Daily Papers

By using ZEUS cluster at Embry-Riddle Aeronautical University we perform extensive numerical simulations based on a two-dimensional Fourier spectral method Fourier spatial discretization and an explicit scheme for time differencing) to find the range of existence of the spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation with cubic and quintic nonlinearities. We start from the parameters used by Akhmediev {\it et. al.} and slowly vary them one by one to determine the regimes where solitons exist as stable/unstable structures. We present eight classes of dissipative solitons from which six are known (stationary, pulsating, vortex spinning, filament, exploding, creeping) and two are novel (creeping-vortex propellers and spinning "bean-shaped" solitons). By running lengthy simulations for the different parameters of the equation, we find ranges of existence of stable structures (stationary, pulsating, circular vortex spinning, organized exploding), and unstable structures (elliptic vortex spinning that leads to filament, disorganized exploding, creeping). Moreover, by varying even the two initial conditions together with vorticity, we find a richer behavior in the form of creeping-vortex propellers, and spinning "bean-shaped" solitons. Each class differentiates from the other by distinctive features of their energy evolution, shape of initial conditions, as well as domain of existence of parameters.

Inverse design of inorganic crystals, in which structures are generated to satisfy a target property while preserving diversity and physical plausibility, remains more demanding than ab initio generation, as property conditioning can degrade the structural quality that current generative models otherwise achieve. We propose a diffusion framework that jointly denoises crystal-structure variables and site-resolved local electronic descriptors through a shared score network. As representative descriptors, we adopt Bader charge and atomic density of states (atomic DOS). Under both band-gap and formation energy conditioned generation, the joint models achieved higher success rates than the structure-only baseline in most target conditions, while simultaneously increasing the fraction of generated structures that satisfy uniqueness, novelty, thermodynamic stability, and physical validity (VSUN criteria). A dummy-variable control confirms that these gains originate from the electronic content of the descriptors rather than from auxiliary site-wise variables. The generated Bader charges agree with DFT references with an MAE of 5.5e-2 e on stable structures, and the generated atomic DOS captures the coarse spectral profile of the DFT reference around the modal accuracy range, although finer details and accuracy vary with elemental species. These results establish local electronic descriptors as effective generative variables that serve two complementary roles: broadening the explored materials space through increased structural diversity, and mitigating the trade-off between property targeting and structural quality by guiding the structural trajectory toward electronically plausible configurations during joint denoising.

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

Formula-Driven Supervised Learning (FDSL) enables vision pre-training without real images, but existing methods cast pre-training as classification on discretized labels, discarding continuity in the generative process. We propose Formula-Driven Supervised Metric Learning (FDSML), which derives relational supervision from image-generation parameters beyond discrete class labels. FDSML combines FineFractalDB, our refined fractal dataset with higher intra-class variation and more stable structures, with a Parameter-Aware Triplet (PA-Triplet) Loss that assigns positives and negatives according to distances in the underlying Iterated Function System parameter space. This objective trains embeddings to respect parameter-derived relative similarity orderings. Experiments show that FDSML improves transferability to image retrieval while remaining competitive on downstream classification and improving robustness under several corruption settings. On ResNet-50, Recall@1 improves from 65.6% to 74.0% on Stanford Online Products and from 56.2% to 78.4% on Stanford Cars over FDSL pre-training. These results suggest that parameter-derived relational supervision provides a stronger synthetic pre-training signal than label-based classification for transfer beyond recognition.

We introduce STAR, a text-to-image model that employs a scale-wise auto-regressive paradigm. Unlike VAR, which is constrained to class-conditioned synthesis for images up to 256times256, STAR enables text-driven image generation up to 1024times1024 through three key designs. First, we introduce a pre-trained text encoder to extract and adopt representations for textual constraints, enhancing details and generalizability. Second, given the inherent structural correlation across different scales, we leverage 2D Rotary Positional Encoding (RoPE) and tweak it into a normalized version, ensuring consistent interpretation of relative positions across token maps and stabilizing the training process. Third, we observe that simultaneously sampling all tokens within a single scale can disrupt inter-token relationships, leading to structural instability, particularly in high-resolution generation. To address this, we propose a novel stable sampling method that incorporates causal relationships into the sampling process, ensuring both rich details and stable structures. Compared to previous diffusion models and auto-regressive models, STAR surpasses existing benchmarks in fidelity, text-image consistency, and aesthetic quality, requiring just 2.21s for 1024times1024 images on A100. This highlights the potential of auto-regressive methods in high-quality image synthesis, offering new directions for the text-to-image generation.

In this work, we introduce PhononBench, the first large-scale benchmark for dynamical stability in AI-generated crystals. Leveraging the recently developed MatterSim interatomic potential, which achieves DFT-level accuracy in phonon predictions across more than 10,000 materials, PhononBench enables efficient large-scale phonon calculations and dynamical-stability analysis for 108,843 crystal structures generated by six leading crystal generation models. PhononBench reveals a widespread limitation of current generative models in ensuring dynamical stability: the average dynamical-stability rate across all generated structures is only 25.83%, with the top-performing model, MatterGen, reaching just 41.0%. Further case studies show that in property-targeted generation-illustrated here by band-gap conditioning with MatterGen--the dynamical-stability rate remains as low as 23.5% even at the optimal band-gap condition of 0.5 eV. In space-group-controlled generation, higher-symmetry crystals exhibit better stability (e.g., cubic systems achieve rates up to 49.2%), yet the average stability across all controlled generations is still only 34.4%. An important additional outcome of this study is the identification of 28,119 crystal structures that are phonon-stable across the entire Brillouin zone, providing a substantial pool of reliable candidates for future materials exploration. By establishing the first large-scale dynamical-stability benchmark, this work systematically highlights the current limitations of crystal generation models and offers essential evaluation criteria and guidance for their future development toward the design and discovery of physically viable materials. All model-generated crystal structures, phonon calculation results, and the high-throughput evaluation workflows developed in PhononBench will be openly released at https://github.com/xqh19970407/PhononBench

We perform a high-throughput computational search for novel phonon-mediated superconductors, starting from the Materials Cloud 3-dimensional structure database of experimentally known inorganic stoichiometric compounds. We first compute the Allen-Dynes critical temperature (T_c) for 4533 non-magnetic metals using a direct and progressively finer sampling of the electron-phonon couplings. For the candidates with the largest T_c, we use automated Wannierizations and electron-phonon interpolations to obtain a high-quality dataset for the most promising 250 dynamically stable structures, for which we calculate spectral functions, superconducting bandgaps, and isotropic Migdal-Eliashberg critical temperatures. For 140 of these, we also provide anisotropic Migdal-Eliashberg superconducting gaps and critical temperatures. The approach is remarkably successful in finding known superconductors, and we find 24 unknown ones with a predicted anisotropic T_{rm c} above 10~K. Among them, we identify a possible double gap superconductor (p-doped BaB_2), a non-magnetic half-Heusler ZrRuSb, and the perovskite TaRu_3C, all exhibiting significant T_{rm c}. Finally, we introduce a sensitivity analysis to estimate the robustness of the predictions.

Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum chemistry by scaling model capacity and training data from quantum chemical calculations. As a generalization task, we evaluate the resulting models' predictions of the bond dissociation energy of neutral H_2, the simplest possible molecule. We find that, regardless of dataset size or model capacity, models trained only on stable structures fail dramatically to even qualitatively reproduce the H_2 energy curve. Only when compressed and stretched geometries are explicitly included in training do the predictions roughly resemble the correct shape. Nonetheless, the largest foundation models trained on the largest and most diverse datasets containing dissociating diatomics exhibit serious failures on simple diatomic molecules. Most strikingly, they cannot reproduce the trivial repulsive energy curve of two bare protons, revealing their failure to learn the basic Coulomb's law involved in electronic structure theory. These results suggest that scaling alone is insufficient for building reliable quantum chemical models.

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging the inherent graph structure of EEG channels to capture the spatial relationships in brain activity. By exploiting task-specific symmetries, we define different pretraining strategies that not only improve model performance across all participant groups but also validate the robustness of the geometric representations. Explainability analysis based on the graph structures reveals consistent group-specific neural signatures that persist across pretraining conditions, suggesting stable geometric structures in the neural representations associated with motor learning and feedback processing. These geometric patterns exhibit partial invariance to certain task space transformations, indicating symmetries that enable generalisation across conditions while maintaining specificity to individual learning strategies. This work demonstrates how GNNs can uncover the effects of previous outcomes on motor planning, in a complex real-world task, providing insights into the geometric principles governing neural representations. Our experimental design bridges the gap between controlled experiments and ecologically valid scenarios, offering new insights into the organisation of neural representations during naturalistic motor learning, which may open avenues for exploring fundamental principles governing brain activity in complex tasks.

We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial distributions of magnetically-trapped ultracold atomic clouds. A Lyapunov function is defined which helps us to prove that stable spatial structures in the atomic clouds exist only for the adiabatic index γ=1+1/n with even n. In the case when n is odd we provide an instability result indicating the divergence of the density function for the atoms. Several numerical solutions, which according to our stability analysis are stable, are also presented.

Generative modeling has emerged as a promising approach for crystal structure discovery. However, existing LLM-based generative models struggle with low-level atomic precision, while diffusion-based methods fall short in integrating high-level scientific knowledge. As a result, generated structures are often invalid, unstable, or do not possess desirable properties. To address this gap, we propose CrystalReasoner (\method), an end-to-end LLM framework that generates crystal structures from natural language instructions through reasoning and alignment. \method introduces physical priors as thinking tokens, which include crystallographic symmetry, local coordination environments and predicted physical properties before generating atomic coordinates. This bridges the gap between natural language and 3D structures. \method then employs reinforcement learning (RL) with a multi-objective, dense reward function to align generation with physical validity, chemical consistency, and thermodynamic stability. For property-conditioned tasks, we design task-specific reward functions and train specialized models for discrete constraints (e.g., space group) and continuous properties (e.g., elasticity, thermal expansion). Empirical results demonstrate that compared to prior works and baselines without thinking traces or RL, \method obtains better performance on diverse metrics, triples S.U.N. ratio, and achieves better performance for property conditioned generation. \method also exhibits adaptive reasoning, increasing reasoning lengths as the number of atoms increases. Our work demonstrates the potential of leveraging thinking traces and RL for generating valid, stable, and property-conditioned crystal structures. Please see our work at https://crystalreasoner.github.io/ .

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMatG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMatG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMatG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and 'de novo' generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMatG, we refine and extend both CSP and DNG metrics compared to previous works. OMatG establishes a new state of the art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science. The OMatG code is available at https://github.com/FERMat-ML/OMatG.

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.

