Daily Papers

This paper challenges the recent paradigm in atomic property prediction that links progress to growing dataset sizes and computational resources. We show that pretraining on a carefully selected, task-relevant dataset can match or even surpass large-scale pretraining, while using as little as 1/24th of the computational cost. We introduce the Chemical Similarity Index (CSI), a novel metric inspired by computer vision's Fr\'echet Inception Distance, for molecular graphs which quantifies the alignment between upstream pretraining datasets and downstream tasks. By selecting the most relevant dataset with minimal CSI distance, we show that models pretrained on a smaller, focused dataset consistently outperform those pretrained on massive, mixed datasets such as JMP, even when those larger datasets include the relevant dataset. Counterintuitively, we also find that indiscriminately adding more data can degrade model performance when the additional data poorly aligns with the task at hand. Our findings highlight that quality often outperforms quantity in pretraining for atomic property prediction.

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

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.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Worldwide image geolocalization-the task of predicting GPS coordinates from images taken anywhere on Earth-poses a fundamental challenge due to the vast diversity in visual content across regions. While recent approaches adopt a two-stage pipeline of retrieving candidates and selecting the best match, they typically rely on simplistic similarity heuristics and point-wise supervision, failing to model spatial relationships among candidates. In this paper, we propose GeoRanker, a distance-aware ranking framework that leverages large vision-language models to jointly encode query-candidate interactions and predict geographic proximity. In addition, we introduce a multi-order distance loss that ranks both absolute and relative distances, enabling the model to reason over structured spatial relationships. To support this, we curate GeoRanking, the first dataset explicitly designed for geographic ranking tasks with multimodal candidate information. GeoRanker achieves state-of-the-art results on two well-established benchmarks (IM2GPS3K and YFCC4K), significantly outperforming current best methods.

Establishing dense correspondence between two images is a fundamental computer vision problem, which is typically tackled by matching local feature descriptors. However, without global awareness, such local features are often insufficient for disambiguating similar regions. And computing the pairwise feature correlation across images is both computation-expensive and memory-intensive. To make the local features aware of the global context and improve their matching accuracy, we introduce DenseGAP, a new solution for efficient Dense correspondence learning with a Graph-structured neural network conditioned on Anchor Points. Specifically, we first propose a graph structure that utilizes anchor points to provide sparse but reliable prior on inter- and intra-image context and propagates them to all image points via directed edges. We also design a graph-structured network to broadcast multi-level contexts via light-weighted message-passing layers and generate high-resolution feature maps at low memory cost. Finally, based on the predicted feature maps, we introduce a coarse-to-fine framework for accurate correspondence prediction using cycle consistency. Our feature descriptors capture both local and global information, thus enabling a continuous feature field for querying arbitrary points at high resolution. Through comprehensive ablative experiments and evaluations on large-scale indoor and outdoor datasets, we demonstrate that our method advances the state-of-the-art of correspondence learning on most benchmarks.

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

Molecular pretrained representations (MPR) has emerged as a powerful approach for addressing the challenge of limited supervised data in applications such as drug discovery and material design. While early MPR methods relied on 1D sequences and 2D graphs, recent advancements have incorporated 3D conformational information to capture rich atomic interactions. However, these prior models treat molecules merely as discrete atom sets, overlooking the space surrounding them. We argue from a physical perspective that only modeling these discrete points is insufficient. We first present a simple yet insightful observation: naively adding randomly sampled virtual points beyond atoms can surprisingly enhance MPR performance. In light of this, we propose a principled framework that incorporates the entire 3D space spanned by molecules. We implement the framework via a novel Transformer-based architecture, dubbed SpaceFormer, with three key components: (1) grid-based space discretization; (2) grid sampling/merging; and (3) efficient 3D positional encoding. Extensive experiments show that SpaceFormer significantly outperforms previous 3D MPR models across various downstream tasks with limited data, validating the benefit of leveraging the additional 3D space beyond atoms in MPR models.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

This paper proposes a simple self-supervised approach for learning a representation for visual correspondence from raw video. We cast correspondence as prediction of links in a space-time graph constructed from video. In this graph, the nodes are patches sampled from each frame, and nodes adjacent in time can share a directed edge. We learn a representation in which pairwise similarity defines transition probability of a random walk, so that long-range correspondence is computed as a walk along the graph. We optimize the representation to place high probability along paths of similarity. Targets for learning are formed without supervision, by cycle-consistency: the objective is to maximize the likelihood of returning to the initial node when walking along a graph constructed from a palindrome of frames. Thus, a single path-level constraint implicitly supervises chains of intermediate comparisons. When used as a similarity metric without adaptation, the learned representation outperforms the self-supervised state-of-the-art on label propagation tasks involving objects, semantic parts, and pose. Moreover, we demonstrate that a technique we call edge dropout, as well as self-supervised adaptation at test-time, further improve transfer for object-centric correspondence.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, large-capacity models, and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-the-shelf image matcher, together with a rapid nonparametric clustering, to construct a graph representing intra- and inter-image keypoint relations. A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inverse-compositional loss, that eliminates the need for a regularization term over the predicted transformations (and thus also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/

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.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

The binding between proteins and ligands plays a crucial role in the realm of drug discovery. Previous deep learning approaches have shown promising results over traditional computationally intensive methods, but resulting in poor generalization due to limited supervised data. In this paper, we propose to learn protein-ligand binding representation in a self-supervised learning manner. Different from existing pre-training approaches which treat proteins and ligands individually, we emphasize to discern the intricate binding patterns from fine-grained interactions. Specifically, this self-supervised learning problem is formulated as a prediction of the conclusive binding complex structure given a pocket and ligand with a Transformer based interaction module, which naturally emulates the binding process. To ensure the representation of rich binding information, we introduce two pre-training tasks, i.e.~atomic pairwise distance map prediction and mask ligand reconstruction, which comprehensively model the fine-grained interactions from both structure and feature space. Extensive experiments have demonstrated the superiority of our method across various binding tasks, including protein-ligand affinity prediction, virtual screening and protein-ligand docking.

Molecular structure recognition is the task of translating a molecular image into its graph structure. Significant variation in drawing styles and conventions exhibited in chemical literature poses a significant challenge for automating this task. In this paper, we propose MolScribe, a novel image-to-graph generation model that explicitly predicts atoms and bonds, along with their geometric layouts, to construct the molecular structure. Our model flexibly incorporates symbolic chemistry constraints to recognize chirality and expand abbreviated structures. We further develop data augmentation strategies to enhance the model robustness against domain shifts. In experiments on both synthetic and realistic molecular images, MolScribe significantly outperforms previous models, achieving 76-93% accuracy on public benchmarks. Chemists can also easily verify MolScribe's prediction, informed by its confidence estimation and atom-level alignment with the input image. MolScribe is publicly available through Python and web interfaces: https://github.com/thomas0809/MolScribe.

