground-truth formula across exact-match accuracy, structural distance, and fingerprint similarity, and it recovers the correct molecular formula as a byproduct about as often as a dedicated predictor without ever using one. MARLIN enables reliable de novo structure elucidation in the realistic discovery regime where the molecular formula is unavailable.
Xujun Che, Xiuxia Du, Depeng Xu
Jul 3, 2026cs.LG

Back to Basics: Improving Molecular Understanding in LLMs via SMILES-Graph Translation

Recent advances in molecular large language models have led to strong performance on molecular understanding and generation tasks, yet these gains often come without reliable structural grounding. In particular, existing approaches conflict with the chemistry principle that structure determines function: despite their downstream success, current molecular LLMs perform poorly on basic structure recognition, suggesting that they fail to capture molecular graphs from canonical SMILES. To remedy this, we propose MolBasic, a structure-first framework that strengthens structural comprehension via SMILES-Graph translation. MolBasic is built around a multi-level structure perception benchmark, where bidirectional SMILES-Graph conversion serves as the core task to align sequential and topological representations. On top of this foundation, we employ a progressive learning scheme with a standardized Chain-of-Thought (CoT) to steer models from structure acquisition toward higher-level molecular reasoning. Experiments show that MolBasic substantially improves structural understanding and yields robust gains on downstream tasks, including property prediction and objective optimization, supporting our structure-first paradigm.
Wenda Wang, Jinjia Feng, Zhewei Wei
Jul 2, 2026cs.LG

Probing Chemical Language Models: Effects of Pre-training and Fine-tuning

Chemical language models (CLMs) are trained with linearized representations such as SMILES, yet it remains unclear which chemically meaningful substructures they encode. To foster a better understanding of CLMs, we conduct a systematic study and probe for 78 molecular substructures across eight pre-trained and six randomly initialized models. We furthermore study how fine-tuning on chemical downstream tasks affects the learned representations of molecular substructures. Our results show that pre-training generally improves molecular structure awareness of CLMs, particularly in the upper layers. Moreover, randomly initialized models already encode ring structures well in the first layer. Our analysis on two chemical downstream tasks further reveals that, interestingly, fine-tuning affects task-relevant molecular substructures more than others, indicating that the changes in the representations follow chemical theory.
Anna Karnysheva, Dietrich Klakow, Ji-Ung Lee
Jun 30, 2026cs.LG

Can Tabular In-Context Learners Generalize to Biomolecular Property Prediction?

Predicting biomolecular properties from limited labeled data is a central bottleneck in protein engineering and small-molecule design. As strong pretrained encoders now supply rich fixed-length representations, the difficulty has shifted from representation learning to building a data-efficient predictor for the few-shot regime. Tabular foundation models such as TabPFN and TabICL are unlikely candidates for this role: they are in-context learners pretrained on synthetic tables drawn from random causal graphs, a generative prior with no obvious correspondence to the processes that produce protein sequences or molecular graphs. That this tabular, causal inductive bias should transfer to biomolecular data at all is counter-intuitive, yet we find it does. Treating each method as a predictor-representation pair, we evaluate across two domains. We find that on protein fitness regression tasks these in-context learning models coupled with ESM Cambrian representations achieve or exceed state-of-the-art results on ProteinGym, and outperform task-specific supervised regressors on a diverse esterase catalytic activity dataset. For small-molecule classification with ECFP/RDKit descriptors, no single predictor-representation pairing dominates across TDC ADMET, MoleculeNet, FS-Mol, and DrugOOD, but they are competitive with the existing task-specific state-of-the-art. Crucially, on both protein and small-molecule few-shot tasks, these predictor-representation pairs offer strong performance. We conclude that tabular foundation models can be strong biomolecular predictors, but only when coupled with expressive representations.
Davy Guan, Lu Zhang, Asiri Wijesinghe +7
Jun 29, 2026cs.LG

Towards Generalizable and Evidential Nuclear Magnetic Resonance-Based Molecular Structure Elucidation via Large Language Model Agent

Nuclear Magnetic Resonance (NMR) spectroscopy is the gold standard for molecular structure elucidation, yet interpreting complex spectra for unknown molecules remains a bottleneck reliant on human expertise. While artificial intelligence has advanced this field, current methods face a critical trade-off: database retrieval cannot identify novel scaffolds, while de novo molecular structure elucidation models operate as black boxes, lacking the atom-level interpretability required for rigorous scientific validation. Here, we present NMRAgent, an evidential reasoning agent powered by large language models (LLMs) that bridges this gap by integrating specialized spectral analysis tools with chemical knowledge graphs. Unlike previous approaches, NMRAgent mimics the deductive reasoning of human experts: it takes experimental NMR spectra and molecular formula as input, plans the elucidation process, proposes candidate structures, verifies peak-atom consistency, and refines misaligned substructure through formula-aware fragment optimization. Enabled by its evidential reasoning, NMRAgent outperforms state-of-the-art methods, improving top-1 accuracy by 46.5% and Tanimoto similarity by 0.502 on a scaffold-split benchmark with novel scaffolds in the test set. Besides, we demonstrate the agent's practical utility by elucidating the structures of two previously unknown natural products isolated from Hydrangea davidii and Vitex trifolia, and by correcting structural misassignments in established literature. By combining high-accuracy prediction with transparent and evidence-based reasoning, NMRAgent establishes a new paradigm for interpretable AI in analytical chemistry.
Zheng Fang, Chen Yang, Yusen Tan +9
Jun 28, 2026physics.chem-ph

Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials

Cl(3,0)\mathrm{Cl}(3,0) interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly. Across ten rMD17 molecules, every L1L \leq 1 baseline in our twelve-model study attains aggregate force-cosine similarity below 0.250.25. The cause is structural. The geometric product of two vectors in R3\mathbb{R}^3 realises only the L=0L=0 and L=1L=1 components of its irreducible representation content, leaving the symmetric-traceless rank-2 component absent from the per-edge bilinear that drives each message-passing layer. We address this with CliffordSTF, which couples the Clifford multivector to closed-form symmetric-traceless tensor tracks at ranks two and three through bilinear cross-track contractions, using a single learned bilinear and no Clebsch--Gordan tables, Wigner-DD matrices, or e3nn calls. On rMD17, CliffordSTF raises aggregate force-cosine similarity from 0.0550.055 (base Clifford) to 0.5510.551, an order-of-magnitude relative directional gain, alongside improved magnitude accuracy (force MAE 15.8%15.8\% lower; energy MAE 10.9%10.9\% lower). It outperforms all CG-free or body-ordered baselines in our study (all 0.17\leq 0.17). On catalysis benchmarks, CliffordSTF achieves the best out-of-distribution S2EF energy MAE on OC22 in our experiments, and the best in-distribution energy MAE among L2L \geq 2 methods on OC22 IS2RE. An eleven-variant ablation shows the two tracks are complementary: neither alone matches the combined model.
Can Polat, Erchin Serpedin, Mustafa Kurban +1
Jun 28, 2026cs.LG

GLACIER: Rethinking Mass Spectrum Prediction as an Object Detection Problem

Predicting tandem mass spectra (MS/MS) from molecular structures represents a central task in analytical chemistry with direct relevance to clinical metabolomics, systems biology, and adjacent disciplines. In this work, we revisit the problem through the lens of object detection on molecular graphs. Molecular fragmentation, a central step in MS/MS prediction, can be approximated as detecting a set of subgraphs (i.e., fragments) and their associated spectral contributions. Existing fragment-based models follow a two-stage paradigm -- first generating candidate fragments and then scoring them -- analogous to two-stage R-CNNs in computer vision. Towards higher accuracy and faster inference, we introduce GLACIER, a single-stage transformer-based fragment detection neural network for molecular graphs. This unified formulation eliminates the need for candidate enumeration, enabling scalable and globally consistent modeling of molecular fragmentation. GLACIER is faster and more accurate than existing state-of-the-art by a significant margin, achieving 70.0% and 69.7% Top-1 retrieval accuracy with and without contrastive finetuning on the MassSpecGym dataset (from the previous SOTA of 64.0%) and 52.5% and 38.5% respectively on the NIST'20 dataset (from 33.2%). Furthermore, GLACIER provides nearly 8-fold inference speedup over our prior two-stage model. Code is available at https://github.com/coleygroup/ms-pred
Rui-Xi Wang, Runzhong Wang, Connor W. Coley
Jun 27, 2026cs.LG

Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps

Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.
RuiKang OuYang, Hanlin Yu, Xinyue Ai +7
Jun 23, 2026cs.LG

Uncertainty-aware reinforcement learning for chemical language models

Reinforcement Learning (RL) has become a powerful paradigm for de novo molecular design, enabling Chemical Language Models (CLMs) to navigate and explore the chemical space while optimizing specific desired properties. However, the existing RL frameworks treat all scoring functions as deterministic oracles, neglecting the inherent uncertainty attached to the predictions of the different molecular properties. This can lead to the exploration of highly-uncertain regions of the chemical space, focusing on the generation of highly scored molecules which are poorly supported by the training data. This can destabilize the optimization process, yielding predictions that are far from their true values. We propose and compare two complementary ways of incorporating predictive uncertainty into RL. In the first one, uncertainty is treated as an additional optimization objective and incorporated along with the rest of the scoring functions, allowing the policy to trade off exploitation against reliability. Secondly, uncertainty is used to modulate policy updates, reducing the influence of molecules whose properties lie far outside the scoring function confidence domain. Both approaches were evaluated across three different settings: (i) a controlled model system, in which the prediction error is modeled as a Gaussian distribution, with a variance proportional to the distance to the training data; and two real-world tasks, making use of (ii) ChemProp models and (iii) a Conformal Prediction wrapper applied to a Random forest classifier. We show that uncertainty-aware RL enables CLMs to explore chemical space more robustly by favoring lower-uncertainty regions. This leads to more reliable hit discovery without compromising molecular score, increasing the true hit rate by 0.25 (from 0.5 to 0.75), and nearly doubling the total number of true hits.
Borja Medina, Jon Paul Janet
Jun 22, 2026cs.AI

Closed-loop Auto Research for Molecular Property Prediction: Discovering and Certifying Generalizable Improvements

Closed-loop Auto Research extends automated machine learning from fixed-dataset fitting to changing the research workflow, with language-model agents editing representations and model code and acquiring external evidence. Molecular property prediction spans many small endpoints. We ask whether this action space yields improvements generalizing beyond the validation signal selecting them. We isolate three Auto Research axes, features, models, and external evidence, under a file-level ablation lock attributing each gain to one axis over a strong baseline. Across 36 endpoints in three benchmark suites we score each selected configuration once on a held-out test whose labels the search never read. A routed pipeline taking each endpoint's best validation axis reaches positive held-out gains of 0.013, 0.011, and 0.042, the transferable axis differing by suite, data on TDC, model on Polaris, feature and model on MoleculeNet. The largest model-search gain falls from 0.041 on validation to 0.003 on test, while curated data reaches 0.022 but negative 0.019 on test, two non-transfer signatures. Curated external data raises held-out CYP2C9-substrate performance by 0.17 and half-life by 0.08, admitted through a contamination filter rejecting same-source files overlapping 64 to 89 percent of test structures, necessary but not sufficient for transfer. A matched-trial automated machine learning control did not reproduce the agent's code-level model intervention, reaching 0.006 against 0.042, and the pipeline stays competitive with an 84M-parameter pretrained 3D model on the shared training split. The experiments stay within molecular property prediction, but separating discovery from held-out certification is a domain-agnostic lesson for any closed-loop system optimising a proxy for a held-out quantity.
Jingjie Ning, Xiaochuan Li, Ji Zeng +2
Jun 18, 2026cs.LG

