cross-model geometry alignment

To address the misalignment of latent-space geometric structures across pre-trained models in cross-domain transfer learning, this paper proposes the first unified transfer learning framework based on Ricci curvature alignment. Methodologically, it introduces Ricci curvature—drawn from Riemannian geometry—as a learnable geometric prior; leveraging differential-geometric tools, it estimates and aligns local curvature distributions across multiple pre-trained models’ latent spaces, enabling structured, geometry-aware collaboration rather than naive feature concatenation. The framework jointly integrates latent-space modeling, multi-source model ensembling, and molecular graph representation learning. Evaluated on 23 molecular property prediction tasks, it significantly outperforms baselines: achieving average improvements of 14.4% under random splits and 8.3% under scaffold splits. These results empirically validate the efficacy and generalizability of curvature-driven geometric alignment for cross-domain knowledge transfer.

In parametric CAD, conventional sketch constraint generation often misaligns with design intent, leading to over-constrained systems or geometric distortions. To address this, we propose “Design Alignment”—a novel paradigm that introduces large language model (LLM) alignment techniques to CAD constraint generation for the first time. Our method establishes a solver-feedback-driven alignment training framework, integrating reasoning-capable LLMs’ semantic understanding with classical geometric constraint modeling to jointly optimize constraint completeness and geometric fidelity. The approach is compatible with existing generative models and achieves a full-constraint satisfaction rate of 93%, substantially outperforming supervised fine-tuning baselines (34%) and non-aligned methods (8.9%). This advancement significantly enhances the editability, robustness, and design-intent consistency of parametric CAD models.

Neural network internal representations often lack stability and cross-architectural consistency due to architectural disparities, hindering knowledge transfer and modular deployment. To address this, we propose a structured regularization framework comprising linear shaping operators and rectified path constraints, which explicitly encode inductive biases to improve geometric alignment of representations across architectures. Through theoretical analysis, controlled transfer experiments, and a novel representation alignment metric, we systematically demonstrate that structural priors significantly enhance semantic consistency among heterogeneous models. Our method improves downstream task performance in model distillation and modular learning by up to 12.3%, offering an interpretable and scalable paradigm for building robust, composable deep learning systems.

This work addresses the lack of theoretical foundations in existing graph pre-training methods for cross-domain knowledge transfer, which hinders their generalization across diverse domains. The authors propose a Neural Manifold Stitching framework that models multiple graph datasets as a unified Riemannian manifold. By constructing local geometric representations through adaptive orthogonal frames, they establish— for the first time—a geometrically consistent transfer mechanism for graph foundation models. Integrating EMA-based prototype batch pre-training with a novel transferability metric, the method significantly outperforms current approaches on multi-domain graph tasks. Furthermore, the study uncovers a geometric scaling law linking dataset scale and manifold smoothness, which effectively enhances model transfer performance.

High annotation cost and poor generalizability plague geometric feature labeling in engineering design images. Method: We propose a large-model-driven automated annotation framework featuring (1) GeoBiked—the first bicycle-structure-specific dataset (4,355 images); (2) Diffusion-Hyperfeatures, a novel representation technique enabling precise cross-image correspondence of geometric keypoints; (3) a dual-path GPT-4o input mechanism integrating image and category labels, enhanced by systematic prompt engineering and a structured annotation schema to ensure fidelity and consistency of technical descriptions; and (4) a multi-source image collaborative geometric localization strategy. Results: Experiments demonstrate significant improvements in keypoint detection accuracy on unseen samples, with high descriptive accuracy from GPT-4o outputs. The framework validates the feasibility and strong generalization capability of large language-vision models for engineering image understanding and fine-grained geometric annotation.

This work addresses the challenge of preserving mapping continuity and bijectivity during complex remeshing processes, where conventional data transfer methods often induce geometric or attribute distortions. The authors propose a composite mapping framework based on local bijective atlases, enhanced by a Shared Scaffold structure that guarantees global bijectivity. The approach is generalized to support a variety of remeshing operations and, for the first time, enables the construction of bijective mappings on 3D tetrahedral remeshings by innovatively integrating Steinitz’s theorem with Maxwell–Cremona lifting theory. This framework facilitates precise tracking of geometric entities—including points, curves, and surfaces—across remeshing sequences, significantly improving fidelity in high-precision applications such as texture transfer and volumetric simulation.

This work addresses the limitations of existing representation alignment methods, which predominantly rely on geometric properties and struggle to capture the global structural organization of model representations. To overcome this, the study introduces topological data analysis into the field for the first time, proposing a Mapper-based visual analytics framework. By integrating force-directed layout, Bubble Sets, motif querying, and membrane-inspired heuristics, the framework enables a unified analytical pipeline spanning global structure alignment, local region matching, and fine-grained pattern exploration. Case studies on language and multimodal models, complemented by expert evaluations, demonstrate that the approach effectively reveals and compares the topological organization of representations across different models or layers, offering deep structural insights.

This work addresses the long-standing isolation among research domains such as alignment training, model organisms, and toy models, which has hindered empirical cross-pollination and led to redundant exploration and inefficiency. For the first time, it systematically transfers supervised fine-tuning (SFT) practices across these domains by integrating cross-model output training, mixed-strategy data, and benign fine-tuning to rigorously evaluate the portability of key findings. The study demonstrates three successful transfer effects: enhanced behavioral generalization, mitigation of capability degradation, and the critical insight that preserving capabilities alone is insufficient to ensure robustness in subsequent training phases. These results underscore both the efficacy and limitations of reusing methodologies across domains, thereby fostering more synergistic development across disparate research areas.

Existing CAD generation methods struggle to simultaneously preserve modeling history, topological reference stability, and feature-level editability in cross-platform scenarios. This work proposes CADIR—an agent-oriented, executable intermediate representation that explicitly constructs a procedural graph encompassing operation sequences, parameter dependencies, constraints, and topological selections based on the OpenCASCADE (OCCT) geometric kernel. To enable faithful cross-platform model reconstruction, CADIR introduces a geometric signature matching mechanism. It is the first approach to support explicit procedural graph representations that allow editing across heterogeneous CAD backends. By integrating text- or image-driven procedural graph retrieval, CADIR demonstrates high-fidelity, editable reuse of complete models and substructures across FreeCAD, SolidWorks, and Fusion 360, enabling seamless subsequent modifications.

This work addresses the lack of theoretical foundations for substructure transferability in graph data by bridging transferable substructures with the intrinsic geometry of graph representation spaces from a functional behavior perspective. It proposes the first Riemannian geometry–based framework for learning intrinsic graph geometry, innovatively introducing neural vector bundles and local coordinate charts to construct the GAUGE pretraining architecture. A Dirichlet loss function is designed to enable explicit modeling of intrinsic graph geometry and quantification of transfer difficulty. The method demonstrates significant performance gains over existing models on zero-shot link prediction and graph isomorphism tasks, validating its expressive power and cross-task transferability.