We derive a series of quantitative bulk-boundary correspondences for 3D bosonic and fermionic symmetry-protected topological (SPT) phases under the assumption that the surface is gapped, symmetric and topologically ordered, i.e., a symmetry-enriched
topological (SET) state. We consider those SPT phases that are protected by the mirror symmetry and continuous symmetries that form a group of $U(1)$, $SU(2)$ or $SO(3)$. In particular, the fermionic cases correspond to a crystalline version of 3D topological insulators and topological superconductors in the famous ten-fold-way classification, with the time-reversal symmetry replaced by the mirror symmetry and with strong interaction taken into account. For surface SETs, the most general interplay between symmetries and anyon excitations is considered. Based on the previously proposed dimension reduction and folding approaches, we re-derive the classification of bulk SPT phases and define a emph{complete} set of bulk topological invariants for every symmetry group under consideration, and then derive explicit expressions of the bulk invariants in terms of surface topological properties (such as topological spin, quantum dimension) and symmetry properties (such as mirror fractionalization, fractional charge or spin). These expressions are our quantitative bulk-boundary correspondences. Meanwhile, the bulk topological invariants can be interpreted as emph{anomaly indicators} for the surface SETs which carry t Hooft anomalies of the associated symmetries whenever the bulk is topologically non-trivial. Hence, the quantitative bulk-boundary correspondences provide an easy way to compute the t Hooft anomalies of the surface SETs. Moreover, our anomaly indicators are complete. Our derivations of the bulk-boundary correspondences and anomaly indicators are explicit and physically transparent.
In this work we investigate the decorated domain wall construction in bosonic group-cohomology symmetry-protected topological (SPT) phases and related quantum anomalies in bosonic topological phases. We first show that a general decorated domain wall
construction can be described mathematically as an Atiyah-Hirzebruch spectral sequence, where the terms on the $E_2$ page correspond to decorations by lower-dimensional SPT states at domain wall junctions. For bosonic group-cohomology SPT phases, the spectral sequence becomes the Lyndon-Hochschild-Serre (LHS) spectral sequence for ordinary group cohomology. We then discuss the physical interpretations of the differentials in the spectral sequence, particularly in the context of anomalous SPT phases and symmetry-enriched gauge theories. As the main technical result, we obtain a full description of the LHS spectral sequence concretely at the cochain level. The explicit formulae are then applied to explain Lieb-Schultz-Mattis theorems for SPT phases, and also derive a new LSM theorem for easy-plane spin model in a $pi$ flux lattice. We also revisit the classifications of symmetry-enriched 2D and 3D Abelian gauge theories using our results.
Extracting temporal relations (e.g., before, after, concurrent) among events is crucial to natural language understanding. Previous studies mainly rely on neural networks to learn effective features or manual-crafted linguistic features for temporal
relation extraction, which usually fail when the context between two events is complex or wide. Inspired by the examination of available temporal relation annotations and human-like cognitive procedures, we propose a new Temporal Graph Transformer network to (1) explicitly find the connection between two events from a syntactic graph constructed from one or two continuous sentences, and (2) automatically locate the most indicative temporal cues from the path of the two event mentions as well as their surrounding concepts in the syntactic graph with a new temporal-oriented attention mechanism. Experiments on MATRES and TB-Dense datasets show that our approach significantly outperforms previous state-of-the-art methods on both end-to-end temporal relation extraction and temporal relation classification.
This paper proposes a question-answering (QA) benchmark for spatial reasoning on natural language text which contains more realistic spatial phenomena not covered by prior work and is challenging for state-of-the-art language models (LM). We propose
a distant supervision method to improve on this task. Specifically, we design grammar and reasoning rules to automatically generate a spatial description of visual scenes and corresponding QA pairs. Experiments show that further pretraining LMs on these automatically generated data significantly improves LMs capability on spatial understanding, which in turn helps to better solve two external datasets, bAbI, and boolQ. We hope that this work can foster investigations into more sophisticated models for spatial reasoning over text.
We propose TRACIE, a novel temporal reasoning dataset that evaluates the degree to which systems understand implicit events -- events that are not mentioned explicitly in natural language text but can be inferred from it. This introduces a new challe
nge in temporal reasoning research, where prior work has focused on explicitly mentioned events. Human readers can infer implicit events via commonsense reasoning, resulting in a more comprehensive understanding of the situation and, consequently, better reasoning about time. We find, however, that state-of-the-art models struggle when predicting temporal relationships between implicit and explicit events. To address this, we propose a neuro-symbolic temporal reasoning model, SYMTIME, which exploits distant supervision signals from large-scale text and uses temporal rules to combine start times and durations to infer end times. SYMTIME outperforms strong baseline systems on TRACIE by 5%, and by 11% in a zero prior knowledge training setting. Our approach also generalizes to other temporal reasoning tasks, as evidenced by a gain of 1%-9% on MATRES, an explicit event benchmark.
