United States

MAX k-SAT is one of the archetypal NP-hard problems. Its variation called random MAX k-SAT problem was introduced in order to understand how hard it is to solve instances of the problem on average. The most common model to sample random instances is the uniform model, which has received a large amount of attention. However, the uniform model often fails to capture important structural properties we observe in the real-world instances.  
	
To address these limitations, a more general (in a certain sense) model has been proposed, the configuration model, which is able to produce instances with an arbitrary distribution of  variables&#39; degrees, and so can simulate biases in instances appearing in various applications. 

Our overall goal is to expand the theory built around the uniform model to the more general configuration model for a wide range of degree distributions. This includes locating satisfiability thresholds and analysing the performance of the standard heuristics applied to instances sampled from the configuration model.
	
In this paper we analyse the performance of the pure literal elimination rule. We provide an equation that given an underlying degree distribution gives the number of clauses the pure literal elimination rule satisfies w.h.p. We also show how the distribution of variable degrees changes over time as the algorithm is being executed.

AAAI 2022

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

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 2021

MAX k-SAT is one of the archetypal NP-hard problems. Its variation called random MAX k-SAT problem was introduced in order to understand how hard it is to solve instances of the problem on average. The most common model to sample random instances is the uniform model, which has received a large amount of attention. However, the uniform model often fails to capture important structural properties we observe in the real-world instances.  
	
To address these limitations, a more general (in a certain sense) model has been proposed, the configuration model, which is able to produce instances with an arbitrary distribution of  variables' degrees, and so can simulate biases in instances appearing in various applications. 

Our overall goal is to expand the theory built around the uniform model to the more general configuration model for a wide range of degree distributions. This includes locating satisfiability thresholds and analysing the performance of the standard heuristics applied to instances sampled from the configuration model.
	
In this paper we analyse the performance of the pure literal elimination rule. We provide an equation that given an underlying degree distribution gives the number of clauses the pure literal elimination rule satisfies w.h.p. We also show how the distribution of variable degrees changes over time as the algorithm is being executed.

technical paper

Learning information-rich and generalizable representations effectively from unlabeled multivariate cardiac signals to identify abnormal heart rhythms (cardiac arrhythmias) is valuable in real-world clinical settings but often challenging due to its complex temporal dynamics. Cardiac arrhythmias can vary significantly in temporal patterns even for the same patient (i.e., intra subject difference). Meanwhile, the same type of cardiac arrhythmia can show different temporal patterns among different patients due to different cardiac structures (i.e., inter subject difference). In this paper, we address the challenges by proposing an Intra-Inter Subject Self-Supervised Learning (ISL) model that is customized for multivariate cardiac signals. Our proposed ISL model integrates medical knowledge into self-supervision to effectively learn from intra-inter subject differences. In intra subject self-supervision, ISL model first extracts heartbeat-level features from each subject using a channel-wise attentional CNN-RNN encoder. Then a stationarity test module is employed to capture the temporal dependencies between heartbeats. In inter subject self-supervision, we design a set of data augmentations according to the clinical characteristics of cardiac signals and perform contrastive learning among subjects to learn distinctive representations for various types of patients. Extensive experiments on three real-world datasets were conducted. In a semi-supervised transfer learning scenario, our pre-trained ISL model leads about 10% improvement over supervised training when only 1% labeled data is available, suggesting strong generalizability and robustness of the model.

Intra-Inter Subject Self-Supervised Learning for Multivariate Cardiac Signals

Off-policy learning plays a pivotal role in optimizing and evaluating policies prior to the online deployment. However, during the real-time serving, we observe varieties of interventions and constraints that cause inconsistency between the online and offline setting, which we summarize and term as runtime uncertainty. Such uncertainty cannot be learned from the logged data due to its abnormality and rareness nature. To assert a certain level of robustness, we perturb the off-policy estimators along an adversarial direction in view of the runtime uncertainty. It allows the resulting estimators to be robust not only to observed but also unexpected runtime uncertainties. Leveraging this idea, we bring runtime-uncertainty robustness to three major off-policy learning methods: the inverse propensity score method, reward-model method, and doubly robust method. We theoretically justify the robustness of our methods to runtime uncertainty, and demonstrate their effectiveness using both the simulation and the real-world online experiments.