MMGNN: Multi-level, multi-color graph neural networks for molecular property prediction

Molecular message-passing neural networks commonly propagate chemically diverse interactions through a single graph, which may mix interaction-specific signals and require deep propagation to capture long-range effects. We introduce the Multi-level, Multi-color Graph Neural Network (MMGNN), a hierarchical framework that decomposes a molecular graph into overlapping atom-type-pair-specific subgraphs while preserving atom-level resolution. MMGNN-2D constructs chemical-colored subgraphs from covalent connectivity, whereas MMGNN-3D constructs geometric-colored subgraphs from spatial proximity and augments their edges with distance, angular, and torsional descriptors. Both variants apply a shared communicative message-passing backbone to each subgraph and combine the resulting representations through atom-wise aggregation and molecular readout. We evaluated MMGNN on five classification and three regression benchmarks from MoleculeNet using common scaffold splits and five independent runs. MMGNN-2D achieved the highest macro-average AUC-ROC of 0.838 across the classification datasets and the lowest RMSE on ESOL (0.803). MMGNN-3D obtained the highest mean AUC-ROC on BBBP (0.956) and the lowest RMSE on FreeSolv (1.793), indicating complementary strengths of topological and geometric representations. Structural and leave-one-out analyses further illustrate how the subgraph decomposition affects learned representations and atom-type-pair sensitivities. These results support overlapping interaction-specific graph decomposition as a competitive strategy for molecular property prediction.
Trung Nguyen, Duc Duy Nguyen
Jun 18, 2026physics.chem-ph

A large-scale foundation model enables simulation-to-real adaptation for nuclear magnetic resonance-based molecular structure analysis

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool for molecular structure analysis, and spectral artificial intelligence offers great potential for its rapid and automated interpretation. However, the scarcity of experimental NMR datasets has constrained deep learning in this domain to narrow, task-specific applications that lack broad generalization. Here, we introduce UltraNMR, a large-scale foundation model for NMR that leverages the intrinsic properties of NMR spectra to learn generalizable spectral representations. We collected 158 million paired simulated 1^{1}H and 13^{13}C NMR spectra to train UltraNMR, employing multiple domain-specific pre-training objectives. UltraNMR captures both intra-spectral and inter-spectral dependencies, enabling seamless simulation-to-real adaptation. We demonstrate that adapting UltraNMR to a range of molecular structure analysis tasks on experimental NMR spectra consistently yields state-of-the-art performance and clearly outperforms UltraNMR variants trained directly on downstream data without simulation pre-training. We also construct a large-scale NMR spectral vector library by encoding simulated NMR spectra using UltraNMR, covering 94 million unique molecules and enabling effective structure-aware retrieval. In real-world applications, UltraNMR facilitates the structural elucidation of two previously unknown natural products from Chinese herbal medicines recorded in the Chinese Pharmacopoeia. These results suggest that large-scale simulation pre-training can effectively bridge the simulation-to-real gap, enabling robust and generalizable molecular structure analysis of real-world NMR spectra.
Chen Yang, Zheng Fang, Hanyu Sun +7
Jun 15, 2026physics.ins-det

Latent space mapping of interpretable structural coordinates from stochastic single-molecule signals

Nanopores are versatile single-molecular sensors, but their utility is fundamentally constrained by stochastic translocation dynamics warping any encoded information. We resolve it by shifting from time-domain analysis to a learned latent-space mapping via a contrastive encoder trained exclusively on simulated signals from a physics-informed model. This encoder maps solid-state nanopore signals of engineered DNA barcodes into an interpretable molecular coordinate system. The learned representation is responsive to structural barcode parameters while remaining invariant to acquisition conditions and translocation conformation, allowing data pooling across devices. Molecule identification requires a single pass through the encoder, reducing computational cost by three orders of magnitude relative to alignment-based methods. We experimentally validate through mixture quantification, rare-variant detection, consensus barcode reconstruction, and real-time signal acquisition. This shift from temporal analysis to mapping structural coordinates into a latent space changes the paradigm behind analyzing stochastic sensor signals by linking classification to interpretable encoded molecular information.
Matteo Cartiglia, Sandro Kuppel, Wouter Botermans Wannes Peeters +7
Jun 8, 2026physics.app-ph

Automating the Expert Eye: A System-Agnostic Deep Learning Framework for Rare Event Discovery in Imbalanced Force Spectroscopy

Single-Molecule Force Spectroscopy (SMFS) provides unprecedented insights into biomolecular mechanics, yet the high-throughput generation of force-extension trajectories creates a severe data curation bottleneck. Identifying rare molecular unbinding events within thousands of noise-dominated curves traditionally relies on tedious, non-scalable manual auditing. Here, we present a system-agnostic, interpretable deep learning framework tailored to overcome extreme class imbalance in automated SMFS triage. Utilizing 1D-to-2D rasterized geometric matrices, we deployed a modified ResNet18 architecture governed by an asymmetric Focal Loss objective function. We evaluated this framework on the complex mechanical unfolding pathways of the R. champanellensis cellulosome. Under hyper-imbalanced test conditions where the target interaction constituted only 1.34% of the dataset (13 true events out of 970 traces), the model achieved an overall accuracy of 0.9196 and a remarkable True Positive Rate (Recall) of 0.9231. By implementing an empirically calibrated dual-threshold triage system, the pipeline automatically discarded 880 unambiguous background noise traces , reducing the manual curation workload by over 90% while safely preserving high-value rare data. Finally, Gradient-weighted Class Activation Mapping (Grad-CAM) visually validated that the network's decisions are firmly anchored in the relevant geometric features of the force curves, specifically localizing on the structural unbinding regions, effectively mitigating 'black-box' skepticism. Built for free cloud-based execution, this open-source tool democratizes scalable, highly precise molecular discovery across the biophysics community.
Jorge Rodriguez-Ramos
Jun 4, 2026cs.LG

