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We theoretically investigate twisted structures where each layer is composed of a strongly correlated material. In particular, we study a twisted t-J model of cuprate multilayers within the slave-boson mean field theory. This treatment encompasses th e Mott physics at small doping and self consistently generates d-wave pairing. Furthermore, including the correct inter-layer tunneling form factor consistent with the symmetry of the Cu $d_{x^2-y^2}$ orbital proves to be crucial for the phase diagram. We find spontaneous time reversal (T) breaking around twist angle of $45^circ$, although only in a narrow window of twist angles. Moreover, the gap obtained is small and the Chern number vanishes, implying a non-topological superconductor. At smaller twist angles, driving an interlayer current however can lead to a gapped topological phase. The energy-phase relation of the interlayer Josephson junction displays notable double-Cooper-pair tunneling which dominates around $45^o$. The twist angle dependence of the Josephson critical current and the Shapiro steps are consistent with recent experiments. Utilizing the moire structure as a probe of correlation physics, in particular of the pair density wave state, is discussed.
We propose 3DETR, an end-to-end Transformer based object detection model for 3D point clouds. Compared to existing detection methods that employ a number of 3D-specific inductive biases, 3DETR requires minimal modifications to the vanilla Transformer block. Specifically, we find that a standard Transformer with non-parametric queries and Fourier positional embeddings is competitive with specialized architectures that employ libraries of 3D-specific operators with hand-tuned hyperparameters. Nevertheless, 3DETR is conceptually simple and easy to implement, enabling further improvements by incorporating 3D domain knowledge. Through extensive experiments, we show 3DETR outperforms the well-established and highly optimized VoteNet baselines on the challenging ScanNetV2 dataset by 9.5%. Furthermore, we show 3DETR is applicable to 3D tasks beyond detection, and can serve as a building block for future research.
223 - Mariana Vicaria 2021
In this paper we study elimination of imaginaries in some classes of henselian valued fields of equicharacteristic zero and residue field algebraically closed. The results are sensitive to the complexity of the value group. We focus first in the case where the ordered abelian group has finite spines, and then prove a better result for the dp-minimal case. An ordered abelian with finite spines weakly eliminates imaginaries once we add sorts for the quotient groups $Gamma/ Delta$ for each definable convex subgroup $Delta$, and sorts for the quotient groups $Gamma/ Delta+ lGamma$ where $Delta$ is a definable convex subgroup and $l in mathbb{N}_{geq 2}$. We refer to these sorts as the quotient sorts. We prove the following two theorems: Theorem: Let $K$ be a valued field of equicharacteristic zero, residue field algebraically closed and value group with finite spines. Then $K$ admits weak elimination of imaginaries once we add codes for all the definable $mathcal{O}$-submodules of $K^{n}$ for each $n in mathbb{N}$, and the quotient sorts for the value group. Theorem: Let $K$ be a henselian valued field of equicharacteristic zero, residue field algebraically closed and dp-minimal value group. Then $K$ eliminates imaginaries once we add codes for all the definable $mathcal{O}$-submodules of $K^{n}$ for each $n in mathbb{N}$, the quotient sorts for the value group and constants to distinguish representatives of the cosets of $Delta+lGamma$ in $Gamma$, where $Delta$ is a convex definable subgroup and $l in mathbb{N}_{geq 2}$.
We consider adversarial machine learning based attacks on power allocation where the base station (BS) allocates its transmit power to multiple orthogonal subcarriers by using a deep neural network (DNN) to serve multiple user equipments (UEs). The D NN that corresponds to a regression model is trained with channel gains as the input and allocated transmit powers as the output. While the BS allocates the transmit power to the UEs to maximize rates for all UEs, there is an adversary that aims to minimize these rates. The adversary may be an external transmitter that aims to manipulate the inputs to the DNN by interfering with the pilot signals that are transmitted to measure the channel gain. Alternatively, the adversary may be a rogue UE that transmits fabricated channel estimates to the BS. In both cases, the adversary carefully crafts adversarial perturbations to manipulate the inputs to the DNN of the BS subject to an upper bound on the strengths of these perturbations. We consider the attacks targeted on a single UE or all UEs. We compare these attacks with a benchmark, where the adversary scales down the input to the DNN. We show that adversarial attacks are much more effective than the benchmark attack in terms of reducing the rate of communications. We also show that adversarial attacks are robust to the uncertainty at the adversary including the erroneous knowledge of channel gains and the potential errors in exercising the attacks exactly as specified.
