arXiv subjects

Haoxuan Li

Publications and source records attributed to Haoxuan Li.

At least 37 records · Page 2Linked to original sources

arXiv2026

The Minimax Cost of Smoothness in Fully First-Order Stochastic Bilevel Optimization

We study the sample complexity of finding a point with expected hypergradient norm at most $ε>0$ in nonconvex--strongly-convex stochastic bilevel optimization using fresh, globally unbiased first-order samples with bounded variance. For lower-variable smoothness order $p\ge1$, F$^2$SA-$p$ achieves $\widetilde O(pε^{-4-2/p})$ (Chen et al., 2026), but necessity of the exponent $4+2/p$ was open. We prove matching upper and lower bounds $Θ_p(ε^{-4-2/p})$ under fixed nondegenerate regularity budgets, with constants allowed to depend on $p$. The lower bound holds for unrestricted randomized algorithms under a fixed sample budget, allows dimension to grow with accuracy, and preserves global unbiasedness and all prescribed lower-variable smoothness bounds, even with a scalar lower variable and exact upper gradients. We further characterize the minimax fixed-budget complexity under $L_j=MΛ^j(j!)^β$ for $j\ge3$: $Q_{p,β}^*(ε)=Θ\left(ε^{-4}\left[\inf_{1\le r\le p,,r\in\mathbb N} r^βε^{-1/r}\right]^2\right)$, for $p\in\mathbb N\cup{\infty}$, with constants independent of $p$. At infinite order, this gives $Θ(ε^{-4})$ for $β=0$ and $Θ(ε^{-4}\log^2(1/ε))$ for $β=1$. A gradient-difference method with weighted independent batches attains these bounds uniformly in order. Thus quantitative smoothness yields precise gains, whereas qualitative analyticity alone still permits $Θ(ε^{-6})$ complexity.

math.OC↗

arXiv2026

Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts

Causal representation learning for time series has developed strong identifiability results in discrete-time latent causal models, but identifiability in continuous-time latent stochastic differential equation (SDE) models remains largely open. We address this gap using environment-induced shifts in diffusion covariance. We study additive-noise latent SDEs observed through an unknown nonlinear diffeomorphism, with shared drift but environment-specific diffusion covariance. We show that two diagonal diffusion regimes with pairwise distinct coordinate-wise variance ratios identify the latent coordinates up to permutation, coordinate-wise scaling, and a possible constant shift, without any sparsity assumption on the drift. We first prove this result for linear Ornstein-Uhlenbeck systems and then extend it to general additive-noise latent SDEs. Under mild smoothness, the instantaneous drift-Jacobian causal graph is identifiable up to the same permutation. We propose a two-stage estimator for latent disentanglement and optional graph recovery; experiments on synthetic systems confirm the predicted identifiability boundary, and an application to Hardanger Bridge monitoring data illustrates the approach on real sensor trajectories.

cs.LG↗

arXiv2026

Adaptive Vision-Language Grasping via Composable Foundation Priors and Generalizable Grasp Synthesis

This paper proposes AdaRoboVLG, a task-adaptive Vision-Language-Grasp (VLG) framework that supports generalizable grasp synthesis across different robotic hands. Unlike existing VLG methods that tightly couple foundation models with end-to-end grasp policies, AdaRoboVLG learns an efficient generalizable base policy that generates and evaluates physically feasible grasp candidates through explicit kinematic mapping and force-closure-based stability estimation, while offloading task-dependent understanding to specialized foundation-model modules. These modules provide composable priors that are integrated into the grasp synthesis process, enabling contextually adaptive grasp synthesis without retraining the underlying grasp policy. Through extensive simulation and real-world experiments, we demonstrate that (i) the base policy exhibits efficient learning and strong cross-hand generalization, (ii) the framework effectively incorporates spatial, cognitive, and temporal priors to address three representative grasping challenges without compromising grasp synthesis performance compared to state-of-the-art methods, and (iii) these priors can operate jointly to enable functional grasping in cluttered and dynamic environments. These results indicate that decoupling physical grasp synthesis from task-dependent understanding provides a scalable paradigm for robotic grasping, allowing future advances in foundation models to be directly translated into improved grasp capabilities without redesigning or retraining the underlying grasp policy. Supplementary videos are available at https://adarobovlg.github.io/

cs.RO↗

arXiv2026

EviLink: Multi-Path Schema Linking with Uncertainty-Guided Evidence Acquisition for Large-Scale Text-to-SQL

