arXiv subjects

Yi Li

Publications and source records attributed to Yi Li.

At least 19 recordsLinked to original sources

arXiv2026

Nonintegral Flux Trapping in Frustrated Josephson Networks of Triplet Superconductors

In a Josephson junction network, anisotropic coupling between spin triplet pairing correlations can lead to frustrated $d$ vector textures that support spontaneous Josephson currents and nonintegral flux trapping. Such networks can appear in superconducting polycrystals, as well as single-crystal superconductors. In analogy to classical spin systems, in which the presence of geometric frustration and anisotropic superexchange can lead to nontrivial spin textures, Josephson networks with anisotropic Josephson couplings cannot simultaneously optimize their $\mathrm{U}(1)$ superconducting phase differences and relative $d$ vector orientations. The internal pairing structure of Cooper pairs twists as they tunnel across the Josephson junction, and the $d$ vector texture enters as an emergent geometric phase which can spontaneously trap fractional flux. For real-valued Josephson couplings between unitary $d$ vectors, the emergent geometric phase reduces to a $\mathbb{Z}_2$ structure, allowing for spontaneous $π$-flux trapping above a critical antisymmetric coupling, distinct from usual half-quantum vortices. Further, we demonstrate a continuously tunable nonintegral flux for complex Josephson couplings. The results of this work reveal new routes to engineer frustrated Josephson networks from the interplay of magnetic textures and spin triplet superconducting pairing order.

cond-mat.supr-con↗

arXiv2026

LEAD: Length-Efficient Adaptive and Dynamic Reasoning for Large Language Models

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness--efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods in our matched comparisons while producing substantially shorter outputs than the base model.

cs.LG↗

arXiv2026

Drafting Agents, Not Just Tokens: Speculative Recursive Self-Improvement for Agentic Systems

Improving an agent through successive revisions requires balancing exploration and evaluation under a limited budget. A narrow search can miss useful sequences of edits, while fully evaluating every intermediate version often exhausts the budget before those sequences yield a verified improvement. Inspired by the draft--verify principle of speculative decoding, we propose Speculative Recursive Self-Improvement (SpecRSI), a two-level framework coupling inner-loop agent search with outer-loop improver learning. SpecRSI drafts successors before their predecessors are fully evaluated, while adopting only fully evaluated, admissible versions. In the inner loop, Verification-Aware Tree Search (VATS) allocates the budget between further edits and outstanding checks using the predicted verified return of a continuation. In the outer loop, Group Verification Optimization (GVO) updates the improver from completed searches while keeping the real evaluator fixed. We evaluate SpecRSI on scientific optimization (including active queue management (AQM) for network infrastructure), coding, and general agent-system benchmarks. Under matched evaluation-call budgets, SpecRSI improves scientific terminal gain over Janus by 60.0%--96.3% and area under the budget curve by 32.1%--91.6%, while achieving higher means across all 50 scientific backbone--task pairs and outperforming MetaRSI-v1 by 1.30--2.70 percentage points (pp) in system score across twenty backbones. On instance-level comparisons, it further improves PyBaMM terminal gain by 142.6% and SWE-Pro success by 6.0 pp at 7.0% and 9.2% lower token cost, respectively. These results demonstrate the efficacy of the proposed approach.

cs.LG↗

arXiv2026

Calibrating Multimodal Test-Time Adaptation under Reliability and Availability Modality Shifts

Multimodal test-time adaptation (TTA) enables pretrained multimodal models to accommodate distribution shifts during inference using only unlabeled test data, without recourse to the original training data. Compared with unimodal adaptation, multimodal adaptation is further complicated by the coexistence and interaction of multiple representation perspectives. This complexity is particularly pronounced under modality reliability shifts, which preserve modality availability but degrade information quality, and modality availability shifts, which render the corresponding modality entirely inaccessible. Category-conditional Gaussian modeling offers a natural starting point for handling such distributional variations, having proven effective in unimodal test-time adaptation for characterizing representation distributions, yet its extension to multimodal settings requires a more elaborate formulation. To this end, we propose Adaptive Probabilistic Gaussian Calibration (AdaPGC), which extends category-conditional Gaussian modeling across modality-specific and multimodal fusion representations for probabilistic calibration under multimodal distribution shifts. AdaPGC continuously updates category-conditional Gaussian models over modality-specific and fusion representations, using the resulting probabilistic predictions to calibrate source model predictions and guide reliability based rectification, while exploiting their joint distributions to recover unavailable fusion representations. Extensive experiments under diverse modality corruption and missingness conditions demonstrate that AdaPGC effectively improves robustness under both modality reliability and availability shifts. Our source code will be released at https://github.com/XuJinglinn/AdaPGC-plus.