Nonlinear manifolds are widespread in deep visual features, where Euclidean distances often fail to capture true similarity. This limitation becomes particularly severe in prototype-based interpretable fine-grained recognition, where subtle semantic distinctions are essential. To address this challenge, we propose a novel paradigm for prototype-based recognition that anchors similarity within the intrinsic geometry of deep features. Specifically, we distill the latent manifold structure of each class into a diffusion space and introduce a differentiable Nystr\"om interpolation, making the geometry accessible to both unseen samples and learnable prototypes. To ensure efficiency, we employ compact per-class landmark sets with periodic updates. This design keeps the embedding aligned with the evolving backbone, enabling fast and scalable inference. Extensive experiments on the CUB-200-2011 and Stanford Cars datasets show that our GeoProto framework produces prototypes focusing on semantically aligned parts, significantly outperforming Euclidean prototype networks.

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.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Autoregressive models (ARMs) have become the workhorse for sequence generation tasks, since many problems can be modeled as next-token prediction. While there appears to be a natural ordering for text (i.e., left-to-right), for many data types, such as graphs, the canonical ordering is less obvious. To address this problem, we introduce a variant of ARM that generates high-dimensional data using a probabilistic ordering that is sequentially inferred from data. This model incorporates a trainable probability distribution, referred to as an order-policy, that dynamically decides the autoregressive order in a state-dependent manner. To train the model, we introduce a variational lower bound on the exact log-likelihood, which we optimize with stochastic gradient estimation. We demonstrate experimentally that our method can learn meaningful autoregressive orderings in image and graph generation. On the challenging domain of molecular graph generation, we achieve state-of-the-art results on the QM9 and ZINC250k benchmarks, evaluated using the Fr\'{e}chet ChemNet Distance (FCD).

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.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

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.

AlphaFold has transformed protein structure prediction, but emerging applications such as virtual ligand screening, proteome-wide folding, and de novo binder design demand predictions at a massive scale, where runtime and memory costs become prohibitive. A major bottleneck lies in the Pairformer backbone of AlphaFold3-style models, which relies on computationally expensive triangular primitives-especially triangle attention-for pairwise reasoning. We introduce Pairmixer, a streamlined alternative that eliminates triangle attention while preserving higher-order geometric reasoning capabilities that are critical for structure prediction. Pairmixer substantially improves computational efficiency, matching state-of-the-art structure predictors across folding and docking benchmarks, delivering up to 4x faster inference on long sequences while reducing training cost by 34%. Its efficiency alleviates the computational burden of downstream applications such as modeling large protein complexes, high-throughput ligand and binder screening, and hallucination-based design. Within BoltzDesign, for example, Pairmixer delivers over 2x faster sampling and scales to sequences ~30% longer than the memory limits of Pairformer.

While deep learning has revolutionized the prediction of rigid protein structures, modelling the conformational ensembles of Intrinsically Disordered Proteins (IDPs) remains a key frontier. Current AI paradigms present a trade-off: Protein Language Models (PLMs) capture evolutionary statistics but lack explicit physical grounding, while generative models trained to model full ensembles are computationally expensive. In this work we critically assess these limits and propose a path forward. We introduce GeoGraph, a simulation-informed surrogate trained to predict ensemble-averaged statistics of residue-residue contact-map topology directly from sequence. By featurizing coarse-grained molecular dynamics simulations into residue- and sequence-level graph descriptors, we create a robust and information-rich learning target. Our evaluation demonstrates that this approach yields representations that are more predictive of key biophysical properties than existing methods.

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.

We present a method for joint alignment of sparse in-the-wild image collections of an object category. Most prior works assume either ground-truth keypoint annotations or a large dataset of images of a single object category. However, neither of the above assumptions hold true for the long-tail of the objects present in the world. We present a self-supervised technique that directly optimizes on a sparse collection of images of a particular object/object category to obtain consistent dense correspondences across the collection. We use pairwise nearest neighbors obtained from deep features of a pre-trained vision transformer (ViT) model as noisy and sparse keypoint matches and make them dense and accurate matches by optimizing a neural network that jointly maps the image collection into a learned canonical grid. Experiments on CUB and SPair-71k benchmarks demonstrate that our method can produce globally consistent and higher quality correspondences across the image collection when compared to existing self-supervised methods. Code and other material will be made available at https://kampta.github.io/asic.

We investigate composed image retrieval with text feedback. Users gradually look for the target of interest by moving from coarse to fine-grained feedback. However, existing methods merely focus on the latter, i.e., fine-grained search, by harnessing positive and negative pairs during training. This pair-based paradigm only considers the one-to-one distance between a pair of specific points, which is not aligned with the one-to-many coarse-grained retrieval process and compromises the recall rate. In an attempt to fill this gap, we introduce a unified learning approach to simultaneously modeling the coarse- and fine-grained retrieval by considering the multi-grained uncertainty. The key idea underpinning the proposed method is to integrate fine- and coarse-grained retrieval as matching data points with small and large fluctuations, respectively. Specifically, our method contains two modules: uncertainty modeling and uncertainty regularization. (1) The uncertainty modeling simulates the multi-grained queries by introducing identically distributed fluctuations in the feature space. (2) Based on the uncertainty modeling, we further introduce uncertainty regularization to adapt the matching objective according to the fluctuation range. Compared with existing methods, the proposed strategy explicitly prevents the model from pushing away potential candidates in the early stage, and thus improves the recall rate. On the three public datasets, i.e., FashionIQ, Fashion200k, and Shoes, the proposed method has achieved +4.03%, +3.38%, and +2.40% Recall@50 accuracy over a strong baseline, respectively.

This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without re-encoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validated that every memory node now has a chance to contribute, and experimentally showed that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at 20+ FPS for multiple objects without bells and whistles.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

This paper presents a vector HD-mapping algorithm that formulates the mapping as a tracking task and uses a history of memory latents to ensure consistent reconstructions over time. Our method, MapTracker, accumulates a sensor stream into memory buffers of two latent representations: 1) Raster latents in the bird's-eye-view (BEV) space and 2) Vector latents over the road elements (i.e., pedestrian-crossings, lane-dividers, and road-boundaries). The approach borrows the query propagation paradigm from the tracking literature that explicitly associates tracked road elements from the previous frame to the current, while fusing a subset of memory latents selected with distance strides to further enhance temporal consistency. A vector latent is decoded to reconstruct the geometry of a road element. The paper further makes benchmark contributions by 1) Improving processing code for existing datasets to produce consistent ground truth with temporal alignments and 2) Augmenting existing mAP metrics with consistency checks. MapTracker significantly outperforms existing methods on both nuScenes and Agroverse2 datasets by over 8% and 19% on the conventional and the new consistency-aware metrics, respectively. The code will be available on our project page: https://map-tracker.github.io.

