arXiv subjects

Xiaoyu Li

Publications and source records attributed to Xiaoyu Li.

At least 19 recordsLinked to original sources

arXiv2026

Low-Degree Polynomial Approximation of the Cross-Polytope

We determine the degree-distortion tradeoff for polynomial approximation of the $d$-dimensional cross-polytope $B_1^d$. For every $1\le t\le d$, every globally nonnegative degree-$2t$ form that is positive away from the origin has multiplicative sandwich distortion at least $(2e)^{-1/2}\sqrt{d/t}$, while an explicit sum-of-squares (SoS) form achieves distortion at most $(2e)^{1/2}\sqrt{d/t}$. Hence both the nonnegative-form and SoS optima are $Θ(\sqrt{d/t})$, and degree $Θ(d)$ is necessary and sufficient for constant distortion. The lower bound is representation-free. Averaging over signed permutations and evaluating on flat points of the $\ell_1$ sphere reduces every candidate to a support-size profile $V(k)=k^{-2t}Q(k)$ with $°Q\le t$ and $Q(0)=0$. After the substitution $u=1/k$, Lagrange interpolation shows that this degree budget cannot keep the profile nearly constant across $d$ support scales. A matching SoS construction averages even powers of sign-vector facet normals and reduces the upper bound to a Rademacher moment. We also isolate a weighted reciprocal-grid lemma, derive consequences for $\ell_p$ balls, and contrast the polar cube. For a general symmetric polytope, weighted facet powers yield a one-sided certificate whose boundary-floor objective is concave and whose worst-direction oracle reduces to convex dual-norm problems; at degree two, its optimizers recover classical optimal design and the John ellipsoid. This is an oracle-model certificate optimization, not an end-to-end complexity result or a characterization of the full SoS optimum.

cs.DS↗

arXiv2026

When the Canonical Completion Is Wrong: Formalizing and Measuring the Jump in Large Language Models

Whether large language models (LLMs) can perform the abductive leap from evidence to a new system of axioms, commonly referred to as a jump, has recently attracted considerable debate. A prominent position holds that LLMs are structurally incapable of such jumps, while recent studies challenge both its mechanism and empirical evidence. One of the main reasons why the debate remains open is the difficulty of defining the jump precisely enough to test it. In this paper, we attempt to develop a formal account of the jump in four steps and measure the second. These steps ask what the default completion of partial data is, when the constraints exclude it, whether the new structure agrees with later observations, and how successive jumps compound. We define a \emph{jump instance} as a finite extension problem whose constraints exclude the canonical completions given by the Kan extensions and leave one correct completion up to renaming. In this setting, a model with a canonical default performs the second step by producing the correct completion under the constraints. We evaluate fourteen models across three certified families. The canonical completion returns once in $13{,}300$ constrained answers across all runs. Several calibrated models also give the correct completion reliably, including three API models that solve $159$ of $162$ primary chain trials, suggesting that they can jump at this step. We further formalize the third and fourth steps, whose empirical evaluation remains future work. We hope our work paves the path for formalizing and measuring the full jump in the future. The code of the paper is available at https://github.com/EEthanShi/kan-jump-test.

cs.CL↗

arXiv2026

RiPPLE: Cross-Space Performance Prediction from Early Training for Neural Architecture Search

Neural architecture search (NAS) evaluates candidate networks, but fully training enough architectures to rank an entire space is expensive. Zero-cost proxies score architectures at initialization, yet their ranking quality varies across search spaces. Learned predictors reduce evaluation cost but typically require fully trained labels or partial-training features for individual candidates. We introduce $\textbf{RiPPLE}$, $\underline{\textbf{R}}$anking v$\underline{\textbf{i}}$a $\underline{\textbf{P}}$refix-$\underline{\textbf{P}}$ropagated $\underline{\textbf{L}}$abel $\underline{\textbf{E}}$xtrapolation, which treats partial training as a source of labels for a small coverage set of anchors. RiPPLE trains these anchors to an early prefix, extrapolates their learning curves to surrogate labels, and propagates the labels over label-free architecture features. The early-training signal remains a label on the anchors rather than a per-candidate feature. Feature, readout, and encoding rules are selected without held-out accuracy and reused across search spaces. We evaluate the method on twelve benchmark cells from four search-space families and on the larger DARTS space. The results examine ranking quality, label efficiency, architecture selection, and the roles of readout, coverage, and propagation. RiPPLE provides a whole-space ranking from a fractional anchor-training budget, with comparisons interpreted under their respective evaluation and cost protocols.

