SearcharxivSearch

arXiv subjects

Yichen Wang

Publications and source records attributed to Yichen Wang.

At least 19 recordsLinked to original sources

Motus2: A Self-Evolving General World Model for Dexterous Manipulation

General embodied agents should perceive, predict, act, evaluate, and improve within a unified system. World models have shown great promise in building such agents, yet existing models typically append an action output head to a world simulator, without coupling them into a closed decision-and-learning loop for policy improvement. We present Motus2, a self-evolving general world model for dexterous manipulation. Motus2 advances world modeling through model scaling and data scaling. For model scaling, a single model with shared weights exposes three control interfaces: a policy (world-action model), a simulator (action-conditioned world model), and an evaluator (value model). The policy proposes candidate action chunks, the simulator predicts their visual consequences, and the evaluator assesses the predicted outcomes. Their coupling forms a closed decision-and-learning loop for policy improvement. This formulation uses curated expert demonstrations for action learning, while failed and suboptimal interactions provide valuable evidence for dynamics modeling and value learning. For data scaling, Motus2 progresses from large-scale monocular egocentric data to synchronized stereo egocentric data, followed by robot-domain adaptation with robot trajectories and supplementary human-robot alignment data. Motus2 further studies global-autoregressive and hybrid-memory extensions of its sliding-window context, adds tactile feedback for contact-aware control, and is instantiated on a fully biomimetic platform with stereo vision, dual arms, dual dexterous hands, and tactile sensing. Together, egocentric data scaling and closed-loop general world model scaling provide a general path toward self-evolving dexterous manipulation.

cs.RO

Inversion Diameter of Planar Graphs

Given an oriented graph $\vec{G}$ and a subset of vertices $X \subseteq V(\vec{G})$, the \emph{inversion} of $X$ is the operation that reverses the orientation of every arc with both endpoints in $X$. For a simple graph $G$, the inversion diameter $\operatorname{diam}(I(G))$ is the maximum distance between two orientations of $G$ under inversions of vertex sets. We prove the sharp bound \[ \operatorname{diam}(I(G))\le 2\chi_a(G)-2, \] where $\chi_a(G)$ is the acyclic chromatic number. Consequently, every planar graph has inversion diameter at most $8$, improving the previously known bound $12$. Using strong-degeneracy arguments, we also obtain upper bounds $7$, $5$, and $4$ for planar graphs of girth at least $4$, $5$, and $6$, respectively.

math.CO

JTA: Joint Testability Architecture for Scenario-Based Validation of Safety-Critical Software

Validation adequacy in safety-critical software depends on more than the system under test. Critical scenarios must be constructed under controlled conditions, execution evidence must be aligned into verdict-ready form, and abnormal outcomes must be attributable to actionable causes. Existing testability research remains largely artifact-centric and offers little architectural support for reasoning about the combined capability of the scenario, the test system, and the system under test. Joint Testability Architecture (JTA) addresses this gap by treating those three elements as a single object of analysis and design. It characterizes validation capability along three dimensions--controllability, observability, and isolability--and organizes them through three domains, three bridges, and an analysis-design-evaluation-refinement loop. JTA also introduces scenario contracts, joint capability assessment, validation blind-spot identification, and bridge-oriented design actions that map capability gaps to concrete improvements in control points, evidence organization, and attribution boundaries. An illustrative analysis of ArduPilot failsafe validation shows that link-loss scenarios are comparatively mature, whereas state-estimation anomaly scenarios remain harder to validate because evidence alignment and attribution semantics are weaker. JTA is not a replacement for existing testing or safety-analysis techniques; it provides an architectural basis for modeling, designing, and assessing scenario-based validation in safety-critical software.

cs.SE

A stability theorem for Berge Hamiltonian cycles under a minimum degree condition

In this paper, we study extremal and stability problems for Berge Hamiltonian cycles in $r$-uniform hypergraphs under a minimum degree condition. Let $ g_r(n,t)=\binom{n-t}{r}+t\binom{t}{r-1}$, and let $t=t(k)$ be the unique integer satisfying $\binom{t-1}{r-1}<k\le \binom{t}{r-1}$. Using a sharp P\'osa-type degree sequence theorem of Salia, we prove an extremal upper bound on the number of hyperedges in an $n$-vertex $r$-uniform hypergraph with minimum degree at least $k$ and with no Berge Hamiltonian cycle. We also prove a stability theorem in the dense range before the first minimizer of $g_r(n,t)$: every near-extremal example is contained in one of two natural non-Hamiltonian constructions.

