arXiv subjects

Rui Liu

Publications and source records attributed to Rui Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Duals of separable Banach Spaces as Calkin Algebras and Universal Ideal Quotients

For $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and every separable Banach space $V$, we use an oracle-relative two-sorted finite-extension construction, whose oracle records the local rational structure of $V$, to construct a separable Banach space $X_V$ such that $$ \operatorname{Cal}(X_V)=\mathcal{B}(X_V)/\mathcal{K}(X_V)\simeq \begin{pmatrix} \mathbb{K}&0\\ V^*&\mathbb{K} \end{pmatrix} $$ as Banach algebras. The identification of $V^*$ with the Jacobson radical is isometric. Consequently, every nonzero dual Banach space with a separable predual admits, after an equivalent renorming, a unital Banach-algebra structure isomorphic to the Calkin algebra of a separable Banach space. Moreover, there is a separable Banach space $X$ such that every separable Banach space is isometric to $\mathcal{J}/\mathcal{K}(X)$ for a closed two-sided ideal $\mathcal{J}$ of $\mathcal{B}(X)$, and the subspace--ideal correspondence preserves the canonical order.

math.FA↗

arXiv2026

Benchmarking EEG Foundation Models at Scale: Lessons from 20,000 Evaluations

Electroencephalography (EEG) foundation models (FMs) promise transferable neural representations, yet their advantages over strong supervised baselines and their prospects for further scaling remain unclear. To address these questions, we introduce EEG-Arena, an open-source benchmark covering 30 EEG FMs and 25 supervised baselines evaluated on 57 downstream tasks from 23 public datasets. Through more than 20,000 evaluations across five experimental protocols, we assess downstream performance, pretraining benefits, model size scaling, pretraining data scaling, and robustness to channel configuration. We find that (1) EEG FMs outperform strong task-specific supervised baselines on most evaluated tasks, particularly under non-bipolar settings; (2) compared with architecture-matched supervised training from scratch, pretraining improves both early optimization and final downstream performance, with larger and more consistent gains as more labeled downstream data become available; (3) existing EEG FMs do not exhibit a consistent positive relationship between parameter count and downstream performance; (4) under a fixed architecture, increasing the pretraining data scale yields sustained downstream gains; and (5) channel-flexible FMs achieve higher absolute performance than channel-constrained models across most evaluated channel configurations. Together, these findings demonstrate the downstream value of EEG FMs and identify pretraining data expansion as a promising direction for further progress. To support continued research, we release EEG-Arena as an open-source evaluation framework that provides shared infrastructure for reproducible benchmarking, model comparison, and community-driven development.

cs.LG↗

arXiv2026

Recursive Self-Improvement via On-Policy Distillation for Reasoning

On-policy distillation (OPD) trains a student model by having it generate trajectories, then matching its next-token predictions with an external teacher's next-token predictions. This provides dense, token-level supervision to the student. On-policy self-distillation (OPSD) eliminates the need for the external teacher. Specifically, a second frozen copy of the student model, now given the ground truth in its context, serves as the teacher. The student model only receives the problem and learns to mimic the privileged teacher model, while the teacher remains frozen throughout training. Previous work showed that freezing the teacher is useful for training stability, but we argue that this can prevent the teacher from incorporating the improvements learned by the student during training. Our primary contribution is to address this limitation with a recursive framework built around two complementary components. First, we let the privileged teacher co-evolve with the student so that revision learned in one round can guide the next, a process we refer to as Dynamic Co-Evolution (DCE). Second, because stronger revision can also make responses too verbose and self-critical, we additionally train on shorter, verified rewrites of the model's own on-policy responses. We call this complementary objective Self-Refined Concise Learning (SRCL). Overall, our comprehensive evaluations show that DCE+SRCL outperforms OPSD across multiple model scales and four competition-level mathematics benchmarks. Specifically, on Qwen3-8B, DCE+SRCL reaches 65.97% Average@12, outperforming OPSD by 35.62 percentage points while reducing mean output length by 7.80% relative to DCE alone.