cs.LG↗

arXiv2026

SIFPBPNet: A Dual-Path Network for Wearable and Cuffless Blood Pressure Estimation via Individualized Steady-state Representation

Continuous and cuffless blood pressure (BP) monitoring using photoplethysmography (PPG) is of great interest for low-cost and personalized cardiovascular health management. However, significant population heterogeneity and the "one-to-many mapping" problem, where similar waveforms across individuals correspond to different BP levels, limit the accuracy of conventional population-based models. To address this challenge, we propose a dual-path architecture termed SIFPBPNet, which separately represents steady-state and instantaneous features, through a Steady-state Feature Path (SFP) and an Instantaneous Feature Path (IFP). The SFP employs a Graph Attention Network (GAT) to extract individual-specific and long-term characteristics from multi-day historical PPG trajectories. In parallel, the IFP captures short-term dynamics from current PPG segments and incorporates the steady-state prior via a cross-attention mechanism. Experiments on a large-scale wearable dataset demonstrate that SIFPBPNet achieves a Mean Absolute Error (MAE) of 8.57 and 5.97 mmHg for systolic and diastolic BP, respectively, outperforming state-of-the-art models. Furthermore, the SFP module consistently improves performance when integrated into various backbone architectures, yielding 2.8-13.1% relative MAE reductions for systolic BP. These results highlight the strong generalizability and plug-and-play transferability of the SFP module, underscoring its great potential for accurate cuffless BP monitoring.

cs.LG↗

arXiv2026

One Spectrum, Two Resources: Data-Memory Scaling in Autoregressive Prediction

How much learned memory is needed to benefit from more data? We show that the two resources are governed by one predictive-energy spectrum in a positive-entropy autoregressive retrieval source. Each coordinate contributes its query probability times the squared radius of its unknown logit. Writing $μ$ for the resulting energy spectrum, we prove the minimax law $\mathfrak R^*_{\rm value}(n,B)\asymp_R Φ_μ(n^{-1})+Φ_μ(τ_B), Φ_μ(t)=\int\min\{x,t\}\,μ(\mathrm dx),$ for $n$ prediction blocks and a learned state with at most $2^B$ values. Data set the resolution $1/n$; memory sets the level $τ_B$ reached by optimal bit allocation. The complete curve also recovers the positive spectrum. Energy-dimension pairing is essential: two causal sources with identical block-energy and block-dimension marginals have different data and memory exponents. A masked query-key attention head learns the route and values, realizing the law with explicit routing, format, and arithmetic errors. Further results give exponent-adaptive allocation, finite-precision realization, and compute-precision laws under two-sided arithmetic assumptions. Experiments recover the data-memory collapse and coupling exponents, explain the routing and allocation mechanisms, and examine weight-only quantization across six pretrained-model scales.

cs.LG↗

arXiv2026

Characterizing Language Generation in the Limit: Finite Witnesses and a Separation-Width Hierarchy

Language generation in the limit asks for valid unseen elements from every exhaustive positive presentation of an unknown infinite language. We characterize this task for arbitrary families over a countable universe. Generation is possible exactly when each target can be assigned a finite positive witness so that the targets activated by any finite sample have an infinite common intersection. The necessary direction follows from a universal normalization: a search through unconfirmed histories converts any successful generator into one depending only on the observed set. We then ask how large compatible witnesses must be. Positive separation width records the smallest uniform size bound, with two further levels for unbounded finite witnesses and the absence of any compatible finite-witness assignment. Every level occurs. Countable families admit singleton witnesses, explicit families realize every finite width, and a union of two families with infinite common cores requires unbounded finite witnesses. Finally, countable-support and finite-profile obstructions explain why local combinatorial data cannot determine generation in the limit. The characterization and full width hierarchy are checked in Lean, including the simplified normalization and a direct diagonal capture lemma. The accompanying Lean development is maintained at https://github.com/xiaoyulics/language-generation-characterization

cs.FL↗

arXiv2026

CoRA-NAS: Coarse Ranking and Anchor-Residual Refinement for Neural Architecture Search

