arXiv subjects

Chen Yuan

Publications and source records attributed to Chen Yuan.

At least 19 recordsLinked to original sources

arXiv2026

Proximity Gaps for Gabidulin Codes and Applications

Proximity gaps are central to the soundness of interactive oracle proofs of proximity (IOPPs) and polynomial commitment schemes (PCSs). An $[n,k,d]$ linear code $C\subseteq\mathbb F^n$ has a $\delta$-proximity gap with error $\epsilon$ if, for every $u_0,u_1\in\mathbb F^n$, either all points on $\ell_{u_0,u_1}=\{u_0+\alpha u_1:\alpha\in\mathbb F\}$ are $\delta$-close to $C$, or at most an $\epsilon$ fraction are. Although proximity gaps for Hamming-metric codes are well understood, their rank-metric counterparts remain largely unexplored despite their applications in coding theory and cryptography. In this work, we study proximity gaps for linear rank-metric codes and their cryptographic applications. First, we show that every $[n,k,d]$ linear rank-metric code $C$ over $\mathbb F_{q^m}$ admits a proximity gap for every $\delta\le(d-1)/(3n)$, with error at most $q^{e+1}/q^m$, where $e=\lfloor\delta n\rfloor$. For Gabidulin codes, we improve the gap to $(d-1)/(2n)$ with error $10q^{n-1}/q^m$. These two proximity gaps match those for general linear Hamming-metric codes and Reed--Solomon (RS) codes, respectively. We prove the $(d-1)/(2n)$ bound is tight by constructing an infinite family of constant-rate Gabidulin codes and affine lines $\ell_{u_0,u_1}$ on which a $1-o(1)$ fraction of points are $d/(2n)$-close to the code, while $u_1$ is at least $3d/(4n)$-far from it. At the $d/(3n)$ gap, we also give a counterexample establishing a lower bound on $\epsilon$. As applications, we construct an IOPP for interleaved Gabidulin codes by adapting the Ligero IOPP for interleaved RS codes. We then adapt the Ligero-based PCS for ordinary polynomials to obtain a $q$-linearized polynomial commitment scheme. To our knowledge, this is the first PCS framework based on rank-metric error-correcting codes.

cs.IT↗

arXiv2026

Asymptotically Optimal List Size of Random Linear Codes

We prove that for every fixed prime power $q$, every $p\in(0,1-1/q)$, and every $\varepsilon>0$ with $1-H_q(p)-\varepsilon>0$, a random linear code over $\mathbb{F}_q$ of rate $1-H_q(p)-\varepsilon$ is $(p,\,\left\lceil\frac{H_q(p)}{\varepsilon}\right\rceil+O_{p,q}(1))\text{-list-decodable}$ with probability at least $1-q^{-\Omega(n)}$. Guruswami, Li, Mosheiff, Resch, Silas, and Wootters showed that, for sufficiently small $\varepsilon$, random linear codes require list size at least $\left\lfloor\frac{H_q(p)}{\varepsilon}+0.99\right\rfloor,$ and conjectured that $\frac{H_q(p)}{\varepsilon}(1+o(1))$ suffices as $\varepsilon\to 0$. This conjecture was previously known for $q=2$, where the upper bound $H_2(p)/\varepsilon+2$ was established. For $q>2$, however, the best known upper bound was $C_{p,q}/\varepsilon$ for a constant $C_{p,q}$ depending on $p$ and $q$. Our result resolves the conjecture for every prime power $q$ and, in fact, establishes the sharper upper bound $\frac{H_q(p)}{\varepsilon}+O_{p,q}(1)$.

cs.IT↗

arXiv2026

Projected Constraints on Primordial Black Holes from Scalar-Induced Gravitational Waves with Taiji

Scalar-induced gravitational waves (SIGWs) provide a direct probe of the enhanced primordial curvature perturbations that may also produce primordial black holes (PBHs). We forecast the capability of the space-based gravitational-wave observatory Taiji to search for an SIGW background generated by a broken-power-law curvature spectrum. A signal-injection study is used to validate the analysis pipeline, after which a pure-noise realization is employed to derive projected upper limits on the curvature-spectrum parameters. We translate these limits into constraints on the PBH abundance using the nonlinear compaction function, critical collapse, and the joint Gaussian distribution of the compaction amplitude and curvature at its peak. The resulting projected $95\%$ upper limits on the PBH dark-matter fraction satisfy $f_{\mathrm{PBH}}^{95\%}<1$ over PBH masses from approximately $6.2\times10^{-18}\,M_\odot$ to $1.7\times10^{-8}\,M_\odot$. We compare the forecast with representative Hawking-evaporation and microlensing bounds. In part of the asteroid-mass interval, the projected Taiji limit is more restrictive than the current Subaru Hyper Suprime-Cam (HSC) microlensing constraint.