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

Recent advancements in self-supervised learning in the point cloud domain have demonstrated significant potential. However, these methods often suffer from drawbacks, including lengthy pre-training time, the necessity of reconstruction in the input space, or the necessity of additional modalities. In order to address these issues, we introduce Point-JEPA, a joint embedding predictive architecture designed specifically for point cloud data. To this end, we introduce a sequencer that orders point cloud patch embeddings to efficiently compute and utilize their proximity based on the indices during target and context selection. The sequencer also allows shared computations of the patch embeddings' proximity between context and target selection, further improving the efficiency. Experimentally, our method achieves competitive results with state-of-the-art methods while avoiding the reconstruction in the input space or additional modality.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching. Our code is available at: https://github.com/daidedou/diffumatch/

Accurate reconstruction of both the geometric and topological details of a 3D object from a single 2D image embodies a fundamental challenge in computer vision. Existing explicit/implicit solutions to this problem struggle to recover self-occluded geometry and/or faithfully reconstruct topological shape structures. To resolve this dilemma, we introduce LIST, a novel neural architecture that leverages local and global image features to accurately reconstruct the geometric and topological structure of a 3D object from a single image. We utilize global 2D features to predict a coarse shape of the target object and then use it as a base for higher-resolution reconstruction. By leveraging both local 2D features from the image and 3D features from the coarse prediction, we can predict the signed distance between an arbitrary point and the target surface via an implicit predictor with great accuracy. Furthermore, our model does not require camera estimation or pixel alignment. It provides an uninfluenced reconstruction from the input-view direction. Through qualitative and quantitative analysis, we show the superiority of our model in reconstructing 3D objects from both synthetic and real-world images against the state of the art.

Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps in a two-stage autoregressive manner, which may miss essential details and lead to error accumulation. Towards precise map element learning, we propose a simple yet effective architecture named PivotNet, which adopts unified pivot-based map representations and is formulated as a direct set prediction paradigm. Concretely, we first propose a novel point-to-line mask module to encode both the subordinate and geometrical point-line priors in the network. Then, a well-designed pivot dynamic matching module is proposed to model the topology in dynamic point sequences by introducing the concept of sequence matching. Furthermore, to supervise the position and topology of the vectorized point predictions, we propose a dynamic vectorized sequence loss. Extensive experiments and ablations show that PivotNet is remarkably superior to other SOTAs by 5.9 mAP at least. The code will be available soon.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

We propose a simple auto-encoder framework for molecule generation. The molecular graph is first encoded into a continuous latent representation z, which is then decoded back to a molecule. The encoding process is easy, but the decoding process remains challenging. In this work, we introduce a simple two-step decoding process. In a first step, a fully connected neural network uses the latent vector z to produce a molecular formula, for example CO_2 (one carbon and two oxygen atoms). In a second step, a graph convolutional neural network uses the same latent vector z to place bonds between the atoms that were produced in the first step (for example a double bond will be placed between the carbon and each of the oxygens). This two-step process, in which a bag of atoms is first generated, and then assembled, provides a simple framework that allows us to develop an efficient molecule auto-encoder. Numerical experiments on basic tasks such as novelty, uniqueness, validity and optimized chemical property for the 250k ZINC molecules demonstrate the performances of the proposed system. Particularly, we achieve the highest reconstruction rate of 90.5\%, improving the previous rate of 76.7\%. We also report the best property improvement results when optimization is constrained by the molecular distance between the original and generated molecules.

In recent years, persistent homology (PH) has been successfully applied to real-world data in many different settings. Despite significant computational advances, PH algorithms do not yet scale to large datasets preventing interesting applications. One approach to address computational issues posed by PH is to select a set of landmarks by subsampling from the data. Currently, these landmark points are chosen either at random or using the maxmin algorithm. Neither is ideal as random selection tends to favour dense areas of the data while the maxmin algorithm is very sensitive to noise. Here, we propose a novel approach to select landmarks specifically for PH that preserves coarse topological information of the original dataset. Our method is motivated by the Mayer-Vietoris sequence and requires only local PH computation thus enabling efficient computation. We test our landmarks on artificial datasets which contain different levels of noise and compare them to standard landmark selection techniques. We demonstrate that our landmark selection outperforms standard methods as well as a subsampling technique based on an outlier-robust version of the k--means algorithm for low sampling densities in noisy data with respect to robustness to outliers.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets (KITTI, NCLT, and Nebula) demonstrate the effectiveness of our method.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends critically on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction taskx2014generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains approx40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 dataset. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms N, and two containing only identical structures but with different unit cells. We also propose a new split for the perov-5 dataset which ensures polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered state-of-the-art in non-rigid shape matching. We first justify that under certain conditions, the learned maps, when represented in the spectral domain, are already cycle consistent. Furthermore, we identify the discrepancy that spectrally consistent maps are not necessarily spatially, or point-wise, consistent. In light of this, we present a novel design of unsupervised Deep Functional Maps, which effectively enforces the harmony of learned maps under the spectral and the point-wise representation. By taking advantage of cycle consistency, our framework produces state-of-the-art results in mapping shapes even under significant distortions. Beyond that, by independently estimating maps in both spectral and spatial domains, our method naturally alleviates over-fitting in network training, yielding superior generalization performance and accuracy within an array of challenging tests for both near-isometric and non-isometric datasets. Codes are available at https://github.com/rqhuang88/Spatiallyand-Spectrally-Consistent-Deep-Functional-Maps.

Accurate potential energy surface (PES) descriptions are essential for atomistic simulations of materials. Universal machine learning interatomic potentials (UMLIPs)^{1-3} offer a computationally efficient alternative to density functional theory (DFT)^4 for PES modeling across the periodic table. However, their accuracy today is fundamentally constrained due to a reliance on DFT relaxation data.^{5,6} Here, we introduce MatPES, a foundational PES dataset comprising sim 400,000 structures carefully sampled from 281 million molecular dynamics snapshots that span 16 billion atomic environments. We demonstrate that UMLIPs trained on the modestly sized MatPES dataset can rival, or even outperform, prior models trained on much larger datasets across a broad range of equilibrium, near-equilibrium, and molecular dynamics property benchmarks. We also introduce the first high-fidelity PES dataset based on the revised regularized strongly constrained and appropriately normed (r^2SCAN) functional^7 with greatly improved descriptions of interatomic bonding. The open source MatPES initiative emphasizes the importance of data quality over quantity in materials science and enables broad community-driven advancements toward more reliable, generalizable, and efficient UMLIPs for large-scale materials discovery and design.

