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We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems.

The historical interaction sequences of users plays a crucial role in training recommender systems that can accurately predict user preferences. However, due to the arbitrariness of user behavior, the presence of noise in these sequences poses a challenge to predicting their next actions in recommender systems. To address this issue, our motivation is based on the observation that training noisy sequences and clean sequences (sequences without noise) with equal weights can impact the performance of the model. We propose a novel self-supervised Auxiliary Task Joint Training (ATJT) method aimed at more accurately reweighting noisy sequences in recommender systems. Specifically, we strategically select subsets from users' original sequences and perform random replacements to generate artificially replaced noisy sequences. Subsequently, we perform joint training on these artificially replaced noisy sequences and the original sequences. Through effective reweighting, we incorporate the training results of the noise recognition model into the recommender model. We evaluate our method on three datasets using a consistent base model. Experimental results demonstrate the effectiveness of introducing self-supervised auxiliary task to enhance the base model's performance.

Exploring intrinsic magnetic topological insulators (TIs) for next-generation spintronic devices is still challenging in recent years. Here, we present a theoretical investigation on the electronic, magnetic and topological properties of monolayer (ML) Janus MnBi2TexSe4-x, derived from two trivial magnetic semiconductors ML MnBi2Se4 and MnBi2Te4. Our band structure analysis reveals that two out of the eight Janus structures exhibit band inversion induced by spin-orbit coupling. These structures are confirmed to have nonzero integer Chern numbers, indicating their topological nature. Moreover, the topological state is robust under moderate biaxial strains. Interestingly, applying compressive strain results in a high Chern number of 2 and enhances their magnetic stability at elevated temperatures. Our findings offer an effective strategy to engineer magnetic TI states within the ML MnBi2Te4 family.

First-principles calculations were conducted to investigate the structural, electronic and magnetic properties of single Fe atoms and Fe dimers on Cu2N/Cu(100). Upon adsorption of an Fe atom onto Cu2N/Cu(100), robust Fe-N bonds form, resulting in the incorporation of both single Fe atoms and Fe dimers within the surface Cu2N layer. The partial occupancy of Fe-3d orbitals lead to large spin moments on the Fe atoms. Interestingly, both single Fe atoms and Fe dimers exhibit in-plane magnetic anisotropy, with the magnetic anisotropy energy (MAE) of an Fe dimer exceeding twice that of a single Fe atom. This magnetic anisotropy can be attributed to the predominant contribution of the component along the x direction of the spin-orbital coupling Hamiltonian. Additionally, the formation of Fe-Cu dimers may further boost the magnetic anisotropy, as the energy levels of the Fe-3d orbitals are remarkably influenced by the presence of Cu atoms. Our study manifests the significance of uncovering the origin of magnetic anisotropy in engineering the magnetic properties of magnetic nanostructures.

Let $0<\alpha,\beta,t<\infty$ and $\mu$ be a positive Borel measure on $\mathbb{C}^n$. We consider the Berezin-type operator $S^{t,\alpha,\beta}_{\mu}$ defined by $$S^{t,\alpha,\beta}_{\mu}f(z):=\left(\int_{\mathbb{C}^n}e^{-\frac{\beta}{2}|z-u|^2}|f(u)|^te^{-\frac{\alpha t}{2}|u|^2}d\mu(u)\right)^{1/t},\quad z\in\mathbb{C}^n.$$ We completely characterize the boundedness and compactness of $S^{t,\alpha,\beta}_{\mu}$ from the weighted Fock space $F^p_{\alpha,w}$ into the Lebesgue space $L^q(wdv)$ for all possible indices, where $w$ is a weight on $\mathbb{C}^n$ that satisfies an $A_{\infty}$-type condition. This solves an open problem raised by Zhou, Zhao and Tang [Banach J. Math. Anal. 18 (2024), Paper No. 20]. As an application, we obtain the description of the boundedness and compactness of Toeplitz-type operators acting between weighted Fock spaces induced by $A_{\infty}$-type weights., Comment: 23 pages

