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Solving Satisfiability is at the core of a wide range of applications from Knowledge Representation to Logic Programming to Software and Hardware Verification. One of the models of Satisfiability, the Random Satisfiability problem, has received much attention in the literature both, as a useful benchmark for SAT solvers, and as an exciting mathematical object. In this paper we tackle a somewhat nonstandard type of Random Satisfiability, the one where instances are not chosen uniformly from a certain class of instances, but rather from a certain nontrivial distribution. More precisely, we use so-called Configuration Model, in which we start with a distribution of degrees (the number of occurrences) of a variable, sample the degree of each variable and then generate a random instance with the prescribed degrees. It has been proposed previously that by properly selecting the starting distribution (to be, say, power law or lognorm) one can approximate at least some aspect of `industrial&#39; instances of SAT.
Here we suggest an algorithm that solves such problems for a wide range of degree distributions and obtain a necessary and a sufficient condition for the satisfiability of such formulas.

AAAI 2021

Satisfiability and Algorithms for Non-Uniform Random k-SAT

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

AAAI 2022

Solving Satisfiability is at the core of a wide range of applications from Knowledge Representation to Logic Programming to Software and Hardware Verification. One of the models of Satisfiability, the Random Satisfiability problem, has received much attention in the literature both, as a useful benchmark for SAT solvers, and as an exciting mathematical object. In this paper we tackle a somewhat nonstandard type of Random Satisfiability, the one where instances are not chosen uniformly from a certain class of instances, but rather from a certain nontrivial distribution. More precisely, we use so-called Configuration Model, in which we start with a distribution of degrees (the number of occurrences) of a variable, sample the degree of each variable and then generate a random instance with the prescribed degrees. It has been proposed previously that by properly selecting the starting distribution (to be, say, power law or lognorm) one can approximate at least some aspect of `industrial' instances of SAT.
Here we suggest an algorithm that solves such problems for a wide range of degree distributions and obtain a necessary and a sufficient condition for the satisfiability of such formulas.

technical paper

We study the problem of fairly allocating indivisible goods and focus on the classic fairness notion of proportionality. The indivisibility of the goods is long known to pose highly non-trivial obstacles to achieving fairness, and a very vibrant line of research has aimed to circumvent them using appropriate notions of approximate fairness. Recent work has established that even approximate versions of proportionality (PROPx) may be impossible to achieve even for small instances, while the best known achievable approximations (PROP1) are much weaker. We introduce the notion of proportionality up to the maximin item (PROPm) and show how to reach an allocation satisfying this notion for any instance involving up to five agents with additive valuations. PROPm provides a well-motivated middle-ground between PROP1 and PROPx, while also capturing some elements of the well-studied maximin share (MMS) benchmark: another relaxation of proportionality that has attracted a lot of attention.

Achieving Proportionality up to the Maximin Item with Indivisible Goods

Most collaborative filtering (CF) models estimate missing ratings with an implicit assumption that the ratings are missing-at-random, which may cause the biased rating estimation and degraded performance since recent deep exploration shows that ratings may likely be missing-not-at-random (MNAR). To debias MNAR rating estimation, we introduce item observability and user selection to depict the generation of MNAR ratings and propose a tripartite CF (TCF) framework to jointly model the triple aspects of rating generation: item observability, user selection, and ratings, and to estimate the MNAR ratings. An item observability variable is introduced to a complete observability model to infer whether an item is observable to a user. TCF also conducts a complete rating model for rating generation and utilizes a user selection model dependent on the item observability and rating values to model user selection of the observable items. We further elaborately instantiate TCF as a Tripartite Probabilistic Matrix Factorization model (TPMF) by leveraging the probabilistic matrix factorization. Besides, TPMF introduces multifaceted dependency between user selection and ratings to model the influence of user selection on ratings. Extensive experiments on synthetic and real-world datasets show that modeling item observability and user selection effectively debias MNAR rating estimation, and TPMF outperforms the state-of-the-art methods in estimating the MNAR ratings.