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their widespread adoption in the biomolecular domain has been limited by a lack of either systematic performance benchmarks or a unified toolkit for interacting with molecular data. To address this, we present ATOM3D, a collection of both novel and existing benchmark datasets spanning several key classes of biomolecules. We implement several classes of three-dimensional molecular learning methods for each of these tasks and show that they consistently improve performance relative to methods based on one- and two-dimensional representations. The specific choice of architecture proves to be critical for performance, with three-dimensional convolutional networks excelling at tasks involving complex geometries, graph networks performing well on systems requiring detailed positional information, and the more recently developed equivariant networks showing significant promise. Our results indicate that many molecular problems stand to gain from three-dimensional molecular learning, and that there is potential for improvement on many tasks which remain underexplored. To lower the barrier to entry and facilitate further developments in the field, we also provide a comprehensive suite of tools for dataset processing, model training, and evaluation in our open-source atom3d Python package. All datasets are available for download from https://www.atom3d.ai .

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.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Deep Metric Learning (DML) methods aim at learning an embedding space in which distances are closely related to the inherent semantic similarity of the inputs. Previous studies have shown that popular benchmark datasets often contain numerous wrong labels, and DML methods are susceptible to them. Intending to study the effect of realistic noise, we create an ontology of the classes in a dataset and use it to simulate semantically coherent labeling mistakes. To train robust DML models, we propose ProcSim, a simple framework that assigns a confidence score to each sample using the normalized distance to its class representative. The experimental results show that the proposed method achieves state-of-the-art performance on the DML benchmark datasets injected with uniform and the proposed semantically coherent noise.

Lines and points are complementary local features, whose combination has proven effective for applications such as SLAM and Structure-from-Motion. The backbone of these pipelines are the local feature matchers, establishing correspondences across images. Traditionally, point and line matching have been treated as independent tasks. Recently, GlueStick proposed a GNN-based network that simultaneously operates on points and lines to establish matches. While running a single joint matching reduced the overall computational complexity, the heavy architecture prevented real-time applications or deployment to edge devices. Inspired by recent progress in point matching, we propose LightGlueStick, a lightweight matcher for points and line segments. The key novel component in our architecture is the Attentional Line Message Passing (ALMP), which explicitly exposes the connectivity of the lines to the network, allowing for efficient communication between nodes. In thorough experiments we show that LightGlueStick establishes a new state-of-the-art across different benchmarks. The code is available at https://github.com/aubingazhib/LightGlueStick.

Can we relocalize in a scene represented by a single reference image? Standard visual relocalization requires hundreds of images and scale calibration to build a scene-specific 3D map. In contrast, we propose Map-free Relocalization, i.e., using only one photo of a scene to enable instant, metric scaled relocalization. Existing datasets are not suitable to benchmark map-free relocalization, due to their focus on large scenes or their limited variability. Thus, we have constructed a new dataset of 655 small places of interest, such as sculptures, murals and fountains, collected worldwide. Each place comes with a reference image to serve as a relocalization anchor, and dozens of query images with known, metric camera poses. The dataset features changing conditions, stark viewpoint changes, high variability across places, and queries with low to no visual overlap with the reference image. We identify two viable families of existing methods to provide baseline results: relative pose regression, and feature matching combined with single-image depth prediction. While these methods show reasonable performance on some favorable scenes in our dataset, map-free relocalization proves to be a challenge that requires new, innovative solutions.

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

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.

Large-scale pre-training has shown promising results on the vision-and-language navigation (VLN) task. However, most existing pre-training methods employ discrete panoramas to learn visual-textual associations. This requires the model to implicitly correlate incomplete, duplicate observations within the panoramas, which may impair an agent's spatial understanding. Thus, we propose a new map-based pre-training paradigm that is spatial-aware for use in VLN. Concretely, we build a local metric map to explicitly aggregate incomplete observations and remove duplicates, while modeling navigation dependency in a global topological map. This hybrid design can balance the demand of VLN for both short-term reasoning and long-term planning. Then, based on the hybrid map, we devise a pre-training framework to learn a multimodal map representation, which enhances spatial-aware cross-modal reasoning thereby facilitating the language-guided navigation goal. Extensive experiments demonstrate the effectiveness of the map-based pre-training route for VLN, and the proposed method achieves state-of-the-art on four VLN benchmarks.

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.

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.

Vectorized HD map is essential for autonomous driving. Remarkable work has been achieved in recent years, but there are still major issues: (1) in the generation of the BEV features, single modality-based methods are of limited perception capability, while direct concatenation-based multi-modal methods fail to capture synergies and disparities between different modalities, resulting in limited ranges with feature holes; (2) in the classification and localization of map elements, only point information is used without the consideration of element infor-mation and neglects the interaction between point information and element information, leading to erroneous shapes and element entanglement with low accuracy. To address above issues, we introduce SuperMapNet for long-range and high-accuracy vectorized HD map construction. It uses both camera images and LiDAR point clouds as input, and first tightly couple semantic information from camera images and geometric information from LiDAR point clouds by a cross-attention based synergy enhancement module and a flow-based disparity alignment module for long-range BEV feature generation. And then, local features from point queries and global features from element queries are tightly coupled by three-level interactions for high-accuracy classification and localization, where Point2Point interaction learns local geometric information between points of the same element and of each point, Element2Element interaction learns relation constraints between different elements and semantic information of each elements, and Point2Element interaction learns complement element information for its constituent points. Experiments on the nuScenes and Argoverse2 datasets demonstrate superior performances, surpassing SOTAs over 14.9/8.8 mAP and 18.5/3.1 mAP under hard/easy settings, respectively. The code is made publicly available1.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Link prediction, a fundamental task on graphs, has proven indispensable in various applications, e.g., friend recommendation, protein analysis, and drug interaction prediction. However, since datasets span a multitude of domains, they could have distinct underlying mechanisms of link formation. Evidence in existing literature underscores the absence of a universally best algorithm suitable for all datasets. In this paper, we endeavor to explore principles of link prediction across diverse datasets from a data-centric perspective. We recognize three fundamental factors critical to link prediction: local structural proximity, global structural proximity, and feature proximity. We then unearth relationships among those factors where (i) global structural proximity only shows effectiveness when local structural proximity is deficient. (ii) The incompatibility can be found between feature and structural proximity. Such incompatibility leads to GNNs for Link Prediction (GNN4LP) consistently underperforming on edges where the feature proximity factor dominates. Inspired by these new insights from a data perspective, we offer practical instruction for GNN4LP model design and guidelines for selecting appropriate benchmark datasets for more comprehensive evaluations.