Schema linking is a difficult and important step in large-scale Text-to-SQL, where systems must identify a compact yet sufficient schema context from large and ambiguous databases. Existing methods often treat schema linking as deterministic selection around a single SQL path, but complex questions may admit multiple valid realizations with different schema needs. We reframe schema linking as uncertainty-aware schema-need inference over multiple plausible SQL paths, where the system distinguishes required schema items from path-dependent uncertain ones and acquires evidence only where needed. We instantiate this reframing with EviLink, which combines multi-hypothesis schema grounding with uncertainty-guided evidence acquisition. Experiments on BIRD-Dev and Spider2-Snow show that this perspective improves the balance among schema completeness, schema relevance, and token cost. On Spider2-Snow, EviLink achieves 93.04% field-level strict recall rate, uses 116.55K average tokens, and improves downstream SQL generation under a fixed generator.

cs.CL↗

arXiv2026

ManiEdit: Sequential Unstructured Knowledge Editing for Language Models from a Manifold Perspective

Large language models (LLMs) inevitably generate some incorrect or outdated content, necessitating efficient and precise mechanisms for continual knowledge updates. However, existing model editing methods struggle to sequentially edit unstructured long-form knowledge, suffering from severe edit forgetting and degradation of general capabilities. To address these challenges, we reframe knowledge editing from a manifold perspective, viewing it as a localized displacement of an edit sub-manifold within the global knowledge manifold. Under this formulation, the problem can be decomposed into two key questions: (i) how to identify representative edit points that effectively anchor the edit sub-manifold, and (ii) how to preserve the remaining manifold structure during the sub-manifold displacement process. Based on this perspective, we propose ManiEdit, a novel manifold-aware autoregressive editing framework consisting of two core components. Pivot Localization addresses the mediocre-point dilemma by identifying high-leverage pivots to anchor the edit sub-manifold. Manifold-Aware Preservation preserves different knowledge types through an energy-weighted penalty combined with recursive null-space alignment. Experiments on two base LLMs and four unstructured editing benchmarks demonstrate that ManiEdit achieves state-of-the-art performance, outperforming the strongest baseline by up to +27.81 BERTScore and +8.50 ROUGE-L, while maintaining near-original general capabilities across six representative downstream tasks. Our code is available at: https://github.com/Areyliu/ManiEdit

cs.CL↗

arXiv2026

Matrix-Vector Complexity of Low-Rank Approximation

We establish matching polynomial query bounds for low-rank approximation from exact matrix--vector products. Given an unknown matrix $A\in\mathbb{R}^{m\times n}$, at each step a randomized algorithm chooses either $v\in\mathbb{R}^n$ and receives $Av$, or $u\in\mathbb{R}^m$ and receives $A^\top u$. The choice may depend measurably on all previous queries and replies and on the algorithm's private randomness; each vector product costs one query. The output is a rank-$k$ right projector with Schatten-$p$ residual at most $1+\varepsilon$ times optimal. Write $N=\min\{m,n\}$ and let $Q_p^*$ denote the worst-case query budget for success probability $2/3$ on every input. For every $1\le k<N$ and sufficiently small $\varepsilon$, our lower bounds, combined with existing Krylov upper bounds, give $Q_p^*=\widetildeΘ\!\left(\min\{N,k\min\{p^{1/6}\varepsilon^{-1/3},\varepsilon^{-1/2}\}\}\right)$ $(2\le p<\infty)$, $Q_\infty^*=\widetildeΘ\!\left(\min\{N,k\varepsilon^{-1/2}\}\right)$. These bounds have universal constants and allow $p$ to vary with the problem parameters, identifying the transition at $p\varepsilon\asymp1$. A complementary result for each fixed $1\le p<2$ gives $\widetildeΘ_p(\min\{N,k\varepsilon^{-1/3}\})$, with constants and an accuracy threshold that may depend on $p$. Together, the results recover this fixed-norm rate for every fixed finite $p$, supplying the multiplicative rank dependence missing from previous lower bounds. Tildes suppress logarithmic factors. The proof extends adaptive Wishart deferred decisions to a rectangular factor with a $k$-dimensional nullspace. Posterior overlap gives a short fixed-norm argument, while persistence of small compression eigenvalues controls growing $p$ and the spectral endpoint. Exact range recovery handles target costs of order $k$; the Wishart family covers the remaining regimes.