High-quality and large-scale data are key to success for AI systems. However, large-scale data annotation efforts are often confronted with a set of common challenges: (1) designing a user-friendly annotation interface; (2) training enough annotators
efficiently; and (3) reproducibility. To address these problems, we introduce Crowdaq, an open-source platform that standardizes the data collection pipeline with customizable user-interface components, automated annotator qualification, and saved pipelines in a re-usable format. We show that Crowdaq simplifies data annotation significantly on a diverse set of data collection use cases and we hope it will be a convenient tool for the community.
Learning from indirect supervision signals is important in real-world AI applications when, often, gold labels are missing or too costly. In this paper, we develop a unified theoretical framework for multi-class classification when the supervision is
provided by a variable that contains nonzero mutual information with the gold label. The nature of this problem is determined by (i) the transition probability from the gold labels to the indirect supervision variables and (ii) the learners prior knowledge about the transition. Our framework relaxes assumptions made in the literature, and supports learning with unknown, non-invertible and instance-dependent transitions. Our theory introduces a novel concept called emph{separation}, which characterizes the learnability and generalization bounds. We also demonstrate the application of our framework via concrete novel results in a variety of learning scenarios such as learning with superset annotations and joint supervision signals.
Real-world applications often require improved models by leveraging a range of cheap incidental supervision signals. These could include partial labels, noisy labels, knowledge-based constraints, and cross-domain or cross-task annotations -- all havi
ng statistical associations with gold annotations but not exactly the same. However, we currently lack a principled way to measure the benefits of these signals to a given target task, and the common practice of evaluating these benefits is through exhaustive experiments with various models and hyperparameters. This paper studies whether we can, in a single framework, quantify the benefits of various types of incidental signals for a given target task without going through combinatorial experiments. We propose a unified PAC-Bayesian motivated informativeness measure, PABI, that characterizes the uncertainty reduction provided by incidental supervision signals. We demonstrate PABIs effectiveness by quantifying the value added by various types of incidental signals to sequence tagging tasks. Experiments on named entity recognition (NER) and question answering (QA) show that PABIs predictions correlate well with learning performance, providing a promising way to determine, ahead of learning, which supervision signals would be beneficial.
Temporal common sense (e.g., duration and frequency of events) is crucial for understanding natural language. However, its acquisition is challenging, partly because such information is often not expressed explicitly in text, and human annotation on
such concepts is costly. This work proposes a novel sequence modeling approach that exploits explicit and implicit mentions of temporal common sense, extracted from a large corpus, to build TACOLM, a temporal common sense language model. Our method is shown to give quality predictions of various dimensions of temporal common sense (on UDST and a newly collected dataset from RealNews). It also produces representations of events for relevant tasks such as duration comparison, parent-child relations, event coreference and temporal QA (on TimeBank, HiEVE and MCTACO) that are better than using the standard BERT. Thus, it will be an important component of temporal NLP.
Abelian Chern-Simons theory, characterized by the so-called $K$ matrix, has been quite successful in characterizing and classifying Abelian fractional quantum hall effect (FQHE) as well as symmetry protected topological (SPT) phases, especially for b
osonic SPT phases. However, there are still some puzzles in dealing with fermionic SPT(fSPT) phases. In this paper, we utilize the Abelian Chern-Simons theory to study the fSPT phases protected by arbitrary Abelian total symmetry $G_f$. Comparing to the bosonic SPT phases, fSPT phases with Abelian total symmetry $G_f$ has three new features: (1) it may support gapless majorana fermion edge modes, (2) some nontrivial bosonic SPT phases may be trivialized if $G_f$ is a nontrivial extention of bosonic symmetry $G_b$ over $mathbb{Z}_2^f$, (3) certain intrinsic fSPT phases can only be realized in interacting fermionic system. We obtain edge theories for various fSPT phases, which can also be regarded as conformal field theories (CFT) with proper symmetry anomaly. In particular, we discover the construction of Luttinger liquid edge theories with central charge $n-1$ for Type-III bosonic SPT phases protected by $(mathbb{Z}_n)^3$ symmetry and the Luttinger liquid edge theories for intrinsically interacting fSPT protected by unitary Abelian symmetry. The ideas and methods used here might be generalized to derive the edge theories of fSPT phases with arbitrary unitary finite Abelian total symmetry $G_f$.
