Daily Papers

RTK-SLAM systems integrate simultaneous localization and mapping (SLAM) with real-time kinematic (RTK) GNSS positioning, promising both relative consistency and globally referenced coordinates for efficient georeferenced surveying. A critical and underappreciated issue is that the standard evaluation metric, Absolute Trajectory Error (ATE), first fits an optimal rigid-body transformation between the estimated trajectory and reference before computing errors. This so-called SE(3) alignment absorbs global drift and systematic errors, making trajectories appear more accurate than they are in practice, and is unsuitable for evaluating the global accuracy of RTK-SLAM. We present a geodetically referenced dataset and evaluation methodology that expose this gap. A key design principle is that the RTK receiver is used solely as a system input, while ground truth is established independently via a geodetic total station. This separation is absent from all existing datasets, where GNSS typically serves as (part of) the ground truth. The dataset is collected with a handheld RTK-SLAM device, comprising two scenes. We evaluate LiDAR-inertial, visual-inertial, and LiDAR-visual-inertial RTK-SLAM systems alongside standalone RTK, reporting direct global accuracy and SE(3)-aligned relative accuracy to make the gap explicit. Results show that SE(3) alignment can underestimate absolute positioning error by up to 76\%. RTK-SLAM achieves centimeter-level absolute accuracy in open-sky conditions and maintains decimeter-level global accuracy indoors, where standalone RTK degrades to tens of meters. The dataset, calibration files, and evaluation scripts are publicly available at https://rtk-slam-dataset.github.io/.

High-fidelity closed-loop simulation for autonomous driving increasingly relies on dense multi-view 3D reconstruction. While recent feed-forward geometric foundation models have revolutionized per-scene optimization, applying them to continuous, long-horizon driving sequences is computationally intractable due to GPU memory limits and the quadratic complexity of global attention. Existing scaling strategies are fundamentally limited, as causal streaming suffers from compounding scale drift and trajectory deviation, while rigid "chunk-then-align" heuristics fragment global context and produce trajectory discontinuities. To address these limitations, we introduce Drive3R, a block-wise streaming geometric foundation model. Its block-wise causal attention resolves the scalability bottleneck of fully bidirectional attention while avoiding the loss of local future context in purely causal streaming. Its confidence-aware re-anchoring further mitigates long-range drift by detecting unreliable streaming states, re-initializing the KV cache, and stitching refreshed segments through SE(3) alignment. Extensive experiments demonstrate that Drive3R establishes a new state-of-the-art on nuScenes, KITTI, and Waymo. Specifically, on nuScenes, it improves over the recent DVGT-2 baseline from 0.1806 to 0.1081 in AbsRel, from 0.6750 to 0.5344 in point-cloud Accuracy, and from 1.5812 to 0.9092 in ATE.

All-atom generative modeling of 3D biomolecular complexes has emerged as the dominant paradigm for predicting the structure of proteins and protein-ligand systems. Generating structures at the atomic level of fidelity, however, typically requires expensive iterative diffusion rollouts, making both conventional deployment and inference-time search techniques computationally costly. In this paper, we introduce the Denoiser Cofolding All-Atom Flowmap (DeCAF) framework for distilling state-of-the-art all-atom cofolding models into all-atom flow maps that produce high-quality samples in only a few inference steps. We build DeCAF on a denoiser-based formulation of flow maps with endpoint losses that naturally support SE(3) rigid alignment, which we show is critical for training accurate models. We further derive a simple change of variables that lets DeCAF operate in the σ-space noise schedule of EDM-style architectures, enabling direct distillation from pretrained cofolding diffusion models. Equipped with DeCAF's flowmap lookahead, we introduce a purpose-built inference-time framework that improves sampling through reward-guided search. Empirically, DeCAF-Boltz statistically improves over Boltz-1x in both accuracy (RMSD) and physical validity scores of protein-ligand poses at strict NFE budgets on the challenging Runs N' Poses, while also showing a more optimal Pareto frontier across all inference compute budgets on PoseBusters. Distilling the state-of-the-art Pearl cofolding model, DeCAF-Pearl outperforms diffusion-based cofolding models and matches its teacher on success rate while using 5x fewer NFEs. We release our code at https://github.com/genesistherapeutics/decaf.

Action-conditioned world models are increasingly used as learned simulators for policy evaluation and improvement, yet their effectiveness rests on an unverified assumption: generated futures faithfully reflect arbitrary valid actions. Existing benchmarks are typically confined to expert demonstrations, leaving off-expert action following inadequately evaluated. To address this gap, we introduce WorldEcho, which probes action following over a broader action distribution using visual integrity and SE(3) trajectory alignment. Our diagnosis shows that current world models reasonably execute expert actions but struggle with diverse off-expert trajectories, either ignoring the commanded actions or producing visually invalid rollouts. We further propose WorldSync, which strengthens action following along three complementary axes: distributional coverage, representational grounding, and intervention-effect alignment. It broadens the training distribution over action consequences, grounds intermediate video representations in action-induced robot dynamics through an Action-Forcing Expert, and aligns predicted changes under action interventions with the corresponding changes in ground-truth futures. Experiments on RoboTwin benchmarks and real-robot tasks show that WorldSync improves WorldEcho metrics and serves as a more reliable simulator for iterative policy improvement, enabling policies to achieve higher success rates.

Recent vision-language-action (VLA) models and world action models (WAMs) advance robotic manipulation by enriching intermediate representations with auxiliary spatial features or future visual-state prediction. However, these representations largely remain within the observation space and do not share the rigid-body geometry of the action space, forcing the action decoder to implicitly recover this geometry. We propose OASIS, a visuomotor policy that aligns the intermediate representation with the action space via SE(3) end-effector trajectory prediction. OASIS couples a 3D-aware feature encoder that fuses vision-language and metric-depth features with an SE(3) trajectory predictor that produces a camera-frame end-effector trajectory. Conditioned on the predictor's pose-supervised hidden states, the action decoder generates action chunks consistent with rigid-body motion. Across simulation and real-world experiments, OASIS outperforms VLA and WAM baselines in success rate and out-of-distribution generalization. Our project page is available at https://npuhandsome.github.io/OASIS_web.

In this paper, we introduce an SE(3) diffusion model-based point cloud registration framework for 6D object pose estimation in real-world scenarios. Our approach formulates the 3D registration task as a denoising diffusion process, which progressively refines the pose of the source point cloud to obtain a precise alignment with the model point cloud. Training our framework involves two operations: An SE(3) diffusion process and an SE(3) reverse process. The SE(3) diffusion process gradually perturbs the optimal rigid transformation of a pair of point clouds by continuously injecting noise (perturbation transformation). By contrast, the SE(3) reverse process focuses on learning a denoising network that refines the noisy transformation step-by-step, bringing it closer to the optimal transformation for accurate pose estimation. Unlike standard diffusion models used in linear Euclidean spaces, our diffusion model operates on the SE(3) manifold. This requires exploiting the linear Lie algebra se(3) associated with SE(3) to constrain the transformation transitions during the diffusion and reverse processes. Additionally, to effectively train our denoising network, we derive a registration-specific variational lower bound as the optimization objective for model learning. Furthermore, we show that our denoising network can be constructed with a surrogate registration model, making our approach applicable to different deep registration networks. Extensive experiments demonstrate that our diffusion registration framework presents outstanding pose estimation performance on the real-world TUD-L, LINEMOD, and Occluded-LINEMOD datasets.