Large Language Models (LLMs) are increasingly deployed as long-term interactive agents, yet their limited context windows make it difficult to sustain coherent behavior over extended interactions. Existing memory systems often store isolated records and retrieve fragments, limiting their ability to consolidate evolving user states and resolve conflicts. We introduce EverMemOS, a self-organizing memory operating system that implements an engram-inspired lifecycle for computational memory. Episodic Trace Formation converts dialogue streams into MemCells that capture episodic traces, atomic facts, and time-bounded Foresight signals. Semantic Consolidation organizes MemCells into thematic MemScenes, distilling stable semantic structures and updating user profiles. Reconstructive Recollection performs MemScene-guided agentic retrieval to compose the necessary and sufficient context for downstream reasoning. Experiments on LoCoMo and LongMemEval show that EverMemOS achieves state-of-the-art performance on memory-augmented reasoning tasks. We further report a profile study on PersonaMem v2 and qualitative case studies illustrating chat-oriented capabilities such as user profiling and Foresight. Code is available at https://github.com/EverMind-AI/EverMemOS.

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system's parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain regions of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result of a competition between focusing nonlinearities and spreading while propagating through medium.

The computational prediction and design of peptide binders targeting specific linear epitopes is crucial in biological and biomedical research, yet it remains challenging due to their highly dynamic nature and the scarcity of experimentally solved binding data. To address this problem, we built an unprecedentedly large-scale library of peptide pairs within stable secondary structures (beta sheets), leveraging newly available AlphaFold predicted structures. We then developed a machine learning method based on the Transformer architecture for the design of specific linear binders, in analogy to a language translation task. Our method, TransformerBeta, accurately predicts specific beta strand interactions and samples sequences with beta sheet-like molecular properties, while capturing interpretable physico-chemical interaction patterns. As such, it can propose specific candidate binders targeting linear epitope for experimental validation to inform protein design.

Target proteins that lack accessible binding pockets and conformational stability have posed increasing challenges for drug development. Induced proximity strategies, such as PROTACs and molecular glues, have thus gained attention as pharmacological alternatives, but still require small molecule docking at binding pockets for targeted protein degradation (TPD). The computational design of protein-based binders presents unique opportunities to access undruggable targets, but have often relied on stable 3D structures or predictions for effective binder generation. Recently, we have leveraged the expressive latent spaces of protein language models (pLMs) for the prioritization of peptide binders from sequence alone, which we have then fused to E3 ubiquitin ligase domains, creating a CRISPR-analogous TPD system for target proteins. However, our methods rely on training discriminator models for ranking heuristically or unconditionally-derived guide peptides for their target binding capability. In this work, we introduce PepMLM, a purely target sequence-conditioned de novo generator of linear peptide binders. By employing a novel masking strategy that uniquely positions cognate peptide sequences at the terminus of target protein sequences, PepMLM tasks the state-of-the-art ESM-2 pLM to fully reconstruct the binder region, achieving low perplexities matching or improving upon previously-validated peptide-protein sequence pairs. After successful in silico benchmarking with AlphaFold-Multimer, we experimentally verify PepMLM's efficacy via fusion of model-derived peptides to E3 ubiquitin ligase domains, demonstrating endogenous degradation of target substrates in cellular models. In total, PepMLM enables the generative design of candidate binders to any target protein, without the requirement of target structure, empowering downstream programmable proteome editing applications.

Generating high-fidelity upper-body 3D avatars from one-shot input image remains a significant challenge. Current 3D avatar generation methods, which rely on large reconstruction models, are fast and capable of producing stable body structures, but they often suffer from artifacts such as blurry textures and stiff, unnatural motion. In contrast, generative video models show promising performance by synthesizing photorealistic and dynamic results, but they frequently struggle with unstable behavior, including body structural errors and identity drift. To address these limitations, we propose a novel approach that combines the strengths of both paradigms. Our framework employs a 3D reconstruction model to provide robust structural and appearance priors, which in turn guides a real-time autoregressive video diffusion model for rendering. This process enables the model to synthesize high-frequency, photorealistic details and fluid dynamics in real time, effectively reducing texture blur and motion stiffness while preventing the structural inconsistencies common in video generation methods. By uniting the geometric stability of 3D reconstruction with the generative capabilities of video models, our method produces high-fidelity digital avatars with realistic appearance and dynamic, temporally coherent motion. Experiments demonstrate that our approach significantly reduces artifacts and achieves substantial improvements in visual quality over leading methods, providing a robust and efficient solution for real-time applications such as gaming and virtual reality. Project page: https://lhyfst.github.io/visa

Few-shot anomaly detection remains challenging due to limited training data. Multi-modal anomaly detection (MAD) offers a viable solution, leveraging 3D geometric cues to enrich 2D RGB representations and compensate for this scarcity. However, existing MAD methods apply spatially uniform feature processing, conflating stable macroscopic structures with high-frequency localized defect signals, exacerbating cross-modal misalignment and inflating false-positive rates. To overcome this, we present CMDS-AD, a Cross-Modal Dual-Stream Anomaly Detection framework. A LoRA-guided diffusion model generates diverse RGB samples to mitigate extreme data scarcity. For 3D normal augmentation, we employ a pre-trained diffusion model as a normal estimator. Crucially, this estimator inherently acts as a non-linear low-pass filter, directly extracting low-frequency normal representations from RGB inputs. This establishes an auxiliary estimated stream of purely low-frequency information, anchoring robust structural templates and assisting the uncompressed real stream, containing coupled high- and low-frequency components, to precisely isolate micro-defects. A Coordinate-Aware Hierarchical Feature Mapper adaptively aligns cross-modal semantics, while a multiplicative scoring mechanism filters modality-specific noise. Under the extreme 1-shot setting, CMDS-AD achieves absolute performance gains of 5.7% (I-AUROC) and 2.0% (AUPRO) on MVTec 3D-AD, alongside 7.7% and 5.6% improvements on EyeCandies, establishing a new state-of-the-art. Code is available at https://github.com/Junhaocai27/CMDS-AD

The field of image-to-video generation has made remarkable progress. However, challenges such as human limb twisting and facial distortion persist, especially when generating long videos or modeling intensive motions. Existing human image animation works address these issues by incorporating human-specific semantic representations, e.g., dense poses or ID embeddings, as additional conditions. However, conditioning on these representations could decrease the generation flexibility. Moreover, their reliance on RGB pixel supervision also lacks emphasis on learning necessary 3D geometric relationships and temporal coherence. In contrast, we introduce a novel approach named SemanticREPA that leverages these semantic representations as supervision signals through representation alignment. Specifically, we begin by training a structure alignment module that aligns the structure representations obtained from video latents with video depth estimation features. We then fix the pretrained module, and utilize it to provide additional supervision on the structure representations of the diffusion models, achieving structure rectification to generate coherent and stable human structures. Simultaneously, we develop an ID alignment module to align the ID representations of the generated videos to face recognition features. We further propose to use the predicted structure representations to refine identity restoration in relevant regions. With structure and ID alignment, our method demonstrates superior quality on extended character motions and enhanced character consistency.

This work investigates how large language models (LLMs) internally represent emotion by analyzing the geometry of their hidden-state space. The paper identifies a low-dimensional emotional manifold and shows that emotional representations are directionally encoded, distributed across layers, and aligned with interpretable dimensions. These structures are stable across depth and generalize to eight real-world emotion datasets spanning five languages. Cross-domain alignment yields low error and strong linear probe performance, indicating a universal emotional subspace. Within this space, internal emotion perception can be steered while preserving semantics using a learned intervention module, with especially strong control for basic emotions across languages. These findings reveal a consistent and manipulable affective geometry in LLMs and offer insight into how they internalize and process emotion.

Protein design aims to compose amino-acid sequences that fold into stable three-dimensional structures while satisfying targeted functional properties. The field is increasingly shifting toward vibe protein design, where a single model is expected to generate novel sequences, engineer existing proteins, and reason about protein characteristics through flexible natural-language constraints. Large language models (LLMs) have emerged as a leading paradigm in this space. However, existing evaluation benchmarks often limit their scope to a partial aspect of protein design, while others restrict design objectives to structured input schemas, lacking an integrated framework that evaluates the broad spectrum of protein design competence under open-ended intents. To this end, we present Vibe Protein design Benchmark (VibeProteinBench), a language-interfaced benchmark that probes generalist capabilities through three complementary stages mirroring a computational protein design workflow: recognition, engineering, and generation. Each stage is grounded in expert-curated mechanistic rationales and multi-faceted in silico validation, to computationally verify whether model outputs are biologically plausible. Evaluations across diverse general-purpose and domain-specialized LLMs reveal that no model achieves strong performance across all three stages, suggesting that generalist protein design remains a substantial open challenge for current LLMs.

Organic crystal structure prediction (CSP) is a requirement for computational modelling of organic solids, but traditionally costs several CPU-years per molecule. Generative models such as OXtal dramatically reduce this cost by sampling stable organic crystal structures directly. However, OXtal forgoes explicit lattice parametrization in favour of modelling large crops of the bulk material with expensive triangle layers, which can incur a computational cost of minutes per molecule. In this paper, we reduce this to seconds with Clari, a large-scale flow matching model that generates redundancy-free unit cells and replaces triangle layers with pure pair-bias attention. Clari requires only atom types and bonds as input and does not need an RDKit-sanitizable input molecule, which expands its applicability to challenging chemistries such as fullerenes, metal complexes, and atom clusters. We further ablate key design choices such as auxiliary losses, timestep distributions, noise priors, and self-conditioning. On OXtal's test sets, we surpass OXtal's solve rate while obtaining a speedup of 15-30times. Because Clari also models explicit hydrogens, it supports inference-time scaling via direct energy ranking, without any decoration or relaxation step. When generating 150 crystals and selecting the top-30 by energy, we further improve solve rate while maintaining a speedup of 5-8times. We also introduce the CSD Teaching Subset as a new test split of diverse and complex molecules for future benchmarking. Our contributions enable CSP within seconds, making large-scale virtual screening of organic solids practical. Code is available at https://github.com/aspuru-guzik-group/clari.

Social media platforms often foster environments where users primarily engage with content that aligns with their existing beliefs, thereby reinforcing their views and limiting exposure to opposing viewpoints. In this paper, we analyze X (formerly Twitter) discussions on climate change throughout 2019, using an unsupervised method centered on chambers--second-order information sources--to uncover ideological patterns at scale. Beyond direct connections, chambers capture shared sources of influence, revealing polarization dynamics efficiently and effectively. Analyzing retweet patterns, we identify echo chambers of climate believers and skeptics, revealing strong chamber overlap within ideological groups and minimal overlap between them, resulting in a robust bimodal structure that characterizes polarization. Our method enables us to infer the stance of high-impact users based on their audience's chamber alignment, allowing for the classification of over half the retweeting population with minimal cross-group interaction, in what we term augmented echo chamber classification. We benchmark our approach against manual labeling and a state-of-the-art latent ideology model, finding comparable performance but with nearly four times greater coverage. Moreover, we find that echo chamber structures remain stable over time, even as their members change significantly, suggesting that these structures are a persistent and emergent property of the system. Notably, polarization decreases and climate skepticism rises during the #FridaysForFuture strikes in September 2019. This chamber-based analysis offers valuable insights into the persistence and fluidity of ideological polarization on social media.

