Fermionic Symmetry Protected Topological Phases and Cobordisms

It has been proposed recently that interacting Symmetry Protected Topological (SPT) phases can be classified using cobordism theory. We test this proposal in the case of fermionic SPT phases with Z/2 symmetry, where Z/2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimension less than or equal to 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.Comment: 26 pages, new references added and a new section on decorated domain walls in v

Holographic entropy inequalities and gapped phases of matter

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area law. In particular, we find that all holographic entropy inequalities are valid in such systems. In gapped systems with topological order, the "cyclic inequalities" derived recently for the holographic entanglement entropy generalize the Kitaev-Preskill formula for the topological entanglement entropy. Finally, we propose a candidate linear inequality for general 4-party quantum states.Comment: 20 pages, 4 figures. v2: section 4 rewritten, where all linear entropy (in)equalities satisfied by area-law systems are derived and an error in their relations to graph theory is correcte

Continual Event Extraction with Semantic Confusion Rectification

We study continual event extraction, which aims to extract incessantly emerging event information while avoiding forgetting. We observe that the semantic confusion on event types stems from the annotations of the same text being updated over time. The imbalance between event types even aggravates this issue. This paper proposes a novel continual event extraction model with semantic confusion rectification. We mark pseudo labels for each sentence to alleviate semantic confusion. We transfer pivotal knowledge between current and previous models to enhance the understanding of event types. Moreover, we encourage the model to focus on the semantics of long-tailed event types by leveraging other associated types. Experimental results show that our model outperforms state-of-the-art baselines and is proficient in imbalanced datasets.Comment: Accepted in the 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP 2023

Differentially Private Vertical Federated Clustering

In many applications, multiple parties have private data regarding the same set of users but on disjoint sets of attributes, and a server wants to leverage the data to train a model. To enable model learning while protecting the privacy of the data subjects, we need vertical federated learning (VFL) techniques, where the data parties share only information for training the model, instead of the private data. However, it is challenging to ensure that the shared information maintains privacy while learning accurate models. To the best of our knowledge, the algorithm proposed in this paper is the first practical solution for differentially private vertical federated k-means clustering, where the server can obtain a set of global centers with a provable differential privacy guarantee. Our algorithm assumes an untrusted central server that aggregates differentially private local centers and membership encodings from local data parties. It builds a weighted grid as the synopsis of the global dataset based on the received information. Final centers are generated by running any k-means algorithm on the weighted grid. Our approach for grid weight estimation uses a novel, light-weight, and differentially private set intersection cardinality estimation algorithm based on the Flajolet-Martin sketch. To improve the estimation accuracy in the setting with more than two data parties, we further propose a refined version of the weights estimation algorithm and a parameter tuning strategy to reduce the final k-means utility to be close to that in the central private setting. We provide theoretical utility analysis and experimental evaluation results for the cluster centers computed by our algorithm and show that our approach performs better both theoretically and empirically than the two baselines based on existing techniques

EFormer: Enhanced Transformer towards Semantic-Contour Features of Foreground for Portraits Matting

The portrait matting task aims to extract an alpha matte with complete semantics and finely-detailed contours. In comparison to CNN-based approaches, transformers with self-attention allow a larger receptive field, enabling it to better capture long-range dependencies and low-frequency semantic information of a portrait. However, the recent research shows that self-attention mechanism struggle with modeling high-frequency information and capturing fine contour details, which can lead to bias while predicting the portrait's contours. To address the problem, we propose EFormer to enhance the model's attention towards semantic and contour features. Especially the latter, which is surrounded by a large amount of high-frequency details. We build a semantic and contour detector (SCD) to accurately capture the distribution of semantic and contour features. And we further design contour-edge extraction branch and semantic extraction branch for refining contour features and complete semantic information. Finally, we fuse the two kinds of features and leverage the segmentation head to generate the predicted portrait matte. Remarkably, EFormer is an end-to-end trimap-free method and boasts a simple structure. Experiments conducted on VideoMatte240K-JPEGSD and AIM datasets demonstrate that EFormer outperforms previous portrait matte methods.Comment: 17 pages, 6 figure

Topological Phases of Matter: Exactly Solvable Models and Classification

In this thesis, we study gapped topological phases of matter in systems with strong inter-particle interaction. They are challenging to analyze theoretically, because interaction not only gives rise to a plethora of phases that are otherwise absent, but also renders methods used to analyze non-interacting systems inadequate. By now, people have had a relatively systematic understanding of topological orders in two spatial dimensions. However, less is known about the higher dimensional cases. In Chapter 2, we will explore three dimensional long-range entangled topological orders in the framework of Walker-Wang models, which are a class of exactly solvable models for three-dimensional topological phases that are not known previously to be able to capture these phases. We find that they can represent a class of twisted discrete gauge theories, which were discovered using a different formalism. Meanwhile, a systematic theory of bosonic symmetry protected topological (SPT) phases in all spatial dimensions have been developed based on group cohomology. A generalization of the theory to group supercohomology has been proposed to classify and characterize fermionic SPT phases in all dimensions. However, it can only handle cases where the symmetry group of the system is a product of discrete unitary symmetries. Furthermore, the classification is known to be incomplete for certain symmetries. In Chapter 3, we will construct an exactly solvable model for the two-dimensional time-reversal-invariant topological superconductors, which could be valuable as a first attempt to a systematic understanding of strongly interacting fermionic SPT phases with anti-unitary symmetries in terms of exactly solvable models. In Chapter 4, we will propose an alternative classification of fermionic SPT phases using the spin cobordism theory, which hopefully can capture all the phases missing in the supercohomology classification. We test this proposal in the case of fermionic SPT phases with Z2 symmetry, where Z2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimensions less than or equal to 3.</p

Exactly solvable model for two-dimensional topological superconductors

In this paper, we present an exactly solvable model for two-dimensional topological superconductors with helical Majorana edge modes protected by time-reversal symmetry. Our construction is based on the idea of decorated domain walls and makes use of the Kasteleyn orientation on a two-dimensional lattice, which was used for the construction of the symmetry protected fermion phase with Z_2 symmetry by Tarantino et al. and Ware et al. By decorating the time-reversal domain walls with spinful Majorana chains, we are able to construct a commuting projector Hamiltonian with zero correlation length ground state wave function that realizes a strongly interacting version of the two-dimensional topological superconductor. From our construction, it can be seen that the T_2 = −1 transformation rule for the fermions is crucial for the existence of such a nontrivial phase; with T_2 = 1, our construction does not work

Twisted gauge theories in three-dimensional Walker-Wang models

Three-dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be “twisted,” in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized in models discovered by Dijkgraaf and Witten. A different framework to systematically construct three-dimensional topological phases was proposed by Walker and Wang and a series of examples have been studied. Can the Walker-Wang construction be used to realize the topological order in twisted gauge theories? This is not immediately clear because the Walker-Wang construction is based on a loop condensation picture while the Dijkgraaf-Witten theory is based on a membrane condensation picture. In this paper, we show that the answer to this question is Yes, by presenting an explicit construction of the Walker-Wang models which realize both the twisted and untwisted gauge theories with gauge group Z_2×Z_2. We identify the topological order of the models by performing modular transformations on the ground-state wave functions and show that the modular matrices exactly match those for the Z_2×Z_2 gauge theories. By relating the Walker-Wang construction to the Dijkgraaf-Witten construction, our result opens up a way to study twisted gauge theories with fermonic charges, and correspondingly strongly interacting fermionic symmetry protected topological phases and their surface states, through exactly solvable models