Zero-cost proxies rank architectures cheaply, but their reliability varies across search spaces. We introduce CoRA-NAS (COarse Ranking + Anchor-residual), a two-stage framework combining a static ranking prior with low-cost learning-curve refinement. CoRA-Rank aggregates capacity and structure-at-initialization proxies through an equal-weight log-rank consensus and a target-free consensus gate. CoRA-Refine samples anchors across this prior, extrapolates their early validation curves, and propagates a learned residual correction with an ExtraTrees model. The refinement uses approximately 1% of the cost of fully training the candidate set. Fully trained architecture-accuracy labels are not used to fit the ranker. One configuration is used across spaces, with space-specific architecture encodings. Across NAS-Bench-201, NAS-Bench-101, TransNAS-Bench-101, and NATS-SSS, CoRA-Refine achieves mean Spearman correlations of 0.946, 0.715, 0.786, and 0.894, respectively. Its worst-space correlation of 0.715 is the highest among the compared methods. On NAS-Bench-201/CIFAR-100, its selected architecture reaches 73.32% accuracy, near the reported ground-truth best of 73.37%. On the pure size space, refinement recovers the static prior's shortfall relative to parameter count, while remaining tied with the strongest capacity proxies within noise. The resulting framework combines cross-space ranking robustness with low-cost architecture selection.

cs.LG↗

arXiv2026

TrajMark: Ownership Attribution and Segment-Level Tamper Localization for Coding-Agent Trajectories

Watermarking the final patch produced by a coding agent provides provenance evidence for the submitted artifact, but does not authenticate the visible process that produced it. Behavioral watermarking methods primarily provide a global detection or identifier-recovery signal, so a locally edited trajectory may retain sufficient ownership evidence without revealing which protected region has become inconsistent. To address this limitation, we propose TrajMark, a training-free, symmetric-key, visible-only trajectory watermarking framework that separates robust ownership attribution from fragile local integrity verification. Our framework consists of two complementary layers: a sparse owner layer that encodes a six-bit deployment identifier by rewriting a keyed subset of naturally occurring READ actions into masked linear equations, and a localization layer that inserts linked Q12 ordinary, group, and terminal seals to commit to protected critical-action segments. This separation allows ownership evidence to accumulate robustly across trajectories, while local modifications perturb nearby keyed commitments and expose the affected protocol region. We further provide a design-level analysis of owner recoverability, integrity collision probability, structural overhead, and localization behavior. Across three coding-agent frameworks and three LLMs, TrajMark recovers the exact owner in all evaluated clean full-watermark batches. Under exhaustive eligible single-site attacks it detects 95.5%-100% of edits, and under random single-action corruption it localizes 95.8% of modified sites to an accepted protocol region rather than to the individual action. Owner marking adds no trajectory actions; the integrity layer adds explicit read-only seals, and matched Pass@1 is 26.9% versus 26.3% for unwatermarked runs.

cs.CR↗

arXiv2026

DRIFT: Removing Diffusion Watermarks by Deflecting the Generative Trajectory

Diffusion watermarking embeds verifiable signals into the generative process and commonly verifies them by recovering trajectory-dependent evidence, making the marks robust to conventional pixel-space distortions. Existing removal attacks either regenerate along deterministic trajectories, which often preserve the watermark-bearing latent structure, or optimize every image separately. We identify the reliance on a recoverable generative trajectory as a common attack surface among the schemes we study. Based on this observation, we propose DRIFT, a black-box attack that combines partial forward diffusion with stochastic reverse resampling. Forward re-noising limits source information available to a fixed-depth recovery pipeline, while stochastic reversal supplies alternative noise-driven paths whose removal benefit we isolate through matched sampler comparisons. Adaptive DRIFT searches a selected ladder for each image's first verifier-rejected rung and refines fidelity while retaining only updates rejected by the same verifier. At fixed depth, we derive information-theoretic and Wasserstein source-dependence bounds; under realized-ladder monotonicity, the first rejected rung is least distorted among rejected rungs on that ladder, and verifier-gated refinement preserves rejection. Across nine watermarks spanning three paradigms, DRIFT achieves 98-100% attack success and the best image quality among the compared attacks, without secret keys, verifier internals, or per-image gradient optimization.