In this paper, we characterize the $d\times d$ matrix weights $W$ on $\mathbb{C}^n$ such that the Fock projection $P_{\alpha}$ is bounded on the vector-valued spaces $L^p_{\alpha,W}(\mathbb{C}^n;\mathbb{C}^d)$ induced by $W$. It is proved that for $1\leq p<\infty$, the Fock projection $P_{\alpha}$ is bounded on $L^p_{\alpha,W}(\mathbb{C}^n;\mathbb{C}^d)$ if and only if $W$ satisfies a restricted $\mathbf{A}_p$-condition. In particular, when $p=1$, our result establishes a strong (1,1) type estimate for the Fock projections, which is quite different with the case of Calder\'{o}n--Zygmund operators., Comment: 19 pages

As inference on Large Language Models (LLMs) emerges as an important workload in machine learning applications, weight quantization has become a standard technique for efficient GPU deployment. Quantization not only reduces model size, but has also been shown to yield substantial speedups for single-user inference, due to reduced memory movement, with low accuracy impact. Yet, it remains open whether speedups are achievable also in \emph{batched} settings with multiple parallel clients, which are highly relevant for practical serving. It is unclear whether GPU kernels can be designed to remain practically memory-bound, while supporting the substantially increased compute requirements of batched workloads. This paper resolves this question positively by describing the design of Mixed-precision Auto-Regressive LINear kernels, called MARLIN. Concretely, given a model whose weights are compressed via quantization to, e.g., 4 bits per element, MARLIN shows that batchsizes up to 16-32 can be supported with close to maximum ($4\times$) quantization speedup, and larger batchsizes up to 64-128 with gradually decreasing, but still significant, acceleration. MARLIN accomplishes this via a combination of techniques, such as asynchronous memory access, complex task scheduling and pipelining, and bespoke quantization support. Our experiments show that MARLIN's near-optimal performance on individual LLM layers across different scenarios can also lead to end-to-end LLM inference speedups (of up to $2.8\times$) when integrated with the popular vLLM serving engine. Finally, MARLIN is extensible to further compression techniques, like NVIDIA 2:4 sparsity, leading to additional speedups.

In this paper, we completely characterize the positive Borel measures $\mu$ on the unit ball $\mathbb{B}_n$ of $\mathbb{C}^n$ such that the Carleson embedding from holomorphic Hardy type tent spaces $\mathcal{HT}^p_{q,\alpha}$ into the tent spaces $T^t_s(\mu)$ is bounded for all $0-n-1$. As an application, we determine the indices $0-n-1$ such that the inclusion $\mathcal{HT}^p_{q,\alpha}\subset\mathcal{HT}^t_{s,\beta}$ holds, which allows us to completely characterize the nonlinear superposition operators between Hardy type tent spaces.

We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the ``split``, followed by a ``fit`` operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware, since a Voronoi partition explicitly reveals both the number of and the connections between the primitives. We design a neural network to predict the Voronoi diagram from an input point cloud or distance field via a binary classification. We show that our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn Voronoi partitions for CAD models from training data and exhibits superior generalization capabilities. Extensive experiments and evaluation demonstrate that the resulting B-Reps, consisting of parametric surfaces, curves, and vertices, are more plausible than those obtained by existing alternatives, with significant improvements in reconstruction quality. Code will be released on https://github.com/yilinliu77/NVDNet., Comment: ACM Transactions on Graphics (SIGGRAPH 2024); Project page: https://vcc.tech/research/2024/BRepVP; Code: https://github.com/yilinliu77/NVDNet

Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space $\mathscr{H}^{\text{weak}}_p(X)$ to the Hardy space $\mathscr{H}^+_p(X)$ of vector-valued Dirichlet series. To obtain this, a Littlewood--Paley inequality for Dirichlet series is established.