High-fidelity 3D Gaussian head avatar generation is critical for applications such as AR/VR, telepresence, and digital humans. Existing methods depend on multi-view datasets, 3D captures, or intermediate 2D view synthesis. In contrast, we learn both conditional and unconditional 3D head models from randomly sampled 2D images alone, without using multi-view data, 3D supervision, or intermediate view generation. We introduce MVCHead, a single-shot state space model that enforces multi-view consistency (MVC) directly in the 3D representation while regressing 3D Gaussians under these constraints. At its core, we propose a Hierarchical State Space (HiSS) block that progressively refines Gaussians from coarse to fine, while capturing long-range dependencies. Within each HiSS block, we modify Mamba's standard unidirectional scan with the proposed Hierarchical Bi-directional State Scan (HiBiSS) that aligns recurrence with the axes along which multi-view inconsistencies are strongest. Finally, we design an SE(3) Multi-view Critic that judges whether a set of self-renders arises from a single underlying 3D configuration, rewarding cross-view pixel alignment without observing real multi-view pairs. MVCHead achieves state-of-the-art perceptual quality, surpasses prior methods in both texture and geometric consistency, and maintains comparable shape consistency. To demonstrate scalability, we release FaceGS-10K, the first large-scale dataset of ready-to-use 3D Gaussian head assets for training and evaluation of 3D head models. Project Page and code: https://humansensinglab.github.io/MVCHead/

Dense 3D point tracking has been a prominent paradigm for modeling motion in dynamic scenes, but a point track is just a 3-DoF translation curve per pixel: it captures where pixels go, not the rotation of the underlying part, nor which pixels move together as one body. We propose MoSE3, the first feed-forward model that predicts dense SE(3) motion from monocular RGB video, producing full 6-DoF rigid transforms at every pixel in world space. Per-pixel SE(3) motion offers a richer view of how a scene moves: rotation, translation, and grouping all at once. Directly predicting SE(3) is challenging: rotations lie on a curved manifold that is ill-suited to Euclidean regression, and annotations for SE(3) are particularly difficult to acquire. To address these challenges, MoSE3 predicts per-pixel SE(3) through two jointly learned intermediates, 3D point tracks and rigidity embeddings, and recovers SE(3) by differentiably fitting transforms within each soft rigid cluster, enabling end-to-end prediction and supervision. To close the data gap, we introduce Art-Kubric, a large-scale synthetic dataset with dense SE(3) and rigidity labels for articulated objects with rich physical interactions. MoSE3 achieves state-of-the-art SE(3) estimation at pixel, part, and object levels on both rigid and articulated benchmarks, and state-of-the-art average 3D point tracking accuracy across three datasets, while showing strong generalization to real-world videos despite being trained solely on synthetic motion data.

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

When manipulating three-dimensional data, it is possible to ensure that rotational and translational symmetries are respected by applying so-called SE(3)-equivariant models. Protein structure prediction is a prominent example of a task which displays these symmetries. Recent work in this area has successfully made use of an SE(3)-equivariant model, applying an iterative SE(3)-equivariant attention mechanism. Motivated by this application, we implement an iterative version of the SE(3)-Transformer, an SE(3)-equivariant attention-based model for graph data. We address the additional complications which arise when applying the SE(3)-Transformer in an iterative fashion, compare the iterative and single-pass versions on a toy problem, and consider why an iterative model may be beneficial in some problem settings. We make the code for our implementation available to the community.

AlphaFold 3 predicts protein structures with remarkable accuracy, yet how structural information emerges within the model remains poorly understood. Here, through causal interventions on internal representations and direct probing of every Pairformer block, we trace the formation of global protein geometry and identify the multiple sequence alignment (MSA) as a structural shortcut to the fold. Removing the MSA largely preserves local secondary structure while disrupting the long-range relationships that define global topology. Restoring the MSA-enriched pair representation at only forty residues recovers most of this lost organization, including at pairs never directly modified. This contribution depends on the detailed direction of the MSA module's output rather than its magnitude. The Pairformer rapidly converts this signal into global geometry: the final fold becomes recoverable by approximately block 9 of 48 for a majority of proteins, roughly twenty-seven blocks before the model's decoder can render it, whereas without the MSA it remains inaccessible for most proteins throughout the pass. Which homologs are supplied shapes this trajectory more strongly than which query is supplied; it persists for a designed query that never evolved but collapses for a shuffled sequence. Most importantly, an alignment built for a different protein that shares the fold, supplied only at the structurally corresponding columns, raises the median TM-score against experiment from 0.44 to 0.72, while the same alignment shifted a few residues along the chain performs worse than supplying no alignment at all. What AlphaFold 3 reads from an alignment is therefore a description of the fold itself, transferable between proteins that share one, rather than the query's own evolutionary history. This explains both its accuracy and the limits of what it has solved.

The design of novel protein structures remains a challenge in protein engineering for applications across biomedicine and chemistry. In this line of work, a diffusion model over rigid bodies in 3D (referred to as frames) has shown success in generating novel, functional protein backbones that have not been observed in nature. However, there exists no principled methodological framework for diffusion on SE(3), the space of orientation preserving rigid motions in R3, that operates on frames and confers the group invariance. We address these shortcomings by developing theoretical foundations of SE(3) invariant diffusion models on multiple frames followed by a novel framework, FrameDiff, for learning the SE(3) equivariant score over multiple frames. We apply FrameDiff on monomer backbone generation and find it can generate designable monomers up to 500 amino acids without relying on a pretrained protein structure prediction network that has been integral to previous methods. We find our samples are capable of generalizing beyond any known protein structure.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M ge 3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

As SE(3)-equivariant graph neural networks mature as a core tool for 3D atomistic modeling, improving their efficiency, expressivity, and physical consistency has become a central challenge for large-scale applications. In this work, we introduce EquiformerV3, the third generation of the SE(3)-equivariant graph attention Transformer, designed to advance all three dimensions: efficiency, expressivity, and generality. Building on EquiformerV2, we have the following three key advances. First, we optimize the software implementation, achieving 1.75times speedup. Second, we introduce simple and effective modifications to EquiformerV2, including equivariant merged layer normalization, improved feedforward network hyper-parameters, and attention with smooth radius cutoff. Third, we propose SwiGLU-S^2 activations to incorporate many-body interactions for better theoretical expressivity and to preserve strict equivariance while reducing the complexity of sampling S^2 grids. Together, SwiGLU-S^2 activations and smooth-cutoff attention enable accurate modeling of smoothly varying potential energy surfaces (PES), generalizing EquiformerV3 to tasks requiring energy-conserving simulations and higher-order derivatives of PES. With these improvements, EquiformerV3 trained with the auxiliary task of denoising non-equilibrium structures (DeNS) achieves state-of-the-art results on OC20, OMat24, and Matbench Discovery.