Large language models (LLMs) often fail to learn effective long chain-of-thought (Long CoT) reasoning from human or non-Long-CoT LLMs imitation. To understand this, we propose that effective and learnable Long CoT trajectories feature stable molecular-like structures in unified view, which are formed by three interaction types: Deep-Reasoning (covalent-like), Self-Reflection (hydrogen-bond-like), and Self-Exploration (van der Waals-like). Analysis of distilled trajectories reveals these structures emerge from Long CoT fine-tuning, not keyword imitation. We introduce Effective Semantic Isomers and show that only bonds promoting fast entropy convergence support stable Long CoT learning, while structural competition impairs training. Drawing on these findings, we present Mole-Syn, a distribution-transfer-graph method that guides synthesis of effective Long CoT structures, boosting performance and RL stability across benchmarks.

Cross-modal ship re-identification (ReID) between optical and synthetic aperture radar (SAR) imagery is fundamentally challenged by the severe radiometric discrepancy between passive optical imaging and coherent active radar sensing. While existing approaches primarily rely on statistical distribution alignment or semantic matching, they often overlook a critical physical prior: ships are rigid objects whose geometric structures remain stable across sensing modalities, whereas texture appearance is highly modality-dependent. In this work, we propose SDF-Net, a Structure-Aware Disentangled Feature Learning Network that systematically incorporates geometric consistency into optical--SAR ship ReID. Built upon a ViT backbone, SDF-Net introduces a structure consistency constraint that extracts scale-invariant gradient energy statistics from intermediate layers to robustly anchor representations against radiometric variations. At the terminal stage, SDF-Net disentangles the learned representations into modality-invariant identity features and modality-specific characteristics. These decoupled cues are then integrated through a parameter-free additive residual fusion, effectively enhancing discriminative power. Extensive experiments on the HOSS-ReID dataset demonstrate that SDF-Net consistently outperforms existing state-of-the-art methods. The code and trained models are publicly available at https://github.com/cfrfree/SDF-Net.

We introduce LimiX-2, a new model in the LimiX family, developed through model and data scaling guided by our previously established scaling laws. LimiX-2 adopts the Contextual Mechanism Networks (CMNs) paradigm and is pretrained with Context-Conditional Masked Modeling (CCMM). CMNs shifts the organizing principle of in-context learning from target-centric prediction to mechanism-oriented joint modeling. Rather than centering the network on the p(y mid x, D_{context}) objective of conventional tabular PFNs, it is designed around learning p(x, y mid D_{context}), a context-dependent representation of the joint structure underlying data generation. Pretraining uses synthetic datasets generated by structural causal models (SCMs) spanning diverse graph structures, functional mechanisms, and observation processes. Evaluations on TabArena, TALENT, and BCCO show that LimiX-2 outperforms current dataset-specific models and tabular foundation models. Beyond predictive performance, the CMN paradigm also promotes causal awareness in LimiX-2: its feature attention encodes direct causal relationships, enabling accurate causal skeleton recovery.

Text-guided image and 3D editing have advanced with diffusion-based models, yet methods like Delta Denoising Score often struggle with stability, spatial control, and editing strength. These limitations stem from reliance on complex auxiliary structures, which introduce conflicting optimization signals and restrict precise, localized edits. We introduce Stable Score Distillation (SSD), a streamlined framework that enhances stability and alignment in the editing process by anchoring a single classifier to the source prompt. Specifically, SSD utilizes Classifier-Free Guidance (CFG) equation to achieves cross-prompt alignment, and introduces a constant term null-text branch to stabilize the optimization process. This approach preserves the original content's structure and ensures that editing trajectories are closely aligned with the source prompt, enabling smooth, prompt-specific modifications while maintaining coherence in surrounding regions. Additionally, SSD incorporates a prompt enhancement branch to boost editing strength, particularly for style transformations. Our method achieves state-of-the-art results in 2D and 3D editing tasks, including NeRF and text-driven style edits, with faster convergence and reduced complexity, providing a robust and efficient solution for text-guided editing.

Transformers have become the de facto architecture for a wide range of machine learning tasks, particularly in large language models (LLMs). Despite their remarkable performance, challenges remain in training deep transformer networks, especially regarding the location of layer normalization. While Pre-Norm structures facilitate easier training due to their more prominent identity path, they often yield suboptimal performance compared to Post-Norm. In this paper, we propose HybridNorm, a straightforward yet effective hybrid normalization strategy that integrates the advantages of both Pre-Norm and Post-Norm approaches. Specifically, HybridNorm employs QKV normalization within the attention mechanism and Post-Norm in the feed-forward network (FFN) of each transformer block. This design not only stabilizes training but also enhances performance, particularly in the context of LLMs. Comprehensive experiments in both dense and sparse architectures show that HybridNorm consistently outperforms both Pre-Norm and Post-Norm approaches, achieving state-of-the-art results across various benchmarks. These findings highlight the potential of HybridNorm as a more stable and effective technique for improving the training and performance of deep transformer models. %Code will be made publicly available. Code is available at https://github.com/BryceZhuo/HybridNorm.

Generating physically realistic 3D molecular structures remains a core challenge in molecular generative modeling. While diffusion models equipped with equivariant neural networks have made progress in capturing molecular geometries, they often struggle to produce equilibrium structures that adhere to physical principles such as force field consistency. To bridge this gap, we propose Reinforcement Learning with Physical Feedback (RLPF), a novel framework that extends Denoising Diffusion Policy Optimization to 3D molecular generation. RLPF formulates the task as a Markov decision process and applies proximal policy optimization to fine-tune equivariant diffusion models. Crucially, RLPF introduces reward functions derived from force-field evaluations, providing direct physical feedback to guide the generation toward energetically stable and physically meaningful structures. Experiments on the QM9 and GEOM-drug datasets demonstrate that RLPF significantly improves molecular stability compared to existing methods. These results highlight the value of incorporating physics-based feedback into generative modeling. The code is available at: https://github.com/ZhijianZhou/RLPF/tree/verl_diffusion.

We present Stable Part Diffusion 4D (SP4D), a framework for generating paired RGB and kinematic part videos from monocular inputs. Unlike conventional part segmentation methods that rely on appearance-based semantic cues, SP4D learns to produce kinematic parts - structural components aligned with object articulation and consistent across views and time. SP4D adopts a dual-branch diffusion model that jointly synthesizes RGB frames and corresponding part segmentation maps. To simplify the architecture and flexibly enable different part counts, we introduce a spatial color encoding scheme that maps part masks to continuous RGB-like images. This encoding allows the segmentation branch to share the latent VAE from the RGB branch, while enabling part segmentation to be recovered via straightforward post-processing. A Bidirectional Diffusion Fusion (BiDiFuse) module enhances cross-branch consistency, supported by a contrastive part consistency loss to promote spatial and temporal alignment of part predictions. We demonstrate that the generated 2D part maps can be lifted to 3D to derive skeletal structures and harmonic skinning weights with few manual adjustments. To train and evaluate SP4D, we construct KinematicParts20K, a curated dataset of over 20K rigged objects selected and processed from Objaverse XL (Deitke et al., 2023), each paired with multi-view RGB and part video sequences. Experiments show that SP4D generalizes strongly to diverse scenarios, including real-world videos, novel generated objects, and rare articulated poses, producing kinematic-aware outputs suitable for downstream animation and motion-related tasks.

Diffusion-based generative models' impressive ability to create convincing images has captured global attention. However, their complex internal structures and operations often make them difficult for non-experts to understand. We present Diffusion Explainer, the first interactive visualization tool that explains how Stable Diffusion transforms text prompts into images. Diffusion Explainer tightly integrates a visual overview of Stable Diffusion's complex components with detailed explanations of their underlying operations, enabling users to fluidly transition between multiple levels of abstraction through animations and interactive elements. By comparing the evolutions of image representations guided by two related text prompts over refinement timesteps, users can discover the impact of prompts on image generation. Diffusion Explainer runs locally in users' web browsers without the need for installation or specialized hardware, broadening the public's education access to modern AI techniques. Our open-sourced tool is available at: https://poloclub.github.io/diffusion-explainer/.

Realistic image super-resolution (Real-ISR) aims to reproduce perceptually realistic image details from a low-quality input. The commonly used adversarial training based Real-ISR methods often introduce unnatural visual artifacts and fail to generate realistic textures for natural scene images. The recently developed generative stable diffusion models provide a potential solution to Real-ISR with pre-learned strong image priors. However, the existing methods along this line either fail to keep faithful pixel-wise image structures or resort to extra skipped connections to reproduce details, which requires additional training in image space and limits their extension to other related tasks in latent space such as image stylization. In this work, we propose a pixel-aware stable diffusion (PASD) network to achieve robust Real-ISR as well as personalized stylization. In specific, a pixel-aware cross attention module is introduced to enable diffusion models perceiving image local structures in pixel-wise level, while a degradation removal module is used to extract degradation insensitive features to guide the diffusion process together with image high level information. By simply replacing the base diffusion model with a personalized one, our method can generate diverse stylized images without the need to collect pairwise training data. PASD can be easily integrated into existing diffusion models such as Stable Diffusion. Experiments on Real-ISR and personalized stylization demonstrate the effectiveness of our proposed approach. The source code and models can be found at https://github.com/yangxy/PASD.

Joint Embedding Predictive Architectures (JEPAs) offer a compelling framework for learning world models in compact latent spaces, yet existing methods remain fragile, relying on complex multi-term losses, exponential moving averages, pre-trained encoders, or auxiliary supervision to avoid representation collapse. In this work, we introduce LeWorldModel (LeWM), the first JEPA that trains stably end-to-end from raw pixels using only two loss terms: a next-embedding prediction loss and a regularizer enforcing Gaussian-distributed latent embeddings. This reduces tunable loss hyperparameters from six to one compared to the only existing end-to-end alternative. With ~15M parameters trainable on a single GPU in a few hours, LeWM plans up to 48x faster than foundation-model-based world models while remaining competitive across diverse 2D and 3D control tasks. Beyond control, we show that LeWM's latent space encodes meaningful physical structure through probing of physical quantities. Surprise evaluation confirms that the model reliably detects physically implausible events.

We propose fine-tuning large language models for generation of stable materials. While unorthodox, fine-tuning large language models on text-encoded atomistic data is simple to implement yet reliable, with around 90% of sampled structures obeying physical constraints on atom positions and charges. Using energy above hull calculations from both learned ML potentials and gold-standard DFT calculations, we show that our strongest model (fine-tuned LLaMA-2 70B) can generate materials predicted to be metastable at about twice the rate (49% vs 28%) of CDVAE, a competing diffusion model. Because of text prompting's inherent flexibility, our models can simultaneously be used for unconditional generation of stable material, infilling of partial structures and text-conditional generation. Finally, we show that language models' ability to capture key symmetries of crystal structures improves with model scale, suggesting that the biases of pretrained LLMs are surprisingly well-suited for atomistic data.