math.OC↗

arXiv2026

Sharp High-Probability Statistical Rates for Heavy-Tailed Nonsmooth Convex Optimization

We establish sharp high-probability statistical rates for nonsmooth stochastic convex optimization under heavy-tailed noise, closing the confidence-dependence gap in both general convex and strongly convex settings. We consider composite objectives with a Lipschitz convex loss and a known proximal regularizer, accessed through fresh unbiased stochastic subgradients. The centered noise has conditional norm and directional $p$th moments bounded by $L^p$ and $s^p$, respectively, where $1<p\le2$ and $0<s\le L$. For $T$ oracle calls and failure probability $0<δ<1/10$, set $q=1-1/p$, $\ell=\log(3/δ)$, and $A=s(L^2/s^2)^q$. With initial distance bound $D$, the minimax objective error is $Θ(D(A+s\ell^q)/T^q)$ in the nonsaturated statistical regime. For a $μ$-strongly convex regularizer, the corresponding quadratic-regime rate is $Θ((A^2+s^2\ell^{2q})/(μT^{2q}))$. These rates require domination of the deterministic and finite-variance terms; matching lower bounds require $d\ge\lceil L^2/s^2\rceil$, while the upper bounds hold in every finite dimension. The new upper bounds attain known statistical lower-bound orders, replacing the previous confidence coefficient $s^{1/p}L^{1-1/p}$ by $s$, and its square by $s^2$ under strong convexity. The key is an online inequality that separates directional fluctuations from the total second moment created by rejection sampling. Localization preserves this separation under strong convexity without additional horizon logarithms. The results characterize oracle complexity with unrestricted internal computation.

math.OC↗

arXiv2026

Joint Lower Bounds for Zeroth-Order Nonconvex Optimization on Euclidean Balls

We prove a joint stochastic zeroth-order lower bound for Goldstein stationarity on a Euclidean query ball, even when the ball is guaranteed to contain a stationary point. In dimension $d$, let $f=\mathbb{E}[F(\cdot;ξ)]$, assume $\mathbb{E}[\operatorname{Lip}(F(\cdot;ξ))^2]\le L_0^2$, and bound the initial objective gap over the ball by $Δ$. For neighborhood radius $δ>0$ and residual tolerance $\varepsilon>0$, our smooth hard family requires $Ω(dL_0^2Δ/(δ\varepsilon^3))$ scalar evaluations for success probability $1/2$, against randomized adaptive algorithms that may retain and repeatedly query each sampled function. The result holds for $\varepsilon\le cL_0$, $Δ\ge Cδ\varepsilon$, and $d\ge C[1+\log(2+ΔL_0^2/(δ\varepsilon^3))]$, on a constructed ball of radius $Θ(Δ/\varepsilon)$. A sequence of localized regions forces repeated direction estimation, and an adaptive Gaussian posterior argument controls sample reuse. The result establishes a joint dimension and accuracy obstruction on solvable bounded-domain instances. The gap is local to the query ball; a matching minimax characterization at a common radius and the corresponding unrestricted global-gap lower bound remain open here.

math.OC↗

arXiv2026

Sharp Minimax Rates for Highly Smooth Strongly Convex Zeroth-Order Optimization

We determine the minimax dimension dependence of noisy zeroth-order optimization for globally strongly convex functions with higher-order smoothness in multilinear operator norm. Each query returns one function value with fresh independent Gaussian noise. For dimension $d$, query budget $T$, and any fixed finite smoothness order $β>2$, the minimax expected objective error satisfies $\mathcal{E}_β(T,d)=Θ_β\left(\min\left\{1,(d^2/T)^{(β-1)/β}\right\}\right)$, with dimension-independent strong-convexity, gradient-smoothness, higher-order-smoothness, noise, and minimizer-radius bounds. Thus, for sufficiently small target error $\varepsilon$, the necessary and sufficient number of noisy values is $Θ_β(d^2\varepsilon^{-β/(β-1)})$, with no logarithmic loss. The new lower bound matches the dimension and budget dependence of the upper bound of Akhavan et al. (2024), and holds for arbitrary randomized adaptive algorithms with unrestricted query points. Its key step localizes a normalized hypercube with one radial cutoff: a query can emphasize one hidden coordinate, but the aggregate information about all coordinates remains small. A self-contained multiscale spherical estimator attains the matching upper bound by cancelling lower-order bias terms. Constants in the rates depend only on the fixed smoothness order under the stated normalization.