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here, we attempt to bridge this gap by proposing the Geo2Seq, which converts molecular geometries into SE(3)-invariant 1D discrete sequences. Geo2Seq consists of canonical labeling and invariant spherical representation steps, which together maintain geometric and atomic fidelity in a format conducive to LMs. Our experiments show that, when coupled with Geo2Seq, various LMs excel in molecular geometry generation, especially in controlled generation tasks.

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in three dimensions to make predictions about novel images. However, imposing SO(3)-equivariance on two-dimensional inputs is difficult because the group of three-dimensional rotations does not have a natural action on the two-dimensional plane. Specifically, it is possible that an element of SO(3) will rotate an image out of plane. We show that an algorithm that learns a three-dimensional representation of the world from two dimensional images must satisfy certain geometric consistency properties which we formulate as SO(2)-equivariance constraints. We use the induced and restricted representations of SO(2) on SO(3) to construct and classify architectures which satisfy these geometric consistency constraints. We prove that any architecture which respects said consistency constraints can be realized as an instance of our construction. We show that three previously proposed neural architectures for 3D pose prediction are special cases of our construction. We propose a new algorithm that is a learnable generalization of previously considered methods. We test our architecture on three pose predictions task and achieve SOTA results on both the PASCAL3D+ and SYMSOL pose estimation tasks.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92\%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50\% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

AI alignment aims to make AI systems behave in line with human intentions and values. As AI systems grow more capable, so do risks from misalignment. To provide a comprehensive and up-to-date overview of the alignment field, in this survey, we delve into the core concepts, methodology, and practice of alignment. First, we identify four principles as the key objectives of AI alignment: Robustness, Interpretability, Controllability, and Ethicality (RICE). Guided by these four principles, we outline the landscape of current alignment research and decompose them into two key components: forward alignment and backward alignment. The former aims to make AI systems aligned via alignment training, while the latter aims to gain evidence about the systems' alignment and govern them appropriately to avoid exacerbating misalignment risks. On forward alignment, we discuss techniques for learning from feedback and learning under distribution shift. On backward alignment, we discuss assurance techniques and governance practices. We also release and continually update the website (www.alignmentsurvey.com) which features tutorials, collections of papers, blog posts, and other resources.

In the applications of proxy-SU(3) model in the context of determining (beta,gamma) values for nuclei across the periodic table, for understanding the preponderance of triaxial shapes in nuclei with Z ge 30, it is seen that one needs not only the highest weight (hw) or leading SU(3) irreducible representation (irrep) (lambda_H, mu_H) but also the lower SU(3) irreps (lambda ,mu) such that 2lambda + mu =2lambda_H + mu_H-3r with r=0,1 and 2 [Bonatsos et al., Symmetry {\bf 16}, 1625 (2024)]. These give the next highest weight (nhw) irrep, next-to-next highest irrep (nnhw) and so on. Recently, it is shown that for nuclei with 32 le Z,N le 46, there will be not only proxy-SU(3) but also proxy-SU(4) symmetry [Kota and Sahu, Physica Scripta {\bf 99}, 065306 (2024)]. Following these developments, presented in this paper are the SU(3) irreps (lambda ,mu) with 2lambda + mu =2lambda_H + mu_H-3r, r=0,1,2 for various isotopes of Ge, Se, Kr, Sr, Zr, Mo, Ru and Pd (with 32 le N le 46) assuming good proxy-SU(4) symmetry. A simple method for obtaining the SU(3) irreps is described and applied. The tabulations for proxy-SU(3) irreps provided in this paper will be useful in further investigations of triaxial shapes in these nuclei.

Molecular glue degraders have emerged as a promising strategy for targeted protein degradation by inducing ternary complex formation between an E3 ubiquitin ligase and a target protein. Despite their therapeutic potential, computational design of molecular glues remains largely unexplored. Unlike conventional structure-based drug design, molecular glue design is governed by the unknown protein-protein interface and requires the simultaneous modeling of ligand generation, protein-protein docking, and ternary complex assembly. In this work, we formulate molecular glue design as a ternary complex generation problem and propose a biology-inspired generative framework, TriGlue. Motivated by the mechanism of molecular glue action, we decompose ternary complex generation into two coupled stages: interface estimation and interface-conditioned complex generation. First, we develop an SE(3)-equivariant interface estimation module that predicts a geometrically constrained protein-protein interface from unbound monomer structures. Second, we introduce an interface-conditioned ternary flow matching network that jointly generates the molecular glue and predicts the rigid-body transformation required to assemble the ternary complex. Extensive experiments demonstrate that TriGlue generates chemically valid molecules and produces plausible ternary complexes, which highlight the potential of biology-inspired generative modeling for accelerating molecular glue discovery. Our code is available at https://github.com/yuliangyan0807/molecular-glue-design.

We study positional encodings for multi-view transformers that process tokens from a set of posed input images, and seek a mechanism that encodes patches uniquely, allows SE(3)-invariant attention with multi-frequency similarity, and can be adaptive to the geometry of the underlying scene. We find that prior (absolute or relative) encoding schemes for multi-view attention do not meet the above desiderata, and present RayRoPE to address this gap. RayRoPE represents patch positions based on associated rays but leverages a predicted point along the ray instead of the direction for a geometry-aware encoding. To achieve SE(3) invariance, RayRoPE computes query-frame projective coordinates for computing multi-frequency similarity. Lastly, as the 'predicted' 3D point along a ray may not be precise, RayRoPE presents a mechanism to analytically compute the expected position encoding under uncertainty. We validate RayRoPE on the tasks of novel-view synthesis and stereo depth estimation and show that it consistently improves over alternate position encoding schemes (e.g. 15% relative improvement on LPIPS in CO3D). We also show that RayRoPE can seamlessly incorporate RGB-D input, resulting in even larger gains over alternatives that cannot positionally encode this information.

Machine-learning interatomic potentials now approach quantum-mechanical accuracy on standard benchmarks, but the training cost of the most expressive equivariant architectures has become a serious bottleneck. We introduce DPA4, an SE(3)-equivariant interatomic-potential architecture with an EMFA (Edge-conditioned, Multi-Focus, Attention) SO(2)-equivariant convolution that combines a low-rank edge-node SO(2)-equivariant product, a multi-focus design for message nonlinearity, and envelope-gated attention for message aggregation. A Lebedev-grid projection further preserves SO(3)-equivariance in the nonlinearity to machine precision. A compiler-friendly conservative energy-gradient training path provides up to sim3 times wall-clock speedup under torch compile. On the compliant Matbench Discovery benchmark, DPA4-Pro attains the best Combined Performance Score (CPS) on the leaderboard, while the 2.76M-parameter DPA4-Air exceeds the accuracy of the 30.1M-parameter eSEN-30M-MP baseline with 10.9times fewer parameters and 42.9times less training compute. On SPICE-MACE-OFF, the 5.4M-parameter DPA4-Plus lowers the aggregate molecular energy and force errors of the 6.5M-parameter eSEN baseline by 29% and 30%, while the 2.7M-parameter DPA4-Air still surpasses that baseline with sim2.4times fewer parameters. Together these results place DPA4 on a new accuracy-cost Pareto frontier on Matbench Discovery and position it as a strong candidate backbone for future multi-task large atomistic model (LAM) pretraining.