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive accuracy, interpretability, and computational efficiency remains a major challenge. In this work, we introduce a novel Graph Neural Network (GNN) architecture that combines compressed higher-order topological signals with standard molecular features. Our approach captures global geometric information while preserving computational tractability and human-interpretable structure. We evaluate our model across a range of benchmarks, from small-molecule datasets to complex material datasets, and demonstrate superior performance using a parameter-efficient architecture. We achieve the best performing results in both accuracy and robustness across almost all benchmarks. We open source all code All code and results can be found on Github https://github.com/rahulkhorana/TFC-PACT-Net.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Large-scale visual localization systems continue to rely on 3D point clouds built from image collections using structure-from-motion. While the 3D points in these models are represented using local image features, directly matching a query image's local features against the point cloud is challenging due to the scale of the nearest-neighbor search problem. Many recent approaches to visual localization have thus proposed a hybrid method, where first a global (per image) embedding is used to retrieve a small subset of database images, and local features of the query are matched only against those. It seems to have become common belief that global embeddings are critical for said image-retrieval in visual localization, despite the significant downside of having to compute two feature types for each query image. In this paper, we take a step back from this assumption and propose Constrained Approximate Nearest Neighbors (CANN), a joint solution of k-nearest-neighbors across both the geometry and appearance space using only local features. We first derive the theoretical foundation for k-nearest-neighbor retrieval across multiple metrics and then showcase how CANN improves visual localization. Our experiments on public localization benchmarks demonstrate that our method significantly outperforms both state-of-the-art global feature-based retrieval and approaches using local feature aggregation schemes. Moreover, it is an order of magnitude faster in both index and query time than feature aggregation schemes for these datasets. Code will be released.

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

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.

Line segments are powerful features complementary to points. They offer structural cues, robust to drastic viewpoint and illumination changes, and can be present even in texture-less areas. However, describing and matching them is more challenging compared to points due to partial occlusions, lack of texture, or repetitiveness. This paper introduces a new matching paradigm, where points, lines, and their descriptors are unified into a single wireframe structure. We propose GlueStick, a deep matching Graph Neural Network (GNN) that takes two wireframes from different images and leverages the connectivity information between nodes to better glue them together. In addition to the increased efficiency brought by the joint matching, we also demonstrate a large boost of performance when leveraging the complementary nature of these two features in a single architecture. We show that our matching strategy outperforms the state-of-the-art approaches independently matching line segments and points for a wide variety of datasets and tasks. The code is available at https://github.com/cvg/GlueStick.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

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 study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

Establishing the relationship between 3D structures and the energy states of molecular systems has proven to be a promising approach for learning 3D molecular representations. However, existing methods are limited to modeling the molecular energy states from classical mechanics. This limitation results in a significant oversight of quantum mechanical effects, such as quantized (discrete) energy level structures, which offer a more accurate estimation of molecular energy and can be experimentally measured through energy spectra. In this paper, we propose to utilize the energy spectra to enhance the pre-training of 3D molecular representations (MolSpectra), thereby infusing the knowledge of quantum mechanics into the molecular representations. Specifically, we propose SpecFormer, a multi-spectrum encoder for encoding molecular spectra via masked patch reconstruction. By further aligning outputs from the 3D encoder and spectrum encoder using a contrastive objective, we enhance the 3D encoder's understanding of molecules. Evaluations on public benchmarks reveal that our pre-trained representations surpass existing methods in predicting molecular properties and modeling dynamics.

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.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

Large-scale pre-training methodologies for chemical language models represent a breakthrough in cheminformatics. These methods excel in tasks such as property prediction and molecule generation by learning contextualized representations of input tokens through self-supervised learning on large unlabeled corpora. Typically, this involves pre-training on unlabeled data followed by fine-tuning on specific tasks, reducing dependence on annotated datasets and broadening chemical language representation understanding. This paper introduces a large encoder-decoder chemical foundation models pre-trained on a curated dataset of 91 million SMILES samples sourced from PubChem, which is equivalent to 4 billion of molecular tokens. The proposed foundation model supports different complex tasks, including quantum property prediction, and offer flexibility with two main variants (289M and 8times289M). Our experiments across multiple benchmark datasets validate the capacity of the proposed model in providing state-of-the-art results for different tasks. We also provide a preliminary assessment of the compositionality of the embedding space as a prerequisite for the reasoning tasks. We demonstrate that the produced latent space is separable compared to the state-of-the-art with few-shot learning capabilities.

Recently, pre-trained foundation models have enabled significant advancements in multiple fields. In molecular machine learning, however, where datasets are often hand-curated, and hence typically small, the lack of datasets with labeled features, and codebases to manage those datasets, has hindered the development of foundation models. In this work, we present seven novel datasets categorized by size into three distinct categories: ToyMix, LargeMix and UltraLarge. These datasets push the boundaries in both the scale and the diversity of supervised labels for molecular learning. They cover nearly 100 million molecules and over 3000 sparsely defined tasks, totaling more than 13 billion individual labels of both quantum and biological nature. In comparison, our datasets contain 300 times more data points than the widely used OGB-LSC PCQM4Mv2 dataset, and 13 times more than the quantum-only QM1B dataset. In addition, to support the development of foundational models based on our proposed datasets, we present the Graphium graph machine learning library which simplifies the process of building and training molecular machine learning models for multi-task and multi-level molecular datasets. Finally, we present a range of baseline results as a starting point of multi-task and multi-level training on these datasets. Empirically, we observe that performance on low-resource biological datasets show improvement by also training on large amounts of quantum data. This indicates that there may be potential in multi-task and multi-level training of a foundation model and fine-tuning it to resource-constrained downstream tasks.