End-to-End Subgraph Detection with GraphDETR

Subgraph detection seeks to identify whether and where instances of query patterns occur within a larger graph. This problem is fundamental across scientific domains and is closely related to subgraph isomorphism, which is NP-complete, limiting combinatorial approaches to small patterns or moderately sized graphs. We introduce GraphDETR, a deep learning framework that formulates subgraph detection as a set prediction problem, analogous to DETR in object detection. GraphDETR encodes the target graph with a graph neural network, and employs a fixed set of learnable query vectors, decoded via a transformer decoder, to predict all pattern occurrences jointly in a single forward pass. This is enabled by training the model end-to-end with bipartite matching. Unlike traditional combinatorial methods that only solve exact structural matching, GraphDETR naturally extends to approximate matching, enabling detection beyond exact pattern correspondence. Empirically, we show that GraphDETR can detect diverse patterns, such as molecular structures, cycles, cliques, and fuzzy patterns of up to 50 nodes, in target graphs with up to 1000 nodes. We further evaluate on molecular functional group detection over the ChEMBL dataset, where GraphDETR predicts the complete set of functional groups per molecule, achieving a strong performance of AP100=91.2\text{AP}_{100} = 91.2.
Dexiong Chen, Till Hendrik Schulz, Karsten Borgwardt
Jun 4, 2026cs.AI

Agentic Molecular Recovery via Molecule-Aware Exploration

Text-guided molecular generation with LLMs often yields invalid SMILES. We argue that invalid drafts should be addressed through a shift from validity-oriented repair to identity-preserving molecular recovery: the objective is not only to restore chemical validity, but also to preserve target-relevant structural cues and recover the molecular identity implied by the description. This perspective reveals the limitations of existing correction strategies. Post-hoc repair can recover validity while distorting key structures, LLM-only correction can introduce unintended global drift, and generic agentic correction remains constrained by greedy single-candidate trajectories even when equipped with executable RDKit edit tools. To address these limitations, we propose AMREC, which couples molecule-aware mismatch tracking with expanded candidate exploration and trajectory-level selection. On invalid ChEBI-20 drafts from three backbone models, AMREC achieves the strongest overall recovery profile across structural, exact-match, and string-level metrics.
Suwan Yoon, Changhee Lee
May 28, 2026cs.LG

OOD-GraphLLM: Graph Large Language Model for Out-of-Distribution Generalized Drug Synergy Prediction

Drug synergy prediction (DSP) aims to identify efficacious drug combinations under various cellular contexts with different targets. However, the continual emergence of novel compounds results in variations in molecular scaffolds and sizes, causing drug synergy data to exhibit out-of-distribution (O.O.D.) shifts with respect to topological structure. Existing works rely on in-distribution (I.D.) assumption, failing to handle the O.O.D. shifts. To solve this problem, we study out-of-distribution generalized drug synergy prediction through a graph large language model for the first time. Nevertheless, O.O.D. generalized DSP is highly non-trivial, posing several challenges: i) how to discover structurally relevant and irrelevant molecular representations with respect to cell targets; ii) how to find the optimal graph neural architectures that accurately calculate molecular representations; and iii) how to jointly leverage molecular structural and semantic information in LLMs. To address these challenges, we propose OOD-GraphLLM, a novel graphLLM framework which is able to accurately predict drug synergy under O.O.D. settings via jointly optimizing molecular graph representation and biomedical semantic language representations in a unified manner. Furthermore, we finetune DrugSyn-LLM, a biomedical LLM, and employ a retrieval-augmented biomedical instruction tuning strategy to align molecular topological information and molecular semantic information with language-based reasoning for O.O.D. generalized DSP. Both the source code (https://github.com/EkkoXiao/Bio-GraphLLM) and released model (https://mn.cs.tsinghua.edu.cn/bio-graphllm/) are publicly available, where users are allowed to download model resources and interactively use the system through a web interface.
Xin Wang, Linxin Xiao, Yang Yao +1
May 26, 2026cs.LG

SCENT: Aligning Mass Spectra with Molecular Structure for Olfactory Perception

Predicting human olfactory perception from molecular structure has seen remarkable progress, yet these approaches require explicit chemical structure at inference, which is not available in practical sensing settings. We address this gap by exploring direct electron ionization mass spectrometry (EI-MS), a sensing technique that acquires chemically informative fragmentation fingerprints in seconds, as an alternative input modality for olfactory prediction. We contribute Spectrum-to-Chemical Embedding alignmeNT (SCENT), a multi-modal contrastive learning framework that aligns EI-MS representations with pretrained chemical structure embeddings, while requiring only mass spectra at inference. On the multi-label odor descriptor prediction task, SCENT significantly outperforms MS-only baselines and achieves performance comparable to structure-based models, despite requiring no explicit molecular structure at test time. The learned representations also better approximate continuous human perceptual ratings and generalize to real-world lab-measured spectra, suggesting that cross-modal alignment is an effective strategy for grounding analytical spectra in chemical semantics.
Ziqi Zhang, Eunyeong Jin, Miguel Vasco +6
May 26, 2026physics.chem-ph

DGLD: Domain-Gated Latent Diffusion for the Discovery of Novel Energetic Materials

