arXiv subjects

Qi Feng

Publications and source records attributed to Qi Feng.

At least 37 records · Page 2Linked to original sources

arXiv2026

Spectrally-large scale geometry in cotangent bundles

In this paper, we prove that the ${\rm Ham}$-orbit space from a fiber of a large family of cotangent bundles, as a metric space with respect to the Floer-theoretic spectral metric, contains a quasi-isometric embedding of an infinite-dimensional normed vector space. The same conclusion holds for the group of compactly supported Hamiltonian diffeomorphisms of some cotangent bundles. To prove this, we generalize a result, relating boundary depth and spectral norm for closed symplectic manifolds in Kislev-Shelukhin's recent work, to Liouville domains. Then we modify Usher's constructions (which were used to obtain Hofer-large scale geometric properties) to achieve our desired conclusions.

math.SG↗

arXiv2026

GraphProp: Training the Graph Foundation Models using Graph Properties

This work focuses on training graph foundation models (GFMs) that have strong generalization ability in graph-level tasks such as graph classification. Effective GFM training requires capturing information consistent across different domains. We discover that graph structures provide more consistent cross-domain information compared to node features and graph labels. However, traditional GFMs primarily focus on transferring node features from various domains into a unified representation space but often lack structural cross-domain generalization. To address this, we introduce GraphProp, which emphasizes structural generalization. The training process of GraphProp consists of two main phases. First, we train a structural GFM by predicting graph invariants. Since graph invariants are properties of graphs that depend only on the abstract structure, not on particular labellings or drawings of the graph, this structural GFM has a strong ability to capture the abstract structural information and provide discriminative graph representations comparable across diverse domains. In the second phase, we use the representations given by the structural GFM as positional encodings to train a comprehensive GFM. This phase utilizes domain-specific node attributes and graph labels to further improve cross-domain node feature generalization. Our experiments demonstrate that GraphProp significantly outperforms the competitors in supervised learning and few-shot learning, especially in handling graphs without node attributes.

cs.LG↗

arXiv2026

Noise estimation of SDE from a single data trajectory

In this paper, we propose a data-driven framework for model discovery of stochastic differential equations (SDEs) from a single trajectory, without requiring the ergodicity or stationary assumption on the underlying continuous process. By combining (stochastic) Taylor expansions with Girsanov transformations, and using the drift function's initial value as input, we construct drift estimators while simultaneously recovering the model noise. This allows us to recover the underlying $\mathbb P$ Brownian motion increments. Building on these estimators, we introduce the first stochastic Sparse Identification of Stochastic Differential Equation (SSISDE) algorithm, capable of identifying the governing SDE dynamics from a single observed trajectory without requiring ergodicity or stationarity. To validate the proposed approach, we conduct numerical experiments with both linear and quadratic drift-diffusion functions. Among these, the Black-Scholes SDE is included as a representative case of a system that does not satisfy ergodicity or stationarity.

q-fin.ST↗

arXiv2026

An Analytic Solution to the Optimal Spherical Dubins Path Problem with Geodesic Curvature Constraints

Computing shortest paths for curvature-constrained Dubins vehicles on the unit sphere is fundamental to many engineering applications, including long-range flight planning, persistent surveillance patterns, and global routing problems where great circles are natural routes. Numerical optimization methods on $\SO(3)$ suffer from sensitivity to initialization, may converge to local minima, and often miss feasible solution branches. This paper proposes a unified analytic computational approach for spherical Dubins CGC and CCC paths that overcomes these limitations. By exploiting the axis-fixing property of rotations and developing a closed-form back-substitution method using geometric projection, the three-dimensional boundary value problem is reduced to solving a quadratic polynomial equation. The proposed analytic solver achieves machine precision accuracy with errors on the order of $10^{-16}$, is approximately $717$ times faster than numerical methods under the same computational environment, and systematically enumerates all feasible solution branches without requiring exhaustive multi-start initialization. The method provides closed-form solutions for optimal path computation in the regime where turning radius $\Rturn \in (0, 1/2]$, corresponding to $U_{\max} \geq \sqrt{3}$.