Towards Robust Off-Policy Learning for Runtime Uncertainty

Using natural-language feedback to guide image generation and manipulation can greatly lower the required efforts and skills. This topic has received increased attention in recent years through refinement of Generative Adversarial Networks (GANs); however, most existing works are limited to single-round interaction, which is not reflective of real world interactive image editing workflows. Furthermore, previous works dealing with multi-round scenarios are limited to predefined feedback sequences, which is also impractical. In this paper, we propose a novel framework for Text-based Interactive image generation and manipulation (TiGAN) that responds to users' natural-language feedback. 
 TiGAN utilizes the powerful pre-trained CLIP model to understand users' natural-language feedback and exploits contrastive learning for a better text-to-image mapping. To maintain the image consistency during interactions, TiGAN generates intermediate feature vectors aligned with the feedback and selectively feeds these vectors to our proposed generative model. Empirical results on several datasets show that TiGAN improves both interaction efficiency and image quality while better avoids undesirable image manipulation during interactions.

Interactive Image Generation with Natural-Language Feedback

Temporal action segmentation classifies the action of each frame in (long) video sequences. Due to the high cost of frame-wise labeling, we propose the first semi-supervised method for temporal action segmentation. Our method hinges on unsupervised representation learning, which, for temporal action segmentation, poses unique challenges. Actions in untrimmed videos vary in length and have unknown labels and start/end times. Ordering of actions across videos may also vary. We propose a novel way to learn frame-wise representations from temporal convolutional networks (TCNs) by clustering input features with added time-proximity conditions and multi-resolution similarity. By merging representation learning with conventional supervised learning, we develop an "Iterative Contrast-Classify (ICC)'' semi-supervised learning scheme. With more labelled data, ICC progressively improves in performance; ICC semi-supervised learning, with 40% labelled videos, performs similarly to fully-supervised counterparts. Our ICC improves MoF by {+1.8, +5.6, +2.5}% on Breakfast, 50Salads, and GTEA respectively for 100% labelled videos.

Iterative Contrast-Classify for Semi-Supervised Temporal Action Segmentation

Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the function that are satisfied by the instance. One drawback of these works is that they do not explicitly treat scenarios where the underlying data is known to be constrained, e.g., certain combinations of features may not exist, may not be observable, or may be required to be disregarded. We propose a more general theory, also based on prime-implicants, tailored to taking constraints into account. The main idea is to view classifiers as describing partial Boolean functions that are undefined on instances that do not satisfy the constraints. We prove that this simple idea results in more parsimonious reasons. That is, not taking constraints into account (e.g., ignoring, or taking them as negative instances) results in reasons that are subsumed by reasons that do take constraints into account. We illustrate this improved succinctness on synthetic classifiers and classifiers learnt from real data.

Sufficient Reasons for Classifier Decisions in the Presence of Domain Constraints

Temporal action detection aims to locate the boundaries of action in the video. The current method based on boundary matching enumerates and calculates all possible boundary matchings to generate proposals. However, these methods neglect the long-range context aggregation in boundary prediction. At the same time, due to the similar semantics of adjacent matchings, local semantic aggregation of densely-generated matchings cannot improve semantic richness and discrimination. In this paper, we propose the end-to-end proposal generation method named Dual Context Aggregation Network (DCAN) to aggregate context on two levels, namely, boundary level and proposal level, for generating high-quality action proposals, thereby improving the performance of temporal action detection. Specifically, we design the Multi-Path Temporal Context Aggregation (MTCA) to achieve smooth context aggregation on boundary level and precise evaluation of boundaries. For matching evaluation, Coarse-to-fine Matching (CFM) is designed to aggregate context on the proposal level and refine the matching map from coarse to fine. We conduct extensive experiments on ActivityNet v1.3 and THUMOS-14. DCAN obtains an average mAP of 35.39% on ActivityNet v1.3 and reaches mAP 54.14% at IoU@0.5 on THUMOS-14, which demonstrates DCAN can generate high-quality proposals and achieve state-of-the-art performance. We release the code at https://github.com/cg1177/DCAN.

DCAN: Improving Temporal Action Detection via Dual Context Aggregation

A weak backdoor, or simply a backdoor, for a Boolean SAT formula F into a class of SAT formulae C is a partial truth assignment T such that F[T] is in C and satisfiability is preserved. The problem of finding a backdoor from class C1 into class C2, or WB(C1,C2), can be stated as follows: Given a formula F in C1, and a natural number k, determine whether there exists a backdoor for F into C2 assigning at most k variables. 
 
