arXiv subjects

Qi Gao

Publications and source records attributed to Qi Gao.

At least 19 recordsLinked to original sources

arXiv2026

Exact and Asymptotically Complete Robust Verifications of Neural Networks via Ising Solvers

We present an Ising-compatible framework for formal neural-network robustness verification under bounded input perturbations. For piecewise activations (both continuous piecewise-linear and discrete piecewise-constant), the Exact Logarithmic Piecewise Model (Log-PW) provides an exact, sound, and complete formulation with a state-optimal logarithmic encoding, reducing the binary variables per neuron from linear $O(κ)$ to information-theoretically minimal logarithmic complexity $O(\lceil \log_2 κ\rceil)$ via logarithmic SOS2 (Log-PWL) and SOS1 (Log-PWC) constraints. For general element-wise activations, the Asymptotic Step-Envelope Model (Step-Env) leverages Log-PWC to construct sound, refinable endpoint enclosures. An exact monotonic reduction based on Jordan decomposition further extends this framework to arbitrary non-monotonic activations. We further develop a hybrid Benders solver with output-sensitive iteration bounds, leveraging a Helly-based conflict compression theory to avoid generic exponential cut explosion. In particular, for shallow networks with fixed input dimension, this establishes an unconditionally polynomial Benders iteration complexity in network size. Interval pruning, certificate transfer for pruned networks, and layerwise classical--Ising partitioning further reduce spin requirements. Experiments demonstrate exact certification fidelity for piecewise-linear networks and near-reference accuracy for non-linear activations under compact spin budgets. On MNIST benchmarks, Log-PW halves binary decision spins over One-Hot formulations, while Helly-based cuts achieve up to a $13.41\times$ speedup and an $87.6\%$ reduction in master queries over standard baselines.

cs.LG↗

arXiv2026

Finite-temperature spectral functions of lattice polarons with process tensors

We develop a process tensor approach for calculating the finite-temperature spectral functions of lattice polarons. We show that the finite-temperature phonon influence functional can be expressed as the elementwise exponential of a low-rank matrix product state, enabling an efficient summation of electron worldlines. An embedding construction embeds worldlines of different propagation times into a single matrix product state. This construction yields the propagator over the full simulated time interval in a single calculation. We benchmark this approach against available finite-temperature density-matrix renormalization group results for the one-dimensional Holstein polaron. We further obtain numerically converged spectra for the two-dimensional Holstein polaron. The spectra reveal a progressive transfer of spectral weight from coherent spectral features into an incoherent background with increasing temperature.

cond-mat.str-el↗

arXiv2026

Quantum--classical break-even in electronic dynamics of macrocyclic molecules

Here we demonstrate quantum--classical break-even for chemical dynamics applications, reaching useful accuracy with a quantum-hardware wall-clock time comparable to that estimated for practical classical computing resources. To this end, we develop a workflow for problems that are hardware-native but classically hard. We target large ring-shaped molecules that map naturally onto quantum hardware with neighboring connections. Exploiting the spatial locality of interactions, we compress short-time evolution within a small region using tensor networks. We then use rotational symmetry to replicate the compressed circuit in space and time, enabling long-time dynamics of large systems with practical classical processing times. We apply the workflow to conjugated macrocycles with rotational periodicity, 12-qubit benzene and 120-qubit [60]annulene, by embedding their electronic structure onto loops of IBM quantum processors. For the annulene, we compared the quantum-processing-unit (QPU) wall-clock times for hole-doped nonequilibrium dynamics to the estimated wall-clock time of two state-of-the-art classical methods, Majorana propagation and matrix-product-state time evolution based on the time-dependent variational principle. We show a situation in which a hybrid quantum--classical strategy is comparable to a classical-only counterpart in terms of both accuracy and computational time for a conventional high-performance computing system under ideal parallelization. These results show that quantum hardware can become a realistic computational option for chemical simulations for practitioners in chemical science and engineering.