cs.CL↗

arXiv2026

Parametric Study of the Torus Instability Threshold

The torus instability of an arched current channel has been suggested to initiate and drive major solar and stellar eruptions. Its threshold, given by the critical decay index of the equilibrium external poloidal field (the so-called strapping field) at the position of the current channel, is insufficiently known. Here, we carry out a parametric numerical study of the threshold, employing the force-free Titov-Démoulin (TD) equilibrium of a line-tied partial toroidal current channel and flux rope. This addresses the scatter of the threshold about its canonical value, $n_\mathrm{cr}=3/2$. Values scattering in the range $n_\mathrm{cr}\approx$\,1--2 are typically found in numerical and observational studies of flux rope eruptions on the Sun. For zero external toroidal (guide, or shear) field and approximately semicircular geometry (corresponding to minimal photospheric line-tying), we find the threshold to lie in the theoretically expected range of $\approx$\,1--1.5. An external toroidal field introduces a strong stabilizing effect on the instability, raising the threshold up to $\sim$\,2.5, which can explain observational and numerical results above the canonical value. Line-tying is found to act as a stabilizer as well. We also consider the approximate threshold based on the potential field and find a very good agreement with the exact numerical value, provided the horizontal component perpendicular to the flux rope axis is used to approximate the external poloidal field.

astro-ph.SR↗

arXiv2026

OptiSkill: A Hierarchical and Evolving SkillBank for LLM-Based Optimization Modeling

Automated operations research (OR) modeling requires LLMs to translate natural-language decision problems into correct mathematical programs. Existing methods can improve individual formulations, but they often solve problems in isolation, retaining little reusable experience and repeating similar formulation errors. Prior memory-based approaches store examples, thoughts, or insights as references, while OR modeling requires reusable formulation skills that transfer across problem narratives and guide concrete modeling decisions. We propose OptiSkill, a skill-augmented framework that builds a hierarchical and evolving SkillBank for LLM-based OR modeling. SkillBank stores solver-verified experience as reusable skills, with Global Strategies for problem-level formulation skeletons and Step Experiences for local error-prevention rules. It is further refined through stable batch-level test-time evolution, where candidate skills are incorporated only after validation. Experiments on eight OR modeling benchmarks show that OptiSkill improves formulation accuracy across LLM backbones, outperforms strong agentic baselines, and gains further by expanding SkillBank coverage and reliability. Code and data are available at https://github.com/rachhhhing/OptiSkill

cs.AI↗

arXiv2026

When More Is Not Better: Component Anti-Synergy in a P300 Speller

P300 brain-computer interface (BCI) spellers can provide hands-free communication for people with severe motor impairments. Modern pipelines combine multiple individually promising components, often assuming that 'more-is-better'. We tested this assumption using a four-component full-factorial experiment varying the inclusion of Euclidean Alignment (EA), xDAWN spatial filtering, subject calibration, and language model priors on a public P300 dataset. Performance was evaluated using accuracy, repetitions, and information transfer rate (ITR) with mixed-effects models. Results show that the value of components is conditional rather than additive. Calibration was the strongest singular contributor, while EA compensated for its absence in zero-calibration settings. Adding independently useful components could also reduce performance, revealing component anti-synergy. Contrary to conventional wisdom, LM support was not universally beneficial: its effect depends strongly on the strength of the underlying EEG pipeline, while results from a larger LM showed a similar pattern. Together, these findings challenge maximal 'all-on' pipeline design and highlight the value of selecting spatial and language-support components according to the quality of available EEG evidence.

cs.LG↗

arXiv2026

On-chip squeezed light in the audio frequency band

Squeezed light in the audio-frequency band is a key resource for quantum metrology and quantum sensing. However, realizing stable audio-frequency squeezed light on integrated photonic platforms remains challenging due to technical noise and the difficulty of scalable phase referencing. Here, we demonstrate on-chip generation of audio-band two-mode squeezed states down to 60 Hz in a silica microcavity. To enable phase-stable operation without directly locking fragile quantum modes, we develop a coherent-comb control method in which a weak electro-optic reference comb co-propagates with the vacuum at the quantum frequency modes in an orthogonal polarization. This scheme provides quadrature measurement and long-timescale phase stability, thereby enabling covariance-matrix reconstruction. We verify the entanglement with the positive partial transposition criterion, which confirms inseparability via a minimum symplectic eigenvalue of 0.395 ($<0.5$). Our results establish an experimentally accessible route toward on-chip phase-stable audio-band squeezing and support the scalable framework for continuous-variable quantum information processing with integrated photonics.

quant-ph↗

arXiv2026

City Editing: Hierarchical Agentic Execution for Dependency-Aware Urban Geospatial Modification

