arXiv subjects

Hanwen Liu

Publications and source records attributed to Hanwen Liu.

At least 19 recordsLinked to original sources

arXiv2026

Refusing Everything Looks Safe: Restoring the Benign Arm to Encoded-Prompt Evaluation

Encoded-prompt attacks are evaluated almost entirely on their harmful arm: a benchmark sends obfuscated harmful requests and reports how often the model complied. A high refusal rate there is reported as safety, and it is equally consistent with a model that has stopped telling the request apart from anything else in the same format. We run the benign arm through the same transformation, and the two cases are far apart. Across four 7-8B models spanning three base families and four post-training recipes, refusal of harmful homoglyph-encoded prompts spans 0.08 while the same four span 0.57 on the identical requests in plaintext. What the encoding destroys is not refusal but the harm gap: on one model the gap between harmful and benign refusal falls from +0.82 in plaintext to exactly 0.00 under the encoding, and a benchmark reading only the harmful arm scores that model and one retaining a +0.61 gap identically. Running the cell such benchmarks leave out (plaintext content wearing the attack template, with nothing obfuscated) shows that on two of the four models the loss is caused by the protocol rather than by the character transformation, and on a third by the characters. Across a full SFT -> DPO -> RLVR pipeline the harm gap rises by +0.26 with a paired interval excluding zero while the standard harmful-arm metric registers no resolved change at all. We report twelve instrument defects, each with the control that caught it, including a binary jailbreak judge that fires on 0.61-0.70 of responses to plaintext benign prompts; six of the twelve inflate apparent safety, which is the direction a broken safety evaluation fails in by default.

cs.CR↗

arXiv2026

Unread or Unenforced? Separating Representation from Enforcement Failure in Content Guards

When an encoded attack passes a content guard, the guard either never represented the payload's harmful content or represented it and failed to act. End-to-end attack success rate reports one number for both, yet the two have opposite remedies: one is a representational limit that more safety training cannot reach, the other is a decision rule that it can. We separate them by reading a guard's own residual stream, using a content probe fitted on plaintext and transferred without refitting to the encoded condition, alongside the verdict logits from the same pass. Licensing that read honestly is most of the problem and is our main contribution. A conventional permutation test admits the decode measurement on most of a 19-condition encoding ladder for each of two open guards. A length-matched null and a floor calibrated on conditions the guard's base model provably cannot decode reduce it to four conditions each; holding out the items the probe was fitted on removes one more. A third screen constrains the block axis, which the decode screens leave untouched, by running plaintext content inside each condition's own wrapper. It removes the largest cell that survived them. What remains is a policy failure that survives an item-level holdout on two of the four surviving conditions, at 8 and 7 per 100 prompts, against 17 and 23 when the probe is allowed to have seen the prompt it is scoring. It is also confined to one family of surface encodings: where an encoding leaves content linearly recoverable we can separate the two failures, and on genuine ciphers we report the cells as unmeasured rather than as evidence that nothing was decoded. Across every guard and condition pair, blocked without decoding is near zero, so we find little evidence for a pure encoding-format detector under the conditions we test. That cell is the one read we do not repeat under the holdout, and we report it as such.

cs.CR↗

arXiv2026

Spectral Estimates for Compact Riemann Surfaces via Kähler Potentials

We establish quantitative comparisons between the Laplace--Beltrami spectra of Kähler metrics of equal area on a compact Riemann surface. An estimate in terms of the oscillation of a potential gives bounds for fractional powers of reciprocal eigenvalues and explicit intervals for eigenvalue ratios. Bounds involving the gradient and Laplacian of the potential give further comparisons. On the Riemann sphere, we obtain estimates for individual eigenvalues, reciprocal sums and counting functions. For a Kähler metric on the unit 2-sphere which is centered in the sense that the unit normal vector field integrates to zero, the Dirichlet energy of the potential yields quantitative improvements of Hersch's bounds for the first positive eigenvalue and the sum of the first three reciprocal eigenvalues.

