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Adapters have been widely explored to alleviate computational and storage costs when fine-tuning pretrained foundation models. However, the adapter itself can exhibit redundancy, leading to unnecessary storage overhead and inferior performance. In this paper, we propose Prune and Share (Pear), a novel adapter-pruning framework for efficient fine-tuning of pretrained visual foundation models. Specifically, we prune certain adapters and share the more important unpruned ones with positions where adapters are pruned, allowing continual adaptation at these positions after pruning. Additionally, a knowledge checkpoint strategy is introduced, which preserves the information of the pruned adapters and further boosts performance. Experimental results on visual adaptation benchmark validate the effectiveness and efficiency of the proposed Pear comparing to other competitive methods. Code is in https://github.com/yibozhong/pear.

This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the Lindblad master equation, alongside a review of typical non-Hermitian free-fermion systems that exhibit unique features. A pedagogical discussion is provided on the relationship between entanglement quantities and the correlation matrix in Hermitian systems. Building on this foundation, we focus on how entanglement concepts are extended to non-Hermitian systems from their Hermitian free-fermion counterparts, with a review of the general properties that emerge. Finally, we highlight various concrete studies, demonstrating that entanglement entropy remains a powerful diagnostic tool for characterizing non-Hermitian physics. The entanglement spectrum also reflects the topological characteristics of non-Hermitian topological systems, while unique non-Hermitian entanglement behaviors are also discussed. The review is concluded with several future directions. Through this review, we hope to provide a useful guide for researchers who are interested in entanglement in non-Hermitian quantum systems., Comment: A Topical Review of the Interplay of Entanglement and Non-Hermitian Physics (to appear in the Special Issue of Non-Hermitian Physics in Chin. Phys. Lett.). version 3; ~15p, 1figure, texts and refs. updated, approximate to final version

Recently, tight-binding models on hyperbolic lattices (discretized AdS space), have gained significant attention, leading to hyperbolic band theory and non-Abelian Bloch states. In this paper, we investigate these quantum systems from the perspective of quantum information, focusing particularly on the scaling of entanglement entropy (EE) that has been regarded as a powerful quantum-information probe into exotic phases of matter. It is known that on $d$-dimensional translation-invariant Euclidean lattice, the EE of band insulators scales as an area law ($\sim L^{d-1}$; $L$ is the linear size of the boundary between two subsystems). Meanwhile, the EE of metals (with finite Density-of-State, i.e., DOS) scales as the renowned Gioev-Klich-Widom scaling law ($\sim L^{d-1}\log L$). The appearance of logarithmic divergence, as well as the analytic form of the coefficient $c$ is mathematically controlled by the Widom conjecture of asymptotic behavior of Toeplitz matrices and can be physically understood via the Swingle's argument. However, the hyperbolic lattice, which generalizes translational symmetry, results in inapplicability of the Widom conjecture and thus presents significant analytic difficulties. Here we make an initial attempt through numerical simulation. Remarkably, we find that both cases adhere to the area law, indicating that the logarithmic divergence arising from finite DOS is suppressed by the background hyperbolic geometry. To achieve the results, we first apply the vertex inflation method to generate hyperbolic lattice on the Poincar\'{e} disk, and then apply the Haydock recursion method to compute DOS. Finally, we study the scaling of EE for different bipartitions via exact diagonalization and perform finite-size scaling. We also investigate how the coefficient of the area law is correlated to bulk gap and DOS. Future directions are discussed., Comment: 15 pages, 11 figures

Low-rank adaptation (LoRA) is a powerful parameter-efficient fine-tuning method that utilizes low-rank projectors $A$ and $B$ to learn weight updates $\Delta W$ for adaptation targets $W$. Previous research has shown that LoRA is essentially a gradient compressor, performing random projections on the gradient using a fixed projection matrix $A_0$. However, this setup restricts the overall weight update to be low-rank, which limits the adaptation performance. In this paper, we propose low-rank interconnected adaptation across layers (Lily). Specifically, we employ a hierarchical framework where low-dimensional projectors (LPs) retained for downward projection at a particular level, while globally-shared high-dimensional projector (HP) experts perform upward projection across all levels of layers. Lily uniquely connects each LP to all HP experts, therefore the gradient projections are no longer dominated by fixed projection matrices, but rather by selective combinations of all the projectors, thereby breaking the low-rank constraint of LoRA. Furthermore, Lily's cross-layer connections facilitate the capture of intricate information and dependencies across different layers, thereby enhancing the model's representational capabilities. Experiments across various modalities, architectures, and model sizes underscore Lily's great performance and efficiency. Code is available on github https://github.com/yibozhong/lily., Comment: 26 pages

