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Luya Wang

Publications and source records attributed to Luya Wang.

15 recordsLinked to original sources
arXiv2026

VisCAD: A Foundation Model Suite with Multimodal Industrial CAD Intelligence

AI-assisted computer-aided design (CAD) for industrial products involves two challenging phases. Part-level generation maps diverse forms of user intent, including renders, text descriptions, 2D drawings, and real photographs, to executable programs in a CAD domain-specific language. Assembly-level generation must additionally handle interacting parts, plan mating relations, estimate poses, and place all parts correctly. Existing specialized CAD models are commonly trained on narrow input domains, such as renders or texts, and often generalize poorly, while general-purpose frontier models cover broader inputs but perform inconsistently across CAD domains. We present VisCAD, a foundation model suite designed to provide both broad generalization and strong CAD capability for realistic industrial products. At its core is VisCAD-M1, a 27B model trained through mid-training and post-training for part-level design generation. On PubCADBench and RealCADBench, VisCAD-M1 achieves the highest average part-level score among the evaluated models, reaching 0.5540 compared with 0.5496 for the strongest frontier model. Reusing VisCAD-M1 as a test-time verifier can further raise the score to 0.5797, an approximately 5 percent relative improvement over the previous state of the art. VisCAD also includes a domain-specific harness that leverages frontier models for complex assembly generation and demonstrates advantages over general-purpose harnesses in both quantitative and qualitative evaluations.

cs.CV↗
arXiv2025

Regular Lagrangians in Lefschetz fibrations

We characterize regularity of Lagrangian submanifolds in Weinstein Lefschetz fibrations, establishing a conjecture of Giroux and Pardon. Our main result is the Weinstein analogue of a closed symplectic Lefschetz pencil result of Auroux, Mu\~noz, and Presas. As an application, given a Legendrian link in tight $S^3$ and an exact filling which is part of an arboreal skeleton for the $4$-ball, we build a Lefschetz fibration such that the image of the filling and all of its mutations are arcs in the base.

math.SG↗
arXiv2025

Properties of contact toric structures and concave boundaries of linear plumbings

We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on the linear plumbing case in this article. We study the properties of the contact structure using two different sets of tools. First, we prove that all such contact manifolds have a global contact toric structure, and use tools from toric geometry to identify when the contact structure is tight versus overtwisted. Second, we study algebraic torsion measurements from embedded contact homology (ECH) for these concavely induced contact manifolds, which has largely been unexplored. We develop a toolkit establishing existence and constraints of pseudoholomorphic curves adapted to the Morse-Bott Reeb dynamics of these plumbing examples, to provide the ECH algebraic torsion and contact invariant calculations for the concave boundaries of linear plumbings.

math.SG↗
arXiv2024

Spinal open books and symplectic fillings with exotic fibers

Spinal open book decompositions provide a natural generalization of open book decompositions. We show that any minimal symplectic filling of a contact 3-manifold supported by a planar spinal open book is deformation equivalent to the complement of a positive multisection in a bordered Lefschetz fibration, which generalizes a result of Wendl. Along the way, we give an explicit local model for a non-compactly supported "singularity at infinity" in a generalized version of bordered Lefschetz fibrations, given by pseudoholomorphic foliations associated to the spinal open books. This provides new tools to classify symplectic fillings of a contact 3-manifold that is not supported by an amenable spinal open book, by studying monodromy factorizations in the newly defined spinal mapping class group. As an application, we complete the classification of strong fillings of all parabolic torus bundles, and make progress towards classifying symplectic fillings of contact 3-manifolds supported by non-planar open books.

math.GT↗
arXiv2023

Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds

We construct $Spin(7)$-instantons on one of Joyce's compact $Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyce is the same as in Lewis' construction of $Spin(7)$-instantons. However, our construction method and the resulting instantons are new. The compact $Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certain local model spaces around the orbifold singularities. We construct our instantons by gluing non-flat connections on the local model spaces to a flat connection on the $Spin(7)$-orbifold. We deliver more than $20,000$ new four-parameter families of examples of $Spin(7)$-instantons within the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$.

math.DG↗
arXiv2023

On Donaldson's 4-6 question

We prove that the examples by Smith and McMullen-Taubes provide infinitely many counterexamples to one direction of Donaldson's 4-6 question and the closely related Stabilising Conjecture. These are the first known counterexamples. In the other direction, we show that the Gromov-Witten invariants of two simply-connected closed symplectic $4$-manifolds, whose products with $(S^2,\omega_{\text{std}})$ are deformation equivalent, agree. In particular, when $b_2^+ \geq 2$, these $4$-manifolds have the same Seiberg-Witten invariants. Furthermore, one can replace $(S^2,\omega_{\text{std}})$ by $(S^2,\omega_{\text{std}})^k$ for any $k \geq 1$ in both results.

math.SG↗
arXiv2023

Infinitely many monotone Lagrangian tori in higher projective spaces

Vianna constructed infinitely many exotic Lagrangian tori in the complex projective plane. We lift these tori to higher-dimensional projective spaces and show that they remain non-symplectomorphic. Our proof is elementary except for an application of the wall-crossing formula by Pascaleff-Tonkonog.

math.SG↗
arXiv2023

A connected sum formula for embedded contact homology

Given two closed contact three-manifolds, one can form their contact connected sum via the Weinstein one-handle attachment. We study how pseudo-holomorphic curves in the symplectization behave under this operation. As a result, we give a connected sum formula for embedded contact homology.