The rapid development of universal machine learning interatomic potentials (uMLIPs) has demonstrated the possibility for generalizable learning of the universal potential energy surface. In principle, the accuracy of uMLIPs can be further improved by bridging the model from lower-fidelity datasets to high-fidelity ones. In this work, we analyze the challenge of this transfer learning problem within the CHGNet framework. We show that significant energy scale shifts and poor correlations between GGA and r^2SCAN pose challenges to cross-functional data transferability in uMLIPs. By benchmarking different transfer learning approaches on the MP-r^2SCAN dataset of 0.24 million structures, we demonstrate the importance of elemental energy referencing in the transfer learning of uMLIPs. By comparing the scaling law with and without the pre-training on a low-fidelity dataset, we show that significant data efficiency can still be achieved through transfer learning, even with a target dataset of sub-million structures. We highlight the importance of proper transfer learning and multi-fidelity learning in creating next-generation uMLIPs on high-fidelity data.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Foundation models have been transformational in machine learning fields such as natural language processing and computer vision. Similar success in atomic property prediction has been limited due to the challenges of training effective models across multiple chemical domains. To address this, we introduce Joint Multi-domain Pre-training (JMP), a supervised pre-training strategy that simultaneously trains on multiple datasets from different chemical domains, treating each dataset as a unique pre-training task within a multi-task framework. Our combined training dataset consists of sim120M systems from OC20, OC22, ANI-1x, and Transition-1x. We evaluate performance and generalization by fine-tuning over a diverse set of downstream tasks and datasets including: QM9, rMD17, MatBench, QMOF, SPICE, and MD22. JMP demonstrates an average improvement of 59% over training from scratch, and matches or sets state-of-the-art on 34 out of 40 tasks. Our work highlights the potential of pre-training strategies that utilize diverse data to advance property prediction across chemical domains, especially for low-data tasks.

Semantic correspondence methods have advanced to obtaining high-quality correspondences employing complicated networks, aiming to maximize the model capacity. However, despite the performance improvements, they may remain constrained by the scarcity of training keypoint pairs, a consequence of the limited training images and the sparsity of keypoints. This paper builds on the hypothesis that there is an inherent data-hungry matter in learning semantic correspondences and uncovers the models can be more trained by employing densified training pairs. We demonstrate a simple machine annotator reliably enriches paired key points via machine supervision, requiring neither extra labeled key points nor trainable modules from unlabeled images. Consequently, our models surpass current state-of-the-art models on semantic correspondence learning benchmarks like SPair-71k, PF-PASCAL, and PF-WILLOW and enjoy further robustness on corruption benchmarks. Our code is available at https://github.com/naver-ai/matchme.

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.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

Most text-based information retrieval (IR) systems index objects by words or phrases. These discrete systems have been augmented by models that use embeddings to measure similarity in continuous space. But continuous-space models are typically used just to re-rank the top candidates. We consider the problem of end-to-end continuous retrieval, where standard approximate nearest neighbor (ANN) search replaces the usual discrete inverted index, and rely entirely on distances between learned embeddings. By training simple models specifically for retrieval, with an appropriate model architecture, we improve on a discrete baseline by 8% and 26% (MAP) on two similar-question retrieval tasks. We also discuss the problem of evaluation for retrieval systems, and show how to modify existing pairwise similarity datasets for this purpose.

Unsigned distance fields (UDFs) provide a versatile framework for representing a diverse array of 3D shapes, encompassing both watertight and non-watertight geometries. Traditional UDF learning methods typically require extensive training on large 3D shape datasets, which is costly and necessitates re-training for new datasets. This paper presents a novel neural framework, LoSF-UDF, for reconstructing surfaces from 3D point clouds by leveraging local shape functions to learn UDFs. We observe that 3D shapes manifest simple patterns in localized regions, prompting us to develop a training dataset of point cloud patches characterized by mathematical functions that represent a continuum from smooth surfaces to sharp edges and corners. Our approach learns features within a specific radius around each query point and utilizes an attention mechanism to focus on the crucial features for UDF estimation. Despite being highly lightweight, with only 653 KB of trainable parameters and a modest-sized training dataset with 0.5 GB storage, our method enables efficient and robust surface reconstruction from point clouds without requiring for shape-specific training. Furthermore, our method exhibits enhanced resilience to noise and outliers in point clouds compared to existing methods. We conduct comprehensive experiments and comparisons across various datasets, including synthetic and real-scanned point clouds, to validate our method's efficacy. Notably, our lightweight framework offers rapid and reliable initialization for other unsupervised iterative approaches, improving both the efficiency and accuracy of their reconstructions. Our project and code are available at https://jbhu67.github.io/LoSF-UDF.github.io.

Vision-Language Models (VLMs) have demonstrated impressive performance on zero-shot classification, i.e. classification when provided merely with a list of class names. In this paper, we tackle the case of zero-shot classification in the presence of unlabeled data. We leverage the graph structure of the unlabeled data and introduce ZLaP, a method based on label propagation (LP) that utilizes geodesic distances for classification. We tailor LP to graphs containing both text and image features and further propose an efficient method for performing inductive inference based on a dual solution and a sparsification step. We perform extensive experiments to evaluate the effectiveness of our method on 14 common datasets and show that ZLaP outperforms the latest related works. Code: https://github.com/vladan-stojnic/ZLaP

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to efficiently navigate chemical space. Scientific foundation models trained on large unlabeled datasets offer a path toward exploring chemical space across diverse application domains. Here we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenization scheme that comprehensively captures nuclear, electronic, and geometric information, MIST learns from a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure -- property relationships and match or exceed state-of-the-art performance across benchmarks spanning physiology, electrochemistry, and quantum chemistry. We demonstrate the ability of these models to solve real-world problems across chemical space, including multiobjective electrolyte solvent screening, olfactory perception mapping, isotope half-life prediction, stereochemical reasoning for chiral organometallic compounds, and binary and multi-component mixture property prediction. Probing MIST models using mechanistic interpretability methods reveals identifiable patterns and trends not explicitly present in the training data, suggesting that the models learn generalizable scientific concepts. We formulate hyperparameter-penalized Bayesian neural scaling laws and use them to reduce the computational cost of model development by an order of magnitude. The methods and findings presented here represent a significant step toward accelerating materials discovery, design, and optimization using foundation models and provide valuable guidance for training compute-optimal scientific foundation models.

