arXiv subjects

Kai Xu

Publications and source records attributed to Kai Xu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Drawstrings and flexibility in the Geroch conjecture

In this paper, we observe new phenomena related to the structure of 3-manifolds satisfying lower scalar curvature bounds. We construct warped-product manifolds of almost nonnegative scalar curvature that converge to pulled string spaces in the Sormani-Wenger intrinsic flat topology. These examples extend the results of Lee-Naber-Neumayer \cite{LNN} to the case of dimension $3$. As a consequence, we produce the first counterexample to a conjecture of Sormani \cite{SormaniConj} on the stability of the Geroch Conjecture. Our example tests the appropriate hypothesis for a related conjecture of Gromov. On the other hand, we demonstrate a $W^{1,p}$-stability statement ($1\leq p<2$) for the Geroch Conjecture in the class of warped products.

math.DG↗

arXiv2026

Layer-Parallel Inference Reduces Encrypted Nonlinear Depth in Transformers

Fully homomorphic encryption (FHE) enables computation on encrypted data, but practical encrypted Transformer inference is bottlenecked by the sequential composition of many nonlinear blocks. We study whether Structured Newton Layer Parallelism (SNLP) can make this inter-layer composition more FHE-friendly: each Transformer block still requires polynomial approximations for operations such as softmax and RMSNorm, but SNLP reduces the layerwise sequential nonlinear depth from L stages to a small number of solver iterations plus linear structured corrections. Using a simulation framework based on Chebyshev polynomial approximations, we measure error accumulation under sequential versus SNLP inference across 8 models and 4 architecture families. On a 0.5B IDN-trained model, SNLP reduces symbolic bootstraps from 53 to 20 (2.65x) with only +1.2% perplexity degradation, while lowering error amplification (1.36x vs. 1.42x). Across all tested models, SNLP has lower amplification than sequential inference. Ablations show that softmax approximation dominates the error budget and CKKS arithmetic noise is negligible in our setting, suggesting that SNLP is complementary to block-level FHE-friendly operator design rather than a replacement for it.

cs.LG↗

arXiv2026

Connectivity-induced surface-loss penalty in superconducting qubit-coupler lattices

Recent advances in design and fabrication have increased the energy-relaxation times of isolated superconducting transmon qubits to the hundreds-of-microseconds regime, with reported values exceeding 500 $μ$s. However, the same progress has not automatically translated to multiqubit processors, where qubits are embedded in connected qubit-coupler lattices and often exhibit much shorter lifetimes than isolated qubits. To identify possible sources of this discrepancy, here we use finite-element simulation to investigate how surface participation ratios and the resulting surface dielectric loss change when a qubit is embedded in a flip-chip qubit-coupler lattice. Controlled comparisons show that higher connectivity can indeed lead to larger surface loss: in the simulated lattice, connecting a qubit to two and four couplers increases the surface loss by factors of 1.3 and 1.8, respectively. We attribute this change to the combined effects of added edge fields from coupling claws, field redistribution over the larger connected metal network, and hybridization with coupler modes. We further examine how this connectivity-induced surface-loss penalty depends on the geometric design parameters of both the qubit electrodes and the coupling claws, and derive guidelines for designing low-loss multiqubit processors.

quant-ph↗

arXiv2026

New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry

We show a sharp and rigid spectral generalization of the classical Bishop--Gromov volume comparison theorem: if a closed Riemannian manifold $(M,g)$ of dimension $n\geq3$ satisfies $$ λ_1\left(-\frac{n-1}{n-2}Δ+\mathrm{Ric}\right)\geq n-1, $$ then $\operatorname{vol}(M)\leq\operatorname{vol}(\mathbb S^{n})$, and $π_1(M)$ is finite. The constant $\frac{n-1}{n-2}$ cannot be improved, and if $\mathrm{vol}(M)=\mathrm{vol}(\mathbb S^n)$ holds, then $M\cong \mathbb S^{n}$. A sharp generalization of the Bonnet--Myers theorem is also shown under the same spectral condition. The proofs involve the use of a new unequally weighted isoperimetric problem, and unequally warped $μ$-bubbles. As an application, in dimensions $3\leq n\leq 5$, we infer sharp results on the isoperimetric structure at infinity of complete manifolds with nonnegative Ricci curvature and uniformly positive spectral biRicci curvature. Furthermore, the main result of this paper is applied in Mazet's recent solution of the stable Bernstein problem in $\mathbb R^6$.