In this paper, we completely give the solution of the problem of Littlewood-type randomization in the Hardy and Bergman spaces of Dirichlet series. The Littlewood-type theorem for Bergman spaces of Dirichlet series is very different from the corresponding version for Hardy spaces of Dirichlet series; but also exhibits various pathological phenomena compared with the setting of analytic Bergman spaces over the unit disk, due to the fact that Dirichlet series behave as power series of infinitely many variables. A description for the inclusion between some mixed norm spaces of Dirichlet series plays an essential role in our investigation. Finally, as another application of the inclusion, we completely characterize the superposition operators between Bergman spaces of Dirichlet series.

We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high probability with (amortized) $O(\mathrm{poly}(\varepsilon^{-1}, \log n))$ time per update. We also obtain the same update time for maintaining a fractional approximate weighted matching (and hence an approximation to the value of the maximum weight matching) and an integral approximate weighted matching in dense graphs. Our unweighted result improves upon the prior state-of-the-art which includes a $\mathrm{poly}(\log{n}) \cdot 2^{O(1/\varepsilon^2)}$ update time [Assadi-Bernstein-Dudeja 2022] and an $O(\sqrt{m} \varepsilon^{-2})$ update time [Gupta-Peng 2013], and our weighted result improves upon the $O(\sqrt{m}\varepsilon^{-O(1/\varepsilon)}\log{n})$ update time due to [Gupta-Peng 2013]. To obtain our results, we generalize a recent optimization approach to dynamic algorithms from [Jambulapati-Jin-Sidford-Tian 2022]. We show that repeatedly solving entropy-regularized optimization problems yields a lazy updating scheme for fractional decremental problems with a near-optimal number of updates. To apply this framework we develop optimization methods compatible with it and new dynamic rounding algorithms for the matching polytope.

The cold-start problem is a common challenge for most recommender systems. The practical application of most cold-start methods is hindered by the deficiency in auxiliary content information for users. Moreover, most methods necessitate simultaneous updates to the extensive parameters of recommender models, leading to significant training costs, particularly in large-scale industrial scenarios. We observe that the model can generate expressive embeddings for warm users with relatively more interactions. Initially, these users were cold-start users, and after transitioning to warm users, they exhibit clustering patterns in their embeddings with consistent initial interactions. Based on this motivation, we propose a Variational Mapping approach for cold-start user Recommendation (VM-Rec), mapping from few initial interactions to expressive embeddings for cold-start users. Specifically, we encode the initial interactions into a latent representation, where each dimension disentangledly signifies the degree of association with each warm user. Subsequently, we utilize this latent representation as the parameters for the mapping function, mapping (decoding) it into an expressive embedding, which can be integrated into a pre-trained recommender model directly. Our method is evaluated on three datasets using the same base model, demonstrating superior performance compared to other popular cold-start methods.

For photonic crystal slab (PCS) structures, bound states in the continuum (BICs) and circularly polarized states (dubbed C-points) are important topological polarization singularities in momentum-space and have attracted burgeoning attention due to their novel topological and optical properties. In our work, the evolution of polarization singularities from BICs to C-points is achieved by breaking the in-plane C2 symmetry of a PCS structure of a square lattice with C4v symmetry. Correspondingly, a BIC is split into two C-points with opposite chirality, incurring distinct optical transmission responses with the incidence of right or left circular polarization (RCP or LCP). Harnessing such chirality selectivity of the C-points, we propose a multifunctional imaging system by integrating the designed PCS into a conventional 4-f imaging system, to realize both the edge imaging and conventional bright-field imaging, determined by the circular polarization state of the light source. In addition to multifunctional imaging, our system also provides a vivid picture about the evolution of the PCS platforms' singularities., Comment: 11 pages, 4 figures