We introduce LegoGPT, the first approach for generating physically stable LEGO brick models from text prompts. To achieve this, we construct a large-scale, physically stable dataset of LEGO designs, along with their associated captions, and train an autoregressive large language model to predict the next brick to add via next-token prediction. To improve the stability of the resulting designs, we employ an efficient validity check and physics-aware rollback during autoregressive inference, which prunes infeasible token predictions using physics laws and assembly constraints. Our experiments show that LegoGPT produces stable, diverse, and aesthetically pleasing LEGO designs that align closely with the input text prompts. We also develop a text-based LEGO texturing method to generate colored and textured designs. We show that our designs can be assembled manually by humans and automatically by robotic arms. We also release our new dataset, StableText2Lego, containing over 47,000 LEGO structures of over 28,000 unique 3D objects accompanied by detailed captions, along with our code and models at the project website: https://avalovelace1.github.io/LegoGPT/.

Schema-guided reasoning pipelines ask LLMs to produce explicit intermediate structures -- rubrics, checklists, verification queries -- before committing to a final decision. But do these structures causally determine the output, or merely accompany it? We introduce a causal evaluation protocol that makes this directly measurable: by selecting tasks where a deterministic function maps intermediate structures to decisions, every controlled edit implies a unique correct output. Across eight models and three benchmarks, models appear self-consistent with their own intermediate structures but fail to update predictions after intervention in up to 60% of cases -- revealing that apparent faithfulness is fragile once the intermediate structure changes. When derivation of the final decision from the structure is delegated to an external tool, this fragility largely disappears; however, prompts which ask to prioritize the intermediate structure over the original input do not materially close the gap. Overall, intermediate structures in schema-guided pipelines function as influential context rather than stable causal mediators.

Magnetic Resonance Imaging (MRI), including diffusion MRI (dMRI), serves as a ``microscope'' for anatomical structures and routinely mitigates the influence of low signal-to-noise ratio scans by compromising temporal or spatial resolution. However, these compromises fail to meet clinical demands for both efficiency and precision. Consequently, denoising is a vital preprocessing step, particularly for dMRI, where clean data is unavailable. In this paper, we introduce Di-Fusion, a fully self-supervised denoising method that leverages the latter diffusion steps and an adaptive sampling process. Unlike previous approaches, our single-stage framework achieves efficient and stable training without extra noise model training and offers adaptive and controllable results in the sampling process. Our thorough experiments on real and simulated data demonstrate that Di-Fusion achieves state-of-the-art performance in microstructure modeling, tractography tracking, and other downstream tasks. Code is available at https://github.com/FouierL/Di-Fusion.

Improving the reliability and completeness of colonoscopic inspection is critical for reducing missed lesions and improving colorectal cancer prevention. Reliable scene understanding is essential for navigation, reconstruction, and assessment of inspection completeness. Anatomical structures such as mucosal folds provide stable geometric cues for endoscope localization, while surgical instruments introduce dynamic occlusions that complicate visual interpretation. However, existing gastrointestinal endoscopy datasets largely focus on disease detection or artifact segmentation, leaving a gap in precise annotations of structural landmarks and instruments. We introduce SegCol, a dataset and benchmark for semantic segmentation of colon fold edges and surgical instruments derived from the EndoMapper dataset. SegCol provides manually annotated pixel-level masks for three instrument classes and thin fold-edge structures across temporally consistent image sequences. It forms the basis of the SegCol Challenge, organized as part of the EndoVis Challenge at MICCAI 2024, evaluating both supervised segmentation and annotation-efficient active learning. We further study segmentation metrics, including Dice, ODS/OIS, AP, and CLDice, under structural perturbations and different object geometries, and analyze participating methods, architectural choices, and active learning strategies. Our findings show that metric behavior strongly depends on target structure, highlighting the need for carefully selected evaluation protocols in endoscopic segmentation. Details are available at https://www.synapse.org/Synapse:syn54124209/wiki/626563, and code at https://github.com/surgical-vision/segcol_challenge.

The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction, directly generating diverse, novel protein structures from neural networks remains difficult. In this work, we present a new diffusion-based generative model that designs protein backbone structures via a procedure that mirrors the native folding process. We describe protein backbone structure as a series of consecutive angles capturing the relative orientation of the constituent amino acid residues, and generate new structures by denoising from a random, unfolded state towards a stable folded structure. Not only does this mirror how proteins biologically twist into energetically favorable conformations, the inherent shift and rotational invariance of this representation crucially alleviates the need for complex equivariant networks. We train a denoising diffusion probabilistic model with a simple transformer backbone and demonstrate that our resulting model unconditionally generates highly realistic protein structures with complexity and structural patterns akin to those of naturally-occurring proteins. As a useful resource, we release the first open-source codebase and trained models for protein structure diffusion.

Current operating systems expose interfaces optimized for human users but not for AI agents. Humans benefit from pixels, icons, windows, visual grouping, mouse movement, and keyboard shortcuts; AI agents instead need compact semantic state, grounded actions, and reliable feedback. As a result, many computer-use agents are forced to interpret screenshots, OCR output, and visual crops, introducing high token costs, visual ambiguity, latency, and coordinate uncertainty. This paper introduces LUMOS (Language Model Unified Machine-Readable Operating-System Semantics), a semantic interaction layer between AI agents and operating systems. LUMOS converts native accessibility metadata and browser UI structures into machine readable semantic blueprints with stable identifiers, roles, names, values, bounds, and action affordances. It also supports live semantic pointer grounding by querying the UI element under or near the cursor through operating-system automation APIs. An LLM then acts through an accessibility grounded observe act loop using constrained visible-UI primitives rather than application-specific scripts. LUMOS does not claim to replace visual agents; instead, it reduces dependence on screenshots when operating systems already provide semantic structure. These results suggest a path toward AI-native operating systems and machine-readable interaction layers.

Reconstructing the early universe from the evolved present-day universe is a challenging and computationally demanding problem in modern astrophysics. We devise a novel generative framework, Cosmo3DFlow, designed to address dimensionality and sparsity, the critical bottlenecks inherent in current state-of-the-art methods for cosmological inference. By integrating 3D Discrete Wavelet Transform (DWT) with flow matching, we effectively represent high-dimensional cosmological structures. The Wavelet Transform addresses the ``void problem'' by translating spatial emptiness into spectral sparsity. It decouples high-frequency details from low-frequency structures, and wavelet-space velocity fields facilitate stable ordinary differential equation (ODE) solvers with large step sizes. Using large-scale cosmological N-body simulations at 128^3 resolution, we achieve up to 46times faster sampling than diffusion models. Our results enable initial conditions to be sampled in seconds, compared to minutes for previous methods.

Text-to-image diffusion models have demonstrated an unparalleled ability to generate high-quality, diverse images from a textual concept (e.g., "a doctor", "love"). However, the internal process of mapping text to a rich visual representation remains an enigma. In this work, we tackle the challenge of understanding concept representations in text-to-image models by decomposing an input text prompt into a small set of interpretable elements. This is achieved by learning a pseudo-token that is a sparse weighted combination of tokens from the model's vocabulary, with the objective of reconstructing the images generated for the given concept. Applied over the state-of-the-art Stable Diffusion model, this decomposition reveals non-trivial and surprising structures in the representations of concepts. For example, we find that some concepts such as "a president" or "a composer" are dominated by specific instances (e.g., "Obama", "Biden") and their interpolations. Other concepts, such as "happiness" combine associated terms that can be concrete ("family", "laughter") or abstract ("friendship", "emotion"). In addition to peering into the inner workings of Stable Diffusion, our method also enables applications such as single-image decomposition to tokens, bias detection and mitigation, and semantic image manipulation. Our code will be available at: https://hila-chefer.github.io/Conceptor/

To serve the intricate and varied demands of image editing, precise and flexible manipulation of image content is indispensable. Recently, DragGAN has achieved impressive editing results through point-based manipulation. However, we have observed that DragGAN struggles with miss tracking, where DragGAN encounters difficulty in effectively tracking the desired handle points, and ambiguous tracking, where the tracked points are situated within other regions that bear resemblance to the handle points. To deal with the above issues, we propose FreeDrag, which adopts a feature-oriented approach to free the burden on point tracking within the point-oriented methodology of DragGAN. The FreeDrag incorporates adaptive template features, line search, and fuzzy localization techniques to perform stable and efficient point-based image editing. Extensive experiments demonstrate that our method is superior to the DragGAN and enables stable point-based editing in challenging scenarios with similar structures, fine details, or under multi-point targets.

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.

In this work, we present Multimodal Equivariant Inverse Design Network (MEIDNet), a framework that jointly learns structural information and materials properties through contrastive learning, while encoding structures via an equivariant graph neural network (EGNN). By combining generative inverse design with multimodal learning, our approach accelerates the exploration of chemical-structural space and facilitates the discovery of materials that satisfy predefined property targets. MEIDNet exhibits strong latent-space alignment with cosine similarity 0.96 by fusion of three modalities through cross-modal learning. Through implementation of curriculum learning strategies, MEIDNet achieves ~60 times higher learning efficiency than conventional training techniques. The potential of our multimodal approach is demonstrated by generating low-bandgap perovskite structures at a stable, unique, and novel (SUN) rate of 13.6 %, which are further validated by ab initio methods. Our inverse design framework demonstrates both scalability and adaptability, paving the way for the universal learning of chemical space across diverse modalities.

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.

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.

Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and the expanded availability of experimental 3D protein structures have accelerated structure prediction, the dynamic nature of protein structures has received limited attention. This study introduces an innovative 4D diffusion model incorporating molecular dynamics (MD) simulation data to learn dynamic protein structures. Our approach is distinguished by the following components: (1) a unified diffusion model capable of generating dynamic protein structures, including both the backbone and side chains, utilizing atomic grouping and side-chain dihedral angle predictions; (2) a reference network that enhances structural consistency by integrating the latent embeddings of the initial 3D protein structures; and (3) a motion alignment module aimed at improving temporal structural coherence across multiple time steps. To our knowledge, this is the first diffusion-based model aimed at predicting protein trajectories across multiple time steps simultaneously. Validation on benchmark datasets demonstrates that our model exhibits high accuracy in predicting dynamic 3D structures of proteins containing up to 256 amino acids over 32 time steps, effectively capturing both local flexibility in stable states and significant conformational changes.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time novel view synthesis (NVS) with impressive quality in indoor scenes. However, achieving high-fidelity rendering requires meticulously captured images covering the entire scene, limiting accessibility for general users. We aim to develop a practical 3DGS-based NVS framework using simple panorama-style motion with a handheld camera (e.g., mobile device). While convenient, this rotation-dominant motion and narrow baseline make accurate camera pose and 3D point estimation challenging, especially in textureless indoor scenes. To address these challenges, we propose LighthouseGS, a novel framework inspired by the lighthouse-like sweeping motion of panoramic views. LighthouseGS leverages rough geometric priors, such as mobile device camera poses and monocular depth estimation, and utilizes the planar structures often found in indoor environments. We present a new initialization method called plane scaffold assembly to generate consistent 3D points on these structures, followed by a stable pruning strategy to enhance geometry and optimization stability. Additionally, we introduce geometric and photometric corrections to resolve inconsistencies from motion drift and auto-exposure in mobile devices. Tested on collected real and synthetic indoor scenes, LighthouseGS delivers photorealistic rendering, surpassing state-of-the-art methods and demonstrating the potential for panoramic view synthesis and object placement.