math.SG↗
arXiv2023

Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysis

A wireless federated learning system is investigated by allowing a server and workers to exchange uncoded information via orthogonal wireless channels. Since the workers frequently upload local gradients to the server via bandwidth-limited channels, the uplink transmission from the workers to the server becomes a communication bottleneck. Therefore, a one-shot distributed principle component analysis (PCA) is leveraged to reduce the dimension of uploaded gradients such that the communication bottleneck is relieved. A PCA-based wireless federated learning (PCA-WFL) algorithm and its accelerated version (i.e., PCA-AWFL) are proposed based on the low-dimensional gradients and the Nesterov's momentum. For the non-convex loss functions, a finite-time analysis is performed to quantify the impacts of system hyper-parameters on the convergence of the PCA-WFL and PCA-AWFL algorithms. The PCA-AWFL algorithm is theoretically certified to converge faster than the PCA-WFL algorithm. Besides, the convergence rates of PCA-WFL and PCA-AWFL algorithms quantitatively reveal the linear speedup with respect to the number of workers over the vanilla gradient descent algorithm. Numerical results are used to demonstrate the improved convergence rates of the proposed PCA-WFL and PCA-AWFL algorithms over the benchmarks.

cs.LG↗
arXiv2023

Legendrian embedded contact homology

We give a construction of embedded contact homology (ECH) for a contact $3$-manifold $Y$ with convex sutured boundary and a pair of Legendrians $\Lambda_+$ and $\Lambda_-$ contained in $\partial Y$ satisfying an exactness condition. The chain complex is generated by certain configurations of closed Reeb orbits of $Y$ and Reeb chords of $\Lambda_+$ to $\Lambda_-$. The main ingredients include: a general Legendrian adjunction formula for curves in $\mathbb{R} \times Y$ with boundary on $\mathbb{R} \times \Lambda$; a relative writhe bound for curves in contact $3$-manifolds asymptotic to Reeb chords; and a Legendrian ECH index with an accompanying ECH index inequality. The (action filtered) Legendrian ECH of any pair $(Y,\Lambda)$ of a closed contact $3$-manifold $Y$ and a Legendrian link $\Lambda$ can also be defined using this machinery after passing to a sutured link complement. This work builds on ideas present in Colin-Ghiggini-Honda's proof of the equivalence of Heegaard-Floer homology and ECH. The independence of our construction of choices of almost complex structure and contact form should require a new flavor of monopole Floer homology. It is beyond the scope of this paper.

math.SG↗
arXiv2023

Fast-BEV: Towards Real-time On-vehicle Bird's-Eye View Perception

Recently, the pure camera-based Bird's-Eye-View (BEV) perception removes expensive Lidar sensors, making it a feasible solution for economical autonomous driving. However, most existing BEV solutions either suffer from modest performance or require considerable resources to execute on-vehicle inference. This paper proposes a simple yet effective framework, termed Fast-BEV, which is capable of performing real-time BEV perception on the on-vehicle chips. Towards this goal, we first empirically find that the BEV representation can be sufficiently powerful without expensive view transformation or depth representation. Starting from M2BEV baseline, we further introduce (1) a strong data augmentation strategy for both image and BEV space to avoid over-fitting (2) a multi-frame feature fusion mechanism to leverage the temporal information (3) an optimized deployment-friendly view transformation to speed up the inference. Through experiments, we show Fast-BEV model family achieves considerable accuracy and efficiency on edge. In particular, our M1 model (R18@256x704) can run over 50FPS on the Tesla T4 platform, with 47.0% NDS on the nuScenes validation set. Our largest model (R101@900x1600) establishes a new state-of-the-art 53.5% NDS on the nuScenes validation set. The code is released at: https://github.com/Sense-GVT/Fast-BEV.

cs.CV↗
arXiv2022

Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil

Given any genus-two, hyperbolic, fibered knot in $S^3$ with nonzero fractional Dehn twist coefficient, we show that its pseudo-Anosov representative has a fixed point. Combined with recent work of Baldwin--Hu--Sivek, this proves that knot Floer homology detects the cinquefoil knot $T(2,5)$, and that the cinquefoil is the only genus-two L-space knot in $S^3$. Our results have applications to Floer homology of cyclic branched covers over knots in $S^3$, to $\mathit{SU}(2)$-abelian Dehn surgeries, and to Khovanov and annular Khovanov homology. Along the way to proving our fixed point result, we describe a small list of train tracks carrying all pseudo-Anosov homeomorphisms in most strata on the punctured disk. As a consequence, we find a canonical track $\tau$ carrying all pseudo-Anosov homeomorphisms in a particular stratum $\mathcal{Q}_0$ on the genus-two surface, and describe every fixed-point-free pseudo-Anosov homeomorphism in $\mathcal{Q}_0$.

math.GT↗
arXiv2022

RePre: Improving Self-Supervised Vision Transformer with Reconstructive Pre-training

Recently, self-supervised vision transformers have attracted unprecedented attention for their impressive representation learning ability. However, the dominant method, contrastive learning, mainly relies on an instance discrimination pretext task, which learns a global understanding of the image. This paper incorporates local feature learning into self-supervised vision transformers via Reconstructive Pre-training (RePre). Our RePre extends contrastive frameworks by adding a branch for reconstructing raw image pixels in parallel with the existing contrastive objective. RePre is equipped with a lightweight convolution-based decoder that fuses the multi-hierarchy features from the transformer encoder. The multi-hierarchy features provide rich supervisions from low to high semantic information, which are crucial for our RePre. Our RePre brings decent improvements on various contrastive frameworks with different vision transformer architectures. Transfer performance in downstream tasks outperforms supervised pre-training and state-of-the-art (SOTA) self-supervised counterparts.

cs.CV↗