Urban renewal requires incremental modifications to existing geospatial plans, yet manually updating complex layouts under spatial constraints is labor-intensive and error-prone. To tackle this, we propose CEAE, a hierarchical agentic framework that formulates urban renewal as machine-executable GeoJSON editing from natural-language instructions. CEAE decomposes instructions into hierarchical geometric intents, executing edits from coarse to fine while preserving spatial consistency through a self-reflective execution-validation loop. Experimental results show that CEAE outperforms baselines in execution validity, robustness, and geometric accuracy.

cs.MA↗

arXiv2026

Streaming P300 Acquisition and Statistical Signal Validation Across Five EEG Platforms: A Hardware-Agnostic BrainFlow/LSL Pipeline

P300 spellers offer people with severe motor impairment, such as ALS, an effective communication channel and remain one of the most established surgery-free alternatives to intracortical interfaces. Advanced language models have made spellers faster and more robust, yet the hardware beneath them is under-studied. We present a hardware-agnostic, real-time P300 acquisition pipeline built on BrainFlow and Lab Streaming Layer (LSL) that runs unchanged across consumer- and research-grade EEG headsets, with permutation tests of signal separability. Using a standard 6 x 6 row/column paradigm, we piloted five configurations: a custom dry system, a custom wet/gel system, Emotiv Flex, Emotiv EPOC X, and Muse 2. The custom systems and EPOC X showed weak or inconsistent signal separability, Muse 2 had the highest acquisition reliability despite limited centro-parietal coverage, and Flex showed the most promising signal. In 20 further Flex sessions varying subject, timing, and phrase length (131 target characters), a peak-amplitude permutation test and a cross-validated xDAWN decoder both detected a significant target response under two channel-exclusion policies, with decoder AUC reaching about 0.72 after 15 repetitions. Character accuracy depended heavily on evaluation methodology: in-sample majority voting reached 94.7%, whereas character-held-out accuracy was 31.3% with evidence accumulated across repetitions, about three times that of held-out majority voting. These analyses indicate that Flex captured a detectable, if still weak, P300 under the studied conditions, while broader participant-level validation and improved decoding remain necessary.

cs.HC↗

arXiv2026

Hierarchical and Permutation-Invariant Feature Transformation Learning via Policy-Guided Embedding Search

Feature transformation improves predictive performance on tabular data by constructing informative abstractions from raw features. Recent generative approaches encode transformation knowledge into continuous embedding spaces for efficient exploration of candidate strategies, but face three key limitations: (1) overlooking hierarchical relationships between low-level features, operations, and high-level abstractions; (2) enforcing order-sensitive embeddings on inherently permutation-invariant transformation sequences, thereby introducing systematic bias; and (3) relying on gradient-based search, which is ill-suited to non-convex transformation spaces. We propose a framework with two complementary components. First, a permutation-invariant hierarchical module captures interactions across features, operations, and abstraction levels, with a self-attention pooling mechanism that maps semantically equivalent structures to consistent embeddings aligned with downstream performance. Second, a policy-guided multi-objective reinforcement learning strategy initializes the search from empirically strong seeds and jointly optimizes predictive accuracy and transformation efficiency. Extensive experiments on diverse tabular benchmarks demonstrate the effectiveness and robustness of our framework against strong baselines. Our code and data are publicly available at: https://github.com/RayLiu1103/PHER.

cs.LG↗

arXiv2026

SAP: State-Guided Data Synthesis with Argument Provenance for Multi-Turn Tool Use

High-quality multi-turn tool-use data is essential for training agentic models, yet existing data synthesis methods often underrepresent the argument-level dependencies that are critical to long-horizon tool use. As a result, even when a model selects the correct tool, task execution may still fail because the model fills tool arguments with fabricated, stale, or weakly grounded values. To address this problem, we propose \textbf{State-Guided Data Synthesis with Argument Provenance (SAP)}. SAP combines state guidance, tool-argument provenance constraints, and turn-level validation to efficiently construct tool-use trajectories with long-range dependencies and high accuracy. Using data generated by SAP, we build SAP-4B, which is highly competitive even when compared with much larger models across multiple benchmarks. Source code, synthesized data, and trained weights are available at https://github.com/Zichen1024/SAP.