cs.CR↗

arXiv2026

Nearly Tight Rademacher Bounds for Sparsely Activated Neural Networks

An input may activate few hidden units even when different inputs collectively use an entire network. We study the statistical complexity of this input-dependent sparsity in the one-hidden-layer ReLU model of Awasthi et al. (COLT 2024). For width $s$, at most $k$ active units per input, and effective weight and bias bounds $W,B$, every size-$m$ sample in the class's fixed radius-$R$ input domain satisfies $\mathcal{R}(S)\le CWR\min\{k,\sqrt{sk/m}\log^{3/2}(2m)\}+kB/\sqrt m$. A support-preserving cover and a single normalized chaining argument remove the previous explicit dimension factor, up to logarithms. Lower bounds on appropriate i.i.d. marginals match up to those logarithms, showing how changing active units across inputs retains a width dependence. The input domain matters: zero-bias networks sparse on the entire ball have at most $2k$ nonzero units and complexity $O(kWR/\sqrt m)$, whereas bias bounds comparable to $WR$ restore the worst-case rate on that same domain in only logarithmic dimension. A spherical-cap construction proves the latter claim without assuming sparsity merely on the sampling support. For a specified normalized bounded loss and biases comparable to $WR$, we also obtain agnostic minimax excess-risk bounds of order $\min\{1,\sqrt{s/(km)}\}$ up to logarithms.

cs.LG↗

arXiv2026

Feature Superposition in Neural Networks: From Theory to Practice

Superposition refers to neural networks representing more features than they have dimensions. It offers a possible explanation for polysemantic neurons and motivates methods for recovering interpretable features from neural activations. Theoretical models typically start with a given set of input features and assumptions about how their values vary across inputs, then study how a network encodes those values in a lower-dimensional hidden representation. Empirical work, by contrast, seeks to identify the features encoded in trained networks and determine their role in computation. In this survey, we review the geometry, learning, and computation of superposed representations, explaining how feature statistics and decoder choice affect the conclusions. To connect these theoretical accounts with evidence from trained networks, we compare practical methods for recovering and analyzing features and examine what their evaluations establish. Since accurate activation reconstruction alone does not establish feature identity or causal use, we discuss the methods' documented failures and applications in light of the evidence available for these different claims. Finally, we assess previously stated open problems and identify remaining theoretical and empirical questions about superposition in trained networks. We hope our work can pave the way for a deeper understanding of superposition and more reliable methods for interpreting neural networks.

cs.LG↗

arXiv2026

Decoupled Analysis-Judging: An Automated Creativity Evaluator Using LLMs in Complex Multi-step Creativity Tasks

Automated evaluation of creativity tasks remains challenging for LLM-as-a-Judge, as LLM is susceptible to biases such as verbosity bias and leniency bias. Such limitations are particularly evident in Contextually-Grounded and Procedurally-Structured Tasks (CGPST), a complex multi-step creativity task where inter-step dependencies, highly subjectivity, and wide scoring ranges lead to more unstable and biased judgments. Existing approaches either rely on task-specific training or directly apply LLM-as-a-Judge, both of which struggle to ensure reliable evaluation under such complexity. To bridge these gaps, we propose CreaEval, an automated creativity evaluator for CGPST that decouples typical LLM-as-a-Judge into analysis and judging. Correspondingly, CreaEval involves two critical phases: Memory-augmented Analysis, a SoT-LLM converts multi-step responses into structured evaluation evidence, incorporating cross-step memory; and Evidence-based Judging, a Judge-LLM uses the extracted evidence for judging without accessing raw responses. Comprehensive experiments show that CreaEval achieves an average performance improvement of 22.74% over the second-best baselines across CGPST and two classic simple creativity tasks, demonstrating its generalizability. The code is available at https://github.com/Jaong/CreaEval.