In this paper, we theoretically study a class of 3D non-liquid states that show exotic boundary phenomena in the thermodynamical limit. More concretely, we focus on a class of 3D fracton topological orders formed via stacking 2D twisted \(\mathbb{Z}_N\) topologically ordered layers along \(z\)-direction. Nearby layers are coupled while maintaining translation symmetry along \(z\) direction. The effective field theory is given by the infinite-component Chern-Simons (iCS) field theory, with an integer-valued symmetric block-tridiagonal Toeplitz \(K\)-matrix whose size is thermodynamically large. With open boundary conditions (OBC) along \(z\), certain choice of \(K\)-matrices exhibits exotic boundary ``Toeplitz braiding'', where the mutual braiding phase angle between two anyons at opposite boundaries oscillates and remains non-zero in the thermodynamic limit. In contrast, in trivial case, the mutual braiding phase angle decays exponentially to zero in the thermodynamical limit. As a necessary condition, this phenomenon requires the existence of boundary zero modes in the \(K\)-matrix spectrum under OBC. We categorize nontrivial \(K\)-matrices into two distinct types. Each type-I possesses two boundary zero modes, whereas each type-II possesses only one boundary zero mode. Interestingly, the integer-valued Hamiltonian matrix of the familiar 1D SSH can be used as a non-trivial $K$-matrix. Importantly, since large-gauge-invariance ensures integer quantized \(K\)-matrix entries, global symmetries are not needed to protect these zero modes. We also present numerical simulation as well as finite size scaling, further confirming the above analytical results. Symmetry fractionalization is also discussed.

Low-rank adaptation (LoRA) has shifted the paradigm of adapting pre-trained Vision Transformers (ViT), achieving great efficiency by updating only a subset of tailored parameters to approximate weight updates. However, the multi-head design of the self-attention mechanism, with the heads working in parallel in the computation flow, exhibiting similar visual patterns and requiring update over all of them, incurs unnecessary storage and computational overhead. In this paper, we propose Head-level responsiveness tuning for low-rank adaptation (Heart-LoRA). The proposed method explores redundancy among the heads and selectively activates task-responsive heads, thus enabling fine-grained head-level tuning. Additionally, given the different responsiveness of heads to diverse visual tasks, our proposed method dynamically activates a subset of the approximated heads that are tailored to the current task. Experimental results show that Heart-LoRA yields superior performance over state-of-the-art PETL approaches on visual adaptation benchmark datasets.

To examine the robustness of the designed 5% $\beta$-limit for high-performance operation in the W7-X stellarator, we undertake nonlinear magnetohydrodynamic (MHD) simulations of pressure-driven instabilities using the M3D-$C^1$ code. Consistent with linear analyses, ideal ballooning instabilities occur as $\beta$ exceeds 5% in the standard configuration. Nonetheless, the modes saturate nonlinearly at relatively low levels without triggering large-scale crashes, even though confinement degradation worsens as $\beta$ increases. In contrast, in an alternative configuration with nearly zero magnetic shear, ideal interchange modes induce a pressure crash at $\beta= 1\%$. These results suggest that the standard W7-X configuration might have a soft $\beta$-limit that is fairly immune to major MHD events, which enhances the appeal of the stellarator approach to steady-state fusion reactors., Comment: 6 pages, 5 figures

The session-based recommendation (SBR) garners increasing attention due to its ability to predict anonymous user intents within limited interactions. Emerging efforts incorporate various kinds of side information into their methods for enhancing task performance. In this survey, we thoroughly review the side information-driven session-based recommendation from a data-centric perspective. Our survey commences with an illustration of the motivation and necessity behind this research topic. This is followed by a detailed exploration of various benchmarks rich in side information, pivotal for advancing research in this field. Moreover, we delve into how these diverse types of side information enhance SBR, underscoring their characteristics and utility. A systematic review of research progress is then presented, offering an analysis of the most recent and representative developments within this topic. Finally, we present the future prospects of this vibrant topic., Comment: This is a survey on side information-driven session-based recommendation

Quantum key distribution (QKD) could help to share secure key between two distant peers. In recent years, twin-field (TF) QKD has been widely investigated because of its long transmission distance. One of the popular variants of TF QKD is sending-or-not-sending (SNS) QKD, which has been experimentally verified to realize 1000-km level fibre key distribution. In this article, the authors introduce phase postselection into the SNS protocol. With this modification, the probability of selecting "sending" can be substantially improved. The numerical simulation shows that the transmission distance can be improved both with and without the actively odd-parity pairing method. With discrete phase randomization, the variant can have both a larger key rate and a longer distance.