math.DG↗

arXiv2026

Connected sum of manifolds with spectral Ricci lower bounds

Let $n > 2$, $γ> \frac{n-1}{n-2}$, and $λ\in \mathbb{R}$. We prove that if $M$ and $N$ are two smooth $n$-manifolds that admit a complete Riemannian metric satisfying \[-γΔ+ \mathrm{Ric} > λ,\]then the connected sum $M \# N$ also admits such a metric. The construction geometrically resembles a Gromov-Lawson tunnel; the range $ γ> \frac{n-1}{n-2} $ is sharp for this to hold.

math.DG↗

arXiv2026

HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulations

Standard pipelines for physics-ready 3D reconstruction rely on a decoupled two-stage paradigm: extracting surface geometry followed by an error-prone tetrahedralization process. While recent Lagrangian methods like TetSphere Splatting attempt to bypass this by directly optimizing volumetric primitives, their homeomorphic constraints prevent topology-adaptive optimization. Consequently, they produce disjoint tetrahedra rather than a single connected mesh, rendering the structures unsuitable for further physical simulations. To address this, we propose a topology-adaptive framework for holistic tetrahedral mesh reconstruction through end-to-end topological and geometric optimization. First, by coupling Gaussian spheres to tetrahedral elements and leveraging edge connections, we estimate a continuous opacity field for differentiable element pruning. Next, jointly minimizing mesh smoothing energy and multi-view Gaussian rendering error drives alternating geometric refinement while preserving topological adaptivity. Consequently, our approach effectively constructs a unified and topologically coherent tetrahedral mesh. Extensive experiments demonstrate that our method outperforms state-of-the-art techniques by achieving superior geometric accuracy and producing coherent, single-connected tetrahedral meshes, thereby effectively bypassing the error-prone conventional tetrahedralization step for reconstructed surface meshes and streamlining downstream physical simulation.

cs.GR↗

arXiv2026

SNLP: Layer-Parallel Inference via Structured Newton Corrections

Autoregressive language models execute Transformer layers sequentially, creating a latency bottleneck that is not removed by conventional tensor or pipeline parallelism. We study whether this layerwise dependency can be relaxed by treating the hidden-state trace across layers as the solution of a nonlinear residual equation and solving it with parallel Newton-style updates. While this view is principled, exact Newton corrections require expensive Jacobian-vector products and naive fixed-point iterations are unstable on trained Transformers. We introduce Structured Newton Layer Parallelism (SNLP), a training and inference framework that replaces exact layer Jacobians with cheap architecture-induced surrogate dynamics. In residual Transformers, this yields Identity Newton (IDN), where the correction reduces to a prefix-sum-like update; in mHC-style architectures, HC Newton (HCN) uses the model's residual mixing matrix. We also study SNLP-aware training, including pretraining regularization and direct SNLP-forward SFT. Experiments on Nanochat-scale Transformers show that SNLP exposes a practical speed-quality frontier: on 0.5B models, it reaches up to 2.58x wall-clock speedup, and a less aggressive configuration reaches 1.40x speedup without increasing PPL. The useful tradeoff comes from the biased finite-iteration computation induced by IDN/HCN rather than exact recovery of the sequential trace. We further show that SNLP-forward SFT can preserve downstream task accuracy, and that SNLP can serve as a drafter for self-speculative decoding while a sequential verifier preserves output correctness.