quant-ph↗

arXiv2026

Solving Large-Scale Parameter Inference in Controllable Nuclear Fusion via Coherent Ising Machines and Block Coordinate Descent

Bayesian inference enables self-consistent plasma parameter inversion in tokamak integrated data analysis by fusing multi-source diagnostics. However, under nonlinear Gaussian likelihoods, finding the maximum a posteriori (MAP) estimate typically relies on sampling methods whose high computational overhead precludes real-time plasma control. To address this bottleneck, we propose a Bayesian inversion framework using a Coherent Ising Machine (CIM)-a quantum computing architecture based on coupled degenerate optical parametric oscillators (DOPOs). With native all-to-all connectivity, the CIM directly maps the negative log-posterior potential onto a spin Hamiltonian and leverages quantum vacuum fluctuations for rapid state-space search during pitchfork bifurcation. Validated on plasma current profile inversion for the EAST tokamak, this method achieves a single-run solution time of approximately 1 ms. Although current qubit limits necessitate a block-wise iterative scheme that prevents full real-time execution today, rapidly scaling quantum hardware offers a clear pathway toward real-time tokamak control.

quant-ph↗

arXiv2026

Rethinking Prediction Horizons: Decoupling Model Queries from State Updates in Few-Step MeanFlow

MeanFlow predicts interval-average velocities, but conventional few-step sampling ties the interval queried from the model to the duration of the state update. We separate these two quantities at inference, fixing the model, update grid, and number of queries while varying the prediction horizon. Our central finding is that the horizon response depends on both query position and the states entering that query. Across seven independently trained CIFAR-10 checkpoints at classifier-free guidance (CFG) scale 2, a longer horizon worsens FID at early steps but improves it at the midpoint. To probe whether query time alone determines this response, we fix the midpoint query and current/subsequent guidance while changing only earlier CFG. In held-out factorial outcomes on five previously studied checkpoints, the mean midpoint horizon benefit increases from 0.109 to 1.308 FID, indicating sensitivity to the incoming-state distribution. A frozen four-query rule reduces mean CIFAR-10 FID by 2.023 without retraining or extra queries, including gains on five checkpoints trained after rule selection. A milder rule also improves mean FID by 1.041 on a stronger frozen grid, with fixed-rule FID gains on the evaluated public ImageNet-256 and AFHQ checkpoints. However, matched-budget calibration favors query-start shifting in historical CIFAR tests, and the tested Horizon allocation adds no FID benefit beyond Grid+Start on two public ImageNet models. Thus, prediction horizon is a distinct, position- and state-sensitive inference control, but not a universally preferred one.

cs.LG↗

arXiv2026

SplatQ: Interaction-Aware Pruning of 3D Gaussian Splatting via Quadratic Selection

Existing 3D Gaussian Splatting (3DGS) pruning methods primarily rely on global Top-K selection based on independent importance scores, lacking regional budget control and ignoring joint deletion effects. Consequently, they cannot ensure balanced reconstruction quality across a scene. We propose SplatQ, a combinatorial pruning algorithm that coordinates regional budget allocation and joint Gaussian selection under a fixed budget. SplatQ partitions Gaussians by spatial proximity and appearance similarity into size-limited blocks, decomposing global selection into subproblems of a specific size. It then smooths importance-based block retention quotas to prevent excessive budget concentration. Finally, it constructs a quadratic approximation of joint deletion effects using the responses of representative pixel colors to changes in Gaussian opacity. Individual responses, pairwise interactions, and quota penalties are incorporated into a quadratic unconstrained binary optimization (QUBO) objective, solved using simulated annealing (SA) or a coherent Ising machine (CIM) to jointly select Gaussians. Experiments on 5 benchmarks demonstrate that SplatQ outperforms state-of-the-art pruning methods in aggregate reconstruction quality, spatial quality balance, and rendering speed. Ablations confirm that budget smoothing improves local detail reconstruction, while interaction modeling improves Gaussian selection quality under a fixed budget.