Molecular Representation Learning (MRL) has proven impactful in numerous biochemical applications such as drug discovery and enzyme design. While Graph Neural Networks (GNNs) are effective at learning molecular representations from a 2D molecular graph or a single 3D structure, existing works often overlook the flexible nature of molecules, which continuously interconvert across conformations via chemical bond rotations and minor vibrational perturbations. To better account for molecular flexibility, some recent works formulate MRL as an ensemble learning problem, focusing on explicitly learning from a set of conformer structures. However, most of these studies have limited datasets, tasks, and models. In this work, we introduce the first MoleculAR Conformer Ensemble Learning (MARCEL) benchmark to thoroughly evaluate the potential of learning on conformer ensembles and suggest promising research directions. MARCEL includes four datasets covering diverse molecule- and reaction-level properties of chemically diverse molecules including organocatalysts and transition-metal catalysts, extending beyond the scope of common GNN benchmarks that are confined to drug-like molecules. In addition, we conduct a comprehensive empirical study, which benchmarks representative 1D, 2D, and 3D molecular representation learning models, along with two strategies that explicitly incorporate conformer ensembles into 3D MRL models. Our findings reveal that direct learning from an accessible conformer space can improve performance on a variety of tasks and models.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

The ability to quickly and accurately compute properties from atomic simulations is critical for advancing a large number of applications in chemistry and materials science including drug discovery, energy storage, and semiconductor manufacturing. To address this need, Meta FAIR presents a family of Universal Models for Atoms (UMA), designed to push the frontier of speed, accuracy, and generalization. UMA models are trained on half a billion unique 3D atomic structures (the largest training runs to date) by compiling data across multiple chemical domains, e.g. molecules, materials, and catalysts. We develop empirical scaling laws to help understand how to increase model capacity alongside dataset size to achieve the best accuracy. The UMA small and medium models utilize a novel architectural design we refer to as mixture of linear experts that enables increasing model capacity without sacrificing speed. For example, UMA-medium has 1.4B parameters but only ~50M active parameters per atomic structure. We evaluate UMA models on a diverse set of applications across multiple domains and find that, remarkably, a single model without any fine-tuning can perform similarly or better than specialized models. We are releasing the UMA code, weights, and associated data to accelerate computational workflows and enable the community to continue to build increasingly capable AI models.

This work presents Prior Depth Anything, a framework that combines incomplete but precise metric information in depth measurement with relative but complete geometric structures in depth prediction, generating accurate, dense, and detailed metric depth maps for any scene. To this end, we design a coarse-to-fine pipeline to progressively integrate the two complementary depth sources. First, we introduce pixel-level metric alignment and distance-aware weighting to pre-fill diverse metric priors by explicitly using depth prediction. It effectively narrows the domain gap between prior patterns, enhancing generalization across varying scenarios. Second, we develop a conditioned monocular depth estimation (MDE) model to refine the inherent noise of depth priors. By conditioning on the normalized pre-filled prior and prediction, the model further implicitly merges the two complementary depth sources. Our model showcases impressive zero-shot generalization across depth completion, super-resolution, and inpainting over 7 real-world datasets, matching or even surpassing previous task-specific methods. More importantly, it performs well on challenging, unseen mixed priors and enables test-time improvements by switching prediction models, providing a flexible accuracy-efficiency trade-off while evolving with advancements in MDE models.

Top-down Bird's Eye View (BEV) maps are a popular representation for ground robot navigation due to their richness and flexibility for downstream tasks. While recent methods have shown promise for predicting BEV maps from First-Person View (FPV) images, their generalizability is limited to small regions captured by current autonomous vehicle-based datasets. In this context, we show that a more scalable approach towards generalizable map prediction can be enabled by using two large-scale crowd-sourced mapping platforms, Mapillary for FPV images and OpenStreetMap for BEV semantic maps. We introduce Map It Anywhere (MIA), a data engine that enables seamless curation and modeling of labeled map prediction data from existing open-source map platforms. Using our MIA data engine, we display the ease of automatically collecting a dataset of 1.2 million pairs of FPV images & BEV maps encompassing diverse geographies, landscapes, environmental factors, camera models & capture scenarios. We further train a simple camera model-agnostic model on this data for BEV map prediction. Extensive evaluations using established benchmarks and our dataset show that the data curated by MIA enables effective pretraining for generalizable BEV map prediction, with zero-shot performance far exceeding baselines trained on existing datasets by 35%. Our analysis highlights the promise of using large-scale public maps for developing & testing generalizable BEV perception, paving the way for more robust autonomous navigation.

Fuzzy similarity join is an important database operator widely used in practice. So far the research community has focused exclusively on optimizing fuzzy join scalability. However, practitioners today also struggle to optimize fuzzy-join quality, because they face a daunting space of parameters (e.g., distance-functions, distance-thresholds, tokenization-options, etc.), and often have to resort to a manual trial-and-error approach to program these parameters in order to optimize fuzzy-join quality. This key challenge of automatically generating high-quality fuzzy-join programs has received surprisingly little attention thus far. In this work, we study the problem of "auto-program" fuzzy-joins. Leveraging a geometric interpretation of distance-functions, we develop an unsupervised Auto-FuzzyJoin framework that can infer suitable fuzzy-join programs on given input tables, without requiring explicit human input such as labeled training data. Using Auto-FuzzyJoin, users only need to provide two input tables L and R, and a desired precision target tau (say 0.9). Auto-FuzzyJoin leverages the fact that one of the input is a reference table to automatically program fuzzy-joins that meet the precision target tau in expectation, while maximizing fuzzy-join recall (defined as the number of correctly joined records). Experiments on both existing benchmarks and a new benchmark with 50 fuzzy-join tasks created from Wikipedia data suggest that the proposed Auto-FuzzyJoin significantly outperforms existing unsupervised approaches, and is surprisingly competitive even against supervised approaches (e.g., Magellan and DeepMatcher) when 50\% of ground-truth labels are used as training data.

Image-text matching remains a challenging task due to heterogeneous semantic diversity across modalities and insufficient distance separability within triplets. Different from previous approaches focusing on enhancing multi-modal representations or exploiting cross-modal correspondence for more accurate retrieval, in this paper we aim to leverage the knowledge transfer between peer branches in a boosting manner to seek a more powerful matching model. Specifically, we propose a brand-new Deep Boosting Learning (DBL) algorithm, where an anchor branch is first trained to provide insights into the data properties, with a target branch gaining more advanced knowledge to develop optimal features and distance metrics. Concretely, an anchor branch initially learns the absolute or relative distance between positive and negative pairs, providing a foundational understanding of the particular network and data distribution. Building upon this knowledge, a target branch is concurrently tasked with more adaptive margin constraints to further enlarge the relative distance between matched and unmatched samples. Extensive experiments validate that our DBL can achieve impressive and consistent improvements based on various recent state-of-the-art models in the image-text matching field, and outperform related popular cooperative strategies, e.g., Conventional Distillation, Mutual Learning, and Contrastive Learning. Beyond the above, we confirm that DBL can be seamlessly integrated into their training scenarios and achieve superior performance under the same computational costs, demonstrating the flexibility and broad applicability of our proposed method. Our code is publicly available at: https://github.com/Paranioar/DBL.