cs.LG↗

arXiv2026

Infinity-harmonic functions and inverse mean curvature flow clusters

An $\infty$-harmonic function is a viscosity solution of $\nabla^2 u(\nabla u,\nabla u)=0$, or equivalently, an absolute minimizer of $\|\nabla u\|_{L^\infty}$. We prove a variety of new structural and regularity results in two dimensions, including: 1. $\infty$-harmonic functions in domains of $\mathbb{R}^2$ are $C^{1,1/3}$. 2. Critical points are isolated, and at each critical point, the solution has a unique quasiradial blow-up. 3. Entire solutions with polynomial growth have unique quasiradial blow-downs, and are determined by their Fourier modes at infinity. These results are consequences of a new theory relating $\infty$-harmonic functions to inverse mean curvature flow (IMCF) clusters -- which are piecewise weak solutions of IMCF with common obstacle-type boundary conditions on the interfaces (a simple example is an embedded family of cuspidal curves evolving by inverse curvature). This connection arises as the $p\to\infty$ limit of the classical duality between $p$-harmonic and $q$-harmonic functions in $\mathbb{R}^2$, where $\frac1p+\frac1q=1$.

math.AP↗

arXiv2026

Inverse mean curvature flow with outer obstacle

We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of the domain serves as an outer obstacle, and the evolving hypersurfaces are assumed to stick tangentially to the boundary upon contact. In smooth bounded domains, we prove an existence and uniqueness theorem for weak solutions, and establish $C^{1,α}$ regularity of the level sets up to the obstacle. The proof combines various techniques, including elliptic regularization, blow-up analysis, and certain parabolic estimates. As an analytic application, we address the well-posedness problem for the usual weak inverse mean curvature flow, showing that the initial value problem always admits a unique maximal (or innermost) weak solution.

math.DG↗

arXiv2026

Few-Step Diffusion Language Models via Trajectory Self-Distillation

Diffusion large language models (DLLMs) have emerged as powerful generative models with the promise of fast text generation through parallel decoding. However, realizing this potential in practice remains challenging: reducing the number of decoding steps, typically causes a substantial degradation in output quality due to token factorization error. To alleviate this, we propose a self-distillation framework that trains a few-step student to match the generative trajectory of a full-step teacher. We theoretically and empirically show that trajectory-level supervision mitigates this factorization error, thereby enabling effective few-step decoding. We further incorporate Direct Discriminative Optimization (DDO), a reverse-KL objective that encourages mode-seeking toward the teacher's modes, yielding stronger performance on challenging reasoning tasks. Across reasoning and code-generation benchmarks, our method substantially narrows the gap between few-step and full-step decoding. The source code is available at https://github.com/Tyrion58/T3D.

cs.CL↗

arXiv2026

DynaMOMA: Instantaneous Prediction of Grasp Poses for Mobile Manipulation of Dynamic Objects

Mobile manipulation is a fundamental robotics task and has advanced rapidly in recent years, enabling robots to navigate, reach, and interact with objects in complex environments. However, mobile manipulation of dynamic objects remains highly challenging, as robots must coordinate the mobile base and arm while adapting to continuously evolving target poses. A key challenge lies in predicting temporally consistent short-horizon grasp trajectories from dynamic observations. In this work, we propose \ours{}, a dynamic mobile manipulation framework that couples instantaneous grasp trajectory prediction with whole-body control policy. Our predictor uses an anchor-based diffusion model to generate temporally consistent short-horizon grasp trajectories conditioned on historical observations. The predicted trajectories are then encoded as compact features and fed to a whole-body reinforcement learning policy, which controls the mobile manipulator for dynamic grasping. We further introduce a anticipation-guided reward that equips the policy with an anticipatory grasping horizon by adaptively shifting the target from the current grasp observation to the instantaneously predicted grasp trajectory. Through extensive experiments in Isaac Gym simulation, we show that our method achieves strong performance in mobile manipulation of dynamic objects across diverse settings and grasping metrics. Furthermore, our predictor and policy demonstrate strong generalizability in real-world experiments.