cs.CV↗

arXiv2026

On the relationships between pressure geometrization and vortex identification

The profound mathematical and conceptual analogy between pressure in fluid mechanics and gravity in general relativity motivates a novel geometric reinterpretation of flows. This article proposes a theoretical framework for geometrizing pressure by establishing a Newton-Cartan geometry and applying a conformal transformation to the spatial metric. The pressure field is reinterpreted as a geometric potential that induces an effective spatial curvature, encoded in the Ricci tensor Rij and the associated Einstein-like tensor Gij. Within this curved effective space, fluid particles under the exclusive influence of pressure follow geodesics, and the classical Euler equation is recovered in the weak-field limit. The pressure Poisson equation emerges naturally as a consequence of the geodesic equation and the Bianchi identity, revealing pressure as an instantaneous geometric constraint rather than an external force. This framework provides a unified geometric interpretation of widely used vortex identification criteria, demonstrating that the prevailing Eulerian and Lagrangian schemes correspond to different geometric invariants or projections of the effective curvature. In the degenerate two-dimensional (2D) limit, the effective spatial tensor vanishes identically, and the global integral of the total curvature vanishes as well. This topological constraint offers a novel interpretation of the dual-cascade scenario in 2D turbulence: the inverse energy cascade arises from geometric condensation of positive-curvature structures toward larger scales, while the forward enstrophy cascade results from geometric dispersion of negative-curvature structures toward smaller scales.

physics.flu-dyn↗

arXiv2026

AnesTRACE: Benchmarking Intraoperative Anesthesia from Multimodal Perception to Multi-step Decision-Making

Intraoperative anesthesia requires systems to interpret evolving multimodal evidence, recommend timely management, and revise decisions as patient states change, yet existing benchmarks usually isolate perception or single-point reasoning. We introduce AnesTRACE, an evaluation suite comprising AnesTRACE-Bench and AnesTRACE-Eval. Built from public perioperative datasets with anesthesiologist annotation, AnesTRACE-Bench evaluates Intraoperative Perception, Single-point Anesthesia Decision-Making, and Multi-step Anesthesia Decision-Making. AnesTRACE-Eval assesses open-ended responses through anesthesiologist-defined criteria for Clinical Correctness, Evidence Grounding, Task Completeness, and Safety, with Temporal Consistency for multi-step decisions; its domain-specific evaluator is trained by supervised fine-tuning and preference alignment on expert-reviewed judgments. Across more than 30 models, fine-grained visual grounding and intervention selection remain difficult: the leading model reaches only 32.2 mIoU for TEE visual grounding and retains a 17.5\% Major/Critical Safety Error Rate in multi-step management. Evaluator alignment with anesthesiologists improves across both training stages, while the best decision quality is accompanied by a 74.3-second P95 Latency. These results show that aggregate performance alone does not establish safe, timely longitudinal decision-making. We release our code at https://zjudbxai.github.io/AnesTRACE/.

cs.CV↗

arXiv2026

Quantum reservoir computing with repeated measurements on superconducting devices

Reservoir computing is a machine learning framework that uses artificial or physical dissipative dynamics to predict time-series data using nonlinearity and memory properties of dynamical systems. Quantum systems are considered promising physical reservoirs, and several quantum reservoir computing (QRC) schemes that exploit intrinsic quantum mechanical properties as computational resources have been proposed. This paper focuses on a particular QRC scheme that was theoretically proposed to use the repeated quantum non-demolition measurement to generate a time series, mainly for the purpose of reducing the total execution time compared to the conventional method without repeated measurement. We experimentally implemented this scheme on IBM superconducting devices and demonstrated that shorter execution time and higher accuracy can be achieved than with a specific conventional method. Then, we study the temporal information processing capacity to quantify the computational capability of the proposed QRC; in particular, we use this quantity to identify the measurement strength that finds the best balance between the amount of available information and the strength of dissipation. An experimental demonstration with a soft robot is also provided, where repeated measurement over 1,000 timesteps was effectively implemented. Finally, we implemented the repeated-measurement QRC scheme using 120 qubits, to test the potential computational power of a large-scale QRC.