Tripartite Collaborative Filtering with Observability and Selection for Debiasing Rating Estimation on Missing-Not-at-Random Data

We propose a general variational framework of fair clustering, which integrates an original Kullback-Leibler (KL) fairness term with a large class of clustering objectives, including prototype or graph based. Fundamentally different from the existing combinatorial and spectral solutions, our variational multi-term approach enables to control the trade-off levels between the fairness and clustering objectives. We derive a general tight upper bound based on a concave-convex decomposition of our fairness term, its Lipschitz-gradient property and the Pinskerâ€™s inequality. Our tight upper bound can be jointly optimized with various clustering objectives, while yielding a scalable solution, with convergence guarantee. Interestingly, at each iteration, it performs an independent update for each assignment variable. Therefore, it can be easily distributed for large-scale datasets. This scalability is important as it enables to explore different trade-off levels between the fairness and clustering objectives. Unlike spectral relaxation, our formulation does not require computing its eigenvalue decomposition. We report comprehensive evaluations and comparisons with state-of-the-art methods over various fair clustering benchmarks, which show that our variational formulation can yield highly competitive solutions in terms of fairness and clustering objectives.

Variational Fair Clustering

Building an intelligent dialogue system with the ability to select a proper response according to a multi-turn context is a great challenging task.
Existing studies focus on building a context-response matching model with various neural architectures or pretrained language models (PLMs)
and typically learning with a single response prediction task.
These approaches overlook many potential training signals contained in dialogue data, which might be beneficial for context understanding and produce better features for response prediction. 
Besides, the response retrieved from existing dialogue systems supervised by the conventional way
still faces some critical challenges, including incoherence and inconsistency.
To address these issues, in this paper, we propose learning a context-response matching model with auxiliary self-supervised tasks designed for the dialogue data based on pre-trained language models.
Specifically, we introduce four self-supervised tasks including next session prediction, utterance restoration, incoherence detection and consistency discrimination, and jointly train the PLM-based response selection model with these auxiliary tasks in a multi-task manner.  
By this means, the auxiliary tasks can guide the learning of the matching model to achieve a better local optimum and select a more proper response.
Experiment results on two benchmarks indicate that the proposed auxiliary self-supervised tasks bring significant improvement for multi-turn response selection in retrieval-based dialogues, and our model achieves new state-of-the-art results on both datasets.

Learning an Effective Context-Response Matching Model with Self-Supervised Tasks for Retrieval-Based Dialogues

Facial landmark localization aims to detect the predefined points of human faces, and the topic has been rapidly improved with the recent development of neural network based methods. However, it remains a challenging task when dealing with faces in unconstrained scenarios, especially with large pose variations. In this paper, we target the problem of facial landmark localization across large poses and address this task based on a split-and-aggregate strategy. To split the search space, we propose a set of anchor templates as references for regression, which well addresses the large variations of face poses. Based on the prediction of each anchor template, we propose to aggregate the results, which can reduce the landmark uncertainty due to the large poses. Overall, our proposed approach, named AnchorFace, obtains state-of-the-art results with extremely efficient inference speed on four challenging benchmarks, i.e. AFLW, 300W, Menpo, and WFLW dataset. Code will be available soon.

AnchorFace: An Anchor-Based Facial Landmark Detector across Large Poses

Explaining black-box models such as deep neural networks is becoming increasingly important as it helps to boost trust and debugging. Popular forms of explanations map the features to a vector indicating their individual importance to a decision on the instance-level. They can then be used to prevent the model from learning the wrong bias in data possibly due to ambiguity. For instance, Ross et al.'s ``right for the right reasons'' propagates user explanations backwards to the network by formulating differentiable constraints based on input gradients. 

Unfortunately, input gradients as well as many other widely used explanation methods form an approximation of the decision boundary and assume the underlying model to be fixed. Here, we demonstrate how to make use of influence functions---a well known robust statistic---in the constraints to correct the modelâ€™s behaviour more effectively. Our empirical evidence demonstrates that this ``right for better reasons''(RBR) considerably reduces the time to correct the classifier at training time and boosts the quality of explanations at inference time compared to input gradients. Besides, we also showcase the effectiveness of RBR in correcting "Clever Hans"-like behaviour in real, high-dimensional domain.