math.CO

The maximum number of odd cycles in planar graphs forbidding shorter odd cycles

Given a graph $H$ and a family of graphs $\mathcal{F}$, the generalized planar Tur\'an number $\mathrm{ex}_\mathcal{P}(n, H, \mathcal{F})$ is the maximum number of copies of $H$ in an $n$-vertex planar graph that contains no graph $F \in \mathcal{F}$ as a subgraph. When only induced copies of $H$ are counted, we denote the corresponding generalized planar Tur\'an number by $\mathrm{ex}_\mathcal{P}(n, H^{\mathrm{ind}}, \mathcal{F})$. Gy\H{o}ri and Karim determined $\mathrm{ex}_\mathcal{P}(n, C_{5}, \{C_3\})$. In this paper, we determine the exact value of $\mathrm{ex}_\mathcal{P}(n, C_{2k+1}, \{C_3,C_5,\ldots,C_{2k-1}\})$ for every $k \ge 3$. Since all shorter odd cycles are forbidden, every $C_{2k+1}$ is induced. This problem is closely related to the inducibility of odd cycles in planar graphs. Ghosh, Gy\H{o}ri, Janzer, Paulos, Salia and Zamora~(and independently Savery) determined the exact value of $\mathrm{ex}_\mathcal{P}(n, C_5^{\mathrm{ind}}, \emptyset)$. Moreover, they established a conjecture for all odd cycles $C_{2k+1}$ with $k \ge 3$. Our result confirms their conjecture under the additional assumption that all shorter odd cycles are forbidden.

math.CO

Shell-Supervised Gaussian Splatting for Urban Real-to-Sim Reconstruction

Real-to-sim reconstruction for embodied AI requires geometry that is useful for collision reasoning, navigation, and agent-environment interaction, not only photorealistic novel-view synthesis. However, close-range urban facades are difficult for video-to-3D reconstruction: glass, reflections, repeated windows, and weak texture can produce visually plausible renderings with unstable surface geometry. We introduce shell-supervised Gaussian Splatting, a reconstruction-stage framework that uses an external facade structural shell as lightweight geometric supervision for video-driven Gaussian reconstruction. The method aligns an exterior shell to the video reconstruction frame, renders per-view depth, camera-space normal, and valid-mask maps, and applies these cues through mask-gated losses during Gaussian optimization. This design preserves RGB-driven appearance while regularizing only visible shell-supported facade regions. Experiments on anonymized close-range urban facade scenes show improved facade orientation and visible-surface point-cloud consistency over photo-only, monocular-cue, and surface-oriented Gaussian baselines, while maintaining comparable held-out rendering quality.

cs.CV

Concordia: JIT-Compiled Persistent-Kernel Checkpointing for Fault-Tolerant LLM Inference

Long-running LLM agents keep valuable state resident on GPUs: KV caches, request schedulers, communication state, and sometimes online adapters. Losing this state after a GPU or communicator failure can discard minutes to hours of work, yet existing recovery mechanisms either restart the whole serving stack or require application-specific checkpoint logic inside every attention and runtime component. This paper argues that fault tolerance for such workloads needs a GPU-resident execution context: checkpoint hooks must run at device synchronization points, observe binary kernels that frameworks and libraries actually execute, and recover without putting the host CPU on the critical path. We present Concordia, a runtime that uses a device-resident persistent kernel as the substrate for fault-tolerant LLM inference. Concordia interposes on GPU module loading and supports PTX- and SASS-level instrumentation, allowing checkpoint and pause hooks to be inserted below framework code and library boundaries. For each registered LLM state region, Concordia JIT-compiles a specialized delta-checkpoint handler -- for example, a KV-block scanner, adapter-page scanner, or recovery applier -- and hot-swaps it into the persistent kernel's operator table. The persistent kernel consumes a lock-free ring buffer of compute, checkpoint, append-log, and recovery tasks, so the same always-on executor triggers dirty-page detection, stages deltas, and appends committed records to a CPU-visible log in CXL memory or host DRAM.

cs.DC

SurGE: Surrogate Gradient-guided Evolution for Co-design of Legged Robots with Parallel Elasticity

Co-design of legged robots with elastic elements is challenging due to the non-differentiability of contact dynamics and mechanism engagement. This paper presents SurGE, a framework that computes surrogate gradients of the design objective through a differentiable pipeline consisting of a kinodynamic single-rigid-body (Kino-SRB) model and a design-aware control policy, and injects them into CMA-ES via mean shift with cosine-annealed step decay. On a 4-DOF design space of a hopping robot with unidirectional parallel spring, SurGE achieves 6 times lower cross-seed standard deviation and 18% tighter population concentration compared to vanilla CMA-ES, while matching or improving the best objective. Hardware experiments on a 2D design subspace show that, starting from a hand-tuned initial design, SurGE reduces the design objective by 37.65% on hardware, with the improvement trend identified in simulation transferring consistently to the physical system. SurGE provides the potential to accelerate non-differentiable co-design problems in legged robots via surrogate model gradients.