While in two-player zero-sum games the Nash equilibrium is a well-established prescriptive notion of optimal play, its applicability as a prescriptive tool beyond that setting is limited. Consequently, the study of decentralized learning dynamics tha t guarantee convergence to correlated solution concepts in multiplayer, general-sum extensive-form (i.e., tree-form) games has become an important topic of active research. The per-iteration complexity of the currently known learning dynamics depends on the specific correlated solution concept considered. For example, in the case of extensive-form correlated equilibrium (EFCE), all known dynamics require, as an intermediate step at each iteration, to compute the stationary distribution of multiple Markov chains, an expensive operation in practice. Oppositely, in the case of normal-form coarse correlated equilibrium (NFCCE), simple no-external-regret learning dynamics that amount to a linear-time traversal of the tree-form decision space of each agent suffice to guarantee convergence. This paper focuses on extensive-form coarse correlated equilibrium (EFCCE), an intermediate solution concept that is a subset of NFCCE and a superset of EFCE. Being a superset of EFCE, any learning dynamics for EFCE automatically guarantees convergence to EFCCE. However, since EFCCE is a simpler solution concept, this begs the question: do learning dynamics for EFCCE that avoid the expensive computation of stationary distributions exist? This paper answers the previous question in the positive. Our learning dynamics only require the orchestration of no-external-regret minimizers, thus showing that EFCCE is more akin to NFCCE than to EFCE from a learning perspective. Our dynamics guarantees that the empirical frequency of play after $T$ iteration is a $O(1/sqrt{T})$-approximate EFCCE with high probability, and an EFCCE almost surely in the limit.
Let S be a smooth del Pezzo surface that is defined over a field K and splits over a Galois extension L. Let G be either the split reductive group given by the root system of $S_L$ in Pic $S_L$, or a form of it containing the Neron-Severi torus. Let $mathcal{G}$ be the G-torsor over $S_L$ obtained by extension of structure group from a universal torsor $mathcal{T}$ over $S_L$. We prove that $mathcal{G}$ does not descend to S unless $mathcal{T}$ does. This is in contrast to a result of Friedman and Morgan that such $mathcal{G}$ always descend to singular del Pezzo surfaces over $mathbb{C}$ from their desingularizations.
Antiferromagnets (AFMs) with zero net magnetization are proposed as active elements in future spintronic devices. Depending on the critical thickness of the AFM thin films and the measurement temperature, bimetallic Mn-based alloys and transition met al oxide-based AFMs can host various coexisting ordered, disordered, and frustrated AFM phases. Such coexisting phases in the exchange coupled ferromagnetic (FM)/AFM-based heterostructures can result in unusual magnetic and magnetotransport phenomena. Here, we integrate chemically disordered AFM IrMn3 thin films with coexisting AFM phases into complex exchange coupled MgO(001)/Ni3Fe/IrMn3/Ni3Fe/CoO heterostructures and study the structural, magnetic, and magnetotransport properties in various magnetic field cooling states. In particular, we unveil the impact of rotating the relative orientation of the disordered and reversible AFM moments with respect to the irreversible AFM moments on the magnetic and magnetoresistance properties of the exchange coupled heterostructures. We further found that the persistence of AFM grains with thermally disordered and reversible AFM order is crucial for achieving highly tunable magnetic properties and multi-level magnetoresistance states. We anticipate that the introduced approach and the heterostructure architecture can be utilized in future spintronic devices to manipulate the thermally disordered and reversible AFM order at the nanoscale.
456 - Tobias Barthel 2021
We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case established in c elebrated work of Benson, Iyengar, and Krause. Further consequences include a verification of the generalized telescope conjecture in this context, a tensor product formula for integral cohomological support, as well as a generalization of Quillens stratification theorem for group cohomology. Our proof makes use of novel descent techniques for stratification in tensor-triangular geometry that are of independent interest.
In batch reinforcement learning, there can be poorly explored state-action pairs resulting in poorly learned, inaccurate models and poorly performing associated policies. Various regularization methods can mitigate the problem of learning overly-comp lex models in Markov decision processes (MDPs), however they operate in technically and intuitively distinct ways and lack a common form in which to compare them. This paper unifies three regularization methods in a common framework -- a weighted average transition matrix. Considering regularization methods in this common form illuminates how the MDP structure and the state-action pair distribution of the batch data set influence the relative performance of regularization methods. We confirm intuitions generated from the common framework by empirical evaluation across a range of MDPs and data collection policies.
Dense retrieval methods have shown great promise over sparse retrieval methods in a range of NLP problems. Among them, dense phrase retrieval-the most fine-grained retrieval unit-is appealing because phrases can be directly used as the output for que stion answering and slot filling tasks. In this work, we follow the intuition that retrieving phrases naturally entails retrieving larger text blocks and study whether phrase retrieval can serve as the basis for coarse-level retrieval including passages and documents. We first observe that a dense phrase-retrieval system, without any retraining, already achieves better passage retrieval accuracy (+3-5% in top-5 accuracy) compared to passage retrievers, which also helps achieve superior end-to-end QA performance with fewer passages. Then, we provide an interpretation for why phrase-level supervision helps learn better fine-grained entailment compared to passage-level supervision, and also show that phrase retrieval can be improved to achieve competitive performance in document-retrieval tasks such as entity linking and knowledge-grounded dialogue. Finally, we demonstrate how phrase filtering and vector quantization can reduce the size of our index by 4-10x, making dense phrase retrieval a practical and versatile solution in multi-granularity retrieval.
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