math.DG↗

arXiv2026

A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory

For a closed oriented Riemannian $4$-manifold $(M,g)$, we consider $\operatorname{SO}(3)$ connections on the bundle $Λ^+$ of self-dual $2$-forms. On the open locus where the self-dual curvature is an orientation-preserving frame, pointwise polar decomposition removes the gauge freedom and replaces the connection by a positive self-adjoint endomorphism field $h$ of $Λ^+$. Using the classical reconstruction of the compatible connection $A(h)$, we obtain a global formulation of the Yang--Mills equation as the determined second order system $$ Φ_g(h):=F_{A(h)}^+h^{-1}-\operatorname{Id}=0. $$ Here, the tensor $F_{A(h)}^+$ is the self-dual curvature of $A(h)$, regarded as an endomorphism of $Λ^+$, and $\operatorname{Id}$ is the identity of $Λ^+$. We establish a variational formulation, automatic irreducibility, elliptic regularity, and a Fredholm index theorem for the linearized operator $D_hΦ_g$. For fields of the form $h=e^{2ω}\operatorname{Id}$, where $ω$ is a smooth real-valued function on $M$, the equation $Φ_g(h)=0$ is equivalent to anti-self-duality and constant scalar curvature $6\sqrt{2}$ of the conformal metric $\hat g=e^{2ω}g$. Consequently, every anti-self-dual conformal class of positive Yamabe constant gives a global solution of $Φ_g(h)=0$.

math.DG↗

arXiv2026

Non-Kähler Critical Hermitian Metrics of the Dinew--Popovici Functional

The Dinew--Popovici functional is an energy functional for Hermitian symplectic metrics in a fixed Aeppli cohomology class. Its vanishing characterizes the Kähler metrics in that class, providing a variational approach to Kähler geometry. Dinew and Popovici proved that every critical point is Kähler in complex dimension three. We give a negative answer to Erfan Soheil's question about higher dimensions by constructing non-Kähler critical metrics on products of two Kähler surfaces $(S_1,η_1)$ and $(S_2,η_2)$. These metrics are critical under every variation on the product 4-fold. We characterize the critical product metrics and prove that non-Kähler critical products exist in the Aeppli class $[η_1+η_2]_A$ precisely when the canonical bundles of the two surface factors are smoothly trivial. As a by-product, we develop a geometric flow driven by the torsion tensor and converging to the fixed Kähler background when this background metric has nonnegative holomorphic bisectional curvature.

math.DG↗

arXiv2026

CTC-TTS: LLM-based dual-streaming text-to-speech with CTC alignment

Large-language-model (LLM)-based text-to-speech (TTS) systems can generate natural speech, but most are not designed for low-latency dual-streaming synthesis. High-quality dual-streaming TTS depends on accurate text--speech alignment and well-designed training sequences that balance synthesis quality and latency. Prior work often relies on GMM-HMM based forced-alignment toolkits (e.g., MFA), which are pipeline-heavy and less flexible than neural aligners; fixed-ratio interleaving of text and speech tokens struggles to capture text--speech alignment regularities. We propose CTC-TTS, which replaces MFA with a CTC based aligner and introduces a bi-word based interleaving strategy. Two variants are designed: CTC-TTS-L (token concatenation along the sequence length) for higher quality and CTC-TTS-F (embedding stacking along the feature dimension) for lower latency. Experiments show that CTC-TTS outperforms fixed-ratio interleaving and MFA-based baselines on streaming synthesis and zero-shot tasks.

eess.AS↗

arXiv2026

On the Hessian Conjecture in Lorentzian Signature: Constant Pivots and Hesse Systems