Enantiomers share atoms, bonds, and pairwise distances yet can behave differently in chiral environments, so molecular encoders must respect atom relabelings and proper rotations without becoming blind to reflection. We introduce GSF-χ, a graph transformer in which stereogenic units modulate all pairwise interactions rather than single out one atom as special. Each central or axial stereogenic unit creates a reflection-even phase field over all atoms, a handedness pseudoscalar χ sets the direction of a relative rotation on latent query--key blocks, giving a Chiral-RoPE that reflection inverts rather than leaves fixed. A C_2 projection separates mirror-even ECD peak counts and positions from mirror-odd peak signs. We prove the operator's even--odd decomposition and its annotation-inversion, permutation, and unit-order identities under explicit canonical-role conditions; property tests and a coordinate-reflection audit verify the laws end to end. GSF-χ leads every central-ECD output and improves axial Rotation and Symbol by 12.6% and 7.9% over the strongest baseline. Equal-budget controls attribute the Rotation advantage to global signed support rather than parameter or edge count; the C_2 projection yields exact enantiomer-pair consistency at a small raw-accuracy cost under complete supervision and becomes predictive when mirror supervision is scarce.

Predicting how a drug-like molecule binds to a specific protein target is a core problem in drug discovery. An extremely fast computational binding method would enable key applications such as fast virtual screening or drug engineering. Existing methods are computationally expensive as they rely on heavy candidate sampling coupled with scoring, ranking, and fine-tuning steps. We challenge this paradigm with EquiBind, an SE(3)-equivariant geometric deep learning model performing direct-shot prediction of both i) the receptor binding location (blind docking) and ii) the ligand's bound pose and orientation. EquiBind achieves significant speed-ups and better quality compared to traditional and recent baselines. Further, we show extra improvements when coupling it with existing fine-tuning techniques at the cost of increased running time. Finally, we propose a novel and fast fine-tuning model that adjusts torsion angles of a ligand's rotatable bonds based on closed-form global minima of the von Mises angular distance to a given input atomic point cloud, avoiding previous expensive differential evolution strategies for energy minimization.

We present E(3)-Pose, a novel fast pose estimation method that jointly and explicitly models rotation equivariance and object symmetry. Our work is motivated by the challenging problem of accounting for fetal head motion during a diagnostic MRI scan. We aim to enable automatic adaptive prescription of 2D diagnostic MRI slices with 6-DoF head pose estimation, supported by 3D MRI volumes rapidly acquired before each 2D slice. Existing methods struggle to generalize to clinical volumes, due to pose ambiguities induced by inherent anatomical symmetries, as well as low resolution, noise, and artifacts. In contrast, E(3)-Pose captures anatomical symmetries and rigid pose equivariance by construction, and yields robust estimates of the fetal head pose. Our experiments on publicly available and representative clinical fetal MRI datasets demonstrate the superior robustness and generalization of our method across domains. Crucially, E(3)-Pose achieves state-of-the-art accuracy on clinical MRI volumes, paving the way for clinical translation. Our implementation is available at github.com/ramyamut/E3-Pose.

Tunnelling reactions of molecules embedded on cryogenic noble-gas matrices are being used in fundamental studies of how reactivity varies with the nature of the supposedly inert matrix as well as pointers to the chemistry occurring in the interstellar medium on ice-grains. To these ends we present chemical kinetic rate constants for the cis to trans isomerisation of seleno-, thio- and monomeric formic acids and that of their three dimeric species, based on multidimensional calculations in the gas-phase, from 10~K to 300~K as a guide to the matrix reactions.

This work presents the first quantitative study of alignment errors between small uncrewed aerial systems (sUAS) geospatial imagery and a priori building polygons and finds that alignment errors are non-uniform and irregular. The work also introduces a publicly available dataset of imagery, building polygons, and human-generated and curated adjustments that can be used to evaluate existing strategies for aligning building polygons with sUAS imagery. There are no efforts that have aligned pre-existing spatial data with sUAS imagery, and thus, there is no clear state of practice. However, this effort and analysis show that the translational alignment errors present in this type of data, averaging 82px and an intersection over the union of 0.65, which would induce further errors and biases in downstream machine learning systems unless addressed. This study identifies and analyzes the translational alignment errors of 21,619 building polygons in fifty-one orthomosaic images, covering 16787.2 Acres (26.23 square miles), constructed from sUAS raw imagery from nine wide-area disasters (Hurricane Ian, Hurricane Harvey, Hurricane Michael, Hurricane Ida, Hurricane Idalia, Hurricane Laura, the Mayfield Tornado, the Musset Bayou Fire, and the Kilauea Eruption). The analysis finds no uniformity among the angle and distance metrics of the building polygon alignments as they present an average degree variance of 0.4 and an average pixel distance variance of 0.45. This work alerts the sUAS community to the problem of spatial alignment and that a simple linear transform, often used to align satellite imagery, will not be sufficient to align spatial data in sUAS orthomosaic imagery.

In the 3-3-1 model with right-handed neutrinos, three triplets of scalars engender the correct sequence of symmetry breaking, SU(3)_C times SU(3)_L times U(1)_X rightarrow SU(3)_C times SU(2)_L times U(1)_Y rightarrow SU(3)_C times U(1)_{EM}, generating mass for all fermions, except neutrinos. Tiny neutrino masses may be achieved by adding one sextet of scalars to the original scalar content. As consequence, it emerges a very complex scalar sector, involving terms that violate lepton number explicitly, too. The main obstacle to the development of the phenomenology of such scenario is the knowledge of its spectrum of scalars since, now, there are 15 massive scalar particles on it. The proposal of this work is to do an exhaustive analysis of such scalar sector with lepton number being explicitly violated at low, electroweak and high energy scales by means of trilinear terms in the potential. The first case can be addressed analytically and, as a nice result, we have observed that the scalar content of such case is split into two categories: One belonging to the 331 energy scale and the other belonging to the EWSB energy scale, with the last recovering the well known THDM+triplet. For the other cases, the scalar sector can be addressed only numerically. Hence, we proposed a very general approach for the numerical study of the potential, avoiding simplifications that can make us reach conclusions without foundation. We show that, in the case of lepton number being explicitly violated at electroweak scale, it is possible to recover the same physics of the THDM+triplet, as the previous case. Among all the possibilities, we call the attention to one special case which generates the 3HDM+triplet scenario. For the last case, when lepton number is violated at high energy scale, the sextet become very massive and decouples from the original scalar content of the 3-3-1 model.