physics.geo-ph↗

arXiv2025

Deep Neural Operator Learning for Probabilistic Models

We propose a deep neural-operator framework for a general class of probability models. Under global Lipschitz conditions on the operator over the entire Euclidean space-and for a broad class of probabilistic models-we establish a universal approximation theorem with explicit network-size bounds for the proposed architecture. The underlying stochastic processes are required only to satisfy integrability and general tail-probability conditions. We verify these assumptions for both European and American option-pricing problems within the forward-backward SDE (FBSDE) framework, which in turn covers a broad class of operators arising from parabolic PDEs, with or without free boundaries. Finally, we present a numerical example for a basket of American options, demonstrating that the learned model produces optimal stopping boundaries for new strike prices without retraining.

cs.LG↗

arXiv2025

Data-driven Feynman-Kac Discovery with Applications to Prediction and Data Generation

In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability measure to recover the backward stochastic differential equation (BSDE) from a single pair of stock and option trajectories. Unlike existing approaches to identifying stochastic differential equations-which typically require ergodicity-our framework leverages the risk-neutral measure, thereby eliminating the ergodicity assumption and enabling BSDE recovery from limited financial time series data. Using this algorithm, we are able not only to make forward-looking predictions but also to generate new synthetic data paths consistent with the underlying probabilistic law.

q-fin.MF↗

arXiv2025

Branched Signature Model

In this paper, we introduce the branched signature model, motivated by the branched rough path framework of [Gubinelli, Journal of Differential Equations, 248(4), 2010], which generalizes the classical geometric rough path. We establish a universal approximation theorem for the branched signature model and demonstrate that iterative compositions of lower-level signature maps can approximate higher-level signatures. Furthermore, building on the existence of the extension map proposed in [Hairer-Kelly. Annales de l'Institue Henri Poincaré, Probabilités et Statistiques 51, no. 1 (2015)], we show how to explicitly construct the extension of the original paths into higher-dimensional spaces via a map $Ψ$, so that the branched signature can be realized as the classical geometric signature of the extended path. This framework not only provides an efficient computational scheme for branched signatures but also opens new avenues for data-driven modeling and applications.

math.NA↗

arXiv2025

Visuospatial Cognitive Assistant

Video-based spatial cognition is vital for robotics and embodied AI but challenges current Vision-Language Models (VLMs). This paper makes two key contributions. First, we introduce ViCA (Visuospatial Cognitive Assistant)-322K, a diverse dataset of 322,003 QA pairs from real-world indoor videos (ARKitScenes, ScanNet, ScanNet++), offering supervision for 3D metadata-grounded queries and video-based complex reasoning. Second, we develop ViCA-7B, fine-tuned on ViCA-322K, which achieves new state-of-the-art on all eight VSI-Bench tasks, outperforming existing models, including larger ones (e.g., +26.1 on Absolute Distance). For interpretability, we present ViCA-Thinking-2.68K, a dataset with explicit reasoning chains, and fine-tune ViCA-7B to create ViCA-7B-Thinking, a model that articulates its spatial reasoning. Our work highlights the importance of targeted data and suggests paths for improved temporal-spatial modeling. We release all resources to foster research in robust visuospatial intelligence.

cs.CV↗

arXiv2025

Towards Visuospatial Cognition via Hierarchical Fusion of Visual Experts

While Multimodal Large Language Models (MLLMs) excel at general vision-language tasks, visuospatial cognition - reasoning about spatial layouts, relations, and dynamics - remains a significant challenge. Existing models often lack the necessary architectural components and specialized training data for fine-grained spatial understanding. We introduce ViCA2 (Visuospatial Cognitive Assistant 2), a novel MLLM designed to enhance spatial reasoning. ViCA2 features a dual vision encoder architecture integrating SigLIP for semantics and Hiera for spatial structure, coupled with a token ratio control mechanism for efficiency. We also developed ViCA-322K, a new large-scale dataset with over 322,000 spatially grounded question-answer pairs for targeted instruction tuning. On the challenging VSI-Bench benchmark, our ViCA2-7B model achieves a state-of-the-art average score of 56.8, significantly surpassing larger open-source models (e.g., LLaVA-NeXT-Video-72B, 40.9) and leading proprietary models (Gemini-1.5 Pro, 45.4). This demonstrates the effectiveness of our approach in achieving strong visuospatial intelligence with a compact model. We release ViCA2, its codebase, and the ViCA-322K dataset to facilitate further research.

cs.CV↗

arXiv2025

Your Pretrained Model Tells the Difficulty Itself: A Self-Adaptive Curriculum Learning Paradigm for Natural Language Understanding

