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The paper proposes a probabilistic generalization of the well-known Strong Backdoor Set (SBS) concept applied to the Boolean Satisfiability Problem (SAT). We call a set of Boolean variables B a Ï-backdoor, if for a fraction of at least Ï of possible assignments of variables from B, assigning their values to variables in a Boolean formula in Conjunctive Normal Form (CNF) results in polynomially solvable formulas. Clearly, a Ï-backdoor with Ï=1 is an SBS. For a given set B it is possible to efficiently construct an (Îµ, Î´)-approximation of parameter Ï using the Monte Carlo method. Thus, we define an (Îµ, Î´)-SBS as such a set B for which the conclusion &quot;parameter Ï deviates from 1 by no more than Îµ&quot; is true with probability no smaller than 1 - Î´. We consider the problems of finding the minimum SBS and the minimum (Îµ, Î´)-SBS. To solve the former problem, one can use the algorithm described by R. Williams, C. Gomes and B. Selman in 2003. In the paper we propose a new probabilistic algorithm to solve the latter problem, and show that the asymptotic estimation of the worst-case complexity of the proposed algorithm is significantly smaller than that of the algorithm by Williams et al. For practical applications, we suggest a metaheuristic optimization algorithm based on the penalty function method to seek the minimal (Îµ, Î´)-SBS. Results of computational experiments show that the use of (Îµ, Î´)-SBSes found by the proposed algorithm allows speeding up solving of test problems related to equivalence checking and hard crafted and combinatorial benchmarks compared to state-of-the-art SAT solvers.

AAAI 2022

On Probabilistic Generalization of Backdoors in Boolean Satisfiability

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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AAAI 2023

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

The paper proposes a probabilistic generalization of the well-known Strong Backdoor Set (SBS) concept applied to the Boolean Satisfiability Problem (SAT). We call a set of Boolean variables B a Ï-backdoor, if for a fraction of at least Ï of possible assignments of variables from B, assigning their values to variables in a Boolean formula in Conjunctive Normal Form (CNF) results in polynomially solvable formulas. Clearly, a Ï-backdoor with Ï=1 is an SBS. For a given set B it is possible to efficiently construct an (Îµ, Î´)-approximation of parameter Ï using the Monte Carlo method. Thus, we define an (Îµ, Î´)-SBS as such a set B for which the conclusion "parameter Ï deviates from 1 by no more than Îµ" is true with probability no smaller than 1 - Î´. We consider the problems of finding the minimum SBS and the minimum (Îµ, Î´)-SBS. To solve the former problem, one can use the algorithm described by R. Williams, C. Gomes and B. Selman in 2003. In the paper we propose a new probabilistic algorithm to solve the latter problem, and show that the asymptotic estimation of the worst-case complexity of the proposed algorithm is significantly smaller than that of the algorithm by Williams et al. For practical applications, we suggest a metaheuristic optimization algorithm based on the penalty function method to seek the minimal (Îµ, Î´)-SBS. Results of computational experiments show that the use of (Îµ, Î´)-SBSes found by the proposed algorithm allows speeding up solving of test problems related to equivalence checking and hard crafted and combinatorial benchmarks compared to state-of-the-art SAT solvers.

technical paper

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. 

Inferring spatial relations in natural language is a crucial ability an intelligent system should possess. The bAbI dataset tries to capture tasks relevant to this domain (task 17 and 19). However, these tasks have several limitations. Most importantly, they are limited to fixed expressions, they are limited in the number of reasoning steps required to solve them, and they fail to test the robustness of models to input that contains irrelevant or redundant information. In this paper, we present a new Question-Answering dataset called StepGame for robust multi-step spatial reasoning in texts. Our experiments demonstrate that state-of-the-art models on the bAbI dataset struggle on the StepGame dataset. Moreover, we propose a Tensor-Product based Memory-Augmented Neural Network (TP-MANN) specialized for spatial reasoning tasks. Experimental results on both datasets show that our model outperforms all the baselines with superior generalization and robustness performance.

StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts

Learning effective representations of entities and relations for knowledge graphs (KGs) is critical to the success of many multi-relational learning tasks. Existing methods based on graph neural networks learn a deterministic embedding function, which lacks sufficient flexibility to explore better choices when dealing with the imperfect and noisy KGs such as the scarce labeled nodes and noisy graph structure. To this end, we propose a novel multi-relational graph Gaussian Process network (GGPN), which aims to improve the flexibility of deterministic methods by simultaneously learning a family of embedding functions, i.e., a stochastic embedding function. Specifically, a Bayesian Gaussian Process (GP) is proposed to model the distribution of this stochastic function and the resulting representations are obtained by aggregating stochastic function values, i.e., messages, from neighboring entities. The two problems incurred when leveraging GP in GGPN are the proper choice of kernel function and the cubic computational complexity. To address the first problem, we further propose a novel kernel function that can explicitly take the diverse relations between each pair of entities into account and be adaptively learned in a data-driven way. We address the second problem by reformulating GP as a Bayesian linear model, resulting in a linear computational complexity. With these two solutions, our GGPN can be efficiently trained in an end-to-end manner. We evaluate our GGPN in link prediction and entity classification tasks, and the experimental results demonstrate the superiority of our method. Our code is available at https://github.com/sysu-gzchen/GGPN.

Multi-Relational Graph Representation Learning with Bayesian Gaussian Process Network

Color Constancy aims to correct image color casts caused by scene illumination. Recently, although the deep learning approaches have remarkably improved on single-camera data, these models still suffer from the seriously insufficient data problem, resulting in shallow model capacity and degradation in multi-camera settings. In this paper, to alleviate this problem, we present a Transfer Learning Color Constancy (TLCC) method that leverages cross-camera RAW data and massive unlabeled sRGB data to support training. Specifically, TLCC consists of the Statistic Estimation Scheme (SE-Scheme) and Color-Guided Adaption Branch (CGA-Branch). SE-Scheme builds a statistic perspective to map the camera-related illumination labels into camera-agnostic form and produce pseudo labels for sRGB data, which greatly expands data for joint training. Then, CGA-Branch further promotes efficient transfer learning from sRGB to RAW data by extracting color information to regularize the backbone's features adaptively. Experimental results show the TLCC has overcome the data limitation and model degradation, outperforming the state-of-the-art performance on popular benchmarks. Moreover, the experiments also prove the TLCC is capable of learning new scenes information from sRGB data to improve accuracy on the RAW images with similar scenes.

Transfer Learning for Color Constancy via Statistic Perspective

This paper presents a model-free reinforcement learning (RL) algorithm for infinite-horizon average-reward Constrained Markov Decision Processes (CMDPs). Considering a learning horizon K, which is sufficiently large, the proposed algorithm achieves sublinear regret and zero constraint violation. The bounds depend on the number of states S, the number of actions A, and two constants which are independent of the learning horizon K.

A Provably-Efficient Model-Free Algorithm for Infinite-Horizon Average-Reward Constrained Markov Decision Processes

Recent studies have shown that strong Natural Language Understanding (NLU) models are prone to relying on annotation biases of the datasets as a shortcut, which goes against the underlying mechanisms of the task of interest. To reduce such biases, several recent works introduce debiasing methods to regularize the training process of targeted NLU models. In this paper, we provide a new perspective with causal inference to find out the bias. On one hand, we show that there is an unobserved confounder for the natural language utterances and their respective classes, leading to spurious correlations from training data. To remove such confounder, the backdoor adjustment with causal intervention is utilized to find the true causal effect, which makes the training process fundamentally different from the traditional likelihood estimation. On the other hand, in inference process, we formulate the bias as the direct causal effect and remove it by pursuing the indirect causal effect with counterfactual reasoning. We conduct experiments on large-scale natural language inference and fact verification benchmarks, evaluating on bias sensitive datasets that are specifically designed to assess the robustness of models against known biases in the training data. Experimental results show that our proposed debiasing framework outperforms previous state-of-the-art debiasing methods while maintaining the original in-distribution performance.

Debiasing NLU Models via Causal Intervention and Counterfactual Reasoning

We study reward design strategies for incentivizing a reinforcement learning agent to adopt a policy from a set of admissible policies. The goal of the reward designer is to modify the underlying reward function cost-efficiently while ensuring that any approximately optimal deterministic policy under the new reward function is admissible and performs well under the original reward function. This problem can be viewed as a dual to the problem of optimal reward poisoning attacks: instead of forcing an agent to adopt a specific policy, the reward designer incentivizes an agent to avoid taking actions that are inadmissible in certain states. Perhaps surprisingly, and in contrast to the problem of optimal reward poisoning attacks, we first show that the reward design problem for admissible policy teaching is computationally challenging, and it is NP-hard to find an approximately optimal reward modification. We then proceed by formulating a surrogate problem whose optimal solution approximates the optimal solution to the reward design problem in our setting, but is more amenable to optimization techniques and analysis. For this surrogate problem, we present characterization results that provide bounds on the value of the optimal solution. Finally, we design a local search algorithm to solve the surrogate problem and showcase its utility using simulation-based experiments.