cs.RO

On the Tur\'an number of blow-ups of $\mathcal{F}_5$

Let $\mathcal{F}_5$ denote the $3$-uniform hypergraph on the vertex set $\{f_1,f_2,\dots,f_5\}$ with hyperedges $\{f_1f_2f_3,f_1f_2f_4,f_3f_4f_5\}$. Recently, Balogh, Clemen and Luo determined the Tur\'an number of a one-vertex blow-up of $\mathcal{F}_5$, more specifically, they blow up the vertex $f_5$ to $t$ vertices, the resulting hypergraph is denoted by $\mathcal{F}_5(f_5;t)$. They show that for infinitely many $t$, $\mathcal{F}_5(f_5;t)$ has exponentially many extremal constructions and positive Tur\'an density. In this paper, we determine the exact Tur\'an number of the hypergraph obtained by blowing up $f_3$ of $\mathcal{F}_5$ to $t$ vertices and show that it also has exponentially many extremal constructions. We also give a general upper bound and lower bound of the Tur\'an number of every blow-up of $\mathcal{F}_5$. For some special blow-ups of $\mathcal{F}_5$, for example, $t$-disjoint copies of $\mathcal{F}_5$, we determine the exact Tur\'an number. We construct a hypergraph $\mathcal{F}_{sim}(t)$ which is a subgraph of a blow-up of $\mathcal{F}_5$, and is contained in the hypergraph obtained by adding any new hyperedge to the Tur\'an hypergraph (the balanced complete $3$-partite hypergraph), but its extremal construction is not the Tur\'an hypergraph. We also determine the exact Tur\'an number of $\mathcal{F}_{sim}(t)$.

math.CO

Algorithm for finding vertex-edge domination number on graphs with bounded treewidth and related problems on planar graphs

Given a graph $G=(V,E)$, a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\in E$, there exists a vertex $u\in S$ such that $u$ ve-dominates $e$. The minimum cardinality among all ve-dominating sets is known as the \textit{vertex-edge domination number} (or simply ve-domination number) and denoted by $\gamma_{ve}(G)$. Finding a minimum ve-dominating set was proved to be NP-complete. Restricted to trees, the problem admits a linear-time algorithm. Treewidth is a commonly used parameter for solving NP-hard problems. In this paper, we present a polynomial-time algorithm for finding a minimum ve-dominating set on graphs with bounded treewidth. Moreover, we show that the treewidth of a planar graph $G$ with ve-domination number $\gamma_{ve}(G)$ is $O(\sqrt{\gamma_{ve}(G)})$ and present an $O(c^{\sqrt{k}}|V(G)|)$-time algorithm for the $k$-ve-domination problem on planar graphs.

math.CO

The Granularity Mismatch in Agent Security: Argument-Level Provenance Solves Enforcement and Isolates the LLM Reasoning Bottleneck

Tool-using LLM agents must act on untrusted webpages, emails, files, and API outputs while issuing privileged tool calls. Existing defenses often mediate trust at the granularity of an entire tool invocation, forcing a brittle choice in mixed-trust workflows: allow external content to influence a call and risk hijacked destinations or commands, or quarantine the call and block benign retrieval-then-act behavior. The key observation behind this paper is that indirect prompt injection becomes dangerous not when untrusted content appears in context, but when it determines an authority-bearing argument. We present \textsc{PACT} (\emph{Provenance-Aware Capability Contracts}), a runtime monitor that assigns semantic roles to tool arguments, tracks value provenance across replanning steps, and checks whether each argument's origin satisfies its role-specific trust contract. Under oracle provenance, \textsc{PACT} achieves 100\% utility and 100\% security on mixed-trust diagnostic suites, while flat invocation-level monitors incur false positives or false negatives. In full AgentDojo deployments across five models, \textsc{PACT} reaches 100\% security on the three strongest models while recovering 38.1--46.4\% utility, 8--16 percentage points above CaMeL at the same security level. Ablations show that both semantic roles and cross-step provenance are necessary. \textsc{PACT} reframes agent security as authority binding, and isolates the remaining deployment bottleneck to provenance inference and contract synthesis.

cs.CR

A generalization of Erd\H{o}s-Hajnal problem on paths with equal-degree endpoints