Energetic-materials performance gains translate directly into reduced propellant mass, smaller warheads, and more efficient civilian gas-generators, yet no new HMX-class compound has been disclosed in fifteen years. Designing one is a sparse-label problem: of ~66 k labelled CHNO molecules only ~3 k carry experimental or DFT-quality measurements, and naive generative models trained on the full mixture either memorise the high-performance tail or extrapolate without calibration. We introduce Domain-Gated Latent Diffusion (DGLD): a label-quality gate at training time, multi-task score-model guidance at sample time, and a four-stage chemistry-validation funnel ending in first-principles DFT audit. The result is 12 DFT-confirmed novel leads. The headline compound, 3,4,5-trinitro-1,2-isoxazole (L1), reaches \r{ho}"cal" =2.09 g/cm3 and D"K-J,cal" =8.25 km/s and is structurally dissimilar from all 65 980 training molecules (nearest-neighbour Tanimoto 0.27). A co-headline lead, E1 (4-nitro-1,2,3,5-oxatriazole), exceeds L1 on calibrated detonation velocity (D_"K-J,cal" =9.00 km/s) from a chemotype family disjoint from L1's. DGLD is the only method to land in the productive quadrant (simultaneously novel and on-target) at DFT level. SMILES-LSTM memorises 18.3% of its outputs exactly; SELFIES-GA's best novel candidate loses 3.5 km/s under DFT audit; REINVENT 4 generates novel high-N heterocycles but peaks at D=9.02 km/s. Code, checkpoints, and 918 mined hard negatives are released on Zenodo (DOI 10.5281/zenodo.19821953); the next compound to enter the HMX-class band can be discovered, validated, and recommended for synthesis at the cost of a few GPU-days.
Yehudit Aperstein, Alexander Apartsin
May 25, 2026q-bio.QM

What Molecular Structure Cannot Tell Us: A Taxonomy of Explainability Gaps in GNN-Based Drug Toxicity Prediction

Not all clinically relevant adverse effects are structurally inferable from molecular graphs - regardless of model quality or architectural complexity. This study introduces an operational taxonomy of the structural information limits that prevent structure-based toxicity prediction, independent of the learning algorithm employed. Graph Neural Networks (GNNs) have emerged as a natural approach for molecular toxicity prediction, operating directly on atomic connectivity without the information loss inherent to fixed-length fingerprints. However, the fraction of a drug's known pharmacological profile that is actually inferable from molecular structure remains systematically underexplored. A systematic case study using acetylsalicylic acid (ASA, Aspirin) - one of the most comprehensively characterized drugs in pharmacology - serves as model compound. A Message Passing Neural Network (MPNN) is trained on the Tox21 benchmark and GNNExplainer is applied to characterize atom-level attribution. Results indicate that molecular structure explains approximately 45% (5/11) of known ASA adverse effects. A four-category Gap Taxonomy (GAP-1 through GAP-4) is introduced distinguishing between principally non-encodable effects, data gaps arising from Missing Not At Random (MNAR) mechanisms, assay panel mismatches, and representation errors. The MNAR gap is empirically quantified via a systematic ChEMBL query (42 documented assays, 0 retrievable bioactivity entries). An attention pooling experiment localizes the representation error to the MPNN message passing layers rather than the aggregation step. The Gap Taxonomy has direct implications for drug safety signal detection and regulatory frameworks including Good Pharmacovigilance Practice (GVP) guidelines and New Approach Methodologies (NAMs). Structural limits identified are confirmed in a companion DDI ablation study.
Juergen Dietrich
May 21, 2026cs.AI

SciCore-Mol: Augmenting Large Language Models with Pluggable Molecular Cognition Modules

Large Language Models (LLMs) are central to the one-for-all intelligent paradigm, but they face a fundamental challenge when dealing with heterogeneous scientific data such as molecules: the inherent gap between discrete linguistic symbols and topological molecular or continuous reaction data leads to significant information loss and semantic noise in text-based reasoning. We propose SciCore-Mol, a modular framework that bridges this gap through three deeply integrated pluggable cognitive modules: a topology-aware perception module, a latent diffusion-based molecular generation module, and a reaction-aware reasoning module. Each module is coupled to the LLM backbone through learned representation interfaces, enabling richer information exchange than is possible with text-only tool feedback. Our experiments on diverse chemical tasks demonstrate that SciCore-Mol achieves strong comprehensive performance across molecular understanding, generation, reaction prediction, and general chemistry knowledge, with an 8B-parameter open-source system that is competitive with and in several dimensions surpasses proprietary large models. This work provides a systematic blueprint for equipping LLMs with scientific expertise through decoupled, pluggable, and flexibly orchestrated modules, with direct implications for drug design, chemical synthesis, and broader scientific discovery.
Yuxuan Chen, Changwei Lv, Yunduo Xiao +5
May 20, 2026cs.LG

Distribution-Aware Reward: Reinforcement Learning over Predictive Distributions for LLM Regression

Large language models can predict real-valued quantities from heterogeneous inputs such as text, code, and molecular strings, but most training objectives score each decoded floating-point number independently, improving point estimates without ensuring calibrated predictive distributions. This limits applications requiring candidate ranking or uncertainty estimation. We introduce Distribution-Aware Reward, an on-policy reinforcement learning objective whose main contribution is to train language models to produce better predictive distributions for regression tasks, rather than only optimizing individual decoded outputs against scalar targets. Our method treats multiple decoded samples as an empirical predictive distribution, evaluates it with the Continuous Ranked Probability Score, and assigns leave-one-out credit based on each rollout's marginal contribution to distribution quality, rewarding predictions that are both accurate and appropriately dispersed. We evaluate our method on a controlled Gaussian-mixture task, code performance prediction, and molecular property prediction from SMILES strings. Across tasks, our method improves over supervised fine-tuning and pointwise reinforcement learning baselines, with strong rank-correlation gains, including a 6-point Spearman improvement on KBSS. On MoleculeNet, it uses only SMILES strings yet remains competitive with strong graph-based and 3D molecular models. Further analyses show that our method mitigates rollout diversity collapse and improves uncertainty diagnostics, suggesting that directly optimizing predictive distributions makes language model regression more robust and better calibrated.
Jungsoo Park, Hyungjoo Chae, Ethan Mendes +4
May 19, 2026cs.LG

MSAlign: Aligning Molecule and Mass Spectra Foundation Models for Metabolite Identification