cs.RO↗

arXiv2026

PAIWorld: A 3D-Consistent World Foundation Model for Robotic Manipulation

World foundation models (WFMs) are powerful simulators, yet they predominantly operate in a single-view setting and lack the multi-view 3D consistency required for robotic manipulation. While robotic systems rely on multiple cameras (egocentric, eye-to-hand, and wrist-mounted) for policy learning, current multi-view world models simply concatenate view tokens without explicit geometric reasoning. This causes cross-view object drift, depth inconsistency, and texture misalignment. We trace these failures to two deficiencies: the absence of an explicit inter-view communication mechanism and the lack of a 3D geometric prior. We argue that resolving both simultaneously is necessary and sufficient. To address this, we present PAIWorld, a framework that augments diffusion-transformer world models via three core components: (1) Geometry-Aware Cross-View Attention blocks that establish an explicit pathway across views, (2) Geometric Rotary Position Embedding that encodes camera ray directions and extrinsic poses into the attention mechanism, and (3) Latent 3D-REPA, which distills 3D-aware features from frozen 3D foundation models to ensure 3D consistency. Built upon a DiT-based world foundation model, PAIWorld achieves state-of-the-art multi-view 3D consistency on robotic manipulation benchmarks, ranking 1st on the WorldArena leaderboard and 2nd on the AgiBot-Challenge2026 leaderboard, while enabling downstream applications such as model-based planning, world action models, and multi-view policy post-training.

cs.RO↗

arXiv2026

S2D2: Fast Decoding for Diffusion LLMs via Training-Free Self-Speculation

Block-diffusion language models offer a promising path toward faster-than-autoregressive generation by combining block-wise autoregressive decoding with within-block parallel denoising. However, in the few-step regime needed for practical acceleration, standard confidence-thresholded decoding is often brittle: aggressive thresholds hurt quality, while conservative thresholds require unnecessary denoising steps. Existing approaches that address this issue either require additional training or incur extra test-time compute. We present S2D2, a training-free self-speculative decoding framework for block-diffusion language models. Our key observation is that a block-diffusion model becomes autoregressive when the block size is reduced to one, allowing the same pretrained model to act as both drafter and verifier. S2D2 inserts a speculative verification step into standard block-diffusion decoding and uses lightweight routing policies to decide when verification is worth its cost. This yields a hybrid decoding trajectory in which diffusion proposes tokens in parallel, while the autoregressive mode acts as a local sequence-level critic. Across three mainstream block-diffusion families, S2D2 consistently improves the accuracy-speed tradeoff over strong confidence-thresholding baselines. On SDAR, we observe up to $4.7\times$ speedup over autoregressive decoding, and up to $1.57\times$ over a tuned dynamic decoding baseline while improving accuracy by up to $4.5$ points. On LLaDA2.1-Mini, S2D2 remains complementary to built-in self-correction, including a conservative setting where it is $4.4\times$ faster than the static baseline with slightly higher accuracy.

cs.CL↗

arXiv2026

A symmetric relaxation method for entire two-dimensional cellular networks and its implications

To simulate the relaxation of an entire 2D cellular network, this study proposes a symmetric relaxation method for both inner and marginal vertices. The relaxations of these two types of vertices are determined by the central angle symmetry of associated cells and the angle symmetry at each vertex, but with different major considerations. Trimmed Voronoi networks with varying irregularity are used as initial networks for the relaxation simulation. In particular, we propose a regular hexagon disordering method to generate Voronoi networks and find that the inner cells of networks with an irregularity value of one exhibit a conserved edge number distribution, as found in other 2D cellular networks. Simulation results agree with the von Neumann-Mullins law for both inner and marginal cells, and a modified equation including a geometric correction term significantly improves prediction quality. The Aboav-Weaire law and Lewis law are also reproduced, with the latter showing that relaxed cells tend to approach the ellipses' maximum inscribed polygons. Analysis of edge length, interior angle, and shape index reveals that symmetric relaxation inhibits T1 (neighbour exchange) topological transitions by reducing short edges while increasing area disparity among neighbouring cells. The findings suggest that T1 events may be triggered when force disequilibrium overcomes the stabilising effect of symmetric relaxation, providing a possible mechanistic explanation for T1 in 2D foams.