math.OC↗

arXiv2026

Matching Upper and Lower Bounds for Higher-Order Nonconvex Finite-Sum Optimization

We establish tight randomized higher-order oracle complexity for finding first-order stationary points of nonconvex finite sums. Let $n$ be the number of components, $Δ>0$ the initial objective-gap bound, $L_p>0$ an individual $p$-th derivative Lipschitz bound, and $ε>0$ the target gradient norm. For every fixed integer $p\ge 2$, the minimax number of exact component queries returning the value and all derivatives through order $p$, with success probability at least $2/3$, is \[ Θ_p\!\left( n+ΔL_p^{1/p}n^{1-1/(2p)} ε^{-(p+1)/p} \right), \] where the constants depend only on $p$ and the worst case ranges over all finite dimensions. The lower bound holds for unrestricted randomized adaptive algorithms and closes the $\sqrt{n}$ gap between the previously known general-order upper and lower bounds in their dependence on $n$. We extend dense weak hiding to complete higher-order replies while keeping each component's regularity independent of the chain length. The matching upper bound retains the known finite-sum exponent, requires only mean-squared $p$-th derivative increments, and removes the fixed-confidence logarithmic loss by verifying entire recursive-estimation epochs with exact function values. The characterization includes the additive $n$ term for every positive parameter regime; it counts oracle calls with unrestricted internal computation.

math.OC↗

arXiv2026

Second-Order Stationarity with Common Random Losses: Matching Tolerance Bounds

We establish tight polynomial tolerance bounds for stochastic second-order stationarity when each fresh oracle response is a derivative of one common random scalar loss. For a population objective $F$ with Lipschitz gradient and Hessian, the target is $\|\nabla F(x)\|\le ε$ and $λ_{\min}(\nabla^2 F(x))\ge -γ$, with independent tolerances $ε,γ>0$. Under bounded gradient variance and almost-surely bounded Hessian error, the minimax number of fresh gradient or Hessian-vector-product calls is $\widetildeΘ\!\left(ε^{-3}+γ^{-5}\right)$. The characterization fixes positive gap, smoothness, and noise parameters, suppresses logarithmic factors, and allows dimension to grow within an explicit polynomial envelope. The upper bound removes the mixed term $ε^{-2}γ^{-2}$ from the earlier fresh-HVP guarantee. Direct random-line Hessian estimates and a dyadic gradient tracker separate gradient drift from randomly signed curvature motion. The lower bound realizes the endpoint costs through globally defined smooth random losses: a smooth partition localizes scalar noise without a chain-length penalty, while exact cancellation limits the information in the entire response. Consequently, the same tolerance exponents hold even for joint value, gradient, and full-Hessian responses with bounded value variance. For a population Hessian with Hölder exponent $ν\in(0,1]$, fresh gradient/HVP complexity becomes $\widetildeΘ\!\left(ε^{-3}+γ^{-(3+2/ν)}\right)$ under the corresponding dimension envelope.

math.OC↗

arXiv2026

Near-Optimal Higher-Order Oracle Complexity for Convex--Concave Minimax Optimization

For smooth convex--concave minimax optimization, the higher-order lower bound of Chen et al. (2026) applies to a restricted tensor-algorithm class with prescribed regularized Taylor-model updates. We establish the same bound for arbitrary adaptive deterministic and randomized algorithms, matching, up to logarithmic factors, the upper bound of Zhang et al. (2026). Fix an integer $p\ge 2$ and let $L_p>0$ bound the Lipschitz constant of the objective's $p$-th derivative on a compact convex product domain of diameter at most $D_Z>0$. Each feasible query returns the objective value and all derivatives through order $p$. For accuracy $ε>0$, set $Q_{\mathrm{tan}}=L_pD_Z^p/ε$ for tangent residual and $Q_{\mathrm{gap}}=L_pD_Z^{p+1}/ε$ for saddle gap. Let $T_E^{\mathrm{det}}(ε)$ and $T_E^{\mathrm{rand}}(ε)$ denote the high-dimensional minimax query complexities for criterion $E\in\{\mathrm{tan},\mathrm{gap}\}$, with randomized success probability at least $2/3$ on every instance. Our lower bounds and the existing upper bound give $c_pQ_E^{2/(3p-1)}\le T_E^{\mathrm{rand}}(ε)\le T_E^{\mathrm{det}}(ε)\le C_pQ_E^{2/(3p-1)}[1+\log(3+Q_E)]^{6(p-1)}$ for sufficiently large $Q_E$, where $c_p,C_p>0$ depend only on $p$. Thus the same accuracy exponent holds beyond tensor update rules, even for randomized queries and arbitrary feasible outputs. The proof constructs a scalar convex--concave chain with exactly flat gates that hide complete derivative information. Direct product-domain error witnesses and adaptive transcript arguments establish the lower bounds for both criteria.