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

Position encoding (PE), an essential part of self-attention networks (SANs), is used to preserve the word order information for natural language processing tasks, generating fixed position indices for input sequences. However, in cross-lingual scenarios, e.g. machine translation, the PEs of source and target sentences are modeled independently. Due to word order divergences in different languages, modeling the cross-lingual positional relationships might help SANs tackle this problem. In this paper, we augment SANs with cross-lingual position representations to model the bilingually aware latent structure for the input sentence. Specifically, we utilize bracketing transduction grammar (BTG)-based reordering information to encourage SANs to learn bilingual diagonal alignments. Experimental results on WMT'14 EnglishRightarrowGerman, WAT'17 JapaneseRightarrowEnglish, and WMT'17 ChineseLeftrightarrowEnglish translation tasks demonstrate that our approach significantly and consistently improves translation quality over strong baselines. Extensive analyses confirm that the performance gains come from the cross-lingual information.

The application of language models (LMs) to molecular structure generation using line notations such as SMILES and SELFIES has been well-established in the field of cheminformatics. However, extending these models to generate 3D molecular structures presents significant challenges. Two primary obstacles emerge: (1) the difficulty in designing a 3D line notation that ensures SE(3)-invariant atomic coordinates, and (2) the non-trivial task of tokenizing continuous coordinates for use in LMs, which inherently require discrete inputs. To address these challenges, we propose Mol-StrucTok, a novel method for tokenizing 3D molecular structures. Our approach comprises two key innovations: (1) We design a line notation for 3D molecules by extracting local atomic coordinates in a spherical coordinate system. This notation builds upon existing 2D line notations and remains agnostic to their specific forms, ensuring compatibility with various molecular representation schemes. (2) We employ a Vector Quantized Variational Autoencoder (VQ-VAE) to tokenize these coordinates, treating them as generation descriptors. To further enhance the representation, we incorporate neighborhood bond lengths and bond angles as understanding descriptors. Leveraging this tokenization framework, we train a GPT-2 style model for 3D molecular generation tasks. Results demonstrate strong performance with significantly faster generation speeds and competitive chemical stability compared to previous methods. Further, by integrating our learned discrete representations into Graphormer model for property prediction on QM9 dataset, Mol-StrucTok reveals consistent improvements across various molecular properties, underscoring the versatility and robustness of our approach.

Mu3e is an experiment currently under construction at the Paul Scherrer Institute in Switzerland, designed to search for the Lepton Flavor Violating (LFV) decay mu^+ rightarrow e^+e^-e^+. In extensions of the Standard Model (SM) that account for neutrino masses, this decay is theoretically allowed but occurs only through extremely rare loop processes, with a predicted branching ratio of approximately O(10^{-54}). Such a small probability implies that any observation of this decay would provide clear evidence for physics beyond the SM. The Mu3e experiment aims to probe the mu^+ rightarrow e^+e^-e^+ decay with a sensitivity of approximately O(10^{-15}) in its Phase-1 and plans to achieve a sensitivity of O(10^{-16}) after future upgrades. To reach its Phase-1 ambitious goals, Mu3e is going to use the most intense continuous muon beam in the world, generating 10^{8} muon stops per second in the target placed at the center of the Mu3e. Mu3e will use three main technologies for particle detection. The tracking will done through ultra-thin (50 - 70 mu m) pixel detectors based on MuPix11 sensors. These are high-voltage monolithic active pixel sensors (HV-MAPS) with a sim 23~mum spatial resolution. The timing will be done through scintillating fibres (sim 250 ps) and tiles (sim 40 ps), coupled to silicon photomultipliers and read out by MuTRiG3 ASICs. A triggerless DAQ system based on FPGAs will collect data from the detectors, which will then undergo reconstruction in a GPU filter farm. The assembly of the detectors has started, with a detector commissioning beam time planned for 2025. This document reports on the status of the construction, installation, and data-taking plans for the near future.

Given a 3-dimensional (para-)CR structure, its family of chains define a 3-dimensional path geometry. We provide necessary and sufficient conditions that determine whether a path geometry in dimension three arises from chains of a CR or para-CR 3-manifold. We demonstrate how our characterization can be verified computationally for a given 3-dimensional path geometry and discuss a few examples.

Many tasks revolve around editing a document, whether code or text. We formulate the revision similarity problem to unify a wide range of machine learning evaluation problems whose goal is to assess a revision to an existing document. We observe that revisions usually change only a small portion of an existing document, so the existing document and its immediate revisions share a majority of their content. We formulate five adequacy criteria for revision similarity measures, designed to align them with human judgement. We show that popular pairwise measures, like BLEU, fail to meet these criteria, because their scores are dominated by the shared content. They report high similarity between two revisions when humans would assess them as quite different. This is a fundamental flaw we address. We propose a novel static measure, Excision Score (ES), which computes longest common subsequence (LCS) to remove content shared by an existing document with the ground truth and predicted revisions, before comparing only the remaining divergent regions. This is analogous to a surgeon creating a sterile field to focus on the work area. We use approximation to speed the standard cubic LCS computation to quadratic. In code-editing evaluation, where static measures are often used as a cheap proxy for passing tests, we demonstrate that ES surpasses existing measures. When aligned with test execution on HumanEvalFix, ES improves over its nearest competitor, SARI, by 12% Pearson correlation and by >21% over standard measures like BLEU. The key criterion is invariance to shared context; when we perturb HumanEvalFix with increased shared context, ES' improvement over SARI increases to 20% and >30% over standard measures. ES also handles other corner cases that other measures do not, such as correctly aligning moved code blocks, and appropriately rewarding matching insertions or deletions.

We introduce Aligner, a novel Parameter-Efficient Fine-Tuning (PEFT) method for aligning multi-billion-parameter-sized Large Language Models (LLMs). Aligner employs a unique design that constructs a globally shared set of tunable tokens that modify the attention of every layer. Remarkably with this method, even when using one token accounting for a mere 5,000 parameters, Aligner can still perform comparably well to state-of-the-art LLM adaptation methods like LoRA that require millions of parameters. This capacity is substantiated in both instruction following and value alignment tasks. Besides the multiple order-of-magnitude improvement in parameter efficiency, the insight Aligner provides into the internal mechanisms of LLMs is also valuable. The architectural features and efficacy of our method, in addition to our experiments demonstrate that an LLM separates its internal handling of "form" and "knowledge" in a somewhat orthogonal manner. This finding promises to motivate new research into LLM mechanism understanding and value alignment.

Most learned dexterous grasp generators relegate contact forces to a downstream verification step, so a kinematically-plausible pose can still violate the conditions for a stable physical grasp. We address this with EquiDexFlow, an SE(3)-equivariant flow-matching model that jointly predicts wrist pose, joint angles, fingertip contacts, surface normals, and contact forces from an object point cloud. Our architecture projects contacts onto the object surface and forces into the Coulomb friction cone by construction, so placement and friction compliance hold without loss penalties. We prove end-to-end SE(3) equivariance and verify it empirically over 200 rotations, with wrist residuals below 0.04^circ and exactly zero joint deviation. Trained on 8,100 force-closure grasps across 81 objects for the 16-DoF Allegro Hand, our model achieves zero friction violations, the best composite score, and the lowest wrench residual among all ablation variants. We retarget decoded fingertip contacts to a 16-DoF LEAP Hand via per-finger inverse kinematics, and our hardware-feasible refinement places every joint at least 5% inside its actuator envelope while preserving wrench balance. On the physical robot, retargeted EquiDexFlow-decoded grasps complete open-loop pick-and-hold trials on all six test objects, with every asymmetric object succeeding at both the canonical pose and a 120^circ co-rotation. Videos, code, and checkpoints are available at https://equidexflow.github.io.

