arXiv subjects

Qi Feng

Publications and source records attributed to Qi Feng.

At least 19 recordsLinked to original sources

arXiv2026

Deep Neural Operator Learning for stochastic heat equations and applications

In this paper, we establish a universal approximation theorem for solution operators of semilinear stochastic heat equations in spatial dimension $d\ge2$, extending deep neural operator approximation results to SPDEs with distribution-valued Gaussian forcing. A smooth Fourier cutoff reduces the forcing to finitely many measurements, while Besov and Schauder estimates control the resulting solution error. The finite-dimensional solution map is then approximated by ReLU branch networks together with grid-based trunk functions, yielding explicit bounds on the numbers of forcing measurements and trunk functions and approximation in every finite stochastic moment. For linear equations, the reduction coincides with truncation of the first Wiener chaos. Lastly, as an application, we prove a high-probability local-in-time approximation theorem for stochastic Navier--Stokes equations, with finite measurements of both the initial condition and forcing and an explicit sensing rate.

cs.LG↗

arXiv2026

Underdamped Anchored Langevin Dynamics

Classical Langevin Monte Carlo algorithms, such as the unadjusted Langevin algorithm (ULA), are based on discretization schemes of the overdamped Langevin dynamics and are widely used for sampling in machine learning because they scale to high dimensions and large datasets. However, they require differentiable log-densities, and are less efficient for sampling heavy-tailed distributions. Although various approaches have been proposed in the literature for sampling non-differentiable and heavy-tailed targets, all of them are developed in the overdamped setting only. We propose a novel momentum-based underdamped anchored Langevin dynamics (UALD), and underdamped anchored Langevin Monte Carlo (UALMC) algorithm based on a discretization scheme of UALD. Our paper is the first to provide a kinetic (momentum-based) Langevin algorithm for non-differentiable and heavy-tailed targets that is free of asymptotic bias. The method replaces the original potential with a smooth reference potential and modifies the underdamped Langevin dynamics via multiplicative scaling in the drift term. We establish non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution and show that the resulting iteration complexity has better dependence on dimension and accuracy level compared to overdamped-based anchored Langevin algorithms. We provide numerical experiments to illustrate the theory and practical performance of our proposed approach.

cs.LG↗

arXiv2026

Initialization Stability and Convergence of Projected Langevin Dynamics

The entropic regularized optimal transport (EOT) plays a fundamental role in the computation of optimal transport. In \cite{CLP}, the authors proposed a gradient flow approach to EOT, and derived a projected Langevin diffusion that converges in distribution to the solution of EOT when initialized with a coupling between the two given marginals. In this paper, motivated by samplings of optimal couplings for EOT, we analyze the projected Langevin dynamics with arbitrary initial distribution, and prove that its long time behavior is the same as if it was initialized from a coupling.

math.PR↗

arXiv2026

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. We demonstrate the effectiveness of the proposed framework through two representative applications: rough volatility calibration and optimal execution.

math.NA↗

arXiv2026

Recall What Is Missing: Composing Evidence from Long-Term Agent Memory

Under a limited context budget, a long-term agent must recall not merely memories that are individually relevant, but evidence that is collectively sufficient for the current query. Conventional memory access retrieves, scores, and truncates memories, often spending multiple context slots on redundant facts while leaving complementary evidence behind. We cast the read phase of long-term memory as query-conditioned evidence composition: each memory is valued by what it adds beyond the evidence already selected. We instantiate this operation with MemPursuit, a training-free mechanism that uses the residual of a sparse convex query reconstruction as a representation-space proxy for what the current memory set is missing. By reusing the query and candidate embeddings already available from retrieval, MemPursuit progressively composes nested evidence contexts without invoking a language model or cross-encoder to score each query--memory pair. The effectiveness of our method is verified on 3 popular benchmarks in comparison to strong baselines. In fixed-budget LoCoMo experiments, MemPursuit improves end-to-end accuracy by 7.2 percentage points at Top-10 and 5.5 percentage points at Top-20, with consistent gains across multiple memory frameworks, while achieving a 32.9$\times$ speedup in median reranking latency over fully batched BGE-v2-m3. Our implementation is available at https://github.com/FengQi-HITSZ/MemPursuit.

cs.AI↗

arXiv2026

Continuous Policy and Value Iteration for Stochastic Control Problems with Inhomogeneous Synchronous Coupling

We propose a continuous policy-value iteration framework for infinite horizon stochastic control problems, in which the policy evolves through Langevin type dynamics driven by the gradient of the inhomogeneous Hamiltonian, while the value function is updated simultaneously with optimal policy iterations, avoiding directly solving its corresponding PDE at each iteration. The iteration scheme enjoys policy improvement under suitable regularity and admissibility assumptions. We show the exponential contraction of the joint policy value dynamics in Wasserstein-2 distance under the Lipschitz condition in expectation via the inhomogeneous synchronous coupling and verify these conditions for linear quadratic problems. Numerical experiments on linear quadratic models and the optimal consumption-investment problems in an incomplete market factor model illustrate policy improvement, convergence toward optimal policies, and the effect of decaying exploration noise.