We present ThinkProbe, a framework for structural analysis of LLM reasoning traces. ThinkProbe converts each trace into a Thought Graph a directed graph with cycles, 8 node types, and 6 edge types and derives a 19-metric five-dimensional cognitive profile (5D-CP: Breadth, Depth, Structure, Metacognitive, Efficiency) through a fully non-generative pipeline combining rule-based segmentation and discriminative semantic linking. Applied to 4{,}200 traces from 7 native reasoning models across 200 open-ended questions and 10 cognitive domains, ThinkProbe reveals that reasoning structure is a stable, model-level property: between-model variance exceeds between-domain variance by up to fourfold across four of five cognitive dimensions, with Structure showing genuine sensitivity to question domain, exposing qualitatively distinct cognitive profiles invisible to accuracy-based evaluation.

Predicting satellite imagery requires a balance between structural accuracy and textural detail. Standard deterministic methods like PredRNN or SimVP minimize pixel-based errors but suffer from the "regression to the mean" problem, producing blurry outputs that obscure subtle geographic-spatial features. Generative models provide realistic textures but often misleadingly reveal structural anomalies. To bridge this gap, we introduce Sat-JEPA-Diff, which combines Self-Supervised Learning (SSL) with Hidden Diffusion Models (LDM). An IJEPA module predicts stable semantic representations, which then route a frozen Stable Diffusion backbone via a lightweight cross-attention adapter. This ensures that the synthesized high-accuracy textures are based on absolutely accurate structural predictions. Evaluated on a global Sentinel-2 dataset, Sat-JEPA-Diff excels at resolving sharp boundaries. It achieves leading perceptual scores (GSSIM: 0.8984, FID: 0.1475) and significantly outperforms deterministic baselines, despite standard autoregressive stability limits. The code and dataset are publicly available on https://github.com/VU-AIML/SAT-JEPA-DIFF.

Self-attention is a ubiquitous primitive in modern sequence models, yet its operator-level geometry is only partially understood. We view a token sequence as a vector field over the token-position graph and identify attention as a connection walk: messages are aggregated by a nonnegative walk matrix while being transported along each edge by a learned linear map. Within this framework, we prove that single-head attention (SHA) is exactly a connection propagation step with constant transport, and that multi-head attention (MHA) is exactly a single edge-dependent connection walk whose effective transport is an attention-gated mixture of headwise transports. We further clarify the conditions under which the corresponding generator reduces to a random-walk connection Laplacian, highlighting the roles of stochasticity, reversibility, and metric-compatible transports. Empirically, we find that trained Transformers across scales (from 124M to 8B) and structures (encoder/decoder) exhibit geometric structure consistent with our theory: effective attention graphs converge to stable geometric operators in deeper layers, learned transports self-organize into approximate scaled isometries, and both phenomena strengthen consistently with scale. Overall, the paper provides a precise connection-walk formalism that links self-attention to classical geometric operators, along with a set of operator-level tools for analyzing transformer models from a geometric perspective.

In this work, we investigate the capability of generating images from pre-trained diffusion models at much higher resolutions than the training image sizes. In addition, the generated images should have arbitrary image aspect ratios. When generating images directly at a higher resolution, 1024 x 1024, with the pre-trained Stable Diffusion using training images of resolution 512 x 512, we observe persistent problems of object repetition and unreasonable object structures. Existing works for higher-resolution generation, such as attention-based and joint-diffusion approaches, cannot well address these issues. As a new perspective, we examine the structural components of the U-Net in diffusion models and identify the crucial cause as the limited perception field of convolutional kernels. Based on this key observation, we propose a simple yet effective re-dilation that can dynamically adjust the convolutional perception field during inference. We further propose the dispersed convolution and noise-damped classifier-free guidance, which can enable ultra-high-resolution image generation (e.g., 4096 x 4096). Notably, our approach does not require any training or optimization. Extensive experiments demonstrate that our approach can address the repetition issue well and achieve state-of-the-art performance on higher-resolution image synthesis, especially in texture details. Our work also suggests that a pre-trained diffusion model trained on low-resolution images can be directly used for high-resolution visual generation without further tuning, which may provide insights for future research on ultra-high-resolution image and video synthesis.

In this work we address the problem of finding reliable pixel-level correspondences under difficult imaging conditions. We propose an approach where a single convolutional neural network plays a dual role: It is simultaneously a dense feature descriptor and a feature detector. By postponing the detection to a later stage, the obtained keypoints are more stable than their traditional counterparts based on early detection of low-level structures. We show that this model can be trained using pixel correspondences extracted from readily available large-scale SfM reconstructions, without any further annotations. The proposed method obtains state-of-the-art performance on both the difficult Aachen Day-Night localization dataset and the InLoc indoor localization benchmark, as well as competitive performance on other benchmarks for image matching and 3D reconstruction.

Event-based cameras are ideal for line-based motion estimation, since they predominantly respond to edges in the scene. However, accurately determining the camera displacement based on events continues to be an open problem. This is because line feature extraction and dynamics estimation are tightly coupled when using event cameras, and no precise model is currently available for describing the complex structures generated by lines in the space-time volume of events. We solve this problem by deriving the correct non-linear parametrization of such manifolds, which we term eventails, and demonstrate its application to event-based linear motion estimation, with known rotation from an Inertial Measurement Unit. Using this parametrization, we introduce a novel minimal 5-point solver that jointly estimates line parameters and linear camera velocity projections, which can be fused into a single, averaged linear velocity when considering multiple lines. We demonstrate on both synthetic and real data that our solver generates more stable relative motion estimates than other methods while capturing more inliers than clustering based on spatio-temporal planes. In particular, our method consistently achieves a 100% success rate in estimating linear velocity where existing closed-form solvers only achieve between 23% and 70%. The proposed eventails contribute to a better understanding of spatio-temporal event-generated geometries and we thus believe it will become a core building block of future event-based motion estimation algorithms.

Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline materials have internal symmetry. However, this is often inadequately addressed by existing generative models, making the consistent generation of stable and symmetrically valid crystal structures a significant challenge. We introduce WyFormer, a generative model that directly tackles this by formally conditioning on space group symmetry. It achieves this by using Wyckoff positions as the basis for an elegant, compressed, and discrete structure representation. To model the distribution, we develop a permutation-invariant autoregressive model based on the Transformer encoder and an absence of positional encoding. Extensive experimentation demonstrates WyFormer's compelling combination of attributes: it achieves best-in-class symmetry-conditioned generation, incorporates a physics-motivated inductive bias, produces structures with competitive stability, predicts material properties with competitive accuracy even without atomic coordinates, and exhibits unparalleled inference speed.

Discovering novel materials is critical for technological advancements such as solar cells, batteries, and carbon capture. However, the development of new materials is constrained by a slow and expensive trial-and-error process. To accelerate this pipeline, we introduce PLaID++, a Large Language Model (LLM) fine-tuned for stable and property-guided crystal generation. We fine-tune Qwen-2.5 7B to generate crystal structures using a novel Wyckoff-based text representation. We show that generation can be effectively guided with a reinforcement learning technique based on Direct Preference Optimization (DPO), with sampled structures categorized by their stability, novelty, and space group. By encoding symmetry constraints directly into text and guiding model outputs towards desirable chemical space, PLaID++ generates structures that are thermodynamically stable, unique, and novel at a sim50\% greater rate than prior methods and conditionally generates structures with desired space group properties. Our experiments highlight the effectiveness of iterative DPO, achieving sim115\% and sim50\% improvements in unconditional and space group conditioned generation, respectively, compared to fine-tuning alone. Our work demonstrates the potential of adapting post-training techniques from natural language processing to materials design, paving the way for targeted and efficient discovery of novel materials.

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.

High-performance GPU kernels are critical to modern machine learning systems, yet developing them remains a manual, expert-driven process. Recent work has explored using LLMs to automate kernel generation, but generated kernels still fall short of carefully tuned references on standardized benchmarks. We present CuTeGen, an agentic GPU kernel synthesis framework that treats kernel development as a structured generate-test-refine workflow over the CuTe abstraction layer. Two design choices distinguish CuTeGen from prior work: targeting CuTe rather than raw CUDA, which exposes performance-critical structures such as tiling and data movement while remaining stable enough for iterative refinement, and a delayed profiling schedule that withholds low-level performance feedback until the kernel's high-level structure has stabilized. On the 209 tasks of KernelBench Level-1 and Level-2, CuTeGen achieves an average speedup of 1.71times over PyTorch and outperforms the prior agentic baseline CudaForge (0.89times) at comparable per-task generation cost. Code available at https://github.com/taratt/cutegen.git

Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.

Recent video inpainting algorithms integrate flow-based pixel propagation with transformer-based generation to leverage optical flow for restoring textures and objects using information from neighboring frames, while completing masked regions through visual Transformers. However, these approaches often encounter blurring and temporal inconsistencies when dealing with large masks, highlighting the need for models with enhanced generative capabilities. Recently, diffusion models have emerged as a prominent technique in image and video generation due to their impressive performance. In this paper, we introduce DiffuEraser, a video inpainting model based on stable diffusion, designed to fill masked regions with greater details and more coherent structures. We incorporate prior information to provide initialization and weak conditioning,which helps mitigate noisy artifacts and suppress hallucinations. Additionally, to improve temporal consistency during long-sequence inference, we expand the temporal receptive fields of both the prior model and DiffuEraser, and further enhance consistency by leveraging the temporal smoothing property of Video Diffusion Models. Experimental results demonstrate that our proposed method outperforms state-of-the-art techniques in both content completeness and temporal consistency while maintaining acceptable efficiency.

Proteins are dynamic molecular machines whose biological functions, spanning enzymatic catalysis, signal transduction, and structural adaptation, are intrinsically linked to their motions. Designing proteins with targeted dynamic properties, however, remains a challenge due to the complex, degenerate relationships between sequence, structure, and molecular motion. Here, we introduce VibeGen, a generative AI framework that enables end-to-end de novo protein design conditioned on normal mode vibrations. VibeGen employs an agentic dual-model architecture, comprising a protein designer that generates sequence candidates based on specified vibrational modes and a protein predictor that evaluates their dynamic accuracy. This approach synergizes diversity, accuracy, and novelty during the design process. Via full-atom molecular simulations as direct validation, we demonstrate that the designed proteins accurately reproduce the prescribed normal mode amplitudes across the backbone while adopting various stable, functionally relevant structures. Notably, generated sequences are de novo, exhibiting no significant similarity to natural proteins, thereby expanding the accessible protein space beyond evolutionary constraints. Our work integrates protein dynamics into generative protein design, and establishes a direct, bidirectional link between sequence and vibrational behavior, unlocking new pathways for engineering biomolecules with tailored dynamical and functional properties. This framework holds broad implications for the rational design of flexible enzymes, dynamic scaffolds, and biomaterials, paving the way toward dynamics-informed AI-driven protein engineering.