Entanglement entropy is a fundamental concept with rising importance in different fields ranging from quantum information science, black holes to materials science. In complex materials and systems, entanglement entropy provides insight into the collective degrees of freedom that underlie the systems' complex behaviours. As well-known predictions, the entanglement entropy exhibits area laws for systems with gapped excitations, whereas it follows the Gioev-Klich-Widom scaling law in gapless fermion systems. Furthermore, the entanglement spectrum provides salient characterizations of topological phases and phase transitions beyond the conventional paradigms. However, many of these fundamental predictions have not yet been confirmed in experiments due to the difficulties in measuring entanglement entropy in physical systems. Here, we report the experimental verification of the above predictions by probing the nonlocal correlations in phononic systems. From the pump-probe responses in phononic crystals, we obtain the entanglement entropy and entanglement spectrum for phononic systems with the fermion filling analog. With these measurements, we verify the Gioev-Klich-Widom scaling law of entanglement entropy for various quasiparticle dispersions in one- and two-dimensions. Moreover, we observe the salient signatures of topological phases in the entanglement spectrum and entanglement entropy which unveil an unprecedented probe of topological phases without relying on the bulk-boundary correspondence. The progress here opens a frontier where entanglement entropy serves as an important experimental tool in the study of emergent phases and phase transitions which can be generalized to non-Hermitian and other unconventional regimes.

Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate serves as a critical indicator of information leakage and directly influences the security of the shared key bits between communicating parties, Alice and Bob. In estimating the upper bound of the phase error rate, phase randomization and subsequent postselection mechanisms serve pivotal roles across numerous QKD protocols. Here we make a precise phase error rate analysis for QKD protocols with phase postselection, which helps us to accurately bound the amount of information an eavesdropper may obtain. We further apply our analysis in sending-or-not-sending twin-field quantum key distribution (SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation results confirm that our precise phase error analysis can noticeably improve the key rate performance especially over long distances in practice. Note that our method does not require alterations to the existing experimental hardware or protocol steps. It can be readily applied within current SNS-TF-QKD and MP-QKD for higher key rate generation.

Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent limitations. In this work, we introduce the \textit{hyperfine structure of entanglement}, which dissects entanglement contours known as the fine structure into particle-number cumulants. This measure exhibits a set of universal properties with its significance in quantum information science. We apply it across diverse contexts: in Fermi gases, establishing connections to mutual information and interacting conformal field theory; in AdS$_3$/CFT$_2$ holographic duality, unveiling finer subregion-subregion duality and extending bulk reconstruction; and in Chern insulators, distinguishing between different quantum phases. Our findings suggest experimental accessibility, offering fresh insights into quantum entanglement across physical systems., Comment: title changed

We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on Sierpinski carpet, we uncover intriguing findings. For gapless ground states exhibiting a finite density of states at the chemical potential, we reveal a super-area law characterized by the presence of a logarithmic correction for area law in the scaling of entanglement entropy. This extends the well-established super-area law observed on translationally invariant Euclidean lattices where the Gioev-Klich-Widom conjecture regarding the asymptotic behavior of Toeplitz matrices holds significant influence. Furthermore, different from the fractal structure of the lattice, we observe the emergence of a novel self-similar and universal pattern termed an ``entanglement fractal'' in the entanglement contour data as we approach the scaling limit. Remarkably, this pattern bears resemblance to intricate Chinese paper-cutting designs. We provide general rules to artificially generate this fractal, offering insights into the universal scaling of entanglement entropy. Meanwhile, as the direct consequence of the entanglement fractal and beyond a single scaling behavior of entanglement contour in translation-invariant systems, we identify two distinct scaling behaviors in the entanglement contour of fractal systems. For gapped ground states, we observe that the entanglement entropy adheres to a generalized area law, with its dependence on the Hausdorff dimension of the boundary between complementary subsystems.