cs.CV↗

arXiv2026

The covering radius of the first-order Reed-Muller code in nine variables is 242

We prove that the covering radius of the binary first-order Reed-Muller code RM(1,9) is exactly 242. Equivalently, the maximum nonlinearity of a Boolean function in nine variables is 242. Our proof combines a one-point rigidity theorem with a spectral and computational exclusion of the two larger candidate nonlinearities. We first show that every nine-variable Boolean function of nonlinearity 243 admits a unique one-point modification that raises its nonlinearity to 244: the point to be changed is the vector sum of its support. This part uses exact Walsh-update identities, integer interpolation, rigidity of a quadratic residue, and a sharp Walsh l1 estimate for cubic Boolean functions. To exclude nonlinearity 244, we use Parseval's identity and congruences of integral Walsh coefficients to force an exceptionally restricted spectrum. An associated cubic residue phase must attain the extremal Walsh l1 bound 10240. We eliminate one equality spectrum by hyperplane slicing; the other forces the original Boolean function from the signs of the cubic phase and yields a double-complement-pairing identity for its cubic top part. The classification of alternating trilinear forms over F2, an exact filter of their representatives, and two exhaustive enumerations of 218 quadratic supplements then rule out every remaining candidate. Together with the known construction attaining nonlinearity 242, these arguments establish the asserted covering radius.

math.NT↗

arXiv2026

Bounding Fidelity of Non-Stabilizer States from Local Pauli Measurements

Nonstabilizerness, commonly referred to as magic, is essential for universal quantum computation. Yet, for pure $n$-qubit states this property is directly linked to the hardness of direct fidelity estimation. We propose a scheme to bound the fidelity on non-stabilizer states by choosing operators with low measurement overhead and using parallel local Pauli measurements to estimate compatible observables. We selectively measure operators that share a permutational symmetry without imposing any assumption on the physical system. This selection reduces the optimization to a linear program with only $O(n)$ variables for bounding fidelity. Our methods can be extended to bound nonlinear quantities like the purity via convex quadratic programs. For hypergraph states that can exhibit extensive nonstabilizerness, we demonstrate for up to $n=500$ qubits that our framework substantially reduces the measurement overhead under both local and global depolarizing noise. These results show that symmetry induced by measurement selection reduces both measurement and computational costs, enabling scalable characterization of magic resources in quantum computing and quantum networks.

quant-ph↗

arXiv2026

Rethinking Positional Encoding and Interaction Granularity for CTR Prediction

Click-through rate (CTR) prediction relies on historical behaviors and contextual features to estimate clicks on a target item. Existing Transformer-based CTR models often adopt index-based or temporal positional encodings and token-level causal interaction. However, we observe that most existing positional encodings do not outperform NoPE, while relaxing causal constraints within target-relative temporal groups also yields gains. These observations motivate a fundamental question: what positional encoding and interaction granularity does CTR prediction actually require? To address this question, we propose \textbf{TRIP}, which combines target-aware rank--time positional encoding with temporal-group interaction modeling. Specifically, Factorized Rank Encoding represents each behavior's ordinal position within the historical sequence through a low-rank factorization, while Target-Relative Time Encoding characterizes its temporal distance to the target on a coarse-to-fine scale. This joint design grounds each behavior's positional representation in its sequence context and temporal relation to the current target. Furthermore, Temporal Group-Causal Interaction enriches intra-group representations through bidirectional interaction and masked reconstruction while preserving inter-group causal order. Finally, behavior representations are condensed into compact group summaries for efficient group-level modeling in subsequent layers. Experiments on four public benchmarks show that TRIP improves AUC by up to 4.45\% relative to the strongest baseline.