astro-ph.CO↗

arXiv2026

Relativistic effects in extreme-mass-ratio inspirals within scalar clouds: Eccentric and inclined orbits

We study extreme-mass-ratio inspirals (EMRIs) evolving in a scalar cloud environment that may form through superradiant instabilities, using a fully relativistic perturbative framework that allows for eccentric and inclined orbits. EMRIs, consisting of a stellar-mass compact object inspiraling into a supermassive black hole, are key sources for space-based gravitational-wave detectors such as LISA. Previous relativistic studies of EMRIs in scalar clouds have been restricted to circular, equatorial motion. Here, instead, we focus on a Schwarzschild black hole background to incorporate eccentricity and orbital inclination. By computing the scalar energy and angular momentum scattered off to spatial infinity and absorbed at the event horizon, we show that orbital eccentricity can induce a dense spectrum of resonances near the last stable orbit, associated with strong relativistic apsidal precession. We further find that orbital inclination can significantly modify the orbital energy and angular momentum losses. In particular, we identify a critical inclination angle below which, at sufficiently small orbital radii, there is a net transfer of energy from the scalar cloud to the orbit. Moreover, for sufficiently large eccentricities, resonances associated with relativistic apsidal precession persist across the full range of inclinations, although their structure changes significantly between prograde and retrograde orbits. These results provide a foundation for future studies of EMRIs in scalar cloud environments on fully generic orbits around spinning black holes.

gr-qc↗

arXiv2026

A Syndrome--Space Approach to Proximity Gaps and Correlated Agreement for Random Linear Codes and Random Reed--Solomon Codes

Proximity gaps and correlated agreement have become central tools in the analysis of interactive oracle proofs of proximity (IOPPs) and code-based SNARKs. Informally, a proximity-gap statement says that for a structured set of words -- such as an affine space, or a curve -- either all points are close to the code, or most are far from it. Such statements are essential in sampling-based proof systems, where a verifier queries only a few random locations on a structured object but must still obtain a global soundness guarantee. In Reed--Solomon-based proof systems, one would ideally like the proximity parameter to approach the information-theoretic limit $1-R$, since this is the largest possible radius for a rate-$R$ code and directly affects protocol efficiency. We establish a direct approach to proximity gaps and correlated agreement for random linear codes in the random parity-check-matrix model, without relying on list decoding of the proof. Our approach is based on a syndrome-space reformulation together with a witness-based reduction argument. It is conceptually different from the existing decoding-driven route for random linear codes, and it also leads to sharper parameters, including the optimal-up-to-$\varepsilon$ large-alphabet radius bound $\rho<1-R-\varepsilon$ for $q=\Theta(n)$, as well as near-capacity bounds over constant alphabets with improved alphabet-size requirements. We apply the same syndrome-space reductions to random Reed--Solomon codes. This yields correlated agreement for random Reed--Solomon codes over affine spaces and polynomial curves up to radius $\rho\le 1-R-\varepsilon$, with field size $q\ge n\cdot 2^{O(\varepsilon^{-3})}$ for affine spaces and $q\ge n\cdot 2^{O_\ell(\varepsilon^{-3})}$ for degree-$\ell$ curves.

cs.IT↗

arXiv2026

Resonances as signatures of scalar clouds in eccentric extreme-mass-ratio inspirals

Ultralight scalars arise naturally in many extensions to the Standard Model and are compelling dark matter candidates. Around spinning black holes, dense scalar clouds could form through the conversion of rotational energy into particles via black hole superradiance. Extreme-mass-ratio inspirals (EMRIs) targeted by future space-based detectors will give us unparalleled access to the environments of massive black holes, allowing us to probe the presence of scalar clouds. We consider EMRIs around a Schwarzschild black hole and show that eccentricity induces a dense sequence of resonances in the scalar fluxes near the last stable orbit. These resonances arise only in a fully relativistic treatment, as they are intrinsically tied to the splitting between the azimuthal and radial orbital frequencies in the strong-field regime. By evolving the orbits adiabatically, we show that the resulting resonant transitions substantially enhance the exchange of energy and angular momentum between the EMRI and the scalar cloud, significantly amplifying the accumulated dephasing in the gravitational waveform relative to circular motion. Our results highlight the importance of eccentricity in shaping the observational signatures of EMRIs embedded in scalar clouds.

gr-qc↗

arXiv2026

Explicit List-Decodable Linearized Reed-Solomon and Folded Linearized Reed-Solomon Subcodes