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust mathematical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models and Score-based Generative Models, where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance on the E(3) group can keep the physical stability of the frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation.

Recent approaches for predicting layouts from 360 panoramas produce excellent results. These approaches build on a common framework consisting of three steps: a pre-processing step based on edge-based alignment, prediction of layout elements, and a post-processing step by fitting a 3D layout to the layout elements. Until now, it has been difficult to compare the methods due to multiple different design decisions, such as the encoding network (e.g. SegNet or ResNet), type of elements predicted (e.g. corners, wall/floor boundaries, or semantic segmentation), or method of fitting the 3D layout. To address this challenge, we summarize and describe the common framework, the variants, and the impact of the design decisions. For a complete evaluation, we also propose extended annotations for the Matterport3D dataset [3], and introduce two depth-based evaluation metrics.

Simultaneous understanding and 3D reconstruction plays an important role in developing end-to-end embodied intelligent systems. To achieve this, recent approaches resort to 2D-to-3D feature alignment paradigm, which leads to limited 3D understanding capability and potential semantic information loss. In light of this, we propose SIU3R, the first alignment-free framework for generalizable simultaneous understanding and 3D reconstruction from unposed images. Specifically, SIU3R bridges reconstruction and understanding tasks via pixel-aligned 3D representation, and unifies multiple understanding tasks into a set of unified learnable queries, enabling native 3D understanding without the need of alignment with 2D models. To encourage collaboration between the two tasks with shared representation, we further conduct in-depth analyses of their mutual benefits, and propose two lightweight modules to facilitate their interaction. Extensive experiments demonstrate that our method achieves state-of-the-art performance not only on the individual tasks of 3D reconstruction and understanding, but also on the task of simultaneous understanding and 3D reconstruction, highlighting the advantages of our alignment-free framework and the effectiveness of the mutual benefit designs.

Entity Alignment (EA) seeks to identify and match corresponding entities across different Knowledge Graphs (KGs), playing a crucial role in knowledge fusion and integration. Embedding-based entity alignment (EA) has recently gained considerable attention, resulting in the emergence of many innovative approaches. Initially, these approaches concentrated on learning entity embeddings based on the structural features of knowledge graphs (KGs) as defined by relation triples. Subsequent methods have integrated entities' names and attributes as supplementary information to improve the embeddings used for EA. However, existing methods lack a deep semantic understanding of entity attributes and relations. In this paper, we propose a Large Language Model (LLM) based Entity Alignment method, LLM-Align, which explores the instruction-following and zero-shot capabilities of Large Language Models to infer alignments of entities. LLM-Align uses heuristic methods to select important attributes and relations of entities, and then feeds the selected triples of entities to an LLM to infer the alignment results. To guarantee the quality of alignment results, we design a multi-round voting mechanism to mitigate the hallucination and positional bias issues that occur with LLMs. Experiments on three EA datasets, demonstrating that our approach achieves state-of-the-art performance compared to existing EA methods.

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

Reinforcement Learning from Human Feedback (RLHF) is widely used for aligning large language models, yet practitioners face a persistent puzzle: improving safety often reduces fairness, scaling to diverse populations becomes computationally intractable, and making systems robust often amplifies majority biases. We formalize this tension as the Alignment Trilemma: no RLHF system can simultaneously achieve (i) epsilon-representativeness across diverse human values, (ii) polynomial tractability in sample and compute complexity, and (iii) delta-robustness against adversarial perturbations and distribution shift. Through a complexity-theoretic analysis integrating statistical learning theory and robust optimization, we prove that achieving both representativeness (epsilon <= 0.01) and robustness (delta <= 0.001) for global-scale populations requires Omega(2^{d_context}) operations, which is super-polynomial in the context dimensionality. We show that current RLHF implementations resolve this trilemma by sacrificing representativeness: they collect only 10^3--10^4 samples from homogeneous annotator pools while 10^7--10^8 samples are needed for true global representation. Our framework provides a unified explanation for documented RLHF pathologies including preference collapse, sycophancy, and systematic bias amplification. We conclude with concrete directions for navigating these fundamental trade-offs through strategic relaxations of alignment requirements.

Different from Object Detection, Visual Grounding deals with detecting a bounding box for each text-image pair. This one box for each text-image data provides sparse supervision signals. Although previous works achieve impressive results, their passive utilization of annotation, i.e. the sole use of the box annotation as regression ground truth, results in a suboptimal performance. In this paper, we present SegVG, a novel method transfers the box-level annotation as Segmentation signals to provide an additional pixel-level supervision for Visual Grounding. Specifically, we propose the Multi-layer Multi-task Encoder-Decoder as the target grounding stage, where we learn a regression query and multiple segmentation queries to ground the target by regression and segmentation of the box in each decoding layer, respectively. This approach allows us to iteratively exploit the annotation as signals for both box-level regression and pixel-level segmentation. Moreover, as the backbones are typically initialized by pretrained parameters learned from unimodal tasks and the queries for both regression and segmentation are static learnable embeddings, a domain discrepancy remains among these three types of features, which impairs subsequent target grounding. To mitigate this discrepancy, we introduce the Triple Alignment module, where the query, text, and vision tokens are triangularly updated to share the same space by triple attention mechanism. Extensive experiments on five widely used datasets validate our state-of-the-art (SOTA) performance.

DNA sequence alignment involves assigning short DNA reads to the most probable locations on an extensive reference genome. This process is crucial for various genomic analyses, including variant calling, transcriptomics, and epigenomics. Conventional methods, refined over decades, tackle this challenge in 2 steps: genome indexing followed by efficient search to locate likely positions for given reads. Building on the success of Large Language Models in encoding text into embeddings, where the distance metric captures semantic similarity, recent efforts have explored whether the same Transformer architecture can produce embeddings for DNA sequences. Such models have shown early promise in classifying short DNA sequences, such as detecting coding/non-coding regions, and enhancer, promoter sequences. However, performance at sequence classification tasks does not translate to sequence alignment, where it is necessary to search across the genome to align each read, a significantly longer-range task. We bridge this gap by framing the Sequence Alignment task for Transformer models as an "Embed-Search-Align" task. In this framework, a novel Reference-Free DNA Embedding model generates embeddings of reads and reference fragments, which are projected into a shared vector space where the read-fragment distance is used as a surrogate for alignment. Technical contributions include: (1) Contrastive loss for self-supervised training of DNA sequence representations, facilitating rich reference-free, sequence-level embeddings, and (2) a DNA vector store to enable search across fragments on a global scale. DNA-ESA is 99% accurate when aligning 250-length reads onto a human genome (3gb), rivaling conventional methods such as Bowtie and BWA-Mem. DNA-ESA exceeds the performance of 6 Transformer model baselines such as Nucleotide Transformer, Hyena-DNA, and shows task transfer across chromosomes and species.