cs.CL↗

arXiv2026

IRIS: Visual-Semantic Binding for Forgery-Resistant Watermarking of Diffusion Images

Most in-generation diffusion watermarks embed patterns independent of the image that carries them, and attackers transplant the marks onto images the generator did not produce, resulting in forgery. Binding the mark to visual semantics prevents such transplantation, yet existing bindings anchor to a proxy image rather than the image they mark. Realizing visual-semantic binding inside generation faces two challenges. The mark derives from the image itself yet enters the sampling trajectory before that image exists, and may itself shift the semantics it binds. The binding also meets opposite sensitivity demands, breaking under semantic change while holding through common processing. We present IRIS, a training-free watermarking scheme that embeds an Intrinsic Ring Identifier from Semantics. IRIS reads a content code from the non-watermarked generated image, derives a one-time ring from the code and a secret key, returns to the final low-noise steps of the same trajectory and blends the ring in, after the semantics it binds are settled. To meet the opposite sensitivity demands, the code is read through a canonicalization shared between embedding and detection, holding through common distortions and mild regeneration while flipping under semantic change. Detection recomputes the ring from the query image and the key alone, and the mark therefore fails on a foreign or spliced image, with acceptance tracking semantic displacement. On three prompt datasets IRIS detects reliably and stays close to its same-seed non-watermarked counterpart, a fidelity prior in-generation marks do not reach. While forgeries transfer fixed-pattern marks and regeneration strips post-hoc marks, IRIS alone among the compared marks withstands both.

cs.CV↗

arXiv2026

Beyond Sparse Weights: When Is Attention Compressible?

KV-cache compression is often justified by attention maps with a few large weights. This is incomplete: large weights may not contain most of the mass, omitted values can cancel, and preserving the attention output may not preserve the task. We separate these questions. Global score gaps -- not threshold counts -- determine how many tokens are needed to retain a target mass. For a realized row, the weighted sum of omitted values is the exact missing statistic. A controlled retrieval--aggregation model explains when truncation helps and when it hurts. These results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion. Under matched budgets, CertKV is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype. Compressibility depends on the mass, values, future queries, and task -- not on a sparse-looking map alone.

cs.LG↗

arXiv2026

Sum-of-Squares Degree Barriers for the Reweighted-Hinge Method in Robust Halfspace Learning: A Christoffel-Function Characterization

A certificate that removes outliers sees the data only through its low-degree moments, and an adversary exploits exactly this, hiding corruption where the clean data already looks typical, in the blind spot no bounded-degree test resolves. That blind spot has an exact size: the Christoffel function of the clean marginal, the quantity data analysis thresholds to detect outliers, here read from the adversary's side as the corruption a certificate cannot remove. We turn this inversion into the organizing principle of the reweighted-hinge approach to robustly learning $γ$-margin halfspaces under malicious noise (Shen 2025; Zeng-Shen 2025): the governing resource is the Sum-of-Squares degree of the certificate, and the resolution principle states that the maximal corruption mass hideable at a center $c$ from a degree-$2t$ certificate is exactly the Christoffel function $λ_{t+1}(c)$. Three consequences follow, all against the certificate method (not information-theoretic). A margin-degree tradeoff: certifying the dense pancake to error $\varepsilon$ costs SoS degree $Ω(\log(1/\varepsilon))$ or margin $Ω(\sqrt{\log(1/\varepsilon)}/\sqrt{d})$, so the $\log(1/\varepsilon)$ margin of Shen (2025) is forced; a weighted-Chebyshev reduction makes the threshold $2t=Θ((|c|/s)^2)$ tight modulo one classical extremal estimate. A degree-2 outlier barrier: an explicit instance on which degree 2 is stuck at $η^{1/2}$ while degree 4 escapes, locating the small breakdown rate in the degree, not the analysis. A degree-$2t$ algorithm tracing the frontier $η^{1-1/2t}$ (recovering Shen 2025 at $t=1$), with an explicit constant gain capped by the pancake density. And an information-theoretic floor of $η/(2(1-η))$, matched exactly from above; under a hard margin its two-point realizations provably require $Θ(1/η)$ mixture components."