math.OC↗

arXiv2026

Amortized Score-Hamiltonian Policy Iteration: A Grid-Free Scheme for Relaxed Stochastic Control Problems

We develop an amortized, grid-free implementation of continuous Langevin dynamics based policy-value iteration for entropy-regularized, infinite-horizon relaxed stochastic control problems. The improvement rate of the exact iteration is a discounted aggregate of relative Fisher information between the policy and the Gibbs law of its Hamiltonian. The associated score residual is the velocity with which the control's Langevin dynamics transport its law. We project this velocity onto a conditional sampler shared across states, instead of one Langevin dynamics per state, and the value dynamics onto a parametric critic, estimating both projections at sampled states to obtain coupled actor--critic flows. The score loss measures the actor's agreement with the current critic, while the policy-evaluation residual measures the critic's agreement with the actor. We also derive gradient and Hessian residuals, including a Feynman--Kac representation for the gradient equation, to control errors not detected by the projected value iteration. An exact decomposition of the HJB residual combines these errors into a policy-suboptimality bound under verification and logarithmic Sobolev assumptions. In the linear-quadratic class, both projections are exact and recover the pointwise iteration, and we provide numerical experiments on general models to demonstrate the coupled actor--critic learning in high-dimensions.

math.OC↗

arXiv2026

Continuous Policy and Value Iteration for Relaxed Stochastic Control Problems and Its Convergence

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This paper focuses on the entropy-regularized relaxed control problem with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By utilizing Langevin-type stochastic differential equations for continuous updates along the policy iteration direction, our approach enables the use of distribution sampling techniques in machine learning to optimize the value function and identify the optimal control simultaneously. Numerical experiments are presented for LQ model with a non-concave reward, and a non-LQ example with a skewed-Laplace optimal control.

math.OC↗

arXiv2026

Learning Local Heterogeneity and Cross-Region Context for Large-Scale Traffic Forecasting

Traffic flow forecasting is essential to intelligent transportation systems. Large-scale traffic forecasting requires jointly modeling local spatial dependencies and cross-region context.Spatial dependencies between geographically neighboring nodes are heterogeneous due to differences in road identity and travel direction, while acquiring global information through allpairs node interactions incurs substantial computational costs. Therefore, capturing local heterogeneity while efficiently acquiring long-range context remains an important challenge in largescale traffic forecasting. To address these challenges, we propose LoReST, a Local-Region Spatial Temporal network that models spatial dependencies at two complementary granularities: node neighborhoods and road network regions. Specifically, relation-aware local aggregation captures heterogeneous dependencies within geographic neighborhoods through road and direction specific feature transformations. Cross-region interaction constructs region representations through mean pooling, exchanges long range context via inter-region attention, and broadcasts it back to nodes. By integrating local information aggregation with crossregion interaction, LoReST is able to effectively achieve spatial dependency learning in large-scale road networks. Experiments on four datasets of the LargeST benchmark show average relative reductions of 4.78%, 3.60%, and 5.75% in MAE, RMSE, and MAPE, respectively.

cs.LG↗

arXiv2026

Sharp hypocoercive convergence estimates for underdamped Langevin dynamics with specular reflection

We study the underdamped (kinetic) Langevin dynamics confined to a bounded domain $Ω\subset\mathbb{R}^d$ by specular reflection of the velocity at the boundary. This process is the natural momentum-based analogue of the normally reflected overdamped Langevin diffusion, and it is used in practice for constrained sampling. Assuming only that the position marginal $μ_x\propto e^{-U}$ satisfies a Poincaré inequality on $Ω$ with constant $m>0$, $\nabla^2U\succeq-K\,\mathrm{Id}$ and $Ω$ is a convex domain, we prove that the law converges to the Gibbs measure exponentially fast in $L^2$, with an explicit rate that scales like $\sqrt m$, which is optimal when $U$ is convex. Since the normally reflected overdamped dynamics converges exactly at rate $m$, this establishes a square-root acceleration for constrained sampling in the small-gap regime when $m$ is small, matching the acceleration known in the unconstrained case. The explicit rate is the same in the unconstrained setting of Fan--Li--Lu. The proof adapts the modified $L^2$ hypocoercivity method of Dolbeault--Mouhot--Schmeiser with the gap-shifted corrector of Fan--Li--Lu. The specular symmetry makes the transport operator antisymmetric, and that the corrector automatically selects the Neumann realization of the overdamped generator, which is precisely the boundary condition that keeps every auxiliary function inside the specular class. The Bochner identity used in the whole-space argument is replaced by a weighted Reilly formula, whose boundary contribution involves the second fundamental form of $\partialΩ$ and is nonnegative for convex $Ω$. Finally, we extend our results to the setting where the domain $Ω$ is non-convex. We obtain an explicit contraction rate that depends on the domain.