quant-ph↗

arXiv2026

Q-DEQ: Discrete Solving and Quantization for Deep Equilibrium Models in Time Series Forecasting under Edge Deployment Coding Constraints

Edge deployment motivates forecasting models with compact parameter storage and low-bit representations. Deep equilibrium models (DEQs) obtain implicit depth by repeatedly applying a shared layer, reducing the parameter cost of explicit layer stacking. Their usual Anderson solver, however, searches for update coefficients in the continuous real domain. We propose Q-DEQ, which formulates local updates in DEQ forward solving as discrete optimization problems. Candidate directions are constructed from the current state and iteration history, and a local quadratic residual model is used to evaluate their combinations. Binary encoding of the direction coefficients yields a quadratic unconstrained binary optimization (QUBO) problem that can be solved by simulated annealing (SA) or a coherent Ising machine (CIM). After fixed-point solving, a re-forward pass applies W8A8 fake quantization to the shared layer's weights and activations. We evaluate Q-DEQ with an iTransformer backbone on five multivariate time series forecasting datasets. Relative MSE differences from the explicit multi-layer baseline range from $-1.16\%$ to $+2.90\%$, with lower MSE on two datasets. DEQ parameter sharing reduces parameter counts by factors of $1.80\times$--$3.82\times$; combined with W8A8, static weight storage is reduced by factors of $4.3\times$--$12.8\times$. Local QUBO problems solved using CPU-based SA and the Kaiwu CIM physical backend produce closely matching downstream forecasts. These results establish local discrete solving as a viable component of DEQ time series forecasting and provide a route for executing fixed-point updates through different combinatorial optimization backends.

cs.LG↗

arXiv2026

Bricks or Cash? Externalities of Housing Upgrading in High-density Cities

We estimate housing externalities in a high-density city, exploiting the staggered rollout of Singapore's nationwide Main Upgrading Programme for public housing. Controlling for nonrandom neighborhood exposure, we find that upgrading raises treated buildings' prices by 11.5% upon completion and neighboring buildings' resale prices by about 2% within 500 meters, decaying to zero beyond. A model with distance-decaying externalities shows that in dense settings spillovers justify the distortions of in-kind provision; this advantage diminishes and reverses at lower densities. Administrative data on over 2 million residents show that upgrading disproportionately retains older incumbents, suggesting age-specific amenities as an underexplored externality channel.

econ.GN↗

arXiv2026

FoundDiff: Foundational Diffusion Model for Generalizable Low-Dose CT Denoising

Low-dose computed tomography (CT) denoising is crucial for reduced radiation exposure while ensuring diagnostically acceptable image quality. Despite significant advancements driven by deep learning (DL) in recent years, existing DL-based methods, typically trained on a specific dose level and anatomical region, struggle to handle diverse noise characteristics and anatomical heterogeneity during varied scanning conditions, limiting their generalizability and robustness in clinical scenarios. In this paper, we propose FoundDiff, a foundational diffusion model for unified and generalizable LDCT denoising across various dose levels and anatomical regions. FoundDiff employs a two-stage strategy: (i) dose-anatomy perception and (ii) adaptive denoising. First, we develop a dose- and anatomy-aware contrastive language-image pre-training model (DA-CLIP) to achieve robust dose and anatomy perception by leveraging specialized contrastive learning strategies to learn continuous representations that quantify ordinal dose variations and identify salient anatomical regions. Second, we design a dose- and anatomy-aware diffusion model (DA-Diff) to perform adaptive and generalizable denoising by synergistically integrating the learned dose and anatomy embeddings from DA-CLIP into diffusion process via a novel dose and anatomy conditional block (DACB) based on Mamba. Extensive experiments on a large simulated multi-dose CT dataset spanning three anatomical regions, together with cross-dataset evaluations on Mayo-2016, CQ500, and piglet datasets, demonstrate superior denoising performance and strong generalization to unseen dose levels and anatomical regions. The codes and models are available at https: //github.com/hao1635/FoundDiff.

