This work considers an asynchronous $\textsf{K}_\text{a}$-active-user unsourced multiple access channel (AUMAC) with the worst-case asynchronicity. The transmitted messages must be decoded within $n$ channel uses, while some codewords are not completely received due to asynchronicities. We consider a constraint of the largest allowed delay of the transmission. The AUMAC lacks the permutation-invariant property of the synchronous UMAC since different permutations of the same codewords with a fixed asynchronicity are distinguishable. Hence, the analyses require calculating all $2^{\textsf{K}_\text{a}}-1$ combinations of erroneously decoded messages. Moreover, transmitters cannot adapt the corresponding codebooks according to asynchronicity due to a lack of information on asynchronicities. To overcome this challenge, a uniform bound of the per-user probability of error (PUPE) is derived by investigating the worst-case of the asynchronous patterns with the delay constraint. Numerical results show the trade-off between the energy-per-bit and the number of active users for different delay constraints. In addition, although the asynchronous transmission reduces interference, the required energy-per-bit increases as the receiver decodes with incompletely received codewords, compared to the synchronous case.
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Bayesian inference for Dirichlet-Multinomial (DM) models has a long and important history. The concentration parameter $\alpha$ is pivotal in smoothing category probabilities within the multinomial distribution and is crucial for the inference afterward. Due to the lack of a tractable form of its marginal likelihood, $\alpha$ is often chosen in an ad-hoc manner, or estimated using approximation algorithms. A constant $\alpha$ often leads to inadequate smoothing of probabilities, particularly for sparse compositional count datasets. In this paper, we introduce a novel class of prior distributions facilitating conjugate updating of the concentration parameter, allowing for full Bayesian inference for DM models. Our methodology is based on fast residue computation and admits closed-form posterior moments in specific scenarios. Additionally, our prior provides continuous shrinkage with its heavy tail and substantial mass around zero, ensuring adaptability to the sparsity or quasi-sparsity of the data. We demonstrate the usefulness of our approach on both simulated examples and on real-world applications. Finally, we conclude with directions for future research.
Large language model (LLM) has achieved promising performance in multilingual machine translation tasks through zero/few-shot prompts or prompt-tuning. However, due to the mixture of multilingual data during the pre-training of LLM, the LLM-based translation models face the off-target issue in both prompt-based methods, including a series of phenomena, namely instruction misunderstanding, translation with wrong language and over-generation. For this issue, this paper introduces an \textbf{\underline{A}}uto-\textbf{\underline{C}}onstriction \textbf{\underline{T}}urning mechanism for \textbf{\underline{M}}ultilingual \textbf{\underline{N}}eural \textbf{\underline{M}}achine \textbf{\underline{T}}ranslation (\model), which is a novel supervised fine-tuning mechanism and orthogonal to the traditional prompt-based methods. In this method, \model automatically constructs a constrained template in the target side by adding trigger tokens ahead of the ground truth. Furthermore, trigger tokens can be arranged and combined freely to represent different task semantics, and they can be iteratively updated to maximize the label likelihood. Experiments are performed on WMT test sets with multiple metrics, and the experimental results demonstrate that \model achieves substantially improved performance across multiple translation directions and reduce the off-target phenomena in the translation.
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory of functional connections, and we refer to partitioned domains endowed with these general forms as functionally connected elements (FCE). We further present a method, incorporating functionally connected elements and a least squares collocation approach, for solving boundary and initial value problems. This method exhibits a spectral-like accuracy, with the free functions involved in the FCE form represented by polynomial bases or by non-polynomial bases of quasi-random sinusoidal functions. The FCE method offers a unique advantage over traditional element-based methods for boundary value problems involving relative boundary conditions. A number of linear and nonlinear numerical examples in one and two dimensions are presented to demonstrate the performance of the FCE method developed herein.
Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like conjugate gradients (CG). However, as datasets increase in magnitude, the kernel matrices become increasingly ill-conditioned and still require $\mathcal{O}(n^2)$ space without partitioning. Thus, while CG increases the size of datasets GPs can be trained on, modern datasets reach scales beyond its applicability. In this work, we propose an iterative method which only accesses subblocks of the kernel matrix, effectively enabling mini-batching. Our algorithm, based on alternating projection, has $\mathcal{O}(n)$ per-iteration time and space complexity, solving many of the practical challenges of scaling GPs to very large datasets. Theoretically, we prove the method enjoys linear convergence. Empirically, we demonstrate its fast convergence in practice and robustness to ill-conditioning. On large-scale benchmark datasets with up to four million data points, our approach accelerates GP training and inference by speed-up factors up to $27\times$ and $72 \times$, respectively, compared to CG.
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $\epsilon$-DP algorithm is $O\left(\frac{\log n}{\sqrt{\epsilon}}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower bound is $\Omega(1/\sqrt{\epsilon})$ [NeurIPS 2019]. In this short note, we give a lower bound of $\tilde{\Omega}\left(\min\left\{\log n, \sqrt{\frac{\log n}{\epsilon}}\right\}\right)$ on the expected approximation ratio of any $\epsilon$-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.
We give an isomorphism test that runs in time $n^{\operatorname{polylog}(h)}$ on all $n$-vertex graphs excluding some $h$-vertex vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time $n^{\operatorname{polylog}(n)}$ (Babai, STOC 2016) and $n^{f(h)}$ for some function $f$ (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and extends previous isomorphism tests for graphs of maximum degree $d$ running in time $n^{\operatorname{polylog}(d)}$ (SIAM J. Comp., 2023) and for graphs of Hadwiger number $h$ running in time $n^{\operatorname{polylog}(h)}$ (SIAM J. Comp., 2023).
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
In semi-supervised domain adaptation, a few labeled samples per class in the target domain guide features of the remaining target samples to aggregate around them. However, the trained model cannot produce a highly discriminative feature representation for the target domain because the training data is dominated by labeled samples from the source domain. This could lead to disconnection between the labeled and unlabeled target samples as well as misalignment between unlabeled target samples and the source domain. In this paper, we propose a novel approach called Cross-domain Adaptive Clustering to address this problem. To achieve both inter-domain and intra-domain adaptation, we first introduce an adversarial adaptive clustering loss to group features of unlabeled target data into clusters and perform cluster-wise feature alignment across the source and target domains. We further apply pseudo labeling to unlabeled samples in the target domain and retain pseudo-labels with high confidence. Pseudo labeling expands the number of ``labeled" samples in each class in the target domain, and thus produces a more robust and powerful cluster core for each class to facilitate adversarial learning. Extensive experiments on benchmark datasets, including DomainNet, Office-Home and Office, demonstrate that our proposed approach achieves the state-of-the-art performance in semi-supervised domain adaptation.
Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via //github.com/Coder-Yu/RecQ.
The chronological order of user-item interactions can reveal time-evolving and sequential user behaviors in many recommender systems. The items that users will interact with may depend on the items accessed in the past. However, the substantial increase of users and items makes sequential recommender systems still face non-trivial challenges: (1) the hardness of modeling the short-term user interests; (2) the difficulty of capturing the long-term user interests; (3) the effective modeling of item co-occurrence patterns. To tackle these challenges, we propose a memory augmented graph neural network (MA-GNN) to capture both the long- and short-term user interests. Specifically, we apply a graph neural network to model the item contextual information within a short-term period and utilize a shared memory network to capture the long-range dependencies between items. In addition to the modeling of user interests, we employ a bilinear function to capture the co-occurrence patterns of related items. We extensively evaluate our model on five real-world datasets, comparing with several state-of-the-art methods and using a variety of performance metrics. The experimental results demonstrate the effectiveness of our model for the task of Top-K sequential recommendation.
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