Accurately identifying metabolites i.e. small molecules from mass spectrometry data remains a core challenge in metabolomics, with broad applications in drug discovery, environmental analysis, and clinical research. We address the Molecule Retrieval task, which consists in recovering the chemical structure of a metabolite from its MS/MS spectrum given a set of candidate molecules. While the recent release of benchmark datasets such as MassSpecGym and Spectraverse has considerably accelerated the development of novel machine learning approaches, the complexity of data preprocessing pipelines and the lack of unified implementations make methods and results difficult to reproduce and compare. We make three contributions. First, we propose a unified framework encompassing recent approaches based on representation alignment and contrastive learning. Second, we introduce MSAlign, inspired by multimodal alignment in vision-language models, which learns a shared representation space by aligning two frozen foundation models (DreaMS for mass spectra and ChemBERTa for molecules) through lightweight MLP projections trained with a candidate-based contrastive objective. MSAlign is simple to implement, fast to train and consistently outperforms existing approaches across all benchmarks. Third, we investigate a long-standing evaluation problem: data splitting strategies in molecule retrieval implicitly trade off data leakage against domain shift. We formalize this tension by introducing a quantitative measure of distribution shift, and use it to evaluate splitting strategies in existing benchmarks. All datasets, splits, candidate sets, and a unified implementation of MSAlign and baselines are publicly released to support reproducible research.
Paul Krzakala, Gabriel Melo, Camille Lançon +4
May 15, 2026q-bio.BM

MoleCode unlocks structural intelligence in large language models

Molecules are graphs, but large language models~(LLMs) are usually asked to reason about them through linear strings. The most popular molecular representation, SMILES, compresses atoms, bonds, branches and rings into a compact sequence in which topology is implicit, forcing LLMs to reconstruct molecular structure before performing the requested chemical operation. Here we introduce MoleCode, an LLM-native, training-free, graph-explicit molecular language in which all molecular components are represented as typed entities with persistent identifiers and explicit relations. MoleCode makes molecular topology directly readable, editable and auditable within the language context, allowing an LLM to operate on structure rather than recover it from syntax. Across molecular reasoning, editing, generation and analysis tasks, this representational shift improves frontier LLMs most strongly when structural access is limiting: unfamiliar molecules, topology-sensitive operations, larger structures and repetitive polymers. It also changes how inference is allocated, replacing long reasoning traces devoted to implicit structural reconstruction with shorter, more chemically directed reasoning over explicit atoms and bonds. In molecular optimization, this enables localized, property-aligned edits that preserve structural similarity to the starting compounds. The same Subgraph--Node--Edge grammar extends beyond small molecules to polymers, Markush structures, mechanism-style transformations and interleaved scientific documents, including research articles and patent disclosures in which chemical information is distributed across text and images. These results suggest that the interface between scientific objects and LLMs should not treat structure as something to be decoded from text. When the object of reasoning is relational, the structure itself should be part of the language.
Zhiyuan Yan, Chen Liu, Boxuan Zhao +8
May 13, 2026cs.LG

Chem-GMNet: A Sphere-Native Geometric Transformer for Molecular Property Prediction

Modern SMILES-based chemical language models obtain strong MoleculeNet performance by treating SMILES as generic text and compensating with multi-million-molecule self-supervised pretraining. We ask: when a domain carries structural priors as rich as chemistry's, does it warrant a domain-native transformer rather than a generic one rescued by scale? We answer affirmatively with \textbf{GM-Net} (Geometric Measure Network), a transformer family in which every module is replaced by a sphere-native counterpart, and instantiate it as \textbf{Chem-GMNet}. Three blocks follow: SH-Embedding (tokens as learnable directions on Sk1S^{k-1} lifted through a Gegenbauer feature map); DualSKA (a per-head fusion of a linear-time gated Sphere-Flow recurrence whose persistent state we prove is the truncated multipole expansion of the input distribution, and a softmax Sphere-Kernel branch over the same Schoenberg-valid kernel); and SH-FFN (sphere projection \to Gegenbauer lift \to moment readout). On canonical DeepChem scaffold splits, against same-shape ChemBERTa-2 baselines under the chemberta3-faithful protocol: (i) random-initialised, Chem-GMNet wins on 7 of 10 MoleculeNet endpoints at  ⁣35%\sim\!35\% fewer parameters; (ii) pretrained on the same 10M-SMILES ZINC corpus as ChemBERTa-2 MLM-10M, it matches or beats the public release on 6 of 8 shared endpoints (5/7 excluding a known ClinTox release anomaly). A (k,L)(k,L) ablation shows that increasing the sphere dimension from k ⁣= ⁣8k\!=\!8 to k ⁣= ⁣10k\!=\!10 at fixed L ⁣= ⁣3L\!=\!3 lowers ESOL RMSE to 0.9380.938 at scratch, beating pretrained ChemBERTa-2 MLM-10M on this endpoint without any pretraining at all.
Deepak Warrier, Raja Sekhar Pappala
May 13, 2026cs.LG

CoRe-Gen: Robust Spectrum-to-Structure Generation under Imperfect Fingerprint Conditions

Molecular structure elucidation from tandem mass spectra (MS/MS) remains challenging, particularly for de novo generation beyond database coverage. A common approach decomposes the task into spectrum-to-fingerprint prediction followed by fingerprint-to-structure decoding, enabling the use of large-scale molecular corpora. However, at deployment, the decoder relies on predicted rather than oracle fingerprints, introducing structured errors that propagate into generation. This results in a fundamental condition mismatch, where models trained on clean inputs must operate under noisy, biased predictions, especially for long-tail substructures. We present CoRe-Gen that explicitly addresses this gap. CoRe-Gen improves the intermediate condition via synthetic-spectrum pretraining of the encoder, matches deployment-time noise through frequency-aware fingerprint corruption during decoder training, and mitigates residual errors using structure-aware autoregressive decoding with compositional SELFIES representations, auxiliary structural supervision, and lightweight chemical constraints. Experiments on standard benchmarks show that CoRe-Gen establishes a new state of the art on NPLIB1, achieving 19.54% Top-1 and 29.92% Top-10 exact-match accuracy, while remaining competitive on the more challenging MassSpecGym benchmark. Importantly, CoRe-Gen preserves the efficiency advantages of autoregressive decoding, providing a practical and scalable solution for robust spectrum-to-structure generation under realistic conditions.
Tianbo Liu, Chixiang Lu, Jing Hao +4
May 11, 2026physics.chem-ph

Physical probes expose and alleviate chemical-environment collapse in molecular representations

Nuclear magnetic resonance (NMR) spectroscopy provides an experimental readout of local chemical environments, but its use in molecular representation learning has been constrained by heterogeneous data and incomplete atom-level assignments. Here we construct complementary high-fidelity experimental and computational 13C NMR resources, which reveal a recurrent form of representational collapse: atoms that are equivalent in molecular topology can remain experimentally distinct in their real chemical environments, whereas explicit 3D descriptions are further limited by static conformations in dynamic regimes. To alleviate this bottleneck, we develop CLAIM (Contrastive Learning for Atom-to-molecule Inference of Molecular NMR), a framework that aligns efficient topological molecular inputs with atom-resolved NMR observables. Through hierarchical chemical priors and cross-level contrastive learning, CLAIM restores lost chemical resolution and markedly improves atom-level molecule-spectrum retrieval. CLAIM remains robust in flexible and tautomeric systems for 13C NMR prediction, improves stereoisomer discrimination without explicit 3D modelling, and transfers to broader molecular property tasks including ADMET prediction and fluorescence estimation. These results establish physically grounded spectral alignment as an effective strategy for alleviating chemical-environment collapse and for guiding experimentally grounded molecular representation learning.
Jiebin Fang, Zidi Yan, Churu Mao +7
May 9, 2026cs.LG

MolWorld: Molecule World Models for Actionable Molecular Optimization

Molecular optimization in drug discovery aims to discover molecules with improved target properties, but practical lead optimization often requires more than high predicted scores. A useful candidate should also be actionable: it should be reachable from known molecules through valid local structural transformations, so that it can be interpreted as a plausible revision within an evolving chemical series. Existing de novo and single-molecule optimization methods do not explicitly model such reachability, especially when both the target molecules and the intermediate molecules connecting them to known compounds are unknown. In this work, we formulate actionable molecular optimization as sequential expansion of a molecule-transfer graph, where nodes are molecules and edges encode valid local transformations. We propose MolWorld, a molecule world model-guided framework that treats the current molecule-transfer graph as an evolving search state. At each iteration, MolWorld selects local anchor contexts, generates candidate molecules conditioned on these contexts, evaluates their properties, and uses a learned world model to update the evolving molecule world by retaining admissible candidates and inserting them into the molecule-transfer graph. The expanded molecule world then guides subsequent optimization. Experiments on property optimization and docking-based tasks show that MolWorld discovers high-property molecules while maintaining substantially stronger structural connectivity, supporting actionable and sequential molecular design.
Yang Qiao, Bo Pan, Hao-Wei Pang +3
May 4, 2026cs.LG

Bolek: A Multimodal Language Model for Molecular Reasoning

Molecular property models increasingly support high-stakes drug-discovery decisions, but their outputs are often difficult to audit: classical predictors return scores without rationale, while language models can produce fluent explanations weakly grounded in the input molecule. We introduce Bolek, a compact multimodal language model that grounds natural-language reasoning in molecular structure by injecting a Morgan fingerprint embedding into an instruction-tuned text decoder. Bolek is fine-tuned on molecular alignment tasks, including molecule description, RDKit descriptor prediction, and substructure detection, and on downstream reasoning over 15 TDC binary classification tasks using synthetic chains-of-thought anchored in concrete molecular features. Across these tasks, Bolek outperforms its Qwen3-4B-Instruct base on all endpoints in yes/no mode and on 13 of 15 in chain-of-thought mode, raising mean ROC/PR AUC from 0.55 to 0.76. It also outperforms TxGemma-9B-Chat on 13 of 15 binary classification tasks despite being less than half its size. Bolek's explanations are more grounded than those of the baseline LLMs: it cites numerical descriptors 10-100x more often per chain-of-thought, and the cited values agree strongly with RDKit for key descriptors such as TPSA, MolLogP, and MolWt (Spearman rho = 0.87-0.91). Generalisation extends beyond the training panel: on 15 unseen TDC classification endpoints, Bolek matches TxGemma on five, and it produces non-trivial rank correlations on three held-out regression endpoints despite never seeing downstream regression during training. These results suggest that targeted modality injection and reasoning supervision tied to verifiable molecular features can yield compact, auditable molecular reasoning models.
Frederic Grabowski, Jacek Szczerbiński, Maciej Jaśkowski +4
May 1, 2026cs.LG

Proteo-R1: Reasoning Foundation Models for De Novo Protein Design

Deep learning in \emph{de novo} protein design has achieved atomic-level fidelity. However, existing models remain largely non-deliberative: they directly synthesize molecular geometries without explicitly reasoning about which residues or interactions are functionally essential. As a result, design decisions are entangled with continuous sampling dynamics, limiting interpretability, controllability, and systematic reuse of biochemical knowledge. We introduce \textbf{Proteo-R1}, a reasoning-guided protein design framework that explicitly decouples \emph{molecular understanding} from \emph{geometric generation}. Proteo-R1 adopts a dual-expert architecture in which a multimodal large language model (MLLM) serves as an \emph{understanding expert}, analyzing protein sequences, structures, and textual context to identify key functional residues that govern binding and specificity. These residue-level decisions are then passed as hard constraints to a separate diffusion-based \emph{generation expert}, which performs conditional co-design while respecting the fixed interaction anchors. This factorization mirrors how human experts approach molecular engineering: first, reasoning about critical interactions, then optimizing geometry subject to those constraints. By operationalizing reasoning as explicit residue-level commitments rather than latent textual guidance, Proteo-R1 achieves stable, interpretable, and modular integration of LLM reasoning with state-of-the-art geometric generative models. Code, data, and demos are available at https://smiles724.github.io/r1/.
Fang Wu, Weihao Xuan, Heli Qi +26
Apr 23, 2026cs.LG