cs.IR↗

arXiv2026

Understanding Python Linters through a Comprehensive and Systematic Empirical Study

Code linters, tools that automatically detect code issues, help developers accelerate development and improve code quality by identifying errors early. Unlike previous studies that focused mainly on single linters or informal comparisons, this paper presents the first large-scale empirical study of five widely used Python linters: Ruff, Pylint, Flake8, Mypy and Black, through four key user concerns: linting rule checks, speed, configuration methods, and linter preferences. We analyze 1,551 linting rules, categorize them into five types, and construct rule mappings, finding that more than 40% are shared between multiple linters, with Ruff and Pylint together covering over 80% of all rules. Pylint has the most rules in the first two categories, and Ruff leads in the last three. Next, we measure their running times on 1,000 GitHub projects under three setups (single-rule, default, all-rules), finding a consistent speed ranking from fastest to slowest: Ruff, Mypy, Flake8, Black, and Pylint. Ruff is extremely fast, with runtimes typically within one second. Then, we summarize four configuration methods and four types of configuration options from 443 available options across the five linters. While all linters support the four configuration methods, they differ in project configuration formats and flexibility in their configuration options. Finally, an analysis of 3,094 GitHub projects using the five linters reveals that over 50% use multiple linters, share strong consensus on option selections and rule suppressions, but exhibit project-specific variations in enabled-rule configurations. Our findings provide actionable insights for linter users and establish a benchmark dataset and taxonomy to support future research, such as cross-linter rule mapping, performance modeling, and automated configuration.

cs.SE↗

arXiv2026

Spectral $Γ_2$ inequalities for the $V$-Laplacian with evolving weighted measures

In this paper, we establish spectral Bakry-Émery $Γ_2$ criteria and their modified counterparts for the $V$-Laplacian on closed Riemannian manifolds equipped with evolving weighted measures. The estimates yield jointly optimized spectral bounds and sharp endpoint constants. When the measures evolve according to the Fokker-Planck equation, these estimates yield monotonicity formulas for the Fisher information associated with Shannon and Tsallis entropies, together with quantitative propagation of Poincaré, logarithmic Sobolev, and nonlinear interpolation inequalities. In the stationary reversible setting, our results specialize to the Witten Laplacian and recover the unweighted Cai-Wang estimates \cite{Cai}.

math.DG↗

arXiv2026

Maximum Velocity of a Liquid Metal Drop Driven by a Time-Dependent Electrocapillary Excitation

Gallium alloys are promising materials in biomedical engineering, electronics, and wireless communications, thanks to their good conductivity, non toxicity and their ability to sustain large deformations. They can be transported in capillaries using purely electric means by continuous electrowetting (CEW). Current models of CEW-driven flows do not address the transient response to fast changes in the excitation, crucial in many applications. Here, we present a theory that describes the CEW-driven oscillatory motion of a drop of Eutectic Gallium-Indium alloy inside a capillary. We consider inertia, viscosity and the transient response of the electrical circuit consisting of the drop plus the electrolyte where it is immersed. The theory describes fairly well the experimental drop velocity and explains the existence of an optimal frequency that maximizes the velocity.

physics.flu-dyn↗

arXiv2026

A Near-Optimal Lower Bound for $\ell_p$-Subspace Embeddings, $1\leq p<2$

For $d \geq 2$, $p \geq 1$ and $ε> 0$, let $N_p(d,ε)$ be the smallest integer $N$ such that for every integer $n$ and every $A\in\mathbb{R}^{n\times d}$, there exists a matrix $Φ\in\mathbb{R}^{N\times n}$ satisfying $(1-ε)\lVert Ax\rVert_p\leq \lVertΦA x\rVert_p\leq (1+ε)\lVert Ax\rVert_p$ for all $x\in\mathbb{R}^d$. For every constant $p\geq 1$ with $p\not\in 2\mathbb{Z}$, when $d\gtrsim_p \log(1/ε)$, the bound \[ N_p(d,ε) \gtrsim_{p} \frac{d}{ε^2 \operatorname{polylog}(d/ε)} \] is established. This improves the previous lower bound $Ω(1/(ε^2\operatorname{polylog}(1/ε)))$ due to Li et al. (SICOMP 2021) and is optimal up to logarithmic factors for $1\leq p<2$. The central technical idea originated from ChatGPT 6 Pro.