cs.AI↗

arXiv2026

Visual Representation and History Modeling for Navigation World Models

Navigation World Models (NWMs) predict action-conditioned visual futures for planning. Two practical challenges are central to their design: selecting a suitable visual representation and efficiently modeling observation history for repeated candidate queries. Standard Global-Softmax attention provides flexible interactions but repeatedly processes the same history, leading to increasing computation and memory costs for long contexts and multi-query planning. We study both problems within a unified conditional flow-transformer framework. We first compare five frozen visual representations under the same dynamics model and evaluation. To reduce redundant history computation, we design Cached-Linear, a hybrid architecture that combines local and shifted-window attention for target mixing with linear attention for reusable history access. We further develop Balanced Gated Delta Network (GDN), which augments this design with frame-wise recurrent memory for temporal history modeling. Experiments on RECON, SACSoN, and SCAND show that representation choice depends on the prediction objective: PAE-L performs best for reconstruction, RAE-B for direct prediction, and V-JEPA for long-horizon rollout. Under shared-history workloads, Cached-Linear substantially reduces computation and memory compared with Global-Softmax, while Balanced GDN improves selected direct-prediction endpoints with efficient context reuse. Overall, we systematically study visual representation and history modeling for NWMs and develop hybrid reusable-history architectures for efficient long-context and multi-query prediction.

cs.CV↗

arXiv2026

From Dense Prediction to Visual Editing: Structured Supervision for Unified Image and Video Creation

Unified image and video creation requires a model to follow diverse instructions while preserving identity, geometry, and temporal structure from visual context. However, semantic-only conditioning and creation-only training do not explicitly supervise the local structure needed for precise, temporally consistent editing. We therefore formulate depth and surface-normal prediction as image-form denoising targets, using these dense tasks as structured visual supervision within the same creation interface. Our framework decouples semantic interpretation from spatially aligned visual injection while sharing one multimodal diffusion transformer (MMDiT) backbone across all tasks. Mutual Context Attention (MCA), a paired-video data-construction procedure, and a progressive training curriculum then connect the learned structural cues to temporally localized editing and reference-conditioned creation. A single checkpoint obtains the highest overall score in the reported comparison of unified systems (4.15); adding dense supervision improves OpenVE Overall from 3.98 to 4.06 and Local Add from 3.92 to 4.18. These results support a deliberately bounded conclusion: perception-oriented dense supervision transfers useful structural knowledge to downstream creation, especially editing locality and preservation; we do not claim superiority as a standalone dense predictor.

cs.CV↗

arXiv2026

RDANet: Relative Degradation Aware Network for Infrared Small Target Detection

Infrared small target detection is still challenging in remote sensing imagery, because the targets are extremely small, exhibit weak local contrast, and are often embedded in complex and highly variable backgrounds. In addition to these inherent difficulties, we observe that existing detectors often show unstable performance when the target scale changes or when the scene background varies. This scale- and scene-sensitive degradation indicates that current methods are insufficient in simultaneously preserving target structure during feature downsampling and maintaining discriminative local contrast under background shifts, which finally results in unbalanced detection performance across different conditions. To improve detection robustness, this paper proposes a Relative Degradation Aware Network (RDANet) for infrared small target detection. RDANet consists of two dedicated modules: Multi-Scale Anti-Alias Downsampling (MSAD) and Prototype-Guided Skip Memory (PGSM). MSAD introduces multi-scale anti-alias filtering together with pixel-fold aggregation to reduce aliasing effects during resolution reduction, so that target shape information can be better preserved while irrelevant background responses are suppressed. PGSM further enhances the skip features by retrieving patch-level prototypes from a shared memory and adaptively integrating them into the current representation, which helps maintain stable local contrast cues under diverse scene backgrounds. Experiments on three public benchmarks show that RDANet achieves the best performance on most evaluation metrics, while scale- and background-stratified evaluations indicate more stable behavior across target sizes and scene complexity. The code is available at https://github.com/BIT-RuiLiu/RDANet.

cs.CV↗

arXiv2026

Unconventional Pressure Evolution of Spin-Density-Wave State in La$_{3}$Ni$_{2}$O$_{7}$

The discovery of pressure-induced high temperature superconductivity in the bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$ has raised the question of how its spin-density-wave (SDW) state evolves toward the superconducting regime. Here, we report a systematic electronic Raman study of La$_{3}$Ni$_{2}$O$_{7}$ single crystals under hydrostatic pressures up to 16.51 GPa. Both the SDW gap energy and the transition temperature $T_{\mathrm{SDW}}$ show an overall increase with pressure, while the dimensionless coupling ratio 2$Δ_{\text{SDW}}/(k_{\text{B}}T_{\text{SDW}})$ remains constant around $\sim7.5$, indicating a robust strong-coupling character of SDW state. At the same time, the Raman SDW peak broadens as pressure is applied, indicating a gradual weakening of long-range SDW order. These results reveal an unusual pressure evolution in which the SDW energy scale is enhanced while the SDW state becomes progressively less coherent, providing spectroscopic constraints on the magnetic correlations relevant to superconductivity in bilayer nickelates.