Curriculum learning is a widely adopted training strategy in natural language processing (NLP), where models are exposed to examples organized by increasing difficulty to enhance learning efficiency and performance. However, most existing approaches rely on manually defined difficulty metrics -- such as text length -- which may not accurately reflect the model's own perspective. To overcome this limitation, we present a self-adaptive curriculum learning paradigm that prioritizes fine-tuning examples based on difficulty scores predicted by pre-trained language models (PLMs) themselves. Building on these scores, we explore various training strategies that differ in the ordering of examples for the fine-tuning: from easy-to-hard, hard-to-easy, to mixed sampling. We evaluate our method on four natural language understanding (NLU) datasets covering both binary and multi-class classification tasks. Experimental results show that our approach leads to faster convergence and improved performance compared to standard random sampling.

cs.CL↗

arXiv2025

Superpositions for General Conditional Mckean-Vlasov Stochastic Differential Equations

In this paper, we study the connection between a general class of Conditional Mckean-Vlasov Stochastic Differential Equations (CMVSDEs) and its corresponding (infinite dimensional) Conditional Fokker-Planck Equation. The CMVSDE under consideration is similar to the one studied in [4], which is a non-trivial generalization of the McKean-Vlasov SDE with common noise and is closely related to a new type of non-linear Zakai equation that has not been studied in the literature. The main purpose of this paper is to establish the superposition principles among the three subjects so that their well-posedness can imply each other. More precisely, we shall first prove the superposition principle between the non-linear Zakai equation, a non-linear measure-valued stochastic PDE, and a CMVSDE; and then prove the superposition principle between an infinite dimensional conditional Fokker-Planck equation and the nonlinear Zakai equations. It is worth noting that none of the (weak) well-posedness of these SDEs/SPDEs in such generality have been investigated in the literature.

math.PR↗

arXiv2025

Non-Reversible Langevin Algorithms for Constrained Sampling

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.

cs.LG↗

arXiv2025

Spectrally-large scale geometry via set-heaviness

We show that there exist infinite-dimensional quasi-flats in the compactly supported Hamiltonian diffeomorphism group of the Liouville domain, with respect to the spectral norm, if and only if the symplectic cohomology of this Liouville domain does not vanish. In particular, there exist infinite-dimensional quasi-flats in the compactly supported Hamiltonian diffeomorphism group of the unit co-disk bundle of any closed manifold. A similar conclusion holds for the ${\rm Ham}$-orbit space of an admissible Lagrangian in any Liouville domain. Moreover, we show that if a closed symplectic manifold contains an incompressible Lagrangian with a certain topological condition, then its Hamiltonian diffeomorphism group admits infinite-dimensional flats. Proofs of all these results rely on the existence of a family of heavy hypersurfaces.

math.SG↗

arXiv2025

Notes on symplectic squeezing in $T^* \mathbb T^n$ and spectra of Finsler dynamics

In this paper, on the one hand, we prove that for $n \geq 2$ any subbundle of $T^* \mathbb T^n$ with bounded fibers symplectically embeds into a trivial subbundle of $T^* \mathbb T^n$ where the fiber is an irrational cylinder. This not only resolves an open problem in Gong-Xue's recent work (which was stated for the 4-dimension case, that is, $n =2$) and also generalizes to any higher-dimensional situation. The proof is based on some version of Dirichlet's approximation theorem. On the other hand, we generalize a main result in Gong-Xue's work mentioned above, showing that any topologically trivial Liouville diffeomorphism on $T^*M$ (for instance, a diffeomorphism induced by an isometry on $M$) does not change the full marked length spectrum of a Finsler metric $F$ on $M$, up to a lifting of the Finsler metric $F$ to the unit codisk bundle $D^*_FM$. The proof is based on persistence module theory.

math.SG↗

arXiv2025

Hypoelliptic entropy dissipation for stochastic differential equations

We study the convergence analysis for general degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to analyze the Fokker-Planck equation, in which the Lyapunov functional is chosen as a weighted relative Fisher information functional. We derive a structure condition and formulate the Lyapunov constant explicitly. We prove the exponential convergence result for the probability density function towards its invariant distribution in the $L_1$ distance. Two examples are presented: underdamped Langevin dynamics with variable diffusion matrices and three oscillator chain models with nearest-neighbor couplings.

math.DS↗

arXiv2025

VERITAS and multiwavelength observations of the Blazar B3 2247+381 in response to an IceCube neutrino alert