Transformer neural operators have recently become an effective approach for surrogate modeling of systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers Re_{tau}approx 180,395,590, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods. By analyzing the attention kernels, we elucidate the reasons why IFactFormer-m converges faster and achieves a stable and accurate long-term prediction compared to IFactFormer-o. Code and data are available at: https://github.com/huiyu-2002/IFactFormer-m.

Large language models (LLMs) remain broadly open and highly steerable: they imitate at scale, accept arbitrary system prompts, and readily adopt multiple personae. By analogy to human development, we hypothesize that progress toward artificial general intelligence (AGI) involves a lock-in phase: a transition from open imitation to identity consolidation, in which goal structures, refusals, preferences, and internal representations become comparatively stable and resistant to external steering. We formalize this phase, link it to known phenomena in learning dynamics, and propose operational metrics for onset detection. Experimentally, we demonstrate that while the behavioral consolidation is rapid and non-linear, its side-effects on general capabilities are not monolithic. Our results reveal a spectrum of outcomes--from performance trade-offs in small models, through largely cost-free adoption in mid-scale models, to transient instabilities in large, quantized models. We argue that such consolidation is a prerequisite for AGI-level reliability and also a critical control point for safety: identities can be deliberately engineered for reliability, yet may also emerge spontaneously during scaling, potentially hardening unpredictable goals and behaviors.

Recently, autoregressive (AR) video diffusion models has achieved remarkable performance. However, due to their limited training durations, a train-test gap emerges when testing at longer horizons, leading to rapid visual degradations. Following Self Forcing, which studies the train-test gap within the training duration, this work studies the train-test gap beyond the training duration, i.e., the gap between the limited horizons during training and open-ended horizons during testing. Since open-ended testing can extend beyond any finite training window, and long-video training is computationally expensive, we pursue a training-free solution to bridge this gap. To explore a training-free solution, we conduct a systematic analysis of AR cache maintenance. These insights lead to Rolling Sink. Built on Self Forcing (trained on only 5s clips), Rolling Sink effectively scales the AR video synthesis to ultra-long durations (e.g., 5-30 minutes at 16 FPS) at test time, with consistent subjects, stable colors, coherent structures, and smooth motions. As demonstrated by extensive experiments, Rolling Sink achieves superior long-horizon visual fidelity and temporal consistency compared to SOTA baselines. Project page: https://rolling-sink.github.io/

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".

Motivated by the peculiar features of the trans-Neptunian object (TNO) Máni and the discovery of ring systems around Centaurs and trans-Neptunian bodies, we investigate the stability of particles around a small irregular body hosting a deep equatorial crater. This study is the third contribution in a sequence devoted to the dynamics around non-spherically symmetric bodies. Using Máni as a reference model, whose crater depth exceeds 10% of its radius, we map the system stability through complementary methods: Poincaré surfaces of section (PSS), survival maps, and the finite-time Lyapunov exponent (FTLE). In the nominal case, the 1!:!1, 2!:!1, 3!:!1, and 4!:!1 spin-orbit resonances (SORs) are consistently identified by all techniques. The prominent 3!:!1 SOR exhibits a bifurcated structure at high eccentricities, matching structural transitions observed at lower Jacobi constant values in the PSSs. Increasing the rotation rate (λ) and crater mass ratio (μ) enlarges resonance widths and promotes overlap, making the 2!:!1 and 4!:!1 SORs progressively dominant. Lower rotation rates allow stable trajectories to persist at higher eccentricities, whereas the 1!:!1 SOR is highly sensitive to stronger perturbations and disappears in the most extreme cases. In contrast to mass-anomaly models, which can clear the region interior to the 2!:!1 SOR, the crater configuration considered here preserves stable regions in this vicinity, suggesting alternative scenarios for the formation and maintenance of debris structures around irregular minor bodies.

Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been one of the most interesting areas to study, and it is also one of the biggest problems of biochemistry. Each protein folds distinctively, and the difficulty of finding its stable shape rapidly increases with an increase in the number of amino acids in the chain. A moderate protein has about 100 amino acids, and the number of combinations one needs to verify to find the stable structure is enormous. At some point, the number of these combinations will be so vast that classical computers cannot even attempt to solve them. In this paper, we examine how this problem can be solved with the help of quantum computing using two different algorithms, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), using Qiskit Nature. We compare the results of different quantum hardware and simulators and check how error mitigation affects the performance. Further, we make comparisons with SoTA algorithms and evaluate the reliability of the method.

Recent advances in video generation have enabled high-fidelity video synthesis from user provided prompts. However, existing models and benchmarks fail to capture the complexity and requirements of professional video generation. Towards that goal, we introduce Stable Cinemetrics, a structured evaluation framework that formalizes filmmaking controls into four disentangled, hierarchical taxonomies: Setup, Event, Lighting, and Camera. Together, these taxonomies define 76 fine-grained control nodes grounded in industry practices. Using these taxonomies, we construct a benchmark of prompts aligned with professional use cases and develop an automated pipeline for prompt categorization and question generation, enabling independent evaluation of each control dimension. We conduct a large-scale human study spanning 10+ models and 20K videos, annotated by a pool of 80+ film professionals. Our analysis, both coarse and fine-grained reveal that even the strongest current models exhibit significant gaps, particularly in Events and Camera-related controls. To enable scalable evaluation, we train an automatic evaluator, a vision-language model aligned with expert annotations that outperforms existing zero-shot baselines. SCINE is the first approach to situate professional video generation within the landscape of video generative models, introducing taxonomies centered around cinematic controls and supporting them with structured evaluation pipelines and detailed analyses to guide future research.

Real-world multivariate time series anomalies are rare and often unlabeled. Additionally, prevailing methods rely on increasingly complex architectures tuned to benchmarks, detecting only fragments of anomalous segments and overstating performance. In this paper, we introduce OracleAD, a simple and interpretable unsupervised framework for multivariate time series anomaly detection. OracleAD encodes each variable's past sequence into a single causal embedding to jointly predict the present time point and reconstruct the input window, effectively modeling temporal dynamics. These embeddings then undergo a self-attention mechanism to project them into a shared latent space and capture spatial relationships. These relationships are not static, since they are modeled by a property that emerges from each variable's temporal dynamics. The projected embeddings are aligned to a Stable Latent Structure (SLS) representing normal-state relationships. Anomalies are identified using a dual scoring mechanism based on prediction error and deviation from the SLS, enabling fine-grained anomaly diagnosis at each time point and across individual variables. Since any noticeable SLS deviation originates from embeddings that violate the learned temporal causality of normal data, OracleAD directly pinpoints the root-cause variables at the embedding level. OracleAD achieves state-of-the-art results across multiple real-world datasets and evaluation protocols, while remaining interpretable through SLS.

Generative models for structure-based drug design (SBDD) have shown promising results in recent years. Existing works mainly focus on how to generate molecules with higher binding affinity, ignoring the feasibility prerequisites for generated 3D poses and resulting in false positives. We conduct thorough studies on key factors of ill-conformational problems when applying autoregressive methods and diffusion to SBDD, including mode collapse and hybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the first SBDD model that operates in the continuous parameter space, together with a novel noise reduced sampling strategy. Empirical results show that our model consistently achieves superior performance in binding affinity with more stable 3D structure, demonstrating our ability to accurately model interatomic interactions. To our best knowledge, MolCRAFT is the first to achieve reference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol). Code is available at https://github.com/AlgoMole/MolCRAFT.

In this paper, we introduce fundamental notions of homotopy theory, including homotopy excision and the Freudenthal suspension theorem. We then explore framed cobordism and its connection to stable homotopy groups of spheres through the Pontryagin-Thom construction. Using this framework, we compute the stable stems in dimensions 0, 1, and 2. This work is primarily expository, revisiting proofs from Pont1 with slight modifications incorporating modern notation. Furthermore, in the final section, we discuss 2-dimensional framed manifolds with Arf invariant one and examine why the result of Pont2 regarding π_2^S is incorrect.

Let X be a nodal curve, and G be the graph dual to X. A stability condition on a graph G is an assignment of integers to the biconnected subsets of vertices of G satisfying some desired properties. Stability conditions yield degeneracy sets, which are certain collections of biconnected subsets of G, but degeneracy sets can also be described without a reference stability condition. We show that the degeneracy sets of a graph G correspond to the single-element extensions of the graphic matroid M(G). Some single-element extensions of the graphic matroid M(G) can be oriented to be single-element extensions of the oriented graphic matroid M(G). Single-element extensions of oriented matroids are in bijection with subdivisions of the Lawrence polytope of the dual oriented matroid. We construct stability conditions on G from subdivisions of the Lawrence polytope of the cographic matroid M^ast(G). Finally, we show that any degeneracy set D of a graph G that has the set of all biconnected subsets of G as a lower bound in the poset of degeneracy sets corresponds to an orientable extension of M(G).

World engines aim to synthesize long, 3D-consistent videos that support interactive exploration of a scene under user-controlled camera motion. However, existing systems struggle under aggressive 6-DoF trajectories and complex outdoor layouts: they lose long-range geometric coherence, deviate from the target path, or collapse into overly conservative motion. To this end, we introduce Captain Safari, a pose-conditioned world engine that generates videos by retrieving from a persistent world memory. Given a camera path, our method maintains a dynamic local memory and uses a retriever to fetch pose-aligned world tokens, which then condition video generation along the trajectory. This design enables the model to maintain stable 3D structure while accurately executing challenging camera maneuvers. To evaluate this setting, we curate OpenSafari, a new in-the-wild FPV dataset containing high-dynamic drone videos with verified camera trajectories, constructed through a multi-stage geometric and kinematic validation pipeline. Across video quality, 3D consistency, and trajectory following, Captain Safari substantially outperforms state-of-the-art camera-controlled generators. It reduces MEt3R from 0.3703 to 0.3690, improves AUC@30 from 0.181 to 0.200, and yields substantially lower FVD than all camera-controlled baselines. More importantly, in a 50-participant, 5-way human study where annotators select the best result among five anonymized models, 67.6% of preferences favor our method across all axes. Our results demonstrate that pose-conditioned world memory is a powerful mechanism for long-horizon, controllable video generation and provide OpenSafari as a challenging new benchmark for future world-engine research.