The sum-rank metric is the mixture of the Hamming and rank metrics. The sum-rank metric found its application in network coding, locally repairable codes, space-time coding, and quantum-resistant cryptography. Linearized Reed-Solomon (LRS) codes are the sum-rank analogue of Reed-Solomon codes and strictly generalize both Reed-Solomon and Gabidulin codes. In this work, we construct an explicit family of $\mathbb{F}_h$-linear sum-rank metric codes over arbitrary fields $\mathbb{F}_h$. Our construction enables efficient list decoding up to a fraction $\rho$ of errors in the sum-rank metric with rate $1-\rho-\varepsilon$, for any desired $\rho \in (0,1)$ and $\varepsilon>0$. Our codes are subcodes of LRS codes, obtained by restricting message polynomials to an $\mathbb{F}_h$-subspace derived from subspace designs, and the decoding list size is bounded by $h^{\mathrm{poly}(1/\varepsilon)}$. Beyond the standard LRS setting, we further extend our linear-algebraic decoding framework to folded Linearized Reed-Solomon (FLRS) codes. We show that folded evaluations satisfy appropriate interpolation conditions and that the corresponding solution space forms a low-dimensional, structured affine subspace. This structure enables effective control of the list size and yields the first explicit positive-rate FLRS subcodes that are efficiently list decodable beyond the unique-decoding radius. To the best of our knowledge, this also constitutes the first explicit construction of positive-rate sum-rank metric codes that admit efficient list decoding beyond the unique decoding radius, thereby providing a new general framework for constructing efficiently decodable codes under the sum-rank metric.

cs.IT↗

arXiv2026

Improvement of the Gilbert-Varshamov Bound for Linear Codes and Quantum Codes

The Gilbert--Varshamov (GV) bound is a central benchmark in coding theory, establishing existential guarantees for error-correcting codes and serving as a baseline for both Hamming and quantum fault-tolerant information processing. Despite decades of effort, improving the GV bound is notoriously difficult, and known improvements often rely on technically heavy arguments and do not extend naturally to the quantum setting due to additional self-orthogonality constraints. In this work we develop a concise probabilistic method that yields an improvement over the classical GV bound for $q$-ary linear codes. For relative distance $\delta=d/n<1-1/q$, we show that an $[n,k,d]_q$ linear code exists whenever $\frac{q^{k}-1}{q-1}\;<\;\frac{c_\delta \sqrt{n}\, q^{n}}{\mathrm{Vol}_q(n,d-1)}$, for positive constant $c_\delta$ depending only on $\delta$, where $\mathrm{Vol}_q(n,d-1)$ denotes the volume of a $q$-ary Hamming ball. We further adapt this approach to the quantum setting by analyzing symplectic self-orthogonal structures. For $\delta<1-1/q^2$, we obtain an improved quantum GV bound: there exists a $q$-ary quantum code $[[n,\,n-k,\,d]]$ provided that $\frac{q^{2n-k}-1}{q-1}<\frac{c_\delta \sqrt{n}\cdot q^{2n}}{\sum_{i=0}^{d-1}\binom{n}{i}(q^2-1)^i}$. In particular, our result improves the standard quantum GV bound by an $\Omega(\sqrt{n})$ multiplicative factor.

cs.IT↗

arXiv2026

One-Loop Tensor Power Spectrum from a Non-Canonical Spectator Field during Inflation

We compute the full one-loop corrections to the primordial tensor power spectrum in an inflationary scenario with a {non-canonical spectator field}, using the in-in formalism. We derive semi-analytic results for the scalar-sourced one-loop tensor spectrum and the effective tensor-to-scalar ratio, $r_{\mathrm{eff}}$. We consider two representative coupling functions: a localized Gaussian dip (Model G), which leads to moderate loop corrections, and a rapidly oscillatory coupling (Model O), which can yield much larger loop contributions. For Model G, we find a $\mathcal{O}(1)$ correction to $r_{\mathrm{eff}}$ while Model O can significantly enhance $r_{\mathrm{eff}}$ by several orders of magnitude (relative to the tree-level value). We further calculate the energy density of primordial gravitational waves. Assuming that primordial black holes with mass $10^{-12}M_{\odot}$ generated in this scenario, constitute all of the dark matter, we find that the results are several orders of magnitude lower than the sensitivities of Taiji/TianQin/LISA.

astro-ph.CO↗

arXiv2026

Efficient Sequential Recommendation for Long Term User Interest Via Personalization