math.OC↗

arXiv2026

Matching Lower Bounds for Randomized First-Order Methods in Hessian-Lipschitz Nonconvex Optimization

We establish a randomized first-order lower bound for finding an $ε$-stationary point, $\|\nabla f(x)\|\le ε$, of a nonconvex function with initial gap at most $Δ$, $L_1$-Lipschitz gradient, and $L_2$-Lipschitz Hessian. Each oracle call returns the exact function value and gradient. Let $Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(ε;Δ,L_1,L_2)$ denote the minimax number of calls, maximized over finite dimensions, for arbitrary adaptive randomized algorithms with per-instance success probability at least $2/3$. In the regime $ε\lesssim L_1^2/L_2$ and $ΔL_2^{1/2}ε^{-3/2}\gtrsim 1$, we prove $ Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(ε;Δ,L_1,L_2) \ge c\,ΔL_1^{1/2}L_2^{1/4}ε^{-7/4}, $ where $c>0$ is an absolute constant. This matches the deterministic restarted accelerated-gradient upper bound of Li and Lin (2023) and extends the sharp deterministic lower bound of Zhou (2026) to unrestricted randomized algorithms. Thus, randomization does not improve the high-dimensional worst-case query rate. The construction keeps quadratic curvature visible while revealing the forcing directions sequentially. Large eigenspaces limit preprocessing, and a scheduled-disclosure coupling makes each fresh direction incur a separate cost.

math.OC↗

arXiv2026

TCMaster: Confidence-Aware Querying and Workload-Guided Physical Design for Multi-Source Traditional Chinese Medicine Knowledge Graphs

Multi-source knowledge graphs (KGs) need query mechanisms that expose reliability and exploit domain structure. This paper presents TCMaster, a property-graph query substrate for confidence-aware traversal and workload-guided physical design over Traditional Chinese Medicine KGs. TCMaster integrates pharmacopoeias, prescriptions, molecular databases, and LLM-extracted micro-semantics into a KG with approximately 221K entities and 723K base edges. It annotates edges with provenance-level confidence, rewrites Cypher queries with confidence predicates, ranks multi-hop paths under PRODUCT, MIN, or weighted-average policies, and uses ontology skew through direction selection, herb-attribute bitmaps, and materialized shortcut edges. On Neo4j, direction selection improves attribute lookup by a factor of 1.47, shortcuts accelerate high-fanout target counting by a factor of 4.42, confidence filtering removes 39.3 percent of low-quality heterogeneous paths, and KG retrieval improves TCMbench QA accuracy by 20.0 percentage points.

cs.AI↗

arXiv2026

LingLan: An Advancing Traditional Chinese Medicine Diagnosis LLM with Multimodal Data

Though artificial intelligence (AI) increasingly transforms modern medicine, its integration into Traditional Chinese Medicine (TCM) has been relatively slow, primarily due to TCM's reliance on holistic, subjective diagnostic methods---namely Inspection, Auscultation and Olfaction, Inquiry, and Palpation(I-AOI-P)---which are difficult to align with quantitative, standardized medical systems. In this work, we introduce a Unification Framework for Multimodal Data (UFMD), which automatically processes tongue and pulse images into structured, clinically standard descriptions, integrating multi-source diagnostic information into a unified digital record of I-AOI-P process. Building on this structured data, we create LingLan-14B, a TCM-specific large language model fine-tuned via supervised learning to emulate the diagnostic logic and workflow of I-AOI-P process. Experimental results show that our method significantly enhances diagnostic accuracy, achieving a relative improvement of 103.5% over the baseline (62.72% vs. 30.82%) and reaching an F1-score of up to 82%.