Drug Synergy Prediction via Residual Graph Isomorphism Networks and Attention Mechanisms

In the treatment of complex diseases, treatment regimens using a single drug often yield limited efficacy and can lead to drug resistance. In contrast, combination drug therapies can significantly improve therapeutic outcomes through synergistic effects. However, experimentally validating all possible drug combinations is prohibitively expensive, underscoring the critical need for efficient computational prediction methods. Although existing approaches based on deep learning and graph neural networks (GNNs) have made considerable progress, challenges remain in reducing structural bias, improving generalization capability, and enhancing model interpretability. To address these limitations, this paper proposes a collaborative prediction graph neural network that integrates molecular structural features and cell-line genomic profiles with drug-drug interactions to enhance the prediction of synergistic effects. We introduce a novel model named the Residual Graph Isomorphism Network integrated with an Attention mechanism (ResGIN-Att). The model first extracts multi scale topological features of drug molecules using a residual graph isomorphism network, where residual connections help mitigate over-smoothing in deep layers. Subsequently, an adaptive Long Short-Term Memory (LSTM) module fuses structural information from local to global scales. Finally, a cross-attention module is designed to explicitly model drug-drug interactions and identify key chemical substructures. Extensive experiments on five public benchmark datasets demonstrate that ResGIN-Att achieves competitive performance, comparing favorably against key baseline methods while exhibiting promising generalization capability and robustness.
Jiyan Song, Wenyang Wang, Chengcheng Yan +2
Apr 21, 2026cs.LG

Graph-Theoretic Models for the Prediction of Molecular Measurements

Graph-theoretic approaches offer simplicity, interpretability, and low computational cost for molecular property prediction. Among these, the model proposed by Mukwembi and Nyabadza, based on the external activity D(G)D(G) and internal activity ζ(G)ζ(G) indices, achieved strong results on a small flavonoid dataset. However, its ability to generalize to larger and chemically diverse datasets has not been tested. This study evaluates the baseline D(G)D(G)-ζ(G)ζ(G) polynomial model on five benchmark datasets from MoleculeNet, covering biological activity (BACE, 1,513 molecules), lipophilicity (LogP synthetic, 14,610 molecules; LogP experimental, 753 molecules), aqueous solubility (ESOL, 1,128 molecules), and hydration free energy (SAMPL, 642 molecules). The baseline model achieves an average R2=0.24R^2 = 0.24, confirming limited transferability. To address this, a systematic enhancement framework is proposed, progressively incorporating Ridge regularization, additional graph descriptors, physicochemical properties, ensemble learning with Gradient Boosting, Lasso feature selection, and a hybrid approach combining topological indices with Morgan fingerprints. The enhanced models raise the average best R2R^2 to 0.79, with individual improvements ranging from 165% to 274%. All improvements are statistically significant (p<0.001p < 0.001). A direct comparison with a Graph Convolutional Network under identical experimental conditions shows that the enhanced classical models match or outperform deep learning on all five datasets. Comparison with the recent GNN+PGM hybrid of Djagba et al.\ further confirms competitiveness, with the enhanced models achieving the best results on two datasets and tying on one. The entire framework requires no GPU, trains in under five minutes, and uses only open-source tools, making it accessible for researchers in resource-limited settings.
Anna Niane, Prudence Djagba
Mar 13, 2026cs.LG

A Multitask Large Reasoning Model for Molecular Science

Artificial intelligence in molecular science must move beyond pattern recognition toward chemically valid and interpretable reasoning. We present a task-adaptive large reasoning model that integrates chemical knowledge through a synergistic multispecialist architecture, chain-of-thought supervision, and molecule-informed reinforcement learning. Task-conditioned routing coordinates prediction and inference specialists across 10 molecular tasks spanning molecular description and generation, nomenclature translation, property prediction, and reaction prediction. The model outperforms more than 20 general-purpose and molecular large language models, improves aggregate performance over the base model by 50.3%, and surpasses the leading molecular multitask baseline on most tasks. Analyses of specialist representations and reasoning pathways reveal task-specific adaptation while retaining interpretable chemical inference. A case study further demonstrates an integrated workflow for central nervous system candidate generation, property screening, molecular interpretation, and retrosynthetic planning. These results demonstrate a versatile multi-task framework for knowledge-guided molecular reasoning and design, with the potential to serve as a core task engine for future molecular science agents.
Pengfei Liu, Shuang Ge, Xiaobo Wang +6
Dec 17, 2025physics.chem-ph

NMIRacle: Multi-modal Generative Molecular Elucidation from IR and NMR Spectra

Molecular structure elucidation from spectroscopic data is a long-standing challenge in Chemistry, traditionally requiring expert interpretation. We introduce NMIRacle, a two-stage generative framework that builds upon recent paradigms in AI-driven spectroscopy with minimal assumptions. In the first stage, NMIRacle learns to reconstruct molecular structures from count-aware fragment representations, capturing both fragment identities and their occurrences. In the second stage, a spectral encoder maps input spectra (IR, 1H-NMR, 13C-NMR) into a latent embedding used to condition the pre-trained generator, which is fine-tuned for direct spectra-to-molecule generation. This formulation bridges fragment-level chemical modeling with spectral evidence, yielding accurate molecular predictions. Empirical results demonstrate that NMIRacle outperforms existing baselines on molecular elucidation, while maintaining robust performance across increasing levels of molecular complexity.
Federico Ottomano, Yingzhen Li, Alex M. Ganose