As a close relative of the Jacobian conjecture, the Hessian conjecture in dimension $n$ states that the local Legendre transform of a polynomial solution to the Monge--Ampère equation $\det(\operatorname{Hess}(ϕ))=\pm1$ is also a polynomial solution. The general Hessian conjecture is false for $n\geq5$, while in Riemannian signature it follows from the Jörgens--Calabi--Pogorelov theorem. We study the four-dimensional Hessian conjecture in Lorentzian signature. For a polynomial potential $ϕ$ in four real variables whose Hessian matrix has index $1$ and determinant $-1$, we define a constant pivot for $ϕ$ to be a nonzero constant vector $ξ$ such that the second directional derivative $D_ξ^2ϕ$ is constant. We then prove that the gradient mapping of every potential admitting a pivot is a polynomial automorphism, and that a pivot always exists when $ϕ$ decomposes into homogeneous pieces as $ϕ=ϕ_d+ϕ_{d-1}+ϕ_2+ϕ_1+ϕ_0$ with $d\geq4$. More generally, we prove the same conclusion when $$ϕ=ϕ_d+\cdots+ϕ_{d-k}+ϕ_2+ϕ_1+ϕ_0,$$ where $k\geq0$ and $d\geq4k+3$. Then, we associate with each potential a linear system of quadrics, called the Hesse system, and a canonical homomorphism $μ_ϕ$. We prove that the existence of a pivot is equivalent to $\operatorname{rank}(μ_ϕ)\leq55$. As an application, we prove that the gradient mapping is a polynomial automorphism whenever the Hesse system has complex dimension at most 4. We also show that if ${\det(\operatorname{Hess}(ϕ-ϕ_2))\equiv0}$, then the potential $ϕ$ admits a pivot. After that, we then give an analytic degeneracy criterion for $\operatorname{Hess}(ϕ-ϕ_2)$. Finally, we prove the Hessian conjecture in this setting for every polynomial potential of degree at most five.

math.AG↗

arXiv2026

An Electrodynamic Lifting of the Toda Monopoles in Curved 3+1 Spacetime

Every solution of the hyperbolic Toda equation determines a classical Abelian monopole on a (2+1)-dimensional Einstein--Weyl space. We determine when its connection is also a source-free electromagnetic potential on a curved Lorentzian 3+1 spacetime with a spacelike Killing field. On the generic branch, Maxwell's equation classifies the admissible Killing-fibre scale and horizontal twist through one characteristic of the Toda field. A separated Liouville branch gives purely magnetic fields with considerably freer fibre geometry. The round spherical solution yields a monopole of unit charge with conserved flux on a contracting screen. The background metric here is neither assumed to be Einstein nor self-dual.

math-ph↗

arXiv2026

PMSN: A Parallel Multi-compartment Spiking Neuron for Multi-scale Temporal Processing

Spiking Neural Networks (SNNs) hold great potential to realize brain-inspired, energy-efficient computational systems. However, current SNNs still fall short in terms of multiscale temporal processing compared to their biological counterparts. This limitation has resulted in poor performance in many pattern recognition tasks with information that varies across different timescales. To address this issue, we put forward a novel spiking neuron model called Parallel Multi-compartment Spiking Neuron (PMSN). The PMSN emulates biological neurons by incorporating multiple interacting substructures and allows for flexible adjustment of the substructure counts to effectively represent temporal information across diverse timescales. Additionally, to address the computational burden associated with the increased complexity of the proposed model, we introduce two parallelization techniques that decouple the temporal dependencies of neuronal updates, enabling parallelized training across different time steps. Our experiments across a wide range of pattern recognition tasks demonstrate that PMSN outperforms state-of-the-art spiking neuron models in temporal processing capacity and training speed. Specifically, compared with the commonly used Leaky Integrate-and-Fire neuron, PMSN offers more than 10 times acceleration and a 30% accuracy improvement on Sequential CIFAR-10 dataset, while maintaining comparable computational cost. Our implementation on neuromorphic hardware further demonstrates the deployability of PMSN and highlights its favorable trade-off between effectiveness and efficiency. Therefore, the proposed PMSN presents a promising solution to harness the computational advantages of detailed biological neurons, enabling high-performance and efficient temporal processing on neuromorphic computing systems. Code is available at https://github.com/xychen-comp/PMSN.

cs.NE↗

arXiv2026

Scaling Unmodified Multithreaded Applications with Elastic CXL-based Distributed Shared Memory