Admissible Policy Teaching through Reward Design

Unlike traditional supervised learning, in many settings only partial feedback is available. We may only observe outcomes for the chosen actions, but not the counterfactual outcomes associated with other alternatives. Such settings encompass a wide variety of applications including pricing, online marketing and precision medicine. A key challenge is that observational data are influenced by historical policies deployed in the system, yielding a biased data distribution. We approach this task as a domain adaptation problem and propose a self-training algorithm which imputes outcomes with categorical values for finite unseen actions in the observational data to simulate a randomized trial through pseudolabelling, which we refer to as Counterfactual Self-Training (CST). CST iteratively imputes pseudolabels and retrains the model. In addition, we show input consistency loss can further improve CST performance which is shown in recent theoretical analysis of pseudolabelling. We demonstrate the effectiveness of the proposed algorithms on both synthetic and real datasets.

Enhancing Counterfactual Classification Performance via Self-Training

Data augmentation has been an important ingredient for boosting performances of learned models. Prior data augmentation methods for few-shot text classification have led to great performance boosts. However, they have not been designed to capture the intricate compositional structure of natural language. As a result, they fail to generate samples with plausible and diverse sentence structures. Motivated by this, we present the data Augmentation using Lexicalized Probabilistic context-free grammars (ALP) that generates augmented samples with diverse syntactic structures with plausible grammar. The lexicalized PCFG parse trees consider both the constituents and dependencies to produce a syntactic frame that maximizes a variety of word choices in a syntactically preservable manner without specific domain experts. Experiments on few-shot text classification tasks demonstrate that ALP enhances many state-of-the-art classification methods. As a second contribution, we delve into the train-val splitting methodologies when a data augmentation method comes into play. We argue empirically that the traditional splitting of training and validation sets is sub-optimal compared to our novel augmentation-based splitting strategies that further expand the training split with the same number of labeled data. Taken together, our contributions on the data augmentation strategies yield a strong training recipe for few-shot text classification tasks.

ALP: Data Augmentation Using Lexicalized PCFGs for Few-Shot Text Classification

From ecology to atmospheric sciences, many academic disciplines deal with data characterized by intricate spatio-temporal complexities, the modeling of which often requires specialized approaches. Generative models of these data are of particular interest, as they enable a range of impactful downstream applications like simulation or creating synthetic training data. Recently, COT-GAN, a new GAN algorithm inspired by the theory of causal optimal transport (COT), was proposed in an attempt to improve generation of sequential data.  However, the task of learning complex patterns over time and space requires additional knowledge of the specific data structures. In this study, we propose a novel loss objective combined with COT-GAN based on an autoregressive embedding to reinforce the learning of spatio-temporal dynamics. We devise SPATE (spatio-temporal association), a new metric measuring spatio-temporal autocorrelation. We compute SPATE for real and synthetic data samples and use it to compute an embedding loss that considers space-time interactions, nudging the GAN to learn outputs that are faithful to the observed dynamics. We test our new SPATE-GAN on a diverse set of spatio-temporal patterns: turbulent flows, log-Gaussian Cox processes and global weather data. We show that our novel embedding loss improves performance without any changes to the architecture of the GAN backbone, highlighting our model's increased capacity for capturing autoregressive structures.

SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss

While Answer-Set Programming (ASP) is a prominent approach to declarative problem solving, optimisation problems can still be a challenge for it. Large-Neighbourhood Search (LNS) is a metaheuristic for optimisation where parts of a solution are alternately destroyed and reconstructed that has high but untapped potential for ASP solving. We present a framework for LNS optimisation in answer-set solving, in which neighbourhoods can be specified either declaratively as part of the ASP encoding, or automatically generated by code. To effectively explore different neighbourhoods, we focus on multi-shot solving as it allows to avoid program regrounding. We illustrate the framework on different optimisation problems, some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production which demonstrate the effectiveness of the LNS approach.

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StepGame: A New Benchmark for Robust Multi-Hop Spatial Reasoning in Texts

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Probabilistic Generalization of Backdoor Trees with Application to SAT

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