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

The Schr\"odinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space R^{D} and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces S^{D}. Notable examples of such sets S are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB which we call Categorical Schr\"odinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images.

In this work, we present a method to generate a configurational level fingerprint for polymers using the Bead-Spring-Model. Unlike some of the previous fingerprinting approaches that employ monomer-level information where atomistic descriptors are computed using quantum chemistry calculations, this approach incorporates configurational information from a coarse-grained model of a long polymer chain. The proposed approach may be advantageous for the study of behavior resulting from large molecular weights. To create this fingerprint, we make use of two kinds of descriptors. First, we calculate certain geometric descriptors like Re2, Rg2 etc. and label them as Calculated Descriptors. Second, we generate a set of data-driven descriptors using an unsupervised autoencoder model and call them Learnt Descriptors. Using a combination of both of them, we are able to learn mappings from the structure to various properties of the polymer chain by training ML models. We test our fingerprint to predict the probability of occurrence of a configuration at equilibrium, which is approximated by a simple linear relationship between the instantaneous internal energy and equilibrium average internal energy.

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.

We introduce a new framework for molecular graph generation with 3D molecular generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps molecular graphs to Euclidean point clouds via synthetic conformer coordinates and learns the inverse map using an E(n)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecular generative models. This approach simplifies the graph generation problem - without relying on molecular fragments nor autoregressive decoding - into a point cloud generation problem followed by node and edge classification tasks. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 30% on ZINC250K and 16% on the large-scale GuacaMol dataset while improving conditional generation by up to 3.9 times.

In deep metric learning, the Triplet Loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that plagues the Triplet Loss is network collapse, an undesirable phenomenon where the network projects the embeddings of all data onto a single point. Researchers predominately solve this problem by using triplet mining strategies. While hard negative mining is the most effective of these strategies, existing formulations lack strong theoretical justification for their empirical success. In this paper, we utilize the mathematical theory of isometric approximation to show an equivalence between the Triplet Loss sampled by hard negative mining and an optimization problem that minimizes a Hausdorff-like distance between the neural network and its ideal counterpart function. This provides the theoretical justifications for hard negative mining's empirical efficacy. In addition, our novel application of the isometric approximation theorem provides the groundwork for future forms of hard negative mining that avoid network collapse. Our theory can also be extended to analyze other Euclidean space-based metric learning methods like Ladder Loss or Contrastive Learning.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

Recent developments in deep learning have made remarkable progress in speeding up the prediction of quantum chemical (QC) properties by removing the need for expensive electronic structure calculations like density functional theory. However, previous methods learned from 1D SMILES sequences or 2D molecular graphs failed to achieve high accuracy as QC properties primarily depend on the 3D equilibrium conformations optimized by electronic structure methods, far different from the sequence-type and graph-type data. In this paper, we propose a novel approach called Uni-Mol+ to tackle this challenge. Uni-Mol+ first generates a raw 3D molecule conformation from inexpensive methods such as RDKit. Then, the raw conformation is iteratively updated to its target DFT equilibrium conformation using neural networks, and the learned conformation will be used to predict the QC properties. To effectively learn this update process towards the equilibrium conformation, we introduce a two-track Transformer model backbone and train it with the QC property prediction task. We also design a novel approach to guide the model's training process. Our extensive benchmarking results demonstrate that the proposed Uni-Mol+ significantly improves the accuracy of QC property prediction in various datasets. We have made the code and model publicly available at https://github.com/dptech-corp/Uni-Mol.

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce Test3R, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets (I_1,I_2,I_3), Test3R generates reconstructions from pairs (I_1,I_2) and (I_1,I_3). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image I_1. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

The automatic analysis of chemical literature has immense potential to accelerate the discovery of new materials and drugs. Much of the critical information in patent documents and scientific articles is contained in figures, depicting the molecule structures. However, automatically parsing the exact chemical structure is a formidable challenge, due to the amount of detailed information, the diversity of drawing styles, and the need for training data. In this work, we introduce MolGrapher to recognize chemical structures visually. First, a deep keypoint detector detects the atoms. Second, we treat all candidate atoms and bonds as nodes and put them in a graph. This construct allows a natural graph representation of the molecule. Last, we classify atom and bond nodes in the graph with a Graph Neural Network. To address the lack of real training data, we propose a synthetic data generation pipeline producing diverse and realistic results. In addition, we introduce a large-scale benchmark of annotated real molecule images, USPTO-30K, to spur research on this critical topic. Extensive experiments on five datasets show that our approach significantly outperforms classical and learning-based methods in most settings. Code, models, and datasets are available.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

Modern optimization in experimental chemistry employs algorithmic search through black-box parameter spaces. Here we demonstrate that pre-trained knowledge in large language models (LLMs) fundamentally changes this paradigm. Using six fully enumerated categorical reaction datasets (768 - 5,684 experiments), we benchmark LLM-guided optimization (LLM-GO) against Bayesian optimization (BO) and random sampling. Frontier LLMs consistently match or exceed BO performance across five single-objective datasets, with advantages growing as parameter complexity increases and high-performing conditions become scarce (<5% of space). BO retains superiority only for explicit multi-objective trade-offs. To understand these contrasting behaviors, we introduce a topology-agnostic information theory framework quantifying sampling diversity throughout optimization campaigns. This analysis reveals that LLMs maintain systematically higher exploration entropy than BO across all datasets while achieving superior performance, with advantages most pronounced in solution-scarce parameter spaces where high-entropy exploration typically fails - suggesting that pre-trained domain knowledge enables more effective navigation of chemical parameter space rather than replacing structured exploration strategies. To enable transparent benchmarking and community validation, we release Iron Mind (https://gomes.andrew.cmu.edu/iron-mind), a no-code platform for side-by-side evaluation of human, algorithmic, and LLM optimization campaigns with public leaderboards and complete trajectories. Our findings establish that LLM-GO excels precisely where traditional methods struggle: complex categorical spaces requiring domain understanding rather than mathematical optimization.

In molecular dynamics (MD) simulations, rare events, such as protein folding, are typically studied by means of enhanced sampling techniques, most of which rely on the definition of a collective variable (CV) along which the acceleration occurs. Obtaining an expressive CV is crucial, but often hindered by the lack of information about the particular event, e.g., the transition from unfolded to folded conformation. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesic interpolations resembling protein folding transitions, thereby improving sampling efficiency without true transition state samples. Leveraging interpolation progress parameters, we introduce a regression-based learning scheme for CV models, which outperforms classifier-based methods when transition state data is limited and noisy