Right for Better Reasons: Training Differentiable Models by Constraining their Influence Function

We introduce Nutri-bullets, a multi-document summarization task for health and nutrition. First, we present two datasets of food and health summaries from multiple scientific studies. Furthermore, we propose a novel extract-compose model to solve the problem in the regime of limited parallel data. We explicitly select key spans from several abstracts using a policy network, followed by composing the selected spans to present a summary via a task specific language model. Compared to state-of-the-art methods, our approach leads to more faithful, relevant and diverse summarization -- properties imperative to this application. For instance, on the BreastCancer dataset our approach gets a more than 50% improvement on relevance and faithfulness.

Nutri-Bullets: Summarizing Health Studies by Composing Segments

Cross-domain named entity recognition (NER) models are able to cope with the scarcity issue of NER samples in target domains. However, most of the existing NER benchmarks lack domain-specialized entity types or do not focus on a certain domain, leading to a less effective cross-domain evaluation. To address these obstacles, we introduce a cross-domain NER dataset (CrossNER), a fully-labeled collection of NER data spanning over five diverse domains with specialized entity categories for different domains. Additionally, we also provide a domain-related corpus since using it to continue pre-training language models (domain-adaptive pre-training) is effective for the domain adaptation. We then conduct comprehensive experiments to explore the effectiveness of leveraging different levels of the domain corpus and pre-training strategies to do domain-adaptive pre-training for the cross-domain task. Results show that focusing on the fractional corpus containing domain-specialized entities and utilizing a more challenging pre-training strategy in domain-adaptive pre-training are beneficial for the NER domain adaptation, and our proposed method can consistently outperform existing cross-domain NER baselines. Nevertheless, experiments also illustrate the challenge of this cross-domain NER task. We hope that our dataset and baselines will catalyze research in the NER domain adaptation area. The code and data are available at https://github.com/zliucr/CrossNER.

CrossNER: Evaluating Cross-Domain Named Entity Recognition

Search-based systems have shown to be effective for planning in zero-sum games. However, search-based approaches have important disadvantages. First, the decisions of search algorithms are mostly non-interpretable, which is problematic in domains where predictability and trust are desired such as commercial games. Second, the computational complexity of search-based algorithms might limit their applicability, especially in contexts where resources are shared among other tasks such as graphic rendering. In this work we introduce a system for synthesizing programmatic strategies for a real-time strategy (RTS) game. In contrast with search algorithms, programmatic strategies are more amenable to explanations and tend to be efficient, once the program is synthesized. Our system uses a novel algorithm for simplifying domain-specific languages (DSLs) and a local search algorithm that synthesizes programs with self play. We performed a user study where we enlisted four professional programmers to develop programmatic strategies for mRTS, a minimalist RTS game. Our results show that the programs synthesized by our approach can outperform search algorithms and be competitive with programs written by the programmers.

Programmatic Strategies for Real-Time Strategy Games

Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks often exhibit a multi-scale structure, in which agents can be grouped into communities, those communities further grouped, and so on, and where interactions among such groups may also exhibit sparsity. We present a general model of multi-scale network games that encodes such multi-level structure. We then develop several algorithmic approaches that leverage this multi-scale structure, and derive sufficient conditions for convergence of these to a Nash equilibrium. Our numerical experiments demonstrate that the proposed approaches enable orders of magnitude improvements in scalability when computing Nash equilibria in such games. For example, we can solve previously intractable instances involving up to 1 million agents in under 15 minutes.

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Achieving Proportionality up to the Maximin Item with Indivisible Goods

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Next from AAAI 2021

Achieving Proportionality up to the Maximin Item with Indivisible Goods

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Analysis of Pure Literal Elimination Rule for Non-Uniform Random (MAX) k-SAT Problem with an Arbitrary Degree Distribution

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