cs.LG↗

arXiv2026

Optimistic Rates for Multiclass PAC Learning

Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself. For a class of Natarajan dimension $d_N$ and Daniely-Shalev-Shwartz dimension $d_{DS}$, the optimal excess risk is known at the two endpoints ($d_{DS}/n$ realizable, $\sqrt{d_N/n}+d_{DS}/n$ agnostic [HMZ24, CEH+26, Pab26]) and open in between. We close the gap: at every fixed oracle risk $L^\star$, the optimal excess risk is $\widetildeΘ(\sqrt{L^\star d_N/n}+d_{DS}/n)$, uniformly in the alphabet size, attained by a learner that knows neither $L^\star$ nor the confidence level. The upper bound composes the cover-menu-compression architecture of [CEH+26], at the realizable rate of [Pab26], with a new comparator-facing relative compression theorem: a size-$k$ compression rule that empirically dominates a comparator $h$ has population risk at most $L(h)+O(\sqrt{L(h)Γ}+Γ)$ with $Γ=(k\log n+\log(1/δ))/n$, without stability; this transfers the comparison principle of the sharp binary theory [MQZ26] while discarding its Boolean-cube geometry, which does not lift to multiclass labels. The lower bound forces both terms using one class and one distribution at every fixed $L^\star$, by a pair-Assouad scheme calibrated to $L^\star$ and a fiber argument on the pseudo-cubes underlying the Natarajan-versus-DS separation of [BCD+22]. Both theorems extend to list learning: against the best $r$-tuple of hypotheses, the same architecture and the same two engines yield an optimistic rate and a lower bound of the same shape, forcing the fluctuation term that [Pab26] expected to be necessary against list comparators, and removing the factor $r$ from the known realizable list lower bound.

cs.LG↗

arXiv2026

LAVA: Layered Audio-Visual Anti-tampering Watermarking for Robust Deepfake Detection and Localization

Proactive watermarking offers a promising approach for deepfake tamper detection and localization in short-form videos. However, existing methods often decouple audio and visual evidence and assume that watermark signals remain reliable under real-world degradations, making tamper localization vulnerable to multimodal misalignment and compression distortions. Moreover, existing semi-fragile visual watermarking methods often degrade significantly under codec compression because their embedding bands overlap with compression-sensitive frequency regions. To address these limitations, we propose Layered Audio-Visual Anti-tampering Watermarking (LAVA), a calibration-aware audio-visual watermark fusion framework for deepfake tamper detection and localization. LAVA leverages cross-modal watermark fusion and calibration-aware alignment to preserve consistent and reliable tamper evidence under compression and audio-visual asynchrony, enabling robust tamper localization. Extensive experiments demonstrate that LAVA achieves near-perfect detection performance (AP = 0.999), remains robust to compression and multimodal misalignment, and significantly improves tamper localization reliability over existing audio-visual fusion baselines.

cs.CV↗

arXiv2026

HI-HCQC: A Tightly-Coupled Hardware Interface with High-Efficiency Communication for Hybrid Classical-Quantum Computing

Hybrid classical-quantum computing requires frequent data exchange between classical processors and quantum control hardware. However, existing superconducting quantum control systems are commonly connected through loosely coupled interfaces such as Ethernet, resulting in high communication latency and limited task throughput. To address this issue, we present HI-HCQC, an RFSoC-based hardware interface for tightly coupled hybrid classical-quantum computing. HI-HCQC integrates high-speed RF-DACs, RF-ADCs, programmable logic, embedded processors, clock synchronization circuits, and a PCIe Gen3 x8 interface, enabling direct microwave pulse synthesis, qubit readout, and high-throughput data transfer between host servers and quantum measurement-control units. Experimental results show that HI-HCQC supports six control channels and one multiplexed readout channel, achieves stable microwave generation and acquisition, and successfully performs qubit spectroscopy, Rabi oscillation, T1 measurement, single-shot readout, randomized benchmarking, and CZ-gate characterization. Compared with a conventional control system, HI-HCQC reduces end-to-end execution latency for representative quantum gate and circuit tasks and significantly improves task throughput. These results demonstrate that PCIe-coupled RFSoC control hardware provides a practical foundation for scalable and efficient hybrid classical-quantum computing systems.

cs.DC↗