While the sources of the diffuse astrophysical neutrino flux detected by the IceCube Neutrino Observatory are still largely unknown, one of the promising methods used towards understanding this is investigating the potential temporal and spatial correlations between neutrino alerts and the electromagnetic radiation from blazars. We report on the multiwavelength target-of-opportunity observations of the blazar B3 2247+381, taken in response to an IceCube multiplet alert for a cluster of muon neutrino events compatible with the source location between May 20, 2022 and November 10, 2022. B3 2247+381 was not detected with VERITAS during this time period. The source was found to be in a low-flux state in the optical, ultraviolet and gamma-ray bands for the time interval corresponding to the neutrino event, but was detected in the hard X-ray band with NuSTAR during this period. We find the multiwavelength spectral energy distribution is well described using a simple one-zone leptonic synchrotron self-Compton radiation model. Moreover, assuming the neutrinos originate from hadronic processes within the jet, the neutrino flux would be accompanied by a photon flux from the cascade emission, and the integrated photon flux required in such a case would significantly exceed the total multiwavelength fluxes and the VERITAS upper limits presented here. The lack of flaring activity observed with VERITAS, combined with the low multiwavelength flux levels, and given the significance of the neutrino excess is at 3$σ$ level (uncorrected for trials), makes B3 2247+381 an unlikely source of the IceCube multiplet. We conclude that the neutrino excess is likely a background fluctuation.

astro-ph.HE↗

arXiv2025

An in-depth study of Gamma rays from the Starburst Galaxy M 82 with VERITAS

Assuming Galactic cosmic rays originate in supernovae and the winds of massive stars, starburst galaxies should produce very-high-energy (VHE; E$>$100 GeV) gamma-ray emission via the interaction of their copious quantities of cosmic rays with the large reservoirs of dense gas within the galaxies. Such VHE emission was detected by VERITAS from the starburst galaxy M 82 in 2008-09. An extensive, multi-year campaign followed these initial observations, yielding a total of 254 h of good quality VERITAS data on M 82. Leveraging modern analysis techniques and the larger exposure, these VERITAS data show a more statistically significant VHE signal ($\sim$6.5 standard deviations ($σ$)). The corresponding photon spectrum is well fit by a power law ($Γ= 2.3 \pm 0.3_{stat} \pm0.2_{sys}$) and the observed integral flux is F($>$450 GeV) = $(3.2 \pm0.6_{stat} \pm 0.6_{sys}) \times 10^{-13}~\mathrm{cm^{-2}~s}^{-1}$, or $\sim$0.4\% of the Crab Nebula flux above the same energy threshold. The improved VERITAS measurements, when combined with various multi-wavelength data, enable modeling of the underlying emission and transport processes. A purely leptonic scenario is found to be a poor representation of the gamma-ray spectral energy distribution (SED). A lepto-hadronic scenario with cosmic rays following a power-law spectrum in momentum (index $s\simeq 2.25$), and with significant bremsstrahlung below $1$~GeV, provides a good match to the observed SED. The synchrotron emission from the secondary electrons indicates that efficient non-radiative losses of cosmic-ray electrons may be related to advective escape from the starburst core.

astro-ph.HE↗

arXiv2024

SyncViolinist: Music-Oriented Violin Motion Generation Based on Bowing and Fingering

Automatically generating realistic musical performance motion can greatly enhance digital media production, often involving collaboration between professionals and musicians. However, capturing the intricate body, hand, and finger movements required for accurate musical performances is challenging. Existing methods often fall short due to the complex mapping between audio and motion, typically requiring additional inputs like scores or MIDI data. In this work, we present SyncViolinist, a multi-stage end-to-end framework that generates synchronized violin performance motion solely from audio input. Our method overcomes the challenge of capturing both global and fine-grained performance features through two key modules: a bowing/fingering module and a motion generation module. The bowing/fingering module extracts detailed playing information from the audio, which the motion generation module uses to create precise, coordinated body motions reflecting the temporal granularity and nature of the violin performance. We demonstrate the effectiveness of SyncViolinist with significantly improved qualitative and quantitative results from unseen violin performance audio, outperforming state-of-the-art methods. Extensive subjective evaluations involving professional violinists further validate our approach. The code and dataset are available at https://github.com/Kakanat/SyncViolinist.

cs.GR↗