Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost stands at roughly \$1.3K/TB, which is dramatically more expensive than reading from existing archival storage solutions today. In this work, we aim to reduce not only the cost but also the latency of DNA storage by studying the DNA coverage depth problem, which aims to reduce the required number of reads to retrieve information from the storage system. Under this framework, our main goal is to understand how to optimally pair an error-correcting code with a given retrieval algorithm to minimize the sequencing coverage depth, while guaranteeing retrieval of the information with high probability. Additionally, we study the DNA coverage depth problem under the random-access setup.
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In this work, we present a generic step-size choice for the ADMM type proximal algorithms. It admits a closed-form expression and is theoretically optimal with respect to a worst-case convergence rate bound. It is simply given by the ratio of Euclidean norms of the dual and primal solutions, i.e., $ ||{\lambda}^\star|| / ||{x}^\star||$. Numerical tests show that its practical performance is near-optimal in general. The only challenge is that such a ratio is not known a priori and we provide two strategies to address it. The derivation of our step-size choice is based on studying the fixed-point structure of ADMM using the proximal operator. However, we demonstrate that the classical proximal operator definition contains an input scaling issue. This leads to a scaled step-size optimization problem which would yield a false solution. Such an issue is naturally avoided by our proposed new definition of the proximal operator. A series of its properties is established.
The emergent behavior of a distributed system is conditioned by the information available to the local decision-makers. Therefore, one may expect that providing decision-makers with more information will improve system performance; in this work, we find that this is not necessarily the case. In multi-agent maximum coverage problems, we find that even when agents' objectives are aligned with the global welfare, informing agents about the realization of the resource's random values can reduce equilibrium performance by a factor of 1/2. This affirms an important aspect of designing distributed systems: information need be shared carefully. We further this understanding by providing lower and upper bounds on the ratio of system welfare when information is (fully or partially) revealed and when it is not, termed the value-of-informing. We then identify a trade-off that emerges when optimizing the performance of the best-case and worst-case equilibrium.
By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$. We will seek a truth assignment to maximize the number of satisfied clauses. This problem is $\textit{NP}$-hard even for its restricted version, the 2-MAXSAT problem by which every clause contains at most 2 literals. In this paper, we discuss an efficient algorithm to solve this problem. Its worst case time complexity is bounded by O($(nm)^2(log_2\;nm)^{log_2\;nm}$). This shows that the 2-MAXSAT problem can be solved in polynomial time.
Dynamic Sparse Training (DST) is a rapidly evolving area of research that seeks to optimize the sparse initialization of a neural network by adapting its topology during training. It has been shown that under specific conditions, DST is able to outperform dense models. The key components of this framework are the pruning and growing criteria, which are repeatedly applied during the training process to adjust the network's sparse connectivity. While the growing criterion's impact on DST performance is relatively well studied, the influence of the pruning criterion remains overlooked. To address this issue, we design and perform an extensive empirical analysis of various pruning criteria to better understand their effect on the dynamics of DST solutions. Surprisingly, we find that most of the studied methods yield similar results. The differences become more significant in the low-density regime, where the best performance is predominantly given by the simplest technique: magnitude-based pruning. The code is provided at //github.com/alooow/fantastic_weights_paper
We consider error-correcting coding for DNA-based storage. We model the DNA storage channel as a multi-draw IDS channel where the input data is chunked into $M$ short DNA strands, which are copied a random number of times, and the channel outputs a random selection of $N$ noisy DNA strands. The retrieved DNA strands are prone to insertion, deletion, and substitution (IDS) errors. We propose an index-based concatenated coding scheme consisting of the concatenation of an outer code, an index code, and an inner synchronization code, where the latter two tackle IDS errors. We further propose a mismatched joint index-synchronization code maximum a posteriori probability decoder with optional clustering to infer symbolwise a posterior probabilities for the outer decoder. We compute achievable information rates for the outer code and present Monte-Carlo simulations for information-outage probabilities and frame error rates on synthetic and experimental data, respectively.
We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system for $n$ equations in $n+m$ variables. Systems with saddle Jacobi number generalize various notions of chained and diagonal systems and form the widest class of systems admitting subsets of state variables as flat output, for which flat parametrization may be computed without differentiating the initial equations. We investigate apparent and intrinsic flat singularities of such systems. As an illustration, we consider the case of a simplified aircraft model, providing new flat outputs and showing that it is flat at all points except possibly in stalling conditions. Finally, we present numerical simulations showing that a feedback using those flat outputs is robust to perturbations and can also compensate model errors, when using a more realistic aerodynamic model.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Neural architecture-based recommender systems have achieved tremendous success in recent years. However, when dealing with highly sparse data, they still fall short of expectation. Self-supervised learning (SSL), as an emerging technique to learn with unlabeled data, recently has drawn considerable attention in many fields. There is also a growing body of research proceeding towards applying SSL to recommendation for mitigating the data sparsity issue. In this survey, a timely and systematical review of the research efforts on self-supervised recommendation (SSR) is presented. Specifically, we propose an exclusive definition of SSR, on top of which we build a comprehensive taxonomy to divide existing SSR methods into four categories: contrastive, generative, predictive, and hybrid. For each category, the narrative unfolds along its concept and formulation, the involved methods, and its pros and cons. Meanwhile, to facilitate the development and evaluation of SSR models, we release an open-source library SELFRec, which incorporates multiple benchmark datasets and evaluation metrics, and has implemented a number of state-of-the-art SSR models for empirical comparison. Finally, we shed light on the limitations in the current research and outline the future research directions.
Dialogue systems are a popular Natural Language Processing (NLP) task as it is promising in real-life applications. It is also a complicated task since many NLP tasks deserving study are involved. As a result, a multitude of novel works on this task are carried out, and most of them are deep learning-based due to the outstanding performance. In this survey, we mainly focus on the deep learning-based dialogue systems. We comprehensively review state-of-the-art research outcomes in dialogue systems and analyze them from two angles: model type and system type. Specifically, from the angle of model type, we discuss the principles, characteristics, and applications of different models that are widely used in dialogue systems. This will help researchers acquaint these models and see how they are applied in state-of-the-art frameworks, which is rather helpful when designing a new dialogue system. From the angle of system type, we discuss task-oriented and open-domain dialogue systems as two streams of research, providing insight into the hot topics related. Furthermore, we comprehensively review the evaluation methods and datasets for dialogue systems to pave the way for future research. Finally, some possible research trends are identified based on the recent research outcomes. To the best of our knowledge, this survey is the most comprehensive and up-to-date one at present in the area of dialogue systems and dialogue-related tasks, extensively covering the popular frameworks, topics, and datasets.
Medical image segmentation requires consensus ground truth segmentations to be derived from multiple expert annotations. A novel approach is proposed that obtains consensus segmentations from experts using graph cuts (GC) and semi supervised learning (SSL). Popular approaches use iterative Expectation Maximization (EM) to estimate the final annotation and quantify annotator's performance. Such techniques pose the risk of getting trapped in local minima. We propose a self consistency (SC) score to quantify annotator consistency using low level image features. SSL is used to predict missing annotations by considering global features and local image consistency. The SC score also serves as the penalty cost in a second order Markov random field (MRF) cost function optimized using graph cuts to derive the final consensus label. Graph cut obtains a global maximum without an iterative procedure. Experimental results on synthetic images, real data of Crohn's disease patients and retinal images show our final segmentation to be accurate and more consistent than competing methods.
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