We consider a distributed multi-user secret sharing (DMUSS) setting in which there is a dealer, $n$ storage nodes, and $m$ secrets. Each user demands a $t$-subset of $m$ secrets. Earlier work in this setting dealt with the case of $t=1$; in this work, we consider general $t$. The user downloads shares from the storage nodes based on the designed access structure and reconstructs its secrets. We identify a necessary condition on the access structures to ensure weak secrecy. We also make a connection between access structures for this problem and $t$-disjunct matrices. We apply various $t$-disjunct matrix constructions in this setting and compare their performance in terms of the number of storage nodes and communication complexity. We also derive bounds on the optimal communication complexity of a distributed secret sharing protocol. Finally, we characterize the capacity region of the DMUSS problem when the access structure is specified.
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We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries can be answered in $O(\log n)$ time. Alternatively, we can achieve a space complexity of $O(n^{9+\varepsilon })$ by relaxing the query time to $O(\log^2 n)$. This is the first improvement upon a conference paper by Chiang and Mitchell from 1999. They present a data structure with $O(n^{11})$ space complexity and $O(\log n)$ query time. Our main result can be extended to include a space-time trade-off. Specifically, we devise data structures with $O(n^{9+\varepsilon}/\hspace{1pt} \ell^{4 + O(\varepsilon )})$ space complexity and $O(\ell \log^2 n )$ query time, for any integer $1 \leq \ell \leq n$. Furthermore, we present improved data structures with $O(\log n)$ query time for the special case where we restrict one (or both) of the query points to lie on the boundary of $P$. When one of the query points is restricted to lie on the boundary, and the other query point is unrestricted, the space complexity becomes $O(n^{6+\varepsilon})$. When both query points are on the boundary, the space complexity is decreased further to $O(n^{4+\varepsilon })$, thereby improving an earlier result of Bae and Okamoto.
We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies in linear and metric spaces, there is very little discussion on depth functions for non-standard data types such as partial orders. We introduce an adaptation of the well-known simplicial depth to the set of all partial orders, the union-free generic (ufg) depth. Moreover, we utilize our ufg depth for a comparison of machine learning algorithms based on multidimensional performance measures. Concretely, we provide two examples of classifier comparisons on samples of standard benchmark data sets. Our results demonstrate promisingly the wide variety of different analysis approaches based on ufg methods. Furthermore, the examples outline that our approach differs substantially from existing benchmarking approaches, and thus adds a new perspective to the vivid debate on classifier comparison.
In this work we study multi-server queues on a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers (users) arrive at the servers according to independent Poisson processes of intensity $\lambda$. However, they probabilistically decide whether to join the queue they arrived at, or move to one of the nearest neighbours. The strategy followed by the customers affects the load on the servers in the long run. In this paper, we are interested in characterizing the fraction of servers that bear a larger load as compared to when the users do not follow any strategy, i.e., they join the queue they arrive at. These are called overloaded servers. In the one-dimensional case ($d=1$), we evaluate the expected fraction of overloaded servers for any finite $N$ when the users follow probabilistic nearest neighbour shift strategies. Additionally, for servers distributed in a $d$-dimensional space we provide expressions for the fraction of overloaded servers in the system as the total number of servers $N\rightarrow \infty$. Numerical experiments are provided to support our claims. Typical applications of our results include electric vehicles queueing at charging stations, and queues in airports or supermarkets.
We consider distributed kernel bandits where $N$ agents aim to collaboratively maximize an unknown reward function that lies in a reproducing kernel Hilbert space. Each agent sequentially queries the function to obtain noisy observations at the query points. Agents can share information through a central server, with the objective of minimizing regret that is accumulating over time $T$ and aggregating over agents. We develop the first algorithm that achieves the optimal regret order (as defined by centralized learning) with a communication cost that is sublinear in both $N$ and $T$. The key features of the proposed algorithm are the uniform exploration at the local agents and shared randomness with the central server. Working together with the sparse approximation of the GP model, these two key components make it possible to preserve the learning rate of the centralized setting at a diminishing rate of communication.
