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In this paper, we provide novel tail bounds on the optimization error of Stochastic Mirror Descent for convex and Lipschitz objectives. Our analysis extends the existing tail bounds from the classical light-tailed Sub-Gaussian noise case to heavier-tailed noise regimes. We study the optimization error of the last iterate as well as the average of the iterates. We instantiate our results in two important cases: a class of noise with exponential tails and one with polynomial tails. A remarkable feature of our results is that they do not require an upper bound on the diameter of the domain. Finally, we support our theory with illustrative experiments that compare the behavior of the average of the iterates with that of the last iterate in heavy-tailed noise regimes.

In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive scaling. Our primary objective is to devise efficient and accurate APNN approaches for resolving multiscale kinetic equations. We have established a neural network based on even-odd decomposition and concluded that enforcing the initial condition for the linear transport equation with inflow boundary conditions is crucial. This APNN method based on even-odd parity relaxes the stringent conservation prerequisites while concurrently introducing an auxiliary deep neural network. Additionally, we have incorporated the conservation laws of mass, momentum, and energy for the Boltzmann-BGK equation into the APNN framework by enforcing exact boundary conditions. This is our second contribution. The most notable finding of this study is that approximating the zeroth, first and second moments of the particle density distribution is simpler than the distribution itself. Furthermore, a compelling phenomenon in the training process is that the convergence of density is swifter than that of momentum and energy. Finally, we investigate several benchmark problems to demonstrate the efficacy of our proposed APNN methods.

Nanopore sequencing, superior to other sequencing technologies for DNA storage in multiple aspects, has recently attracted considerable attention. Its high error rates, however, demand thorough research on practical and efficient coding schemes to enable accurate recovery of stored data. To this end, we consider a simplified model of a nanopore sequencer inspired by Mao \emph{et al.}, incorporating intersymbol interference and measurement noise. Essentially, our channel model passes a sliding window of length \(\ell\) over a \(q\)-ary input sequence that outputs the \textit{composition} of the enclosed \(\ell\) bits and shifts by \(\delta\) positions with each time step. In this context, the composition of a \(q\)-ary vector $\bfx$ specifies the number of occurrences in \(\bfx\) of each symbol in \(\lbrace 0,1,\ldots, q-1\rbrace\). The resulting compositions vector, termed the \emph{read vector}, may also be corrupted by \(t\) substitution errors. By employing graph-theoretic techniques, we deduce that for \(\delta=1\), at least \(\log \log n\) symbols of redundancy are required to correct a single (\(t=1\)) substitution. Finally, for \(\ell \geq 3\), we exploit some inherent characteristics of read vectors to arrive at an error-correcting code that is of optimal redundancy up to a (small) additive constant for this setting. This construction is also found to be optimal for the case of reconstruction from two noisy read vectors.

This paper presents a novel approach to human image colorization by fine-tuning the InstructPix2Pix model, which integrates a language model (GPT-3) with a text-to-image model (Stable Diffusion). Despite the original InstructPix2Pix model's proficiency in editing images based on textual instructions, it exhibits limitations in the focused domain of colorization. To address this, we fine-tuned the model using the IMDB-WIKI dataset, pairing black-and-white images with a diverse set of colorization prompts generated by ChatGPT. This paper contributes by (1) applying fine-tuning techniques to stable diffusion models specifically for colorization tasks, and (2) employing generative models to create varied conditioning prompts. After finetuning, our model outperforms the original InstructPix2Pix model on multiple metrics quantitatively, and we produce more realistically colored images qualitatively. The code for this project is provided on the GitHub Repository //github.com/AllenAnZifeng/DeepLearning282.

Non-IID data present a tough challenge for federated learning. In this paper, we explore a novel idea of facilitating pairwise collaborations between clients with similar data. We propose FedAMP, a new method employing federated attentive message passing to facilitate similar clients to collaborate more. We establish the convergence of FedAMP for both convex and non-convex models, and propose a heuristic method to further improve the performance of FedAMP when clients adopt deep neural networks as personalized models. Our extensive experiments on benchmark data sets demonstrate the superior performance of the proposed methods.

We consider an interesting problem-salient instance segmentation in this paper. Other than producing bounding boxes, our network also outputs high-quality instance-level segments. Taking into account the category-independent property of each target, we design a single stage salient instance segmentation framework, with a novel segmentation branch. Our new branch regards not only local context inside each detection window but also its surrounding context, enabling us to distinguish the instances in the same scope even with obstruction. Our network is end-to-end trainable and runs at a fast speed (40 fps when processing an image with resolution 320x320). We evaluate our approach on a publicly available benchmark and show that it outperforms other alternative solutions. We also provide a thorough analysis of the design choices to help readers better understand the functions of each part of our network. The source code can be found at \url{//github.com/RuochenFan/S4Net}.

We present MMKG, a collection of three knowledge graphs that contain both numerical features and (links to) images for all entities as well as entity alignments between pairs of KGs. Therefore, multi-relational link prediction and entity matching communities can benefit from this resource. We believe this data set has the potential to facilitate the development of novel multi-modal learning approaches for knowledge graphs.We validate the utility ofMMKG in the sameAs link prediction task with an extensive set of experiments. These experiments show that the task at hand benefits from learning of multiple feature types.

The key issue of few-shot learning is learning to generalize. In this paper, we propose a large margin principle to improve the generalization capacity of metric based methods for few-shot learning. To realize it, we develop a unified framework to learn a more discriminative metric space by augmenting the softmax classification loss function with a large margin distance loss function for training. Extensive experiments on two state-of-the-art few-shot learning models, graph neural networks and prototypical networks, show that our method can improve the performance of existing models substantially with very little computational overhead, demonstrating the effectiveness of the large margin principle and the potential of our method.

In this paper, we introduce the Reinforced Mnemonic Reader for machine reading comprehension tasks, which enhances previous attentive readers in two aspects. First, a reattention mechanism is proposed to refine current attentions by directly accessing to past attentions that are temporally memorized in a multi-round alignment architecture, so as to avoid the problems of attention redundancy and attention deficiency. Second, a new optimization approach, called dynamic-critical reinforcement learning, is introduced to extend the standard supervised method. It always encourages to predict a more acceptable answer so as to address the convergence suppression problem occurred in traditional reinforcement learning algorithms. Extensive experiments on the Stanford Question Answering Dataset (SQuAD) show that our model achieves state-of-the-art results. Meanwhile, our model outperforms previous systems by over 6% in terms of both Exact Match and F1 metrics on two adversarial SQuAD datasets.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax