arXiv subjects

Menghan Jia

Publications and source records attributed to Menghan Jia.

6 recordsLinked to original sources

arXiv2026

Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at https://github.com/JingXiao10/GUA.

cs.LG↗

arXiv2026

RealmEye: Virtual Machine Introspection for Arm CCA Realm VMs

Confidential VMs (CVMs) have become the dominant substrate for sensitive cloud workloads, from financial services to privacy-preserving AI inference. The hardware isolation that protects these CVMs from a malicious cloud also blinds their owners to what runs inside them: kernel rootkits planted via network or supply-chain attacks can hide processes, tamper with kernel data, and exfiltrate model weights under the cover of the same isolation that defends the VM. Tenants therefore need to inspect a running CVM from outside, yet classical VM introspection (VMI) presupposes a trusted Hypervisor, which CVMs exclude from the TCB. The state-of-the-art CVM-VMI system, 00SEVen, restores introspection on AMD SEV-SNP via an in-VM agent at a privileged tier (VMPL0), a mechanism that does not exist on Arm CCA, leaving Realm VMs without any introspection solution. We present RealmEye, the first VMI system for Arm CCA Realm VMs. RealmEye places the entire introspection logic inside the Realm Management Monitor (RMM) at R-EL2, achieving hardware-enforced separation between the monitor and the monitored VM: no agent runs inside the Realm, and the Realm remains unmodified. RealmEye reads Realm memory and registers, suspends the VM for consistent snapshots, and traps page-level accesses, without relying on any in-VM interface. A periodic, self-driven trigger mode keeps scan timing internal to the RMM, preventing the Hypervisor from colluding with in-Realm rootkits. Results are returned to the remote owner over a hardware-attested channel, and a CCA driver backend lets existing tools such as LibVMI and DRAKVUF interoperate with RealmEye unchanged. On the Arm FVP, RealmEye detects process hiding and syscall-table hooking by Diamorphine, and its in-RMM cost is linearly predictable from primitive invocation counts.

cs.CR↗

arXiv2026

Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery

Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity.

cs.LG↗

arXiv2025

Hierarchy-Aware Neural Subgraph Matching with Enhanced Similarity Measure

Subgraph matching is challenging as it necessitates time-consuming combinatorial searches. Recent Graph Neural Network (GNN)-based approaches address this issue by employing GNN encoders to extract graph information and hinge distance measures to ensure containment constraints in the embedding space. These methods significantly shorten the response time, making them promising solutions for subgraph retrieval. However, they suffer from scale differences between graph pairs during encoding, as they focus on feature counts but overlook the relative positions of features within node-rooted subtrees, leading to disturbed containment constraints and false predictions. Additionally, their hinge distance measures lack discriminative power for matched graph pairs, hindering ranking applications. We propose NC-Iso, a novel GNN architecture for neural subgraph matching. NC-Iso preserves the relative positions of features by building the hierarchical dependencies between adjacent echelons within node-rooted subtrees, ensuring matched graph pairs maintain consistent hierarchies while complying with containment constraints in feature counts. To enhance the ranking ability for matched pairs, we introduce a novel similarity dominance ratio-enhanced measure, which quantifies the dominance of similarity over dissimilarity between graph pairs. Empirical results on nine datasets validate the effectiveness, generalization ability, scalability, and transferability of NC-Iso while maintaining time efficiency, offering a more discriminative neural subgraph matching solution for subgraph retrieval. Code available at https://github.com/liuzhouyang/NC-Iso.

cs.LG↗

arXiv2025

UGM2N: An Unsupervised and Generalizable Mesh Movement Network via M-Uniform Loss

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies.In this paper, we present an Unsupervised and Generalizable Mesh Movement Network (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level.Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

cs.AI↗

arXiv2024

State-space Decomposition Model for Video Prediction Considering Long-term Motion Trend

Stochastic video prediction enables the consideration of uncertainty in future motion, thereby providing a better reflection of the dynamic nature of the environment. Stochastic video prediction methods based on image auto-regressive recurrent models need to feed their predictions back into the latent space. Conversely, the state-space models, which decouple frame synthesis and temporal prediction, proves to be more efficient. However, inferring long-term temporal information about motion and generalizing to dynamic scenarios under non-stationary assumptions remains an unresolved challenge. In this paper, we propose a state-space decomposition stochastic video prediction model that decomposes the overall video frame generation into deterministic appearance prediction and stochastic motion prediction. Through adaptive decomposition, the model's generalization capability to dynamic scenarios is enhanced. In the context of motion prediction, obtaining a prior on the long-term trend of future motion is crucial. Thus, in the stochastic motion prediction branch, we infer the long-term motion trend from conditional frames to guide the generation of future frames that exhibit high consistency with the conditional frames. Experimental results demonstrate that our model outperforms baselines on multiple datasets.

cs.CV↗