Erd\H{o}s and Hajnal proposed a problem that: is it true that every $(2n+1)$-vertex graph with $n^2+n+1$ edges contains two vertices of equal degree connected by a path of length three? The edge bound is sharp by the complete bipartite graph $K_{n,n+1}$. Recently, Chen and Ma [Journal of Combinatorial Theory, Series B, 179:1-18, 2026] answered this problem affirmatively for every $n \ge 600$. In the same paper, they further conjectured that for sufficiently large $n$, the statement is true if we replace the path of length three by a path of fixed odd length. In this paper, we confirm their conjecture.

math.CO

Hu\'i S\`u: Co-constructing a Dual Feedback Apparatus

This performance presents a duet between two intelligent musical instruments, S\`u (to trace back; to go upstream) and Agentier (playing on agentic clavier), and their human performers, connected through feedback loops. Rather than treating AI as a tool that responds predictably to input, both systems operate recursively, where past actions continuously influence future behaviour. The S\`u operates in the audio space through latent representation. Its performer uses Make Noise 0-series synthesisers and MIDI controllers to work with a neural feedback synthesis system based on a RAVE model, with a latent feedback loop embedded within the model's internal structure. This allows the instrument to remember and reuse its own internal states, influencing ongoing sound generation through its recent sonic history. The Agentier functions in the control space. Its performer interacts with the system using a Roland S-1 synthesiser and Keith McMillen QuNeo touchpad, where control gestures are routed into a recurrent neural network that feeds back into the synthesis process. Through this feedback loop, the system actively shapes the evolution of control signals over time. Contrasting feedback in the audio and control domains, the performance explores shared agency, resistance, and negotiation between humans and intelligent musical systems. Musical phenomena are co-produced through the entangled states of interaction, rather than through pre-existing system configuration or fixed mappings.

cs.SD

Transferable Physical-World Adversarial Patches Against Object Detection in Autonomous Driving

Deep learning drives major advances in autonomous driving (AD), where object detectors are central to perception. However, adversarial attacks pose significant threats to the reliability and safety of these systems, with physical adversarial patches representing a particularly potent form of attack. Physical adversarial patch attacks pose severe risks but are usually crafted for a single model, yielding poor transferability to unseen detectors. We propose AdvAD, a transfer-based physical attack against object detection in autonomous driving. Instead of targeting a specific detector, AdvAD optimizes adversarial patches over multiple detection models in a unified framework, encouraging the learned perturbations to capture shared vulnerabilities across architectures. The optimization process adaptively balances model contributions and enforces robustness to physical variations. It further employs data augmentation and geometric transformations to maintain patch effectiveness under diverse physical conditions. Experiments in both digital and real-world settings show that AdvAD consistently outperforms state-of-the-art (SOTA) attacks in performance and transferability.

cs.CV

On the largest chromatic number of $F$-free hypergraphs

Given a hypergraph $F$, what is the largest chromatic number that an $F$-free hypergraph can have? In the case of graphs, this question is easy to answer: the chromatic number is unbounded if $F$ contains a cycle, and the largest chromatic number of $F$-free graphs is $k-1$ if $F$ is a forest on $k$ vertices. The situation is more complicated for hypergraphs. The strong coloring of a hypergraph is a coloring of the vertices such that every hyperedge is rainbow. The weak coloring of a hypergraph is a coloring of the vertices such that no hyperedge is monochromatic. The strong/weak chromatic number of a hypergraph is the minimum number of colors in a strong/weak coloring of the hypergraph. Our question has been completely answered for the weak chromatic number, similarly to the graph case. We characterize the hypergraphs $F$ such that $F$-free hypergraphs have bounded strong chromatic number. The only remaining case is when $F$ is the 3-uniform expansion $S_k^+$ of a star with $k$ edges. Concerning the strong chromatic number of $S_k^+$-free hypergraphs, we give bounds that are asymptitically sharp as $k\rightarrow\infty$. We also consider the same problem when the Berge copies of a graph $F$ are forbidden. We characterize when the strong/weak chromatic numbers are bounded in this case, and obtain sharp results or bounds for specific trees. In particular, when $F$ is a path, we give a tight bound when $r=3$ and an asymptotically sharp bound when $r=4$.