The retrieval phase is a vital component in recommendation systems, requiring the model to be effective and efficient. Recently, generative retrieval has become an emerging paradigm for document retrieval, showing notable performance. These methods enjoy merits like being end-to-end differentiable, suggesting their viability in recommendation. However, these methods fall short in efficiency and effectiveness for large-scale recommendations. To obtain efficiency and effectiveness, this paper introduces a generative retrieval framework, namely SEATER, which learns SEmAntic Tree-structured item identifiERs via contrastive learning. Specifically, we employ an encoder-decoder model to extract user interests from historical behaviors and retrieve candidates via tree-structured item identifiers. SEATER devises a balanced k-ary tree structure of item identifiers, allocating semantic space to each token individually. This strategy maintains semantic consistency within the same level, while distinct levels correlate to varying semantic granularities. This structure also maintains consistent and fast inference speed for all items. Considering the tree structure, SEATER learns identifier tokens' semantics, hierarchical relationships, and inter-token dependencies. To achieve this, we incorporate two contrastive learning tasks with the generation task to optimize both the model and identifiers. The infoNCE loss aligns the token embeddings based on their hierarchical positions. The triplet loss ranks similar identifiers in desired orders. In this way, SEATER achieves both efficiency and effectiveness. Extensive experiments on three public datasets and an industrial dataset have demonstrated that SEATER outperforms state-of-the-art models significantly., Comment: 9 main pages

We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard., Comment: 10 pages

Accurate depth estimation under out-of-distribution (OoD) scenarios, such as adverse weather conditions, sensor failure, and noise contamination, is desirable for safety-critical applications. Existing depth estimation systems, however, suffer inevitably from real-world corruptions and perturbations and are struggled to provide reliable depth predictions under such cases. In this paper, we summarize the winning solutions from the RoboDepth Challenge -- an academic competition designed to facilitate and advance robust OoD depth estimation. This challenge was developed based on the newly established KITTI-C and NYUDepth2-C benchmarks. We hosted two stand-alone tracks, with an emphasis on robust self-supervised and robust fully-supervised depth estimation, respectively. Out of more than two hundred participants, nine unique and top-performing solutions have appeared, with novel designs ranging from the following aspects: spatial- and frequency-domain augmentations, masked image modeling, image restoration and super-resolution, adversarial training, diffusion-based noise suppression, vision-language pre-training, learned model ensembling, and hierarchical feature enhancement. Extensive experimental analyses along with insightful observations are drawn to better understand the rationale behind each design. We hope this challenge could lay a solid foundation for future research on robust and reliable depth estimation and beyond. The datasets, competition toolkit, workshop recordings, and source code from the winning teams are publicly available on the challenge website., Comment: Technical Report; 65 pages, 34 figures, 24 tables; Code at https://github.com/ldkong1205/RoboDepth

We offer two very transparent digital signature schemes: one using non-square matrices and the other using scrap automorphisms. The former can be easily converted to a public key encryption scheme., Comment: 10 pages

This paper evaluates the feasibility of helicon current drive (HCD) in a hybrid scenario for the China Fusion Engineering Test Reactor (CFETR). Utilizing the GENRAY/CQL3D package, a large number of simulations (over 5 000) were conducted, with parametric scans in the antenna's poloidal position, launched parallel refractive index, and wave frequency. The analysis reveals that helicon has excellent accessibility under reactor-level conditions, and smaller n|| and higher wave frequency result in enhanced wave absorption. The simulations demonstrate an optimal launched parallel refractive index of approximately 1.6 for the CFETR hybrid scenario. The best launch position is found to be within a poloidal angle range of 25 degrees to 65 degrees. Additionally, it is preferable to have a narrow parallel refractive index spectrum for wave absorption when operating below the threshold value of {\Delta}n|| (~0.6), beyond which the effect of {\Delta}n|| on wave absorption is negligible. This study provides valuable insights into the potential application of HCD in CFETR.

This paper studies grading algorithms for randomized exams. In a randomized exam, each student is asked a small number of random questions from a large question bank. The predominant grading rule is simple averaging, i.e., calculating grades by averaging scores on the questions each student is asked, which is fair ex-ante, over the randomized questions, but not fair ex-post, on the realized questions. The fair grading problem is to estimate the average grade of each student on the full question bank. The maximum-likelihood estimator for the Bradley-Terry-Luce model on the bipartite student-question graph is shown to be consistent with high probability when the number of questions asked to each student is at least the cubed-logarithm of the number of students. In an empirical study on exam data and in simulations, our algorithm based on the maximum-likelihood estimator significantly outperforms simple averaging in prediction accuracy and ex-post fairness even with a small class and exam size.