We study a variant of Collaborative PAC Learning, in which we aim to learn an accurate classifier for each of the $n$ data distributions, while minimizing the number of samples drawn from them in total. Unlike in the usual collaborative learning setup, it is not assumed that there exists a single classifier that is simultaneously accurate for all distributions. We show that, when the data distributions satisfy a weaker realizability assumption, sample-efficient learning is still feasible. We give a learning algorithm based on Empirical Risk Minimization (ERM) on a natural augmentation of the hypothesis class, and the analysis relies on an upper bound on the VC dimension of this augmented class. In terms of the computational efficiency, we show that ERM on the augmented hypothesis class is NP-hard, which gives evidence against the existence of computationally efficient learners in general. On the positive side, for two special cases, we give learners that are both sample- and computationally-efficient.
The optimization problem associated to fitting two-layer ReLU networks having $d$~inputs, $k$~neurons, and labels generated by a target network, is considered. Two types of infinite families of spurious minima, giving one minimum per $d$, were recently found. The loss at minima belonging to the first type converges to zero as $d$ increases. In the second type, the loss remains bounded away from zero. That being so, how may one avoid minima belonging to the latter type? Fortunately, such minima are never detected by standard optimization methods. Motivated by questions concerning the nature of this phenomenon, we develop methods to study distinctive analytic properties of hidden minima. By existing analyses, the Hessian spectrum of both types agree modulo $O(d^{-1/2})$-terms -- not promising. Thus, rather, our investigation proceeds by studying curves along which the loss is minimized or maximized, generally referred to as tangency arcs. We prove that apparently far removed group representation-theoretic considerations concerning the arrangement of subspaces invariant to the action of subgroups of $S_d$, the symmetry group over $d$ symbols, relative to ones fixed by the action yield a precise description of all finitely many admissible types of tangency arcs. The general results used for the loss function reveal that arcs emanating from hidden minima differ, characteristically, by their structure and symmetry, precisely on account of the $O(d^{-1/2})$-eigenvalue terms absent in previous work, indicating in particular the subtlety of the analysis. The theoretical results, stated and proved for o-minimal structures, show that the set comprising all tangency arcs is topologically sufficiently tame to enable a numerical construction of tangency arcs and so compare how minima, both types, are positioned relative to adjacent critical points.
In current text-based task-oriented dialogue (TOD) systems, user emotion detection (ED) is often overlooked or is typically treated as a separate and independent task, requiring additional training. In contrast, our work demonstrates that seamlessly unifying ED and TOD modeling brings about mutual benefits, and is therefore an alternative to be considered. Our method consists in augmenting SimpleToD, an end-to-end TOD system, by extending belief state tracking to include ED, relying on a single language model. We evaluate our approach using GPT-2 and Llama-2 on the EmoWOZ benchmark, a version of MultiWOZ annotated with emotions. Our results reveal a general increase in performance for ED and task results. Our findings also indicate that user emotions provide useful contextual conditioning for system responses, and can be leveraged to further refine responses in terms of empathy.
Privacy policies are crucial for informing users about data practices, yet their length and complexity often deter users from reading them. In this paper, we propose an automated approach to identify and visualize data practices within privacy policies at different levels of detail. Leveraging crowd-sourced annotations from the ToS;DR platform, we experiment with various methods to match policy excerpts with predefined data practice descriptions. We further conduct a case study to evaluate our approach on a real-world policy, demonstrating its effectiveness in simplifying complex policies. Experiments show that our approach accurately matches data practice descriptions with policy excerpts, facilitating the presentation of simplified privacy information to users.
Building a single universal speech enhancement (SE) system that can handle arbitrary input is a demanded but underexplored research topic. Towards this ultimate goal, one direction is to build a single model that handles diverse audio duration, sampling frequencies, and microphone variations in noisy and reverberant scenarios, which we define here as "input condition invariant SE". Such a model was recently proposed showing promising performance; however, its multi-channel performance degraded severely in real conditions. In this paper we propose novel architectures to improve the input condition invariant SE model so that performance in simulated conditions remains competitive while real condition degradation is much mitigated. For this purpose, we redesign the key components that comprise such a system. First, we identify that the channel-modeling module's generalization to unseen scenarios can be sub-optimal and redesign this module. We further introduce a two-stage training strategy to enhance training efficiency. Second, we propose two novel dual-path time-frequency blocks, demonstrating superior performance with fewer parameters and computational costs compared to the existing method. All proposals combined, experiments on various public datasets validate the efficacy of the proposed model, with significantly improved performance on real conditions. Recipe with full model details is released at //github.com/espnet/espnet.
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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