cs.DS↗

arXiv2026

An Attribute-Based Measure of Video Complexity

A new framework for the estimation of the complexity posed by video-question pairs to video-LLMs, Video Attribute-Based Complexity (VideoABC), is proposed. Video complexity is defined as the probability of failure of a video-LLM for a given video-question pair. VideoABC is a non-parametric complexity measure, using a reference video dataset and a pre-defined vocabulary of video attributes informative of complexity, e.g. the scene complexity or the speed of the video event relevant to the question. In a training phase, reference videos are projected into the space of these attributes, which is then quantized. The expected ABC of each quantization cell is then computed. Given a new video and its projection into the attribute space, complexity is estimated by the expected ABC of the associated quantization cell. To enable the use of VideoABC with small reference video datasets, two quantizers are combined: a k-means quantizer that enables accurate complexity estimates for samples in the distribution of the reference dataset and a universal lattice quantizer that guarantees generalization to out-of-distribution samples. A synthetic video generation procedure, inspired by target-distractor manipulations of psychophysics studies, is proposed to populate the cells of the lattice quantizer during training, enabling the computation of their expected ABCs. Experimental results show that VideoABC is effective even with very low-dimensional attribute representations, substantially outperforming approaches like 'video-LLM as judge' with much less complexity. Finally, the explainable nature of the VideoABC score, in terms of well-defined attributes, is shown to provide insights on how the attribute composition of benchmarks affects their complexity.

cs.CV↗

arXiv2026

ClunoGS: Compact Language 3D Gaussian Splatting via Unified Optimization

Language 3D Gaussian Splatting enables open-vocabulary scene understanding by associating Gaussian primitives with language features. These semantic attributes increase model storage, while most existing 3DGS compression methods are designed mainly to preserve RGB rendering quality. One straightforward approach is to apply sparsification and quantization sequentially. However, pruning based only on rendering quality can remove Gaussians that have small RGB contributions but are important for semantic prediction. Once removed, their semantic information cannot be recovered by later quantization. We propose ClunoGS, a compact framework for Language 3DGS that combines semantics-aware Gaussian sparsification and vector quantization in a unified constrained objective. Semantic supervision is used during sparsification, and the objective jointly considers rendering quality, semantic accuracy, and compactness. We optimize the unified objective with alternating primal, sparsification, quantization, and dual updates. We evaluate ClunoGS on open-vocabulary localization and segmentation using the LERF and ScanNet-10 benchmarks. Under aggressive compression, our unified, semantics-aware formulation substantially alleviates the degradation of semantic representations caused by sequential compression and semantics-agnostic Gaussian sparsification. Ablations further show that jointly coordinating sparsification and quantization better preserves semantic accuracy than applying them independently.

cs.CV↗

arXiv2026

Kinetic-inductance Parametric Amplification in Superconducting Hybrid Magnonics

Parametric amplification enables sensitive microwave detection and signal processing by amplifying weak signals with minimal added noise. Here, we demonstrate kinetic inductance mediated parametric amplification in a hybrid magnonic system comprising a nonlinear NbN nanowire resonator strongly coupled to a yttrium iron garnet sphere. The resonator exhibits four wave mixing and nonlinear frequency pulling, enabling parametric amplification both away from and within the magnon-photon strong coupling regime. In the magnon detuned regime, we observe 7 dB gain, while coupling to the YIG magnon shifts the parametric amplification response by ~20 MHz and yields 3.4 dB gain in the hybrid mode. Thus, magnon photon coupling provides a route to magnetically tune the spectral position of kinetic inductance parametric amplification. At higher pump powers, the system transitions to a self oscillatory regime featuring comb-like sidebands and probe activated nonlinear mode mixing. These results establish hybrid magnonics as a platform for tunable nonlinear microwave amplification and dynamics.