It is a long-standing challenge in modern recommender systems to effectively make recommendations for new users, namely the cold-start problem. Cross-Domain Recommendation (CDR) has been proposed to address this challenge, but current ways to represent users' interests across systems are still severely limited. We introduce Personal Knowledge Graph (PKG) as a domain-invariant interest representation, and propose a novel CDR paradigm named MeKB-Rec. We first link users and entities in a knowledge base to construct a PKG of users' interests, named MeKB. Then we learn a semantic representation of MeKB for the cross-domain recommendation. To efficiently utilize limited training data in CDR, MeKB-Rec employs Pretrained Language Models to inject world knowledge into understanding users' interests. Beyond most existing systems, our approach builds a semantic mapping across domains which breaks the requirement for in-domain user behaviors, enabling zero-shot recommendations for new users in a low-resource domain. We experiment MeKB-Rec on well-established public CDR datasets, and demonstrate that the new formulation % is more powerful than previous approaches, achieves a new state-of-the-art that significantly improves HR@10 and NDCG@10 metrics over best previous approaches by 24\%--91\%, with a 105\% improvement for HR@10 of zero-shot users with no behavior in the target domain. We deploy MeKB-Rec in WeiXin recommendation scenarios and achieve significant gains in core online metrics. MeKB-Rec is now serving hundreds of millions of users in real-world products., Comment: 13 pages, 4 figures, conference

With the recent progress in large-scale vision and language representation learning, Vision Language Pre-training (VLP) models have achieved promising improvements on various multi-modal downstream tasks. Albeit powerful, these models have not fully leveraged world knowledge to their advantage. A key challenge of knowledge-augmented VLP is the lack of clear connections between knowledge and multi-modal data. Moreover, not all knowledge present in images/texts is useful, therefore prior approaches often struggle to effectively integrate knowledge, visual, and textual information. In this study, we propose REtrieval-based knowledge Augmented Vision Language (REAVL), a novel knowledge-augmented pre-training framework to address the above issues. For the first time, we introduce a knowledge-aware self-supervised learning scheme that efficiently establishes the correspondence between knowledge and multi-modal data and identifies informative knowledge to improve the modeling of alignment and interactions between visual and textual modalities. By adaptively integrating informative knowledge with visual and textual information, REAVL achieves new state-of-the-art performance uniformly on knowledge-based vision-language understanding and multi-modal entity linking tasks, as well as competitive results on general vision-language tasks while only using 0.2% pre-training data of the best models. Our model shows strong sample efficiency and effective knowledge utilization., Comment: arXiv admin note: text overlap with arXiv:2210.09338 by other authors

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $\delta$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schl\"uter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schl\"uter current density scaling as $J\sim1/\Delta\iota$, where $\Delta\iota$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $\Delta\iota$, the scaling relation $J\sim1/\Delta\iota\sim1/s$ will lead to a paradox that the Pfirsch--Schl\"uter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schl\"uter current density but also the diamagnetic current density are divergent as $\sim1/\Delta\iota$. However, due to the formation of a Dirac $\delta$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(\Delta\iota)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox., Comment: Minor corrections of typos

Complementary recommendation gains increasing attention in e-commerce since it expedites the process of finding frequently-bought-with products for users in their shopping journey. Therefore, learning the product representation that can reflect this complementary relationship plays a central role in modern recommender systems. In this work, we propose a logical reasoning network, LOGIREC, to effectively learn embeddings of products as well as various transformations (projection, intersection, negation) between them. LOGIREC is capable of capturing the asymmetric complementary relationship between products and seamlessly extending to high-order recommendations where more comprehensive and meaningful complementary relationship is learned for a query set of products. Finally, we further propose a hybrid network that is jointly optimized for learning a more generic product representation. We demonstrate the effectiveness of our LOGIREC on multiple public real-world datasets in terms of various ranking-based metrics under both low-order and high-order recommendation scenarios., Comment: 6 pages, 3 figures

Quantum key distribution (QKD) allows two remote parties to share information-theoretically secure keys. In recent years, a revolutionary breakthrough called twin-field (TF) QKD has been developed to overcome the linear key-rate constraint and greatly increases the achievable distance. Phase-randomization and subsequent postselection play important roles in its security proof. Later, no-phase-postselection TF-QKD was proposed and became a popular variant, since the removal of phase postselection leads to a higher key rate. However, the achievable distance is decreased compared to the original one. Here, we propose a TF-QKD protocol with partial phase postselection. Namely, its code mode is still free from global phase randomization and postselection to make sure the advantage of the high key rate remains. On other hand, phase postselection is introduced in the decoy mode to improve the performance. Applying an operator dominance condition, we prove universal security of the proposed protocol in the finite-key case under coherent attacks, and numerical simulations confirm its potential advantages in terms of key rate and achievable distance.