physics.bio-ph↗

arXiv2026

TextMesh4D: Zero-shot Text-to-4D Mesh Generation

Large-scale, high-quality dynamic 3D (4D) assets are essential for learning physically grounded representations, but remain costly to capture and annotate at scale. This limits the viability of supervised 4D learning and motivates zero-shot text-to-4D generation leveraging pretrained diffusion priors. To model complex dynamics, prior methods typically adopt implicit 3D representations (e.g., NeRFs or 3DGS) for their deformation capacity. However, their implicit nature provides limited control over surface topology, which hinders high-fidelity geometry and makes temporally coherent surface reconstruction challenging. To address these limitations, we explore zero-shot text-to-4D mesh generation. However, a structural mismatch arises when combining diffusion-based guidance with topology-constrained meshes: the guidance is noisy and spatially inconsistent, while meshes impose severe topological constraints, making direct vertex-level deformation unstable. In this paper, we introduce TextMesh4D, the first zero-shot framework for text-to-4D that directly generates dynamic meshes by addressing the above challenge at two complementary levels. Geometrically, we shift deformation modeling from vertices to faces via a Jacobian Deformation Field (JDF), enabling topology-aware surface reconstruction through an integrability-enforcing integration formulation. Semantically, we propose a Local-Global Semantic Regularizer (LGSR) that preserves identity over time by jointly constraining local deformation plausibility and global shape consistency. Extensive experiments demonstrate state-of-the-art temporal consistency, structural fidelity, and visual quality, while remaining efficient on a single 24GB GPU.

cs.CV↗

arXiv2026

A Scoping Review of Mixed Initiative Visual Analytics in the Automation Renaissance

Artificial agents are increasingly integrated into data analysis workflows, carrying out tasks that were primarily done by humans. Our research explores how the introduction of automation recalibrates the dynamic between humans and automating technology. To explore this question, we conducted a scoping review encompassing twenty years of mixed-initiative visual analytic systems. To describe and contrast the relationship between humans and automation, we developed an integrated taxonomy to delineate the objectives of these mixed-initiative visual analytics tools, how much automation they support, and the assumed roles of humans. Here, we describe our qualitative approach of integrating existing theoretical frameworks with new codes we developed. Our analysis shows that the visualization research literature lacks consensus on the definition of mixed-initiative systems and explores a limited potential of the collaborative interaction landscape between people and automation. Our research provides a scaffold to advance the discussion of human-AI collaboration during visual data analysis. Our integrated taxonomy is available in the form of a web application on https://smonadjemi.github.io/miva.

cs.HC↗

arXiv2026

On BPS Branes

We study supersymmetric BPS branes (BPS-B) in supergravity theories. Some of these states are anticipated by BPS black-brane (BPS-BB) solutions of supergravity. In particular, we define and distinguish the cone generated by BPS branes from the subcone of charges that admit BPS black-brane attractor solutions in the infrared limit of the supergravity effective field theory. We denote these cones by $C_{\rm BPS-B}$ and $C_{\rm BPS-BB}$, respectively. We conjecture that, in any supersymmetric theory of quantum gravity, every integrally charged state lying in $C_{\rm BPS-BB}$ is realized by a BPS state in the spectrum. Furthermore, we conjecture and present evidence that when $C_{\rm BPS-B}$ is moduli independent, it can be determined as the cone dual to the $C_{\rm BPS-BB}$ under the electric-magnetic pairing.

hep-th↗

arXiv2026

Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiability

Inference-Time Scaling (ITS) has largely succeeded in verifiable domains like math and coding, where cheap verification enables scalable output selection. However, extending ITS to tasks prone to systematic failure - driven by faulty initial assumptions or unmet multidimensional constraints - typically relies on costly external solvers or brittle, model-based verifiers. Our key insight is that the intrinsic statistics of parallel sample sets, specifically length-adjusted tail entropy, provide a robust discriminative signal for solution quality without access to ground truth. Crucially, these statistics serve as a difficulty gate for adaptive compute allocation, dynamically routing problems across scaling regimes. First, Intrinsic Selection (iS) ranks candidates post-hoc, matching consensus-based algorithms across three domains and improving engineering design selection by 20% over pass@1 baselines. Second, Intrinsic Particle Filtering (iPF) generalizes this to step-level resampling, guiding generation toward high-confidence reasoning trajectories to improve pass@1 by 6.1 points on average on hard math problems. Finally, Particle Distillation (dPF) injects privileged guidance via early logit blending and KL-guided resampling, steering generation past systematic reasoning errors to satisfy expert rubrics, yielding up to 26.5% gains on complex clinical responses. Our pipeline applies seamlessly across broad-purpose, domain-specialized, and multimodal architectures, successfully extending ITS to open-ended domains without requiring trained reward models or exact ground-truth verification.

cs.LG↗