cond-mat.mes-hall↗

arXiv2026

PRET is a few-shot system for pan-cancer recognition without example training

Pathological examination stands as the cornerstone in cancer diagnosis, impacting millions worldwide annually. With the shortage of pathologists globally, artificial intelligence (AI) has emerged rapidly to automate the diagnostics process. However, conventional AI models require substantial labeled data for each disease, posing huge challenges in scalability and practicality. Therefore, we introduce PRET (pan-cancer recognition without examples training), a few-shot system to achieve flexible, scalable, and effective cancer recognition across diverse organs, hospitals and tasks without training. Evaluated on 23 international benchmarks comprising 4,484 whole-slide images, our method outperforms existing approaches across 20 tasks, achieving over 97% area under the curve on 15 benchmarks with a maximum improvement of 36.76%. Notably, PRET delivers clinical-grade diagnostic performance in lymph node metastasis detection using only eight slide examples, outperforming 11 pathologists. By offering a flexible and cost-effective solution for pan-cancer recognition, PRET paves the way for accessible and equitable AI-based pathology systems, particularly benefiting minority populations and underserved regions.

cs.CV↗

arXiv2026

Non-Monotonic Exciton Transport Efficiency in Multi-layer Ring-shaped Quantum Networks inspired by Photosystem I

Photosystem I (PSI) is one of the most efficient natural photosynthetic complexes and serves as a structural prototype for understanding excitation energy transfer (EET) and designing artificial light-harvesting systems. Here, we construct a multilayer elliptical-conical quantum network inspired by PSI to investigate how antenna architecture affects EET. Excitation dynamics are simulated using the quantum jump approach combined with coherent modified Redfield theory (QJA-CMRT). The transfer efficiency exhibits a pronounced nonmonotonic dependence on pigment density, reaching a maximum of 0.86 at x=6 in the five-layer network. The optimal configuration contains 91 pigments, close to the number of core antenna pigments in natural PSI. Our combined density-of-states and kinetic analyses reveal that this nonmonotonic dependence originates from a trade-off: at low pigment densities, enhanced band overlap promotes energy transfer, whereas at high densities, excessive exciton delocalization compromises funnel directionality and reduces efficiency; the optimal configuration is consequently achieved at x=6. These findings provide insights into PSI antenna organization and offer guidelines for designing efficient artificial light-harvesting systems.

cond-mat.soft↗

arXiv2026

Long-time existence of the Laplacian flow with Weyl tensor

We establish integral extension criteria for the Laplacian flow of closed $G_2$-structures on compact $7$-dimensional manifolds $M$. Assuming a uniform lower bound for the scalar curvature, we prove that a finite-time solution extends smoothly whenever the spatial $L^p$ norm of the $77$-dimensional Weyl component $W_{77}$ remains uniformly bounded for some $p\ge 7/2$. We also obtain a mixed space--time extension criterion under the condition \[ W_{77}\in L^q(0,T;L^p(M,g(t))), \qquad \frac{7}{2}<p<\infty,\quad 1\le q<\infty,\quad \frac{1}{q}+\frac{7}{p}\le 2. \] In particular, finite space-time $L^4$ integrability of $W_{77}$ is sufficient for extension.

math.DG↗

arXiv2026

Coherent optical control of a thousand qubits in a three-dimensional trapped-ion crystal

Leading quantum platforms are largely limited to one or two dimensions, whereas three-dimensional Coulomb crystals of trapped ions self-assemble into dense qubit arrays with no rearrangement overhead. Coherent optical control of such crystals has nonetheless been out of reach, because the optical transition couples to nearly all $3N$ collective modes, i.e., a thermally occupied quasi-continuum bath. Here we cool about 3,600 modes of a crystal of over 1,200 ions below single-phonon occupation, using a continuous cooling band that spans more than five octaves in vibrational spectrum, from about 50 kHz to 2.1 MHz. The crystal then serves as a register of optical qubits, allowing global initialization, coherent manipulation and collective detection. We demonstrate ensemble optical coherence of 21.6 milliseconds and reduce the optical-transition frequency uncertainty from 389 Hz for a single ion to 12 Hz for over a thousand ions, approaching the expected projection-noise scaling. Our approach could be extended to even larger crystals with phonon-mediated many-body couplings, opening a route towards entanglement-enhanced precision metrology and three-dimensional quantum simulation, particularly with spatial-shaped illumination for region-resolved collective control.

quant-ph↗