cs.CV↗

arXiv2026

Towards Provable and Scalable Training of Quantized Neural Networks with Ising Optimization

Training quantized neural networks remains fundamentally challenging due to non-convex loss landscapes and discrete parameter spaces. We introduce an exact Quadratic Constrained Binary Optimization (QCBO) framework with provable guarantees. We first characterize the stratified topology of network zero-loss level sets: generic interior strata are smooth, yet globally optimal components can remain disconnected even under overparameterization. To address this non-convex obstruction, we compile finite-depth architectures with parameter codebooks and Forward Interval Propagation (FIP)-bounded states into bounded QCBOs, yielding an exact completely positive convex formulation that preserves the global discrete optimum with zero relaxation gap. To overcome monolithic sample scaling, we formulate sample-wise Decomposed Lower-Bound Optimization (DLBO) to reduce each Ising call from dataset to single-sample scale. The DLBO moment hierarchy also forms a Hamiltonian-locality hierarchy, with order two giving an auxiliary-free pairwise QUBO oracle and higher orders trading interaction locality for tighter bounds. Strictly feasible discrete parameters are recovered via Spectral--ADMM and randomized rounding. Experiments on a coherent Ising machine achieve $94.95\%$ accuracy on binary Fashion-MNIST (coats vs. sandals) at 1.1-bit precision, demonstrating resilience against low-bit representational collapse. Multi-class DLBO evaluations on 3-class Fashion-MNIST, 3-class Wine, and 3-class Digits further validate scalable convergence.

cs.LG↗

arXiv2026

Quantum Simulations for Extreme Ultraviolet Photolithography

A key challenge of extreme ultraviolet (EUV) lithography in semiconductor fabrication is the line edge roughness or "blur" produced by the electron cascades following absorption of a high-energy photon. Here we present quantum algorithms to compute EUV absorption and photoelectron emission spectra, which are key to predicting blur. The first is a time-domain algorithm resolving absorption at a given frequency; the second is a first-quantized plane-wave algorithm computing the photoemission spectrum via real-time dynamics that treats bound and continuum states on equal footing. For a model photoresist monomer IMePh, 92 eV absorption requires $200$ logical qubits and $10^{9}$ non-Clifford gates per circuit with $10^3$ shots, while the photoemission spectrum needs $\geq 10^{14}$ gates, $10^4$ shots, and several thousand logical qubits. These results establish high-fidelity quantum simulations as a key component to parameterize the multi-scale macroscopic models required to overcome the electron blur bottleneck in semiconductor miniaturization.

quant-ph↗

arXiv2026

UI-Mate: Advancing Open-Weight Foundation GUI Agents with In-Context Demonstrations

Foundation GUI agents can automate complex digital tasks, but deployment is hindered by scarce and biased training data, ambiguous prompts, and unreliable execution. Routine workflows rely on user-specific tools and tacit conventions, so unstated instructions can produce arbitrary variations across runs. We present UI-Mate, a foundation GUI agent that integrates an environment-grounded training stack with in-context demonstration learning. UI-Mate makes three contributions: A Scalable Environment-Grounded Training Stack: A closed-loop data engine automates task generation, environment construction, rollout, filtering, capability balancing, SFT, and online RL across massively parallel environments via unified task-verifier bundles. In-Context Demonstration Learning: A mechanism that transforms multimodal demonstrations into flexible subtask-level workflows, follows relevant demonstrated steps, and re-plans from the live interface. OSWorkerBench Benchmark and Insights: A benchmark of 100 long-horizon office tasks across 41 applications that supports instruction-only and demonstration-guided evaluation. Its demonstration resources separate a 33-task self-demo setting, built from successful strong-agent rollouts of the same targets, from a 45-task variant-demo setting, built from human recordings of related but non-identical tasks. Experiments show that UI-Mate-27B sets a new open-weight state of the art on general computer-use benchmarks, scoring 77.0% on OSWorld-Verified and 66.2% on WindowsAgentArena. On OSWorkerBench, it reaches 41.0% strict success and 76.9% progress, outperforming its Qwen3.6-27B base by 17.7 and 24.5 points. On the 33-task self-demo subset, one demonstration raises strict success from 17.2% to 35.4% and progress from 67.9% to 81.1%, substantially improving long-horizon reliability. Project page: https://ui-mate.github.io.

