The Kolmogorov-Arnold Network (KAN) has recently gained attention as an alternative to traditional multi-layer perceptrons (MLPs), offering improved accuracy and interpretability by employing learnable activation functions on edges. In this paper, we introduce the Kolmogorov-Arnold Auto-Encoder (KAE), which integrates KAN with autoencoders (AEs) to enhance representation learning for retrieval, classification, and denoising tasks. Leveraging the flexible polynomial functions in KAN layers, KAE captures complex data patterns and non-linear relationships. Experiments on benchmark datasets demonstrate that KAE improves latent representation quality, reduces reconstruction errors, and achieves superior performance in downstream tasks such as retrieval, classification, and denoising, compared to standard autoencoders and other KAN variants. These results suggest KAE's potential as a useful tool for representation learning. Our code is available at \url{https://github.com/SciYu/KAE/}.

We study deep ReLU feed forward neural networks (NN) and their injectivity abilities. The main focus is on \emph{precisely} determining the so-called injectivity capacity. For any given hidden layers architecture, it is defined as the minimal ratio between number of network's outputs and inputs which ensures unique recoverability of the input from a realizable output. A strong recent progress in precisely studying single ReLU layer injectivity properties is here moved to a deep network level. In particular, we develop a program that connects deep $l$-layer net injectivity to an $l$-extension of the $\ell_0$ spherical perceptrons, thereby massively generalizing an isomorphism between studying single layer injectivity and the capacity of the so-called (1-extension) $\ell_0$ spherical perceptrons discussed in [82]. \emph{Random duality theory} (RDT) based machinery is then created and utilized to statistically handle properties of the extended $\ell_0$ spherical perceptrons and implicitly of the deep ReLU NNs. A sizeable set of numerical evaluations is conducted as well to put the entire RDT machinery in practical use. From these we observe a rapidly decreasing tendency in needed layers' expansions, i.e., we observe a rapid \emph{expansion saturation effect}. Only $4$ layers of depth are sufficient to closely approach level of no needed expansion -- a result that fairly closely resembles observations made in practical experiments and that has so far remained completely untouchable by any of the existing mathematical methodologies.

The growing need for accurate and efficient 3D identification of tumors, particularly in liver segmentation, has spurred considerable research into deep learning models. While many existing architectures offer strong performance, they often face challenges such as overfitting and excessive computational costs. An adjustable and flexible architecture that strikes a balance between time efficiency and model complexity remains an unmet requirement. In this paper, we introduce proKAN, a progressive stacking methodology for Kolmogorov-Arnold Networks (KANs) designed to address these challenges. Unlike traditional architectures, proKAN dynamically adjusts its complexity by progressively adding KAN blocks during training, based on overfitting behavior. This approach allows the network to stop growing when overfitting is detected, preventing unnecessary computational overhead while maintaining high accuracy. Additionally, proKAN utilizes KAN's learnable activation functions modeled through B-splines, which provide enhanced flexibility in learning complex relationships in 3D medical data. Our proposed architecture achieves state-of-the-art performance in liver segmentation tasks, outperforming standard Multi-Layer Perceptrons (MLPs) and fixed KAN architectures. The dynamic nature of proKAN ensures efficient training times and high accuracy without the risk of overfitting. Furthermore, proKAN provides better interpretability by allowing insight into the decision-making process through its learnable coefficients. The experimental results demonstrate a significant improvement in accuracy, Dice score, and time efficiency, making proKAN a compelling solution for 3D medical image segmentation tasks.

Open-set object detection (OSOD) is highly desirable for robotic manipulation in unstructured environments. However, existing OSOD methods often fail to meet the requirements of robotic applications due to their high computational burden and complex deployment. To address this issue, this paper proposes a light-weight framework called Decoupled OSOD (DOSOD), which is a practical and highly efficient solution to support real-time OSOD tasks in robotic systems. Specifically, DOSOD builds upon the YOLO-World pipeline by integrating a vision-language model (VLM) with a detector. A Multilayer Perceptron (MLP) adaptor is developed to transform text embeddings extracted by the VLM into a joint space, within which the detector learns the region representations of class-agnostic proposals. Cross-modality features are directly aligned in the joint space, avoiding the complex feature interactions and thereby improving computational efficiency. DOSOD operates like a traditional closed-set detector during the testing phase, effectively bridging the gap between closed-set and open-set detection. Compared to the baseline YOLO-World, the proposed DOSOD significantly enhances real-time performance while maintaining comparable accuracy. The slight DOSOD-S model achieves a Fixed AP of $26.7\%$, compared to $26.2\%$ for YOLO-World-v1-S and $22.7\%$ for YOLO-World-v2-S, using similar backbones on the LVIS minival dataset. Meanwhile, the FPS of DOSOD-S is $57.1\%$ higher than YOLO-World-v1-S and $29.6\%$ higher than YOLO-World-v2-S. Meanwhile, we demonstrate that the DOSOD model facilitates the deployment of edge devices. The codes and models are publicly available at https://github.com/D-Robotics-AI-Lab/DOSOD.

While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the topological information of a graph using persistence diagrams. However, these attempts have faced the problem of losing node embedding information, which in turn prevents them from providing a more expressive graph representation. To tackle this issue, we shift our focus to edge filtration and introduce a novel edge filtration-based persistence diagram, named Topological Edge Diagram (TED), which is mathematically proven to preserve node embedding information as well as contain additional topological information. To implement TED, we propose a neural network based algorithm, named Line Graph Vietoris-Rips (LGVR) Persistence Diagram, that extracts edge information by transforming a graph into its line graph. Through LGVR, we propose two model frameworks that can be applied to any message passing GNNs, and prove that they are strictly more powerful than Weisfeiler-Lehman type colorings.

Image to point cloud global localization is crucial for robot navigation in GNSS-denied environments and has become increasingly important for multi-robot map fusion and urban asset management. The modality gap between images and point clouds poses significant challenges for cross-modality fusion. Current cross-modality global localization solutions either require modality unification, which leads to information loss, or rely on engineered training schemes to encode multi-modality features, which often lack feature alignment and relation consistency. To address these limitations, we propose, SaliencyI2PLoc, a novel contrastive learning based architecture that fuses the saliency map into feature aggregation and maintains the feature relation consistency on multi-manifold spaces. To alleviate the pre-process of data mining, the contrastive learning framework is applied which efficiently achieves cross-modality feature mapping. The context saliency-guided local feature aggregation module is designed, which fully leverages the contribution of the stationary information in the scene generating a more representative global feature. Furthermore, to enhance the cross-modality feature alignment during contrastive learning, the consistency of relative relationships between samples in different manifold spaces is also taken into account. Experiments conducted on urban and highway scenario datasets demonstrate the effectiveness and robustness of our method. Specifically, our method achieves a Recall@1 of 78.92% and a Recall@20 of 97.59% on the urban scenario evaluation dataset, showing an improvement of 37.35% and 18.07%, compared to the baseline method. This demonstrates that our architecture efficiently fuses images and point clouds and represents a significant step forward in cross-modality global localization. The project page and code will be released.

At the heart of neural network force fields (NNFFs) is the architecture of neural networks, where the capacity to model complex interactions is typically enhanced through widening or deepening multilayer perceptrons (MLPs) or by increasing layers of graph neural networks (GNNs). These enhancements, while improving the model's performance, often come at the cost of a substantial increase in the number of parameters. By applying the Trainable Adaptive Activation Function Structure (TAAFS), we introduce a method that selects distinct mathematical formulations for non-linear activations, thereby increasing the precision of NNFFs with an insignificant addition to the parameter count. In this study, we integrate TAAFS into a variety of neural network models, resulting in observed accuracy improvements, and further validate these enhancements through molecular dynamics (MD) simulations using DeepMD.

Due to its efficiency, Post-Training Quantization (PTQ) has been widely adopted for compressing Vision Transformers (ViTs). However, when quantized into low-bit representations, there is often a significant performance drop compared to their full-precision counterparts. To address this issue, reconstruction methods have been incorporated into the PTQ framework to improve performance in low-bit quantization settings. Nevertheless, existing related methods predefine the reconstruction granularity and seldom explore the progressive relationships between different reconstruction granularities, which leads to sub-optimal quantization results in ViTs. To this end, in this paper, we propose a Progressive Fine-to-Coarse Reconstruction (PFCR) method for accurate PTQ, which significantly improves the performance of low-bit quantized vision transformers. Specifically, we define multi-head self-attention and multi-layer perceptron modules along with their shortcuts as the finest reconstruction units. After reconstructing these two fine-grained units, we combine them to form coarser blocks and reconstruct them at a coarser granularity level. We iteratively perform this combination and reconstruction process, achieving progressive fine-to-coarse reconstruction. Additionally, we introduce a Progressive Optimization Strategy (POS) for PFCR to alleviate the difficulty of training, thereby further enhancing model performance. Experimental results on the ImageNet dataset demonstrate that our proposed method achieves the best Top-1 accuracy among state-of-the-art methods, particularly attaining 75.61% for 3-bit quantized ViT-B in PTQ. Besides, quantization results on the COCO dataset reveal the effectiveness and generalization of our proposed method on other computer vision tasks like object detection and instance segmentation.

Optimization techniques are pivotal in neural network training, shaping both predictive performance and convergence efficiency. This study introduces Foxtsage, a novel hybrid optimisation approach that integrates the Hybrid FOX-TSA with Stochastic Gradient Descent for training Multi-Layer Perceptron models. The proposed Foxtsage method is benchmarked against the widely adopted Adam optimizer across multiple standard datasets, focusing on key performance metrics such as training loss, accuracy, precision, recall, F1-score, and computational time. Experimental results demonstrate that Foxtsage achieves a 42.03% reduction in loss mean (Foxtsage: 9.508, Adam: 16.402) and a 42.19% improvement in loss standard deviation (Foxtsage: 20.86, Adam: 36.085), reflecting enhanced consistency and robustness. Modest improvements in accuracy mean (0.78%), precision mean (0.91%), recall mean (1.02%), and F1-score mean (0.89%) further underscore its predictive performance. However, these gains are accompanied by an increased computational cost, with a 330.87% rise in time mean (Foxtsage: 39.541 seconds, Adam: 9.177 seconds). By effectively combining the global search capabilities of FOX-TSA with the stability and adaptability of SGD, Foxtsage presents itself as a robust and viable alternative for neural network optimization tasks.

Conventional cardiac cine MRI methods rely on retrospective gating, which limits temporal resolution and the ability to capture continuous cardiac dynamics, particularly in patients with arrhythmias and beat-to-beat variations. To address these challenges, we propose a reconstruction framework based on subspace implicit neural representations for real-time cardiac cine MRI of continuously sampled radial data. This approach employs two multilayer perceptrons to learn spatial and temporal subspace bases, leveraging the low-rank properties of cardiac cine MRI. Initialized with low-resolution reconstructions, the networks are fine-tuned using spoke-specific loss functions to recover spatial details and temporal fidelity. Our method directly utilizes the continuously sampled radial k-space spokes during training, thereby eliminating the need for binning and non-uniform FFT. This approach achieves superior spatial and temporal image quality compared to conventional binned methods at the acceleration rate of 10 and 20, demonstrating potential for high-resolution imaging of dynamic cardiac events and enhancing diagnostic capability.