 The class 0-Val contains all Boolean formulae with at least one negative literal in each clause. We design a new algorithm for WB(3CNF, 0-Val) by reducing it to a local search variant of 3-SAT. We show that our algorithm runs in time O*(2.562^k), improving on the previous state-of-the-art of O*(2.85^k). Here, the O* notation is a variant of the big-O notation that allows to omit polynomial factors in the input size. 
 
 Next, we look at WB(3CNF, Null), where Null is the class consisting of the empty formula. This problem was known to have a trivial running time upper bound of O*(6^k) and can easily be solved in O*(3^k) time. We use a reduction to Conflict-Free-d-Hitting-Set to prove an upper bound of O*(2.2738^k), and also prove a lower bound of 2^o(k) assuming the Exponential Time Hypothesis. 
 
 Finally, Horn is the class of formulae with at most one positive literal per clause. We improve the previous O*(4.54^k) running time for WB(3CNF, Horn) problem to O*(4.17^k), by exploiting the structure of the SAT instance to give a novel proof of the non-existence of the slowest cases after a slight restructuring of the branching priorities.

Faster Algorithms for Weak Backdoors

We study the problem of allocating indivisible goods among strategic agents. We focus on settings wherein monetary transfers are not available and each agent's private valuation is a submodular function with binary marginals, i.e., the agents' valuations are matroid-rank functions. In this setup, we establish a notable dichotomy between two of the most well-studied fairness notions in discrete fair division; specifically, between envy-freeness up to one good (EF1) and maximin shares (MMS).   

First, we show that a known Pareto-efficient mechanism is group strategy-proof for finding EF1 allocations, under matroid-rank valuations. The group strategy-proofness guarantee strengthens an existing result that establishes truthfulness (individually for each agent) in the same context. Our result also generalizes prior work from binary additive valuations to the matroid-rank case.  

Next, we establish that an analogous positive result cannot be achieved for MMS, even when considering truthfulness on an individual level. Specifically, we prove that, for matroid-rank valuations, there does not exist a truthful mechanism that is index oblivious, Pareto efficient, and maximin fair.   

For establishing our results, we develop a characterization of truthful mechanisms for matroid-rank functions. This characterization in fact holds for a broader class of valuations (specifically, holds for binary XOS functions) and might be of independent interest.

Truthful and Fair Mechanisms for Matroid-Rank Valuations

In multiwinner approval voting, the goal is to select k-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large cohesive group of voters remains unrepresented. However, the JR axiom may conflict with other desiderata, such as coverage (maximizing the number of voters who approve at least one committee member) or social welfare (maximizing the number of approvals obtained by committee members). In this work, we investigate the impact of imposing the JR axiom (as well as the more demanding EJR axiom) on social welfare and coverage. Our approach is threefold: we derive worst-case bounds on the loss of welfare/coverage that is caused by imposing JR, study the computational complexity of finding 'good' committees that provide JR (obtaining a hardness result, an approximation algorithm, and an exact algorithm for one-dimensional preferences), and examine this setting empirically on several synthetic datasets.

The Price of Justified Representation

Relation prediction in knowledge graphs is dominated by embedding based methods which mainly focus on the transductive setting. Unfortunately, they are not able to handle inductive learning where unseen entities and relations are present and cannot take advantage of prior knowledge. Furthermore, their inference process is not easily explainable. In this work, we propose an all-in-one solution, called BERTRL (BERT-based Relational Learning), which leverages pre-trained language model and fine-tunes it by taking relation instances and their possible reasoning paths as training samples. BERTRL outperforms the SOTAs in 15 out of 18 cases in both inductive and transductive settings. Meanwhile, it demonstrates strong generalization capability in few-shot learning and is explainable. The data and code can be found at https://github.com/zhw12/BERTRL.

Downloads

Next from AAAI 2022

Intra-Inter Subject Self-Supervised Learning for Multivariate Cardiac Signals

Similar lecture

Satisfiability and Algorithms for Non-Uniform Random k-SAT

.css-70qvj9{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-align-items:center;-webkit-box-align:center;-ms-flex-align:center;align-items:center;}Downloads

Next from AAAI 2022

Intra-Inter Subject Self-Supervised Learning for Multivariate Cardiac Signals

Similar lecture

Satisfiability and Algorithms for Non-Uniform Random k-SAT

Downloads