cs.AI↗

arXiv2026

Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws

In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs). However, solving PDEs with discontinuous solutions, such as hyperbolic conservation laws, remains challenging for neural network-based methods such as physics-informed neural networks (PINNs). Existing methods often rely on strong prior assumptions such as knowledge of discontinuity locations, or they introduce artificial smoothing terms that degrade accuracy. However, accurately solving these conservation laws and predicting the formation and propagation of discontinuities in solutions is crucial in many practical applications, including gas dynamics and traffic flow modeling. In this paper, we introduce a novel Weak-Entropy PINN (WEPINN) framework for hyperbolic conservation laws with discontinuous solutions. The method enforces the governing equations in their weak (integral) formulation and incorporates the entropy condition to select the physically admissible solution, while employing the discrete fast Fourier transform (DFFT) for efficient numerical integration. Our method is tested through extensive numerical experiments on a variety of scalar conservation laws and systems of conservation laws in one and two dimensional spaces. These experiments demonstrate that our method can accurately resolve sharp discontinuities while effectively capturing interactions between multiple shock and rarefaction waves.

math.NA↗

arXiv2026

Topological properties and phase diagram of the triangular Hofstadter model with staggered flux

We study the topological properties and phase diagram of the triangular Hofstadter model with staggered flux in adjacent triangles in this work. This lattice can be used to describe the low energy physics of the twisted bilayer transition metal dichalcogenides (TMD) in a certain range of the electric displacement field between the two layers. We show that the Hofstadter spectrum of this model is generally asymmetric except at specific staggered flux $3ϕ= π/2 \mod π$ due to an additional P symmetry at such $ϕ$. Breaking the translation symmetry by dimerization lifts the P symmetry and results in rich topological phases in the system. The dimerized model with different rational external magnetic flux $Φ_B = 2πp/q$ has phase diagram with the following common features. For even q, the dimerized model generally has three gapped regimes. The one with small dimerization has finite Chern number and the other two have zero Chern number. For odd q, the model is gapped with zero Chern number at any finite dimerization. For both q even and odd, the two regimes with zero Chern number can be further characterized by the inversion symmetry of the parametrized one-dimensional chains of the system at ϕ= 0 \mod π/3$, and one regime is topologically non-trivial and the other is trivial. Our results may be tested in twisted bilayer TMD with weak interaction or cold atom systems in optical lattice or photonic crystals achieved in recent experiments.

cond-mat.other↗

arXiv2026

Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux

We study the Hofstadter model on a hexagonal lattice with irrational magnetic flux in this work. The Hofstadter model of the square lattice with irrational flux has been solved mathematically by Avila and his collaborators in his Fields medal work. However, this theory is usually not applicable to lattices with internal degrees of freedom, such as spin or sublattice. In this work, we show that for the hexagonal lattice with only nearest neighbor hopping, the system can still be characterized by a two by two transfer matrix and solved exactly by the Avila global theory although this lattice has two sublattices. We obtained the exact localization phase diagram of the hexagonal lattice with irrational flux by this theory, which reveals three pure phases, i.e., the extended, localized and critical states but no mobility edge due to the chiral symmetry. We used the renormalization group (RG) theory to verify these results, which can determine part of the phase diagram. We then computed the fractal dimension of the remaining part numerically. The results from both the RG theory and numerical analysis confirmed the phase diagram we get from the Avila global theory. Our results can be tested in various hexagonal Moire lattices and artificial superlattices in recent experiments.

cond-mat.mes-hall↗