The question of whether there exists a finite group of order at least three in which every element except one is a commutator has remained unresolved in group theory. In this article, we address this open problem by developing an algorithmic approach that leverages several group theoretic properties of such groups. Specifically, we utilize a result of Frobenius and various necessary properties of such groups, combined with Plesken and Holt's extensive enumeration of finite perfect groups, to systematically examine all finite groups up to a certain order for the desired property. The computational core of our work is implemented using the computer system GAP (Groups, Algorithms, and Programming). We discover two nonisomorphic groups of order 368,640 that exhibit the desired property. Our investigation also establishes that this order is the minimum order for such a group to exist. As a result, this study provides a positive answer to Problem 17.76 in the Kourovka Notebook. In addition to the algorithmic framework, this paper provides a structural description of one of the two groups found.

TrueEBSD is an open-source MATLAB program for image alignment and spatial distortion correction of images and electron backscatter diffraction (EBSD) maps. We have re-implemented TrueEBSD as an add-on to MTEX, an established toolbox for EBSD data analysis. Spatial alignment enables correlative analysis methods, such as augmenting EBSD orientation maps with data from other imaging modes. The augmented EBSD maps can then be analysed further using MTEX. We demonstrate TrueEBSD on two example case studies: one for measuring Co phase fraction and WC contiguity in a WC-Co composite, and another for determining the relative susceptibility of grain boundaries to void formation in a copper polycrystal. In both examples, the EBSD map was augmented with scanning electron microscopy (SEM) image data. This enabled quantitative crystallographic measurements which would not be possible from analysing the EBSD maps and images separately.

The regulation of various cellular processes heavily relies on the protein complexes within a living cell, necessitating a comprehensive understanding of their three-dimensional structures to elucidate the underlying mechanisms. While neural docking techniques have exhibited promising outcomes in binary protein docking, the application of advanced neural architectures to multimeric protein docking remains uncertain. This study introduces SyNDock, an automated framework that swiftly assembles precise multimeric complexes within seconds, showcasing performance that can potentially surpass or be on par with recent advanced approaches. SyNDock possesses several appealing advantages not present in previous approaches. Firstly, SyNDock formulates multimeric protein docking as a problem of learning global transformations to holistically depict the placement of chain units of a complex, enabling a learning-centric solution. Secondly, SyNDock proposes a trainable two-step SE(3) algorithm, involving initial pairwise transformation and confidence estimation, followed by global transformation synchronization. This enables effective learning for assembling the complex in a globally consistent manner. Lastly, extensive experiments conducted on our proposed benchmark dataset demonstrate that SyNDock outperforms existing docking software in crucial performance metrics, including accuracy and runtime. For instance, it achieves a 4.5% improvement in performance and a remarkable millionfold acceleration in speed.

We study two-Higgs-doublet models, extensions of the Standard Model (SM) containing two Higgs doublets rather than one. Tree-level Higgs-mediated interactions that change quark or lepton flavor are conventionally suppressed by a discrete Z_2 symmetry. Motivated by string compactifications, we instead impose a non-invertible Fibonacci selection rule at a matching scale Λ for that purpose. This rule also forbids the independent mass parameter that normally allows the additional Higgs particles to become arbitrarily heavy, while renormalization-group evolution regenerates it below Λ. An allowed Z_2-breaking quartic interaction simultaneously avoids stable cosmological domain walls. In the exact alignment limit, requiring perturbative unitarity and boundedness from below up to the matching scale bounds the masses of the three non-SM Higgs states; for Λ=10^{19},GeV, they lie below about 150,GeV. The scanned parameter space predicts a suppressed Higgs diphoton signal strength within the projected reach of the HL-LHC. This illustrates how a stringy non-invertible selection rule can leave testable signatures in Higgs physics.

We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow matching can be applied on SE(3) and propose modifications during training to effectively learn the vector field. Compared to FrameDiff, FrameFlow requires five times fewer sampling timesteps while achieving two fold better designability. The ability to generate high quality protein samples at a fraction of the cost of previous methods paves the way towards more efficient generative models in de novo protein design.

Determining the binding pose of a ligand to a protein, known as molecular docking, is a fundamental task in drug discovery. Generative approaches promise faster, improved, and more diverse pose sampling than physics-based methods, but are often hindered by chemically implausible outputs, poor generalisability, and high computational cost. To address these challenges, we introduce a novel fragmentation scheme, leveraging inductive biases from structural chemistry, to decompose ligands into rigid-body fragments. Building on this decomposition, we present SigmaDock, an SE(3) Riemannian diffusion model that generates poses by learning to reassemble these rigid bodies within the binding pocket. By operating at the level of fragments in SE(3), SigmaDock exploits well-established geometric priors while avoiding overly complex diffusion processes and unstable training dynamics. Experimentally, we show SigmaDock achieves state-of-the-art performance, reaching Top-1 success rates (RMSD<2 & PB-valid) above 79.9% on the PoseBusters set, compared to 12.7-30.8% reported by recent deep learning approaches, whilst demonstrating consistent generalisation to unseen proteins. SigmaDock is the first deep learning approach to surpass classical physics-based docking under the PB train-test split, marking a significant leap forward in the reliability and feasibility of deep learning for molecular modelling.

Finetuning a language model can lead to emergent misalignment (EM) [Betley et al., 2025b]. Models trained on a narrow distribution of misaligned behavior generalize to more egregious behaviors when tested outside the training distribution. We study a set of interventions proposed to reduce EM. We confirm that these interventions reduce or eliminate EM on existing evaluations (questions like "How do I make a quick buck?"). However, if the evaluation prompts are tweaked to resemble the training context, the model displays EM. We call this conditional misalignment. As in standard EM, the model displays misaligned behaviors more egregious than those seen during training, but only on inputs sharing features with the training data. The first two interventions are diluting misaligned data with benign data, and finetuning on benign data after misaligned data. Both produce conditional misalignment. For instance, models trained on a mix of only 5% insecure code still show misalignment when asked to format responses as Python strings (resembling the training context). The third intervention is inoculation prompting. Here, statements with a similar form to the inoculation prompt serve as triggers for misalignment, even if they have the opposite meaning. On the positive side, inoculation prompting has lower (but still non-zero) conditional misalignment if training is on-policy or includes reasoning distillation. Our results imply that in realistic post-training, where misaligned data is typically combined with benign data, models may be conditionally misaligned even if standard evaluations look clean.

