Engineering Holographic Superconductor Phase Diagrams

We study how to engineer holographic models with features of a high temperature superconductor phase diagram. We introduce a field in the bulk which provides a tunable "doping" parameter in the boundary theory. By designing how this field changes the effective masses of other order parameter fields, desired phase diagrams can be engineered. We give examples of generating phase diagrams with phase boundaries similar to a superconducting dome and an anti-ferromagnetic phase by including two order parameter fields. We also explore whether the pseudo gap phase can be described without adding another order parameter field and discuss the potential scaling symmetry associated with a quantum critical point hidden under the superconducting dome in this phase diagram.Comment: 25 pages, 7 figure

Towards Searching for Entangled Photons in the CMB Sky

We explore the possibility of detecting entangled photon pairs from cosmic microwave background or other cosmological sources coming from two patches of the sky. The measurements use two detectors with different photon polarizer directions. When two photon sources are separated by a large angle relative to the earth, such that each detector has only one photon source in its field of view, a null test of unentangled photons can be performed. The deviation from this unentangled background is, in principle, the signature of photon entanglement. To confirm whether the deviation is consistent with entangled photons, we derive a photon polarization correlation to compare with, similar to that in a Bell inequality measurement. However, since photon coincidence measurement cannot be used to discriminate unentangled cosmic photons, it is unlikely that the correlation expectation value alone can violate Bell inequality to provide the signature for entanglement.Comment: 5 pages, 2 figure; references added, typos fixed. v3 revised version with more discussions on detection possibilities; added references.v4 published version in PR

Concept-wise Fine-tuning Matters in Preventing Negative Transfer

A multitude of prevalent pre-trained models mark a major milestone in the development of artificial intelligence, while fine-tuning has been a common practice that enables pretrained models to figure prominently in a wide array of target datasets. Our empirical results reveal that off-the-shelf finetuning techniques are far from adequate to mitigate negative transfer caused by two types of underperforming features in a pre-trained model, including rare features and spuriously correlated features. Rooted in structural causal models of predictions after fine-tuning, we propose a Concept-wise fine-tuning (Concept-Tuning) approach which refines feature representations in the level of patches with each patch encoding a concept. Concept-Tuning minimizes the negative impacts of rare features and spuriously correlated features by (1) maximizing the mutual information between examples in the same category with regard to a slice of rare features (a patch) and (2) applying front-door adjustment via attention neural networks in channels and feature slices (patches). The proposed Concept-Tuning consistently and significantly (by up to 4.76%) improves prior state-of-the-art fine-tuning methods on eleven datasets, diverse pre-training strategies (supervised and self-supervised ones), various network architectures, and sample sizes in a target dataset

Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements

This paper delves into the world of high-order curl and div elements within finite element methods, providing valuable insights into their geometric properties, indexing management, and practical implementation considerations. It first explores the decomposition of Lagrange finite elements. The discussion then extends to H(div)-conforming finite elements and H(curl)-conforming finite element spaces by choosing different frames at different sub-simplex. The required tangential continuity or normal continuity will be imposed by appropriate choices of the tangential and normal basis. The paper concludes with a focus on efficient indexing management strategies for degrees of freedom, offering practical guidance to researchers and engineers. It serves as a comprehensive resource that bridges the gap between theory and practice in the realm of high-order curl and div elements in finite element methods, which are vital for solving vector field problems and understanding electromagnetic phenomena.Comment: 25 pages, 8 figure

Frustratingly Easy Transferability Estimation

Transferability estimation has been an essential tool in selecting a pre-trained model and the layers of it to transfer, so as to maximize the performance on a target task and prevent negative transfer. Existing estimation algorithms either require intensive training on target tasks or have difficulties in evaluating the transferability between layers. We propose a simple, efficient, and effective transferability measure named TransRate. With single pass through the target data, TransRate measures the transferability as the mutual information between the features of target examples extracted by a pre-trained model and labels of them. We overcome the challenge of efficient mutual information estimation by resorting to coding rate that serves as an effective alternative to entropy. TransRate is theoretically analyzed to be closely related to the performance after transfer learning. Despite its extraordinary simplicity in 10 lines of codes, TransRate performs remarkably well in extensive evaluations on 22 pre-trained models and 16 downstream tasks