Lemma 1. Assume that Assumptions 1 and 2 hold, the iterations satisfy the following inequality for all k 2 N: Combine Assumption 2 with Definition 4.6, we have the second moment of g(W Summing both sides of this inequality for k 2{1,...,K} and recalling Assumption 2 (a) gives Rearranging above inequality and dividing further by K yields the result. The second condition in Eq. 4.10 ensures that lim Summing both sides of this inequality for k 2{1,...,K} and recalling Assumption 2(a) gives It guarantees that the model moves towards the descending direction of the loss function. Following the experimental setup in Section 5.1, we demonstrate that the proposed method empirically satisfies Assumption 2(b), and visualize in Figure 7 the sufficient direction constant µ for the (partial) convolutional layers of the four models during the end-to-end training using TREC. For SqueezeNet and ResNet-34, we show one block as the representative, since the other blocks have similar performance. Several insights can be drawn from Figure 7. (i) The value of µ of each convolutional layer is consistently greater than zero, indicating that Assumption 2(b) is satisfied, further ensuring the convergence of the TREC-equipped CNNs.

The intensive computations in convolutional neural networks (CNNs) pose challenges for resource-constrained devices; eliminating redundant computations from convolution is essential. This paper gives a principled method to detect and avoid transient redundancy, a type of redundancy existing in input data or activation maps and hence changing across inferences. By introducing a new form of convolution (TREC), this new method makes transient redundancy detection and avoidance an inherent part of the CNN architecture, and the determination of the best configurations for redundancy elimination part of CNN backward propagation. We provide a rigorous proof of the robustness and convergence of TREC-equipped CNNs. TREC removes over 96% computations and achieves 3.51 average speedups on microcontrollers with minimal (about 0.7%) accuracy loss.

Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues - their performance significantly deteriorates on clean instances with crafted perturbations. To enhance robustness, we propose an ensemble-based Collaborative Neural Framework (CNF) w.r.t. the defense of neural VRP methods, which is crucial yet underexplored in the literature. Given a neural VRP method, we adversarially train multiple models in a collaborative manner to synergistically promote robustness against attacks, while boosting standard generalization on clean instances. A neural router is designed to adeptly distribute training instances among models, enhancing overall load balancing and collaborative efficacy. Extensive experiments verify the effectiveness and versatility of CNF in defending against various attacks across different neural VRP methods. Notably, our approach also achieves impressive out-of-distribution generalization on benchmark instances.

In each triplet, we present the input image and two 3D shapes retrieved using OpenShape embeddings from the Objaverse [2] dataset. Input images are from unsplash.com. In each triplet, we present the input point cloud and two 3D shapes retrieved using OpenShape embeddings from the Objaverse [2] dataset. In each row, we show the input point clouds on the left and the generated captions on the right. Each row shows three examples (input point clouds and generated images).

Lately, there has been a surge in interest surrounding generative modeling of time series data. Most existing approaches are designed either to process short sequences or to handle long-range sequences. This dichotomy can be attributed to gradient issues with recurrent networks, computational costs associated with transformers, and limited expressiveness of state space models. Towards a unified generative model for varying-length time series, we propose in this work to transform sequences into images. By employing invertible transforms such as the delay embedding and the short-time Fourier transform, we unlock three main advantages: i) We can exploit advanced diffusion vision models; ii) We can remarkably process short-and long-range inputs within the same framework; and iii) We can harness recent and established tools proposed in the time series to image literature.

Notably, this still does not fix the oversaturation and corruption at low noise levels, suggesting multiple sources for the detrimental effects of excessive iteration. Further research will be required to better understand the root causes of these observed effects.

Visual grounding is a common vision task that involves grounding descriptive sentences to the corresponding regions of an image. Most existing methods use independent image-text encoding and apply complex hand-crafted modules or encoder-decoder architectures for modal interaction and query reasoning. However, their performance significantly drops when dealing with complex textual expressions. This is because the former paradigm only utilizes limited downstream data to fit the multi-modal feature fusion. Therefore, it is only effective when the textual expressions are relatively simple. In contrast, given the wide diversity of textual expressions and the uniqueness of downstream training data, the existing fusion module, which extracts multimodal content from a visual-linguistic context, has not been fully investigated.