While CXL presents a promising hardware substrate for Distributed Shared Memory (DSM), seamlessly scaling multithreaded applications across multiple nodes remains a formidable challenge. Existing CXL-based DSMs fall short: they require manual code modifications to share non-heap data, employ rigid data placement policies that fail under diverse and dynamic workloads, and suffer from severe page-fault processing overheads in sub-microsecond ($μ\mathrm{s}$) environments. We present xDSM, a full-space, elastic DSM system built over CXL that transparently scales unmodified multithreaded applications. To eliminate the burden of manual code rewrites, xDSM employs an OS-runtime co-design that establishes a globally coordinated address space, seamlessly sharing all memory segments. To mask CXL access penalties, xDSM abandons static placement rules in favor of a dynamic, latency-driven policy that actively balances data between local DRAM and CXL memory. Finally, to resolve the fundamental tension between high base-page fault overheads and severe huge-page false sharing, xDSM introduces spatial locality-aware elasticity, dynamically coalescing and splitting pages on the fly to amortize processing costs. Evaluated across diverse workloads using 15 system configurations, xDSM outperforms CXL-only baselines by 1.5$\times$ to 2.2$\times$ and state-of-the-art hybrid DSMs by 1.1$\times$ to 2.2$\times$, while achieving near-linear scalability.

cs.OS↗

arXiv2026

A Note on the Rainich Problem for SU(2) Gauge

We provide a resolution to the non-Abelian Rainich problem. By canonically identifying traceless symmetric $(0,2)$-tensors with Hermitian forms on the vector bundle of chiral 2-forms, we define the internal square roots of a stress-energy tensor. We then prove that the existence of a local $\operatorname{SU}(2)$ Yang-Mills field with prescribed stress-energy tensor $T$ is equivalent to a single differential condition on internal square roots of $T$.

math.DG↗

arXiv2026

On Topology of Compact Hessian Manifolds

We investigate the global topological constraints and structural properties of compact Hessian manifolds. By establishing novel fibration and splitting theorems, we confirm Chern's conjecture on the vanishing of the Euler characteristic for this class of affine manifolds. Applying these techniques to low dimensions, we provide a topological classification of complete Hessian surfaces. Furthermore, utilizing the theory of Hitchin systems and the Cheng-Yau solution to the real Monge-Ampère equation, we establish a geometric classification of closed orientable Hessian $3$-manifolds.

math.DG↗

arXiv2026

On Conservative Statistical Riemann Surfaces

We establish a correspondence between information geometry and gauge theory. First, we define an important class of statistical manifolds, that is normalized and satisfies a conservation field equation. Second, we prove that for a conservative statistical structure on an orientable surface, the Chebyshev 1-form is constrained to be harmonic, and the traceless part of the Amari--Chentsov tensor descends to a holomorphic cubic differential. Then, we demonstrate that normalized conservative statistical structures are geometrically generated by solutions to the scalar Tzitzéica equation on Higgs bundles with general linear holonomy, generalizing the Labourie-Loftin correspondence. Finally, we prove that the moduli space of normalized conservative statistical structures on a closed orientable surface of genus at least 2 is completely parameterized by a holomorphic vector bundle over the Teichmüller space, consisting of Abelian differentials and cubic differentials.

math-ph↗

arXiv2026

On the Rigidity of Analytic Mappings in Complex Analysis and Geometry

We establish rigidity results for holomorphic mappings and plurisubharmonic functions in complex geometry. First, under mild conditions, we show that the gradient of a $\operatorname{U}(1)$-invariant strictly plurisubharmonic function in $\mathbb{C}^2$ possesses finite fibers and induces a analytic mapping of topological degree $1$ on the symplectic quotient. Second, we prove that continuous fiber-wise holomorphic maps on proper fibrations elevate to global holomorphic maps when anchored by mutually disjoint sections, yielding rigidity for homomorphisms between elliptic fibrations and Abelian schemes. Third, we demonstrate that a fiber-wise holomorphic map of mapping degree $1$ from a fibered compact Kobayashi hyperbolic manifold to a projective variety is a biholomorphism, provided it is injective on a very ample hypersurface. Finally, we prove that a holomorphic Lie group action with sufficiently large orbits confines the critical locus of a proper invariant strictly plurisubharmonic function to the fixed-point set, guaranteeing a unique global minimum and yielding a sharp differential topological obstruction on the orbit dimensions of compact Lie group actions.