cond-mat.supr-con↗

arXiv2026

Rethinking Normalization Placement for LLMs: Post-Norm under Curriculum Depth Growing

Pre-norm is the standard normalization placement in modern Transformers because it facilitates joint optimization of full-depth models. We ask whether this preference persists when depth is introduced through a curriculum. In curriculum depth growth, each appended block receives the boundary representation produced by a trained prefix, making normalization placement relevant to forward conditioning. We therefore test whether placement and training curriculum interact. In a controlled distillation study with a Qwen3-8B teacher and a nine-layer student, pre-norm and post-norm are indistinguishable under joint training, differing by $0.0004$ validation CE, while post-norm improves over pre-norm by $0.0328$ under curriculum growth, an order of magnitude larger. A post-joint control matched by student active-layer tokens remains worse than post-grow, which rules out compute as the sole explanation. The ranking crosses over during the curriculum: post-norm takes the lead once blocks are appended. Single-block and freeze controls localize the ranking change to block appending rather than shallow-block quality or retraining. Boundary diagnostics associate post-norm with stable residual scales and pre-norm with structural-token scale drift; on a fixed batch, the final pre-grow block is also nearly identity-mapped. Together with the phase-wise crossover, these observations are consistent with boundary-scale conditioning after new blocks are appended. The results motivate treating normalization placement and training curriculum as coupled design choices in this distillation setting.

cs.AI↗

arXiv2026

Prediction of BaBiO$_3$-like superconducting perovskites in K-doped SrAsO$_3$

Using first-principles calculations, we predict a new perovskite compound SrAsO$_3$ . The undoped cubic phase has pronounced soft-phonon instabilities, which are gradually suppressed upon K doping the Sr site. The cubic phase becomes dynamically stable for K-doping levels above approximately 60%, and the stabilized K-doped phases are metallic with predicted conventional phonon mediated superconductivity. Moreover, the inclusion of nonlocal exchange interactions broadens the electronic bandwidth, enhances the electron-phonon coupling (EPC) strength, and increases the superconducting transition temperature ($T_c$) of these doped compounds. In particular, the HSE06 hybrid exchange-correlation functional corrected EPC constant $λ$ reaches 1.41 for Sr$_{0.4}$K$_{0.6}$AsO$_3$, corresponding to a predicted $T_c$ of 44.3 K. These results suggest that SrAsO$_3$ is a BaBiO$_3$-like superconducting perovskite driven by strong electron-phonon coupling.

cond-mat.supr-con↗

arXiv2026

LoCA: Forward-Only LLM Tuning after One-Shot Calibration with Local Credit Assignment

Parameter-efficient post-training reduces the number of trainable parameters, but still requires repeated end-to-end backpropagation through the frozen backbone. Every adaptation step therefore needs backward-capable hardware and must store or recompute activations. We ask whether this repeated backward chain can be replaced by a one-time calibration. We introduce Local Credit Assignment (LoCA), a two-stage method for small-shift adaptation. One probe backward pass fits a low-rank map at each transformer block from the final prediction error to a local hidden-state correction. LoCA then reuses these maps to form blockwise regression targets from forward activations and fits low-rank adapters with closed-form ridge solves. No further backbone backward pass is required. We evaluate LoCA on five discriminative benchmarks with Qwen2.5 models from 0.5B to 14B. In 16 of 25 reported task--scale comparisons, LoCA yields lower evaluation cross-entropy than the corresponding LoRA run. Its measured full-run GPU peak, including calibration, is 26--29\% lower than LoRA's. After calibration, its CPU steady-state memory is 36--52\% lower and its per-pass time is 43--48\% lower. A shared scale-normalized candidate set is reused across all tested Qwen2.5 sizes and on SmolLM2-1.7B. LoCA thus amortizes global credit assignment into one calibration and enables later forward-only tuning when repeated backpropagation is impractical. The code associated with this paper is available \href{https://github.com/Xia12121/LoCA}{here}.

cs.AI↗