math.PR↗

arXiv2026

Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation

Normalizing flow Boltzmann generators retain a tractable pushforward density, but training with forward KL depends on target samples that may be biased or omit modes. As a result, a flow can miss target mass while its observed importance weights give a high effective sample size. We introduce the log-ratio variation $\X_ω$, the mean absolute pairwise difference of the target-to-pushforward log-density ratio under a weighting measure $ω$, and use it to define KLXX, a new loss function. Two log-ratio variations are added to the forward KL (denoted by the two X's): one weighted by the target to improve accuracy, the other by a mixture of quench and temper samples with pushforward samples to search candidate modes. We derive the Fisher--Rao gradient flow of KLXX, where both variations contribute nonpositive dissipation, and a fixed-surrogate error bound for KLXX. We use KLXX in an adaptive-staging Boltzmann generator, with importance reweighting at every stage. We bound the sampling error of its inference scheme when the stage weights are essentially bounded, and prove it asymptotically unbiased in the sample size. In the numerical tests, KLXX improves mode coverage over forward KL. It also improves the generator's per-stage diagnostics against the loss that built the schedule. The observables the generator recovers are close to independent references. The log-ratio variations thus supply information that the forward KL loss usually omits.

stat.ML↗

arXiv2026

Design and Performance of the Upgraded Prototype Schwarzschild-Couder Telescope Camera Module

The Cherenkov Telescope Array Observatory (CTAO) is a ground-based observatory that will improve upon the sensitivities of the current generation of very-high-energy gamma-ray instruments. The Schwarzschild-Couder Telescope (SCT) is a dual-mirror candidate design for a CTAO Medium-Sized Telescope (MST). The prototype Schwarzschild-Couder Telescope (pSCT) was inaugurated in 2019 at Fred Lawrence Whipple Observatory (FLWO) in Arizona and observed significant gamma-ray emission from the Crab Nebula with a partially populated camera. The pSCT camera is currently being upgraded to fully instrument the focal plane with 11,328 silicon photomultiplier (SiPM) pixels split between 177 camera modules. Additionally, the modules will feature upgraded electronics designed to reduce electronics crosstalk and noise. A module calibration procedure has been developed using a preproduction test module. Following this calibration procedure, performance testing shows that the upgrade module has low noise, minimal electronics crosstalk, and excellent charge resolution. After calibration and optimization, the 177 production modules will be installed in the pSCT camera for commissioning. This will be followed by observations of known VHE gamma-ray sources for camera performance validation.

astro-ph.IM↗

arXiv2026

An extensible software platform for automated operational and characterization testing of scientific cameras

Multi-detector programs such as Earth 2.0 (ET) require detector characterization across different technologies, operating conditions, and production batches, together with consistent procedures for operation, characterization, and device selection. Traditional laboratory workflows often distribute camera control, illumination, image analysis, and report generation across detector-specific programs and manual steps, slowing iterative development and hindering standardized characterization. We address this gap with PixelXVision, a layered software platform that combines a common camera SDK, preset-based configuration, and a runtime plugin system. Detector-specific behavior is configured through declarative presets, allowing the same host interface to operate CCD, CMOS, and infrared detectors without model-specific core changes. Characterization procedures are implemented as plugins that use a shared object manager to access camera, illumination, storage, and database services. Each run links raw frames, measured operating conditions, configuration, analysis products, and reports into a traceable archive with a queryable index. The platform supports lightweight deployment for iterative single-detector development and structured workflows for multi-detector campaigns. The platform has been applied in characterization testing across CMOS, CCD, and HgCdTe cameras, and its configurable architecture can accommodate additional camera models for subsequent CCD testing for WFST without model-specific changes to the core host software. For operational troubleshooting, the platform integrates ChatPixel, a knowledge-base assistant that provides answers with cited sources when it has relevant information.

physics.ins-det↗

arXiv2026

The Retriever Should Remember: Experience-Amortized Reranking for Long-Term Agent Memory