math.CO

The Tur\'{a}n number of the Cartesian product of a star and an edge

Let $C_k$ denote the cycle of length $k$, $S_t$ be a star with $t$ edges. And let $B_t$ be the graph consisting of $t$ copies of $C_4$ sharing one fixed edge. Equivalently, $B_t=K_2 \mathbin{\square} S_t$, which is the Cartesian product of a star with $t$ edges and an edge. Recently, Gao, Janzer, Liu and Xu [\textit{Israel J. Math. 269(2025)}] proved that the Tur\'an number of $K_2\mathbin{\square} C_{2l}$ is $\Theta(n^{\frac{3}{2}})$ for every $l\ge 4$. In this paper, we obtain upper and lower estimates for the Tur\'an number of $B_t$ in both the general and bipartite settings for every $t\geq 2$. For the lower bound, we use random construction based on the extremal structure of $C_4$. These results imply that $\frac{1}{2\sqrt{2}}\leq \lim_{t\to \infty} \frac{\mathrm{ex}(n,B_t)}{\sqrt{t}}\leq \frac{1}{2}$, and $\frac{1}{4}\leq \lim_{t\to \infty} \frac{\mathrm{ex}_{bip}(n,B_t)}{\sqrt{t}}\leq \frac{1}{2\sqrt{2}}.$ In the case of $B_2$, we obtain sharper estimates. We show that the Tur\'an number of $B_2$ is approximately between $(0.518+o(1))n^{\frac{3}{2}}$ and $(0.603+o(1))n^{\frac{3}{2}}$. And in the bipartite setting, it is approximately between $(0.385+o(1))n^{\frac{3}{2}}$ and $(0.468+o(1))n^{\frac{3}{2}}$. Moreover, in the bipartite setting, we give a more general result, which shows that for every tree $T$ with $t$ edges, the bipartite Tur\'an number of $K_2\mathbin{\square}T$ is at most $\frac{\sqrt{t}}{2\sqrt{2}}(1+o(1))n^{\frac{3}{2}}$.

math.CO

Forbidding matching as trace in uniform hypergraphs

We say a hypergraph $\mathcal{H}$ contains a hypergraph $\mathcal{G}$ as trace if there exists a vertex subset $S \subseteq V(\mathcal{H})$ such that $|S| = |V(\mathcal{G})|$ and $\{e \cap S: e \in E(\mathcal{H})\}$ contains $\mathcal{G}$ as a sub-hypergraph. We use $\mathrm{ex}_r(n, \mathrm{Tr}_r(\mathcal{G}))$ to denote the maximum number of hyperedges in an $r$-uniform hypergraph on $n$ vertices not containing $\mathcal{G}$ as a trace. The study of Tur\'{a}n numbers for traces was initiated by Mubayi and Zhao who studied the case when $\mathcal{G}$ is a complete graph. Let $M_{s+1}$ denote the graph of a matching with $s+1$ edges. In this paper, we give the upper bound of $\mathrm{ex}_r(n, \mathrm{Tr}_r(M_{s+1}))$ which is sharp asymptotically. When $r=3$, we give the exact value of $\mathrm{ex}_3 (n, \mathrm{Tr}_3 (M_{s+1}))$. We also consider the generalized Tur\'{a}n number in the case of matching. That is, the maximum number of copies of clique $\mathcal{K}_t^r$ in hypergraphs forbidding $\mathrm{Tr}_r (M_{s+1})$ as a trace. We give an upper bound which is sharp asymptotically and when $r=3$, we give the exact value. The Tur\'{a}n number of forbidding a matching and the other graph is another well studied topic initiated by Alon and Frankl. We also consider an analogue problem for the trace version, i.e., forbidding trace of matching and trace of complete graph as subgraphs.

math.CO

The number of induced paths in outerplanar graphs

Let $P_k$ denote the path with $k$ vertices, and $\mathrm{ex}_{\mathcal{OP}}(n,H^{\mathrm{ind}},\emptyset)$ be the maximum number of induced copies of $H$ in an $n$-vertex outerplanar graph. In this paper, we determine the exact value of $\mathrm{ex}_{\mathcal{OP}}(n,P_3^{\mathrm{ind}},\emptyset)$ for all $n$, and give an asymptotic value of $\mathrm{ex}_{\mathcal{OP}}(n,P_4^{\mathrm{ind}},\emptyset)$. For general $k$, Matolcsi and Nagy proved that $\lim_{k\to \infty} {\left( \mathrm{ex}_{\mathcal{OP}}(n, P_{k+1},\emptyset)\right)^{1/k}} =4$. In the induced case, we prove that \[ fib(k-1)\frac{{(n-2k+3)}^2}{4} \le \mathrm{ex}_{\mathcal{OP}}(n, P_{k+1}^{\mathrm{ind}},\emptyset) \le fib(k+1) \binom{n}{2}, \] where $fib(k)$ is the Fibonacci number. This implies that $\lim_{k\to \infty} {\left( \mathrm{ex}_{\mathcal{OP}}(n, P_{k+1}^{\mathrm{ind}},\emptyset)\right)^{1/k}} = \frac{\sqrt{5}+1}{2}\approx 1.618$.

math.CO