Producing long, coherent video sequences with stable 3D structure remains a major challenge, particularly in streaming scenarios. Motivated by this, we introduce Endless World, a real-time framework for infinite, 3D-consistent video generation.To support infinite video generation, we introduce a conditional autoregressive training strategy that aligns newly generated content with existing video frames. This design preserves long-range dependencies while remaining computationally efficient, enabling real-time inference on a single GPU without additional training overhead.Moreover, our Endless World integrates global 3D-aware attention to provide continuous geometric guidance across time. Our 3D injection mechanism enforces physical plausibility and geometric consistency throughout extended sequences, addressing key challenges in long-horizon and dynamic scene synthesis.Extensive experiments demonstrate that Endless World produces long, stable, and visually coherent videos, achieving competitive or superior performance to existing methods in both visual fidelity and spatial consistency. Our project has been available on https://bwgzk-keke.github.io/EndlessWorld/.

Recent studies have shown that autoencoder-based models can achieve superior performance on anomaly detection tasks due to their excellent ability to fit complex data in an unsupervised manner. In this work, we propose a novel autoencoder-based model, named StackVAE-G that can significantly bring the efficiency and interpretability to multivariate time series anomaly detection. Specifically, we utilize the similarities across the time series channels by the stacking block-wise reconstruction with a weight-sharing scheme to reduce the size of learned models and also relieve the overfitting to unknown noises in the training data. We also leverage a graph learning module to learn a sparse adjacency matrix to explicitly capture the stable interrelation structure among multiple time series channels for the interpretable pattern reconstruction of interrelated channels. Combining these two modules, we introduce the stacking block-wise VAE (variational autoencoder) with GNN (graph neural network) model for multivariate time series anomaly detection. We conduct extensive experiments on three commonly used public datasets, showing that our model achieves comparable (even better) performance with the state-of-the-art modelsand meanwhile requires much less computation and memory cost. Furthermore, we demonstrate that the adjacency matrix learned by our model accurately captures the interrelation among multiple channels, and can provide valuable information for failure diagnosis applications.

Concept erasure methods that operate via linear projection assume that features occupy separable subspaces. We show this assumption fails under dense superposition: when two features are forced into an antipodal pair sharing a single subspace, state-of-the-art linear erasure destroys both, not just the target. Networks trained with gradient descent instead solve this problem non-linearly, but not uniformly: they converge to one of two distinct circuit-level solutions depending on initialization, which we call mirror and shadow solutions. We map this bifurcation as a function of feature entanglement, show it reflects a stable attractor structure rather than an artifact of our setup, and use targeted causal interventions to demonstrate that both solutions leave a substantial, measurable trace of the erased feature's representation intact, recoverable through a single scalar patch rather than requiring any further training. This mirrors a failure mode recently observed empirically in LLM unlearning, where suppression rather than deletion allows forgotten knowledge to resurface; our results offer a mechanistic, causally-validated account of why that failure mode occurs.

This paper studies reference-free style-conditioned character generation in text-to-image diffusion models, where high-quality synthesis requires both stable character structure and consistent, fine-grained style expression across diverse prompts. Existing approaches primarily rely on text-only prompting, which is often under-specified for visual style and tends to produce noticeable style drift and geometric inconsistency, or introduce reference-based adapters that depend on external images at inference time, increasing architectural complexity and limiting deployment flexibility.We propose PokeFusion Attention, a lightweight decoder-level cross-attention mechanism that fuses textual semantics with learned style embeddings directly inside the diffusion decoder. By decoupling text and style conditioning at the attention level, our method enables effective reference-free stylized generation while keeping the pretrained diffusion backbone fully frozen.PokeFusion Attention trains only decoder cross-attention layers together with a compact style projection module, resulting in a parameter-efficient and plug-and-play control component that can be easily integrated into existing diffusion pipelines and transferred across different backbones.Experiments on a stylized character generation benchmark (Pokemon-style) demonstrate that our method consistently improves style fidelity, semantic alignment, and character shape consistency compared with representative adapter-based baselines, while maintaining low parameter overhead and inference-time simplicity.

We examine whether richer visual representations yield more human-aligned measures of urban engagement, using 61 first-person city-walk videos from YouTube segmented into over 50,000 ten-second clips and represented across four modalities: spatiotemporal video features, temporally averaged images (TAIs), audio embeddings, and text-based semantic descriptions. Spearman correlation analysis reveals the expected ordering along the temporal-richness continuum, with video features showing the strongest continuous alignment. However, this ordering breaks down under binary classification of high- versus low-engagement moments (the paradigm most commonly used to train perceptual scoring models), where TAIs consistently match or outperform video across most classifiers and quantile thresholds. An independent two-alternative forced-choice study on Amazon Mechanical Turk confirms that this parity reflects human judgment: participants identified engaging moments with comparable accuracy from TAIs and full video clips, while text performed substantially worse and audio remained near chance. Gap analysis reveals a functional dissociation: video features are advantaged in activity-driven scenes with dynamic content, whereas TAIs better align with human judgments in composition-driven scenes dominated by stable spatial structure. These findings challenge the assumption that richer representations are inherently more human-aligned, and suggest that perceptually grounded temporal compression can be a principled alternative to full video encoding.

We study diffeomorphisms of Banach spaces satisfying generalized hyperbolicity: the stable and unstable subspaces are invariant only up to inclusion, need not depend continuously on the point, and expansivity may fail. On closed manifolds, this condition is equivalent to Axiom~A with strong transversality. We introduce a continuous-selection method that converts uniform orbitwise estimates into bounded continuous solutions of cohomological equations for generalized-hyperbolic cocycles. For diffeomorphisms in the uniform global \(C^1\) category, this yields continuous semiconjugacies in both directions under sufficiently small bounded Lipschitz perturbations, and topological stability in the sense of Walters. For the infinite product of one-dimensional Morse-Smale systems on \(\ell^p(\mathbb Z)\), \(1\leq p\leq\infty\), we construct compatible forward and reverse cohomological solution operators and prove structural stability, including for perturbations that couple coordinates, although the product is not expansive. For \(p=\infty\) this gives a structurally stable diffeomorphism with uncountably many hyperbolic fixed points, in contrast with the finitely many basic sets of Axiom~A diffeomorphisms. The cocycle analysis yields Lipschitz shadowing for the induced operator on bounded continuous vector fields.

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

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.

Predicting transcriptional responses to genetic perturbations could reduce the experimental burden of functional genomics, but extrapolation to genes that were never perturbed during training remains difficult. We present Stable-Shift, a structured method for estimating unseen-gene responses. Stable-Shift aggregates single-cell measurements into perturbation-level expression shifts, fits a low-rank response basis using training perturbations only, and predicts an unseen gene's coordinates in that basis from biological context. The context combines STRING interactions, network structure, control-cell expression statistics, and Gene Ontology annotations; the evaluated implementation uses graph convolution to integrate these inputs. On the supplied K562 Perturb-seq benchmark, Stable-Shift obtained 0.592 cosine similarity, compared with 0.569 for GEARS, together with higher Spearman correlation and top-gene precision among the evaluated methods. Its mean cosine similarity over five unseen-gene splits was 0.589 +/- 0.008. The same ordering was observed in the supplied graph-aware, residualized, gene-space, and Norman-dataset comparisons. These results support further study of biologically structured latent-response prediction, while the lower gene-space accuracy and sensitivity to sparse graph neighborhoods limit the scope of the present conclusions.

We develop a modular wall crossing theory for quasimaps to a projective variety, allowing independent variation of the boundary coefficients and the quasimap weight. Building on the K-stability of quasimaps introduced by Hashizume and the first author, we construct projective moduli spaces in the stable, Calabi--Yau, and log Fano regimes, together with wall crossing morphisms. A central construction is the moduli theory of boundary polarized Calabi--Yau quasimaps, which retains an ample polarization at the numerically trivial locus and allows comparison with suitable perturbations toward the stable and log Fano regions. The stable theory applies in arbitrary genus, while the comparisons through the Calabi--Yau locus concern genus zero. For degree-one boundary divisors, the resulting framework relates weighted stable maps and quasimaps to Hassett spaces and GIT quotients of weighted points on mathbb P^1. In a companion paper, we apply this framework to give a modular interpolation between Miranda's GIT compactification of rational elliptic surfaces and the Baily--Borel compactification of an eight-dimensional ball quotient.

Structural fidelity is essential to scientific methodology diagrams. To communicate research logic, these diagrams must faithfully render components, directional relations, and textual annotations. Since a single error, such as a reversed arrow or an unreadable equation, can invalidate the entire figure, structural fidelity is inherently conjunctive: correctness on one axis cannot compensate for failure on another. Current open-source models fail to satisfy this criterion. Supervised fine-tuning (SFT) learns plausible layouts but cannot reliably ensure structural correctness, while scalar reward-based post-training obscures which structural dimension has failed. To address this, we introduce SciForma, a framework for the structure faithful generation of scientific methodology diagrams. Specifically, SciForma decomposes diagram quality into three structural axes: Component, Arrow, and Text, guided by a structural inventory. Built on this foundation, we curate SciFormaData-700K for structured training and SciFormaBench-2K for logic-verified evaluation. To close the gap left by SFT, we develop Multi-Dimensional Conjunctive Preference Optimization (M-DPO), which enforces simultaneous correctness across all axes and adaptively routes gradients to the most deficient dimension in post-training. The same structural inventory also enables iterative editing at inference time to correct residual errors. This combination allows SciForma-9B to exceed all open-source baselines and GPT-Image-1.5 on both SciFormaBench-2K and AIBench, bringing open scientific diagram generation close to proprietary-level structural fidelity. Our code and data will be available at: https://github.com/microsoft/SciForma.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

Motivated by applications in Diophantine approximation, we develop a new fibering mechanism for non-degenerate manifolds in R^n, showing that they admit local decompositions into families of non-degenerate curves with uniform quantitative non-degeneracy properties. The manifolds are required to be C^N with the essentially optimal bound Ngeq maxlbrace n,l+1rbrace, where the manifold is l non-degenerate. Furthermore, we show that this uniform quantitative local control can be globalised into a qualitative statement, so that almost every point of a non-degenerate manifold lies on a non-degenerate curve contained in the manifold. Our approach is perturbative and shows that the fibering structure arising in the analytic setting is stable under sufficiently small C^N perturbations. The method provides a framework for extending fibering based results in Diophantine approximation from curves to manifolds. Such applications are considered in the paper.