cs.AI↗

arXiv2026

Syndrome, Synergy, and Safety: Structured Reasoning and Knowledge-Driven Alignment for TCM Prescription Generation

Applying large language models to Traditional Chinese Medicine (TCM) prescription generation reveals three clinically critical gaps: models produce end-to-end mappings without auditable reasoning following the li-fa-fang-yao paradigm (SR Gap), treat each encounter in isolation without follow-up adjustment via sui zheng jia jian (LA Gap), and fail to enforce absolute contraindication rules such as Shi Ba Fan (SC Gap). We propose a progressive four-stage framework (SFT $\to$ PG-CoT $\to$ Dynamic $\to$ K-RL) that addresses each gap: PG-CoT constrains CoT distillation under the li-fa-fang-yao paradigm to produce auditable diagnostic chains, Dynamic SFT models patient trajectories with explicit transition reasoning, and K-RL encodes deterministic pharmacological rules as rule-based DPO preference signals. Across 12 fine-tuned models and 6 zero-shot baselines, our framework substantially improves prescription quality over zero-shot baselines---with a 7B model (Mistral-7B) surpassing zero-shot GPT-5 on all three TCM evaluation metrics.

cs.CL↗

arXiv2026

Sharp Fresh-Gradient Complexity of Nonconvex-Strongly-Concave Minimax Optimization

We characterize the fresh-gradient oracle complexity of smooth nonconvex-strongly-concave minimax optimization, with matching upper and lower bounds up to logarithmic factors. Let $Φ(x)=\max_y f(x,y)$, where $f$ is jointly $L$-smooth and $μ$-strongly concave in $y$ on unconstrained Euclidean domains, and set $κ=L/μ$. Each query returns a fresh unbiased joint gradient with conditional variance at most $σ^2$. Given initial primal gap at most $Δ$ and dual residual $\|\nabla_y f(x_0,y_0)\|\le G$, the fixed-budget complexity of finding $\|\nablaΦ(\widehat x)\|\leε$ with probability at least $2/3$ is $\widetildeΘ(\sqrtκLΔ/ε^2+κLΔσ^2/ε^4+κ^2σ^2/ε^2+\sqrtκ\log_+(G/(ε\sqrtκ)))$, where $\log_+u=\log\max\{1,u\}$. This characterization holds when $κ$ and $LΔ/ε^2$ exceed universal constants, uniformly over finite dimensions, and the suppressed logarithms are independent of $G$. It establishes the necessity of linear condition-number dependence in the global stochastic cost and identifies a separate statistical refinement cost. A proximal method separates coarse primal progress from one final refinement, while the lower bounds apply to arbitrary adaptive randomized algorithms. Dual initialization contributes only an additive logarithmic cost, yet removing its control eliminates every finite dimension-free complexity bound, even with exact gradients.

math.OC↗

arXiv2026

Bridge3D: Enabling Vision-Language-Action Models to See and Act in 3D

Vision-Language-Action (VLA) models have demonstrated remarkable generalization in robotic manipulation via large-scale multimodal pretraining. However, VLA models are mainly trained on 2D-centric observations, which inherently constrains their capacity for precise spatial manipulation. Previous methods enhance 3D awareness by introducing implicit spatial priors, but still lack explicit geometry guidance. In this paper, we propose Bridge3D that integrates both implicit and explicit 3D geometry guidance into pre-trained 2D VLA models, enabling them to ''see'' and ''act'' in 3D. Bridge3D introduces two strategies: 1) Implicit Fusion, which enriches visual tokens with features from 3D foundation models to improve ''seeing'' in 3D; 2) Explicit Conditioning, which integrates action denoising with an explicit 3D semantic field to achieve ''acting'' in 3D. Furthermore, we utilize the proposed layer-wise linear probing to improve learning efficiency. Experiments show that Bridge3D achieves superior performance against state-of-the-art methods. On the RoboTwin 2.0 benchmark, Bridge3D exceeds $π_0$ by 14.0 percentage points, while in real-world experiments, it outperforms Spatial Forcing by 11.7 percentage points. These results demonstrate Bridge3D's strong capabilities in high-precision and spatial-sensitive manipulation tasks.

cs.RO↗