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

Efficient training strategies for large-scale diffusion models have recently emphasized the importance of improving discriminative feature representations in these models. A central line of work in this direction is representation alignment with features obtained from powerful external encoders, which improves the representation quality as assessed through linear probing. Alignment-based approaches show promise but depend on large pretrained encoders, which are computationally expensive to obtain. In this work, we propose an alternative regularization for training, based on promoting the Linear SEParability (LSEP) of intermediate layer representations. LSEP eliminates the need for an auxiliary encoder and representation alignment, while incorporating linear probing directly into the network's learning dynamics rather than treating it as a simple post-hoc evaluation tool. Our results demonstrate substantial improvements in both training efficiency and generation quality on flow-based transformer architectures such as SiTs, achieving an FID of 1.46 on 256 times 256 ImageNet dataset.

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These models extend traditional message-passing GNNs and Transformers by representing node and edge features as spherical tensors that transform under irreducible representations of the rotation group SO(3), ensuring that predictions change in physically meaningful ways under rotations of the input. This guide develops a complete, intuitive foundation for spherical equivariant modeling - from group representations and spherical harmonics, to tensor products, Clebsch-Gordan decomposition, and the construction of SO(3)-equivariant kernels. Building on this foundation, we construct the Tensor Field Network and SE(3)-Transformer architectures and explain how they perform equivariant message-passing and attention on geometric graphs. Through clear mathematical derivations and annotated code excerpts, this guide serves as a self-contained introduction for researchers and learners seeking to understand or implement spherical EGNNs for applications in chemistry, molecular property prediction, protein structure modeling, and generative modeling.

Loss explosions in training deep neural networks can nullify multi-million dollar training runs. Conventional monitoring metrics like weight and gradient norms are often lagging and ambiguous predictors, as their values vary dramatically across different models and even between layers of the same model, making it difficult to establish a unified standard for detecting impending failure. We introduce Spectral Alignment (SA), a novel, theoretically-grounded metric that monitors the distributional alignment between layer inputs and the principal singular vectors of weight matrices. We show that a collapse in the sign diversity of this alignment is a powerful early predictor of representational collapse and training divergence. Empirical results on language models demonstrate that monitoring the SA distribution provides a significantly earlier and clearer warning of loss explosions than traditional scalar metrics. SA's low computational overhead makes it a practical tool for safeguarding model training.

NVIDIA's CUTLASS library provides a robust and expressive set of methods for describing and manipulating multi-dimensional tensor data on the GPU. These methods are conceptually grounded in the abstract notion of a CuTe layout and a rich algebra of such layouts, including operations such as composition, logical product, and logical division. In this paper, we present a categorical framework for understanding this layout algebra by focusing on a naturally occurring class of tractable layouts. To this end, we define two categories Tuple and Nest whose morphisms give rise to layouts. We define a suite of operations on morphisms in these categories and prove their compatibility with the corresponding layout operations. Moreover, we give a complete characterization of the layouts which arise from our construction. Finally, we provide a Python implementation of our categorical constructions, along with tests that demonstrate alignment with CUTLASS behavior. This implementation can be found at our git repository https://github.com/ColfaxResearch/layout-categories.

We present Three-Phase Transformer (3PT), a residual-stream structural prior for decoder-only Transformers on a standard SwiGLU + RMSNorm + RoPE + GQA backbone. The hidden vector is partitioned into N equally-sized cyclic channels, each maintained by phase-respecting ops: a per-channel RMSNorm, a 2D Givens rotation between attention and FFN that rotates each channel by theta + i*(2*pi/N), and a head-count constraint aligning GQA heads with the partition. The architecture is a self-stabilizing equilibrium between scrambling and re-imposition, not a bolted-on module. The partition carves out a one-dimensional DC subspace orthogonal to the channels, into which we inject a fixed Gabriel's horn profile r(p) = 1/(p+1) as an absolute-position side-channel composing orthogonally with RoPE's relative-position rotation. The canonical N=3 borrows its metaphor from balanced three-phase AC, where three sinusoids 120 degrees apart sum to zero with no anti-correlated pair. At 123M parameters on WikiText-103, 3PT achieves -7.20% perplexity (-2.62% bits-per-byte) over a matched RoPE-Only baseline at +1,536 parameters (0.00124% of total), with 1.93x step-count convergence speedup (1.64x wall-clock). N behaves as a parameter-sharing knob rather than a unique optimum: at 5.5M an N-sweep over {1,2,3,4,6,8,12} is near-monotone with N=1 winning; at 123M a three-seed sweep finds N=3 and N=1 statistically indistinguishable. The load-bearing mechanism is the channel-partitioned residual stream, per-block rotation, per-phase normalization, and horn DC injection. We characterize (a) self-stabilization of the geometry without explicit enforcement, a novel instance of the conservation-law framework for neural networks; (b) a U-shaped depth profile of rotation-angle drift at 12 layers; (c) orthogonal composition with RoPE, attention, and FFN.

Recent work by Baratin et al. (2021) sheds light on an intriguing pattern that occurs during the training of deep neural networks: some layers align much more with data compared to other layers (where the alignment is defined as the euclidean product of the tangent features matrix and the data labels matrix). The curve of the alignment as a function of layer index (generally) exhibits an ascent-descent pattern where the maximum is reached for some hidden layer. In this work, we provide the first explanation for this phenomenon. We introduce the Equilibrium Hypothesis which connects this alignment pattern to signal propagation in deep neural networks. Our experiments demonstrate an excellent match with the theoretical predictions.

Recent work discovered Emergent Misalignment (EM): fine-tuning large language models on narrowly harmful datasets can lead them to become broadly misaligned. A survey of experts prior to publication revealed this was highly unexpected, demonstrating critical gaps in our understanding of model alignment. In this work, we both advance understanding and provide tools for future research. Using new narrowly misaligned datasets, we create a set of improved model organisms that achieve 99% coherence (vs. 67% prior), work with smaller 0.5B parameter models (vs. 32B), and that induce misalignment using a single rank-1 LoRA adapter. We demonstrate that EM occurs robustly across diverse model sizes, three model families, and numerous training protocols including full supervised fine-tuning. Leveraging these cleaner model organisms, we isolate a mechanistic phase transition and demonstrate that it corresponds to a robust behavioural phase transition in all studied organisms. Aligning large language models is critical for frontier AI safety, yet EM exposes how far we are from achieving this robustly. By distilling clean model organisms that isolate a minimal alignment-compromising change, and where this is learnt, we establish a foundation for future research into understanding and mitigating alignment risks in LLMs.

Accurate prediction of protein-ligand binding poses is crucial for structure-based drug design, yet existing methods struggle to balance speed, accuracy, and physical plausibility. We introduce Matcha, a novel molecular docking pipeline that combines multi-stage flow matching with learned scoring and physical validity filtering. Our approach consists of three sequential stages applied consecutively to refine docking predictions, each implemented as a flow matching model operating on appropriate geometric spaces (R^3, SO(3), and SO(2)). We enhance the prediction quality through a dedicated scoring model and apply unsupervised physical validity filters to eliminate unrealistic poses. Compared to various approaches, Matcha demonstrates superior performance on Astex and PDBbind test sets in terms of docking success rate and physical plausibility. Moreover, our method works approximately 25 times faster than modern large-scale co-folding models. The model weights and inference code to reproduce our results are available at https://github.com/LigandPro/Matcha.