We introduce the Dual-View Pheromone Pathway Network (DPPN), an architecture that routes sparse attention through a persistent pheromone field over latent slot transitions, and use it to discover two independent requirements for persistent structural memory in neural networks. Through five progressively refined experiments using up to 10 seeds per condition across 5 model variants and 4 transfer targets, we identify a core principle: persistent memory requires a stable coordinate system, and any coordinate system learned jointly with the model is inherently unstable. We characterize three obstacles -- pheromone saturation, surface-structure entanglement, and coordinate incompatibility -- and show that neither contrastive updates, multi-source distillation, Hungarian alignment, nor semantic decomposition resolves the instability when embeddings are learned from scratch. Fixed random Fourier features provide extrinsic coordinates that are stable, structure-blind, and informative, but coordinate stability alone is insufficient: routing-bias pheromone does not transfer (10 seeds, p>0.05). DPPN outperforms transformer and random sparse baselines for within-task learning (AULC 0.700 vs 0.680 vs 0.670). Replacing routing bias with learning-rate modulation eliminates negative transfer: warm pheromone as a learning-rate prior achieves +0.003 on same-family tasks (17 seeds, p<0.05) while never reducing performance. A structure completion function over extrinsic coordinates produces +0.006 same-family bonus beyond regularization, showing the catch-22 between stability and informativeness is partially permeable to learned functions. The contribution is two independent requirements for persistent structural memory: (a) coordinate stability and (b) graceful transfer mechanism.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

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.

Deep ResNet architectures have achieved state of the art performance on many tasks. While they solve the problem of gradient vanishing, they might suffer from gradient exploding as the depth becomes large (Yang et al. 2017). Moreover, recent results have shown that ResNet might lose expressivity as the depth goes to infinity (Yang et al. 2017, Hayou et al. 2019). To resolve these issues, we introduce a new class of ResNet architectures, called Stable ResNet, that have the property of stabilizing the gradient while ensuring expressivity in the infinite depth limit.

We prove stability for a class of heterogeneous catalysis models in the L_p-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a reasonable condition on the involved parameters, we show that given equilibria are normally stable, i.e. solutions are attracted at an exponential rate. The potential incidence of instability is discussed as well.

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing diversity-stability debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as, if not more, important to consider when studying the stability of large ecological systems.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ= 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ= 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρapprox 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2times greater geometric change than CKA during post-training alignment (up to 5.23times in Llama) while providing earlier warning in 73\% of models and maintaining a 6times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

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.

We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, mutually compatible (i.e. a bimonoidal structure). If the underlying monoidal category is cartesian monoidal, a bimonoidal structure is given uniquely by a commutative strength. However, if the underlying monoidal category is not cartesian monoidal, a strength is not enough to guarantee all the desired properties of joints and marginals. A bimonoidal structure is then the correct requirement for the more general case. We explain the theory and the operational interpretation, with the help of the graphical calculus for monoidal categories. We give a definition of stochastic independence based on the bimonoidal structure, compatible with the intuition and with other approaches in the literature for cartesian monoidal categories. We then show as an example that the Kantorovich monad on the category of complete metric spaces is a bimonoidal monad for a non-cartesian monoidal structure.

We identify seven new 192-periodic infinite families of elements in the 2-primary stable homotopy groups of spheres. Although their Hurewicz image is trivial for topological modular forms, they remain nontrivial after T(2)- as well as K(2)-localization. We also obtain new information about 2-torsion and 2-divisibility of some of the previously known 192-periodic infinite families in the stable stems.

We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of Fontaine-Illusie. First, we identify both local and global obstructions to d-semistability. In order to analyze the existence of smoothings, we develop a logarithmic deformation theory of foliations and show that the corresponding moduli functor admits a versal hull.

We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.

Inverse materials design is a long-standing goal of computational materials discovery. Generative models for crystalline materials are typically trained to match the distribution of a structure database, while nothing in their training objective points them at specific design goals such as targeted properties. We use group-relative policy optimization (GRPO) to align a generative model based on stochastic interpolants and discrete flow matching with general black-box reward functions through reinforcement learning. Atom types are generated by a discrete flow and the policy gradient of our generalization of GRPO directly acts on the likelihoods of the atom-type transitions, which differentiates our work from previous reinforcement-learning approaches for diffusion and flow-based generative models of crystalline materials. We introduce a reward function that raises the yield of metastable, unique and novel structures (mSUN) from 13.4% for the pretrained model to 45.5% for the reinforced model, as evaluated by a community benchmark. Our reward also improves the performance of a reinforcement learning framework for crystalline materials based on latent denoising diffusion models. At the same time, we find that directly reinforcing atom-type transition likelihoods enables reward exploitation that has to be prevented with explicit guards. The same analysis also exposes a gap in the community metric. Single-element structures in distinct packings are counted as metastable, unique and novel materials and inflate mSUN without yielding any new compounds. A stability claim is only as good as its reference hull. We report every result split by the number of reference phases behind it and argue that benchmarks should do the same.

World models are central to building agents that can reason, plan, and generalize beyond their training data. However, research on world models is currently fragmented, with disparate codebases, data pipelines, and evaluation protocols hindering reproducibility and fair comparison. Current practice is further limited by three key bottlenecks: fragile one-off codebases, slow video data loading, and the lack of standardized generalization benchmarks. We present stable-worldmodel (swm), an open-source platform for standardized and reproducible world modeling research and evaluation. It delivers (1) a high-performance Lance-based data layer with native support and conversion tools for MP4, HDF5, and LeRobot datasets, (2) clean, well-tested implementations of modern world model baselines and planning solvers, and (3) a broad suite of environments and tasks extended with controllable visual, geometric, and physical factors of variation for systematic in-silico evaluation of dynamics understanding, control performance, representation quality, and out-of-distribution generalization. By unifying the full pipeline under a single, scalable framework, swm dramatically reduces research overhead and accelerates trustworthy progress toward reliable world models.

We investigate the KdV-Burgers and Gardner equations with dissipation and external perturbation terms by the approach of dynamical systems and Shil'nikov's analysis. The stability of the equilibrium point is considered, and Hopf bifurcations are investigated after a certain scaling that reduces the parameter space of a three-mode dynamical system which now depends only on two parameters. The Hopf curve divides the two-dimensional space into two regions. On the left region the equilibrium point is stable leading to dissapative periodic orbits. While changing the bifurcation parameter given by the velocity of the traveling waves, the equilibrium point becomes unstable and a unique stable limit cycle bifurcates from the origin. This limit cycle is the result of a supercritical Hopf bifurcation which is proved using the Lyapunov coefficient together with the Routh-Hurwitz criterion. On the right side of the Hopf curve, in the case of the KdV-Burgers, we find homoclinic chaos by using Shil'nikov's theorem which requires the construction of a homoclinic orbit, while for the Gardner equation the supercritical Hopf bifurcation leads only to a stable periodic orbit.

Let (M omega) be a two dimensional symplectic manifold, phi: M to M a symplectomorphism with hyperbolic fixed point x and transversely intersecting stable and unstable manifolds W^s(phi, x) cap W^u(phi, x)=:H(phi, x). The intersection points are called homoclinic points, and the stable and unstable manifold are in this situation Lagrangian submanifolds. For this Lagrangian intersection problem with its infinite number of intersection points and wild oscillation behavior, we first define a Floer homology generated by finite sets of so-called contractible homoclinic points. This generalizes very significantly the Floer homologies generated by (semi)primary points defined by us in earlier works. Nevertheless these Floer homologies only consider quite `local' aspects of W^s(phi, x) cap W^u(phi, x) since their generator sets are finite, but the number of all contractible homoclinic points is infinite. To overcome this issue, we construct a direct limit of these `local' homoclinic Floer homologies over suitable index sets. These direct limits thus accumulate the information gathered by the finitely generated local' homoclinic Floer homologies.

Stable Diffusion is a recent open-source image generation model comparable to proprietary models such as DALLE, Imagen, or Parti. Stable Diffusion comes with a safety filter that aims to prevent generating explicit images. Unfortunately, the filter is obfuscated and poorly documented. This makes it hard for users to prevent misuse in their applications, and to understand the filter's limitations and improve it. We first show that it is easy to generate disturbing content that bypasses the safety filter. We then reverse-engineer the filter and find that while it aims to prevent sexual content, it ignores violence, gore, and other similarly disturbing content. Based on our analysis, we argue safety measures in future model releases should strive to be fully open and properly documented to stimulate security contributions from the community.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) Non-uniqueness: there are many different eigendecompositions of the same Laplacian, and (2) Instability: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a "hard partition" of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to "softly partition" eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.

A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.

Using a set of LambdaCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

We present new insights and a novel paradigm (StEik) for learning implicit neural representations (INR) of shapes. In particular, we shed light on the popular eikonal loss used for imposing a signed distance function constraint in INR. We show analytically that as the representation power of the network increases, the optimization approaches a partial differential equation (PDE) in the continuum limit that is unstable. We show that this instability can manifest in existing network optimization, leading to irregularities in the reconstructed surface and/or convergence to sub-optimal local minima, and thus fails to capture fine geometric and topological structure. We show analytically how other terms added to the loss, currently used in the literature for other purposes, can actually eliminate these instabilities. However, such terms can over-regularize the surface, preventing the representation of fine shape detail. Based on a similar PDE theory for the continuum limit, we introduce a new regularization term that still counteracts the eikonal instability but without over-regularizing. Furthermore, since stability is now guaranteed in the continuum limit, this stabilization also allows for considering new network structures that are able to represent finer shape detail. We introduce such a structure based on quadratic layers. Experiments on multiple benchmark data sets show that our new regularization and network are able to capture more precise shape details and more accurate topology than existing state-of-the-art.

Watermark has been widely deployed by industry to detect AI-generated images. A recent watermarking framework called Stable Signature (proposed by Meta) roots watermark into the parameters of a diffusion model's decoder such that its generated images are inherently watermarked. Stable Signature makes it possible to watermark images generated by open-source diffusion models and was claimed to be robust against removal attacks. In this work, we propose a new attack to remove the watermark from a diffusion model by fine-tuning it. Our results show that our attack can effectively remove the watermark from a diffusion model such that its generated images are non-watermarked, while maintaining the visual quality of the generated images. Our results highlight that Stable Signature is not as stable as previously thought.

Foundation models and self-supervised learning (SSL) have become central to modern AI, yet research in this area remains hindered by complex codebases, redundant re-implementations, and the heavy engineering burden of scaling experiments. We present stable-pretraining, a modular, extensible, and performance-optimized library built on top of PyTorch, Lightning, Hugging Face, and TorchMetrics. Unlike prior toolkits focused narrowly on reproducing state-of-the-art results, stable-pretraining is designed for flexibility and iteration speed: it unifies essential SSL utilities--including probes, collapse detection metrics, augmentation pipelines, and extensible evaluation routines--within a coherent and reliable framework. A central design principle is logging everything, enabling fine-grained visibility into training dynamics that makes debugging, monitoring, and reproducibility seamless. We validate the library by demonstrating its ability to generate new research insights with minimal overhead, including depthwise representation probing and the analysis of CLIP degradation under synthetic data finetuning. By lowering barriers to entry while remaining scalable to large experiments, stable-pretraining aims to accelerate discovery and expand the possibilities of foundation model research.

We investigate modified gravity with quadratic curvature terms (R^2, R_{AB}R^{AB}, and R_{ABCD}R^{ABCD}). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay (|x|toinfty) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function r(u).