Long-term language-model agents accumulate memories across interactions, but their retrievers typically do not accumulate retrieval experience. Semantic retrieval is efficient, but embedding similarity does not always reflect whether a memory contains evidence relevant to the current query. Large language model (LLM) rerankers provide stronger query-conditioned relevance scores, yet stateless reranking repeatedly scores a large candidate pool and discards these scores after each query. We introduce EARM, an experience-amortized reranking framework that treats previously acquired LLM relevance scores as reusable retrieval experience. EARM stores sparse query--memory relevance scores in an online matrix, learns their shared structure through causal matrix completion, and combines a small set of newly observed scores with estimated scores to rerank the remaining candidates. The scoring budget decreases as experience accumulates, changing LLM reranking from a repeated per-query expense into a retrieval capability learned over an agent's lifetime. Experiments on long-term conversational memory show that mixed observed-and-estimated reranking improves answer accuracy over semantic retrieval by up to 6.62% and remains effective when only 17.5% of candidates receive direct LLM relevance scores, thereby substantially reducing the inference overhead of LLM reranking. These results motivate a broader view of agent memory: a long-lived agent should remember not only past content, but also how that content has proved useful for retrieval.

cs.AI↗

arXiv2026

Néel-order-dependent transverse transport in noncoplanar antiferromagnet $\text{MnTe}_{2}$

Antiferromagnets hold appealing potential in next-generation spintronic devices with higher frequency and scalability, thanks to their alternating spin orientations that cancel out net magnetization. However, the lack of a nonzero magnetization makes the detection of the magnetic configuration of antiferromagnet difficult, hampering the applications of antiferromagnets. Here, we report a new transverse transport effect in noncoplanar antiferromagnet $\text{MnTe}_{2}$. This effect is antisymmetric in both magnetic field and Néel order, but symmetric in its two indices. It can be understood in terms of the contribution induced by both magnetic field and geometric quantities, as confirmed by our theoretical calculations. Our discovery of a new Néel-order-dependent transverse transport effect provides opportunities to the advancing antiferromagnetic spintronics.

cond-mat.mtrl-sci↗

arXiv2026

Symplectic dynamics via a tube construction

This is the first in a series of papers studying symplectic dynamics on Liouville domains $(W, λ)$ from a geometric approach. We employ Usher's tube construction to build a higher-dimensional Liouville domain from $(W,λ; H)$, where $H$ is a Hamiltonian function on $(W, λ)$, possibly non-autonomous. We establish dynamical stabilities with respect to a new Thompson-type pseudo-metric on Hamiltonians, bounded below by Banach--Mazur type distances. We also explore relations between the topological entropies of the Hamiltonian dynamics and its induced Reeb dynamics, examine symplectic capacities, especially the Gromov width, under the tube construction, and give a categorification of the Thompson-type metric via a generalized tube construction (called the tunnel construction). Finally, we investigate the relation between the filtered symplectic homology of the resulting tube and the Hamiltonian Floer homologies of the input Hamiltonians, as well as their iterates, on the given base $(W, λ)$.

math.SG↗

arXiv2026

Interpreting Swift and NuSTAR Observations of the Low-Luminosity Active Galactic Nucleus NGC 4278 with Radiatively Inefficient Accretion Flows and Implications for Neutrino Emission

We report the first NuSTAR hard X-ray observations of the low-luminosity active galactic nucleus NGC 4278. The source is clearly detected beyond 10 keV with a hard X-ray spectrum consistent with a power law of photon index between 2.2 and 2.5 without evidence for a high-energy cutoff. The X-ray flux is low compared to the active state in 2021, but exhibits variability by a factor of ~2 on a timescale of a month. We discuss the origin of the hard X-ray emission and explore its connection to gamma rays and high-energy neutrinos. We explain the X-ray data, including both quiescent and active states, using a radiatively inefficient accretion flow (RIAF) model with a variable accretion rate. We also show that TeV gamma rays cannot escape from the RIAF disk, and very high-energy gamma rays observed in LHAASO are likely to originate from outer regions such as jets and winds, which is consistent with our results favoring a magnetically arrested disk. We also discuss hidden neutrino emission from RIAFs together with possible connections to coronae of active galactic nuclei with standard, radiatively efficient disks.

astro-ph.HE↗

arXiv2026

A Multiwavelength Study of a Long-Duration VHE Flare from BL Lacertae with VERITAS

We report the first observations of a long-duration very-high-energy (VHE; $E > 100$ GeV) flare from BL Lacertae (VER J2202+422), taken with the Very Energetic Radiation Imaging Telescope Array System (VERITAS). On October 15, 2022, the Fermi-Large Area Telescope (LAT) detected elevated GeV activity originating from this blazar. This triggered a multiwavelength campaign, which includes observations from VERITAS, Swift, NuSTAR, and select optical and radio observatories. VERITAS observed the source for a total of $\sim 9.8$ hours between September 1, 2022 and December 1, 2022. An analysis of these data yields a $\sim 28 σ$ detection of the source. While previously observed VHE flares from BL Lacertae have lasted on time-scales of minutes to days, VERITAS continued to detect flaring activity from the source for over a month ($\sim 40$ days) after the original flaring activity was detected with Fermi-LAT. Broadband spectral modeling shows that a synchrotron self-Compton (SSC) model with an external inverse-Compton (EC) component is preferred over a one-zone SSC model.

astro-ph.HE↗