Cross-modal 3D shape retrieval is a crucial and widely applied task in the field of 3D vision. Its goal is to construct retrieval representations capable of measuring the similarity between instances of different 3D modalities. However, existing methods face challenges due to the performance bottlenecks of single-modal representation extractors and the modality gap across 3D modalities. To tackle these issues, we propose a Heterogeneous Dynamic Graph Representation (HDGR) network, which incorporates context-dependent dynamic relations within a heterogeneous framework. By capturing correlations among diverse 3D objects, HDGR overcomes the limitations of ambiguous representations obtained solely from instances. Within the context of varying mini-batches, dynamic graphs are constructed to capture proximal intra-modal relations, and dynamic bipartite graphs represent implicit cross-modal relations, effectively addressing the two challenges above. Subsequently, message passing and aggregation are performed using Dynamic Graph Convolution (DGConv) and Dynamic Bipartite Graph Convolution (DBConv), enhancing features through heterogeneous dynamic relation learning. Finally, intra-modal, cross-modal, and self-transformed features are redistributed and integrated into a heterogeneous dynamic representation for cross-modal 3D shape retrieval. HDGR establishes a stable, context-enhanced, structure-aware 3D shape representation by capturing heterogeneous inter-object relationships and adapting to varying contextual dynamics. Extensive experiments conducted on the ModelNet10, ModelNet40, and real-world ABO datasets demonstrate the state-of-the-art performance of HDGR in cross-modal and intra-modal retrieval tasks. Moreover, under the supervision of robust loss functions, HDGR achieves remarkable cross-modal retrieval against label noise on the 3D MNIST dataset. The comprehensive experimental results highlight the effectiveness and efficiency of HDGR on cross-modal 3D shape retrieval.

Rotation invariant point cloud analysis is essential for many real-world applications where objects can appear in arbitrary orientations. Traditional local rotation-invariant methods rely on lossy region descriptors, limiting the global comprehension of 3D objects. Conversely, global features derived from pose alignment can capture complementary information. To leverage both local and global consistency for enhanced accuracy, we propose the Global-Local-Consistent Hypergraph Cross-Attention Network (GLC-HCAN). This framework includes the Global Consistent Feature (GCF) representation branch, the Local Consistent Feature (LCF) representation branch, and the Hypergraph Cross-Attention (HyperCA) network to model complex correlations through the global-local-consistent hypergraph representation learning. Specifically, the GCF branch employs a multi-pose grouping and aggregation strategy based on PCA for improved global comprehension. Simultaneously, the LCF branch uses local farthest reference point features to enhance local region descriptions. To capture high-order and complex global-local correlations, we construct hypergraphs that integrate both features, mutually enhancing and fusing the representations. The inductive HyperCA module leverages attention techniques to better utilize these high-order relations for comprehensive understanding. Consequently, GLC-HCAN offers an effective and robust rotation-invariant point cloud analysis network, suitable for object classification and shape retrieval tasks in SO(3). Experimental results on both synthetic and scanned point cloud datasets demonstrate that GLC-HCAN outperforms state-of-the-art methods.

We present the lifted proximal operator machine (LPOM) to train fully-connected feed-forward neural networks. LPOM represents the activation function as an equivalent proximal operator and adds the proximal operators to the objective function of a network as penalties. LPOM is block multi-convex in all layer-wise weights and activations. This allows us to develop a new block coordinate descent (BCD) method with convergence guarantee to solve it. Due to the novel formulation and solving method, LPOM only uses the activation function itself and does not require any gradient steps. Thus it avoids the gradient vanishing or exploding issues, which are often blamed in gradient-based methods. Also, it can handle various non-decreasing Lipschitz continuous activation functions. Additionally, LPOM is almost as memory-efficient as stochastic gradient descent and its parameter tuning is relatively easy. We further implement and analyze the parallel solution of LPOM. We first propose a general asynchronous-parallel BCD method with convergence guarantee. Then we use it to solve LPOM, resulting in asynchronous-parallel LPOM. For faster speed, we develop the synchronous-parallel LPOM. We validate the advantages of LPOM on various network architectures and datasets. We also apply synchronous-parallel LPOM to autoencoder training and demonstrate its fast convergence and superior performance.