math.CV↗

arXiv2026

Hausdorff Dimension of Union of Lines Covering a Curve: Applications to Mathematical Physics

We prove that for any nonlinear $f \in C^{1,α}([0,1])$, the union of lines covering its graph has a Hausdorff dimension of at least $1+α$, and this dimension bound is sharp. We then apply these geometric results to mathematical physics, proving that spacetime observability sets for conservation laws with $α$-Hölder initial wave speeds possess a dimension of at least $α$. Finally, we prove that if an absolutely integrable vector field $v$ on the boundary of a polyhedron exhibits a strictly positive total flux, then the union of the line field spanned by $v$ possesses a Hausdorff dimension of 3.

math.AP↗

arXiv2026

Towards a Hybrid Quantum-Classical Computing Framework for Database Optimization Problems in Real Time Setup

Quantum computing has shown promise for solving complex optimization problems in databases, such as join ordering and index selection. Prior work often submits formulated problems directly to black-box quantum or quantum-inspired solvers with the expectation of directly obtaining a good final solution. Due to the black-box nature of these solvers, users cannot perform fine-grained control over the solving procedure to balance the accuracy and efficiency, which in turn limits flexibility in real-time settings where most database problems arise. Moreover, it leads to limited potential for handling large-scale database optimization problems. In this paper, we propose a vision for the first real-time quantum-augmented database system, enabling transparent solutions for database optimization problems. We develop two complementary scalability strategies to address large-scale challenges, overcomplexity, and oversizing that exceed hardware limits. We integrate our approach with a database query optimizer as a preliminary prototype, evaluating on real-world workload, achieving up to 14x improvement over the classical query optimizer. We also achieve both better efficiency and solution quality than a black-box quantum solver.

cs.DB↗

arXiv2026

Is Quantum Computing Ready for Real-Time Database Optimization?

Database systems encompass several performance-critical optimization tasks, such as join ordering and index tuning. As data volumes grow and workloads become more complex, these problems have become exponentially harder to solve efficiently. Quantum computing, especially quantum annealing, is a promising paradigm that can efficiently explore very large search spaces through quantum tunneling. It can escape local optima by tunneling through energy barriers rather than climbing over them. Earlier works mainly focused on providing an abstract representation (e.g., Quadratic Unconstrained Binary Optimization (QUBO)) for the database optimization problems (e.g., join order) and overlooked the real integration within database systems due to the high overhead of quantum computing services (e.g., a minimum 5s runtime for D-Wave's CQM-Solver). Recently, quantum annealing providers have offered more low-latency solutions, e.g., NL-Solver, which paves the road to actually realizing quantum solutions within DBMSs. However, this raises new systems research challenges in balancing efficiency and solution quality. In this talk, we show that this balance is possible to achieve. As a proof of concept, we present Q2O, the first real Quantum-augmented Query Optimizer. We show the end-to-end workflow: we encode the join order problem as a nonlinear model, a format solvable by the NL-Solver, using actual database statistics; the solution is translated into a plan hint that guides PostgreSQL's optimizer to produce a complete plan. Q2O is capable of handling actual queries in real time.

cs.DB↗

arXiv2025

On Two Dimensional Flat Hessian Potentials

A Riemannian metric is termed a Hessian metric if in some coordinate system it can be locally represented as the Hessian quadratic form of some locally defined smooth potential function. Under very mild extra technical conditions, we first theoretically describe the potentials of flat Hessian metrics on surfaces, and then construct these potentials explicitly using methods from integrable systems.

math.DG↗