Recent years have witnessed success of sequential modeling, generative recommender, and large language model for recommendation. Though the scaling law has been validated for sequential models, it showed inefficiency in computational capacity when considering real-world applications like recommendation, due to the non-linear(quadratic) increasing nature of the transformer model. To improve the efficiency of the sequential model, we introduced a novel approach to sequential recommendation that leverages personalization techniques to enhance efficiency and performance. Our method compresses long user interaction histories into learnable tokens, which are then combined with recent interactions to generate recommendations. This approach significantly reduces computational costs while maintaining high recommendation accuracy. Our method could be applied to existing transformer based recommendation models, e.g., HSTU and HLLM. Extensive experiments on multiple sequential models demonstrate its versatility and effectiveness. Source code is available at \href{https://github.com/facebookresearch/PerSRec}{https://github.com/facebookresearch/PerSRec}.

cs.IR↗

arXiv2025

Gravitational wave cosmology

Gravitational waves (GWs) originating from cosmological sources offer direct insights into the physics of the primordial Universe, the fundamental nature of gravity, and the cosmic expansion of the Universe. In this review paper, we present a comprehensive overview of our recent advances in GW cosmology, supported by the national key research and development program of China, focusing on cosmological GW sources and their implications for fundamental physics and cosmology. We first discuss the generation mechanisms and characteristics of stochastic gravitational wave backgrounds generated by physical processes occurred in the early Universe, including those from inflation, phase transitions, and topological defects, and summarize current and possible future constraints from pulsar timing array and space-based detectors. Next, we explore the formation and observational prospects of primordial black holes as GW sources and their potential connection to dark matter. We then analyze how GWs are affected by large-scale structure, cosmological perturbations, and possible modifications of gravity on GW propagation, and how these effects can be used to test fundamental symmetry of gravity. Finally, we discuss the application of GW standard sirens in measuring the Hubble constant, the expansion history, and dark energy parameters, including their combination with electromagnetic observations. These topics together show how GW observations, especially with upcoming space-based detectors, such as LISA, Taiji, and Tianqin, can provide new information about the physics of the early Universe, cosmological evolution, and the nature of gravity.

gr-qc↗

arXiv2025

List Decoding of Reed-Solomon Codes and Folded Reed-Solomon Codes Over Galois Ring

List decoding of codes can be seen as the generalization of unique decoding of codes while list decoding over finite fields has been extensively studied, extending these results to more general algebraic structures such as Galois rings remains an important challenge. Due to recent progress in zero knowledge systems, there is a growing demand to investigate the proximity gap of codes over Galois rings in Yizhou Yao(2025). The proximity gap is closely related to the decoding capability of codes. It was shown in Eli Ben-Sasson(2020) that the proximity gap for RS codes over finite field can be improved to $1-\sqrt{r}$ if one consider list decoding instead of unique decoding. However, we know very little about RS codes over Galois ring which might hinder the development of zero knowledge proof system for ring-based arithmetic circuit. In this work, we first extend the list decoding procedure of Guruswami and Sudan to Reed-Solomon codes over Galois rings, which shows that RS codes with rate $r$ can be list decoded up to radius $1-\sqrt{r}$. Then, we investigate the list decoding of folded Reed-Solomon codes over Galois rings. We show that the list decoding radius of folded Reed-Solomon codes can reach the Singlton bound as its counterpart over finite field. We also extend the deterministic pruning method of Vikrant Ashvinkumar(2026) to Galois rings, showing how to prune the affine free module obtained from the linear-algebraic decoder and recover the candidate codewords. Finally, we improve the list size of our folded Reed-Solomon code to $O(1/\varepsilon^2)$ by extending recent work in Shashank Srivastava(2025) to Galois Rings. By developing the recent work of Yeyuan Chen(2025), we show that folded Reed-Solomon codes over Galois rings satisfy the relaxed generalized Singleton bound in the average-radius sense with optimal list size $O(1/\varepsilon)$.

cs.IT↗

arXiv2025

Constraining the Swift Memory Burden Effect with GW250114-like Events

Black hole spectroscopy allows to infer the properties of the remnant of a binary black hole coalescence. Motivated by the recent proposal that a black hole's information load can alter its classical response to small perturbations, an effect known as the swift memory burden, we develop a minimal phenomenological framework to analyze the ringdown of a binary black hole merger and confront it with the data from the GW250114 event. We perform a Bayesian analysis combining the frequencies of the (220) and (440) quasi-normal modes and obtain a lower bound $\log_{10}p \gtrsim 2$, where $p$ controls how the gaps reopen when the black hole's master mode occupation departs from the critical value. Moreover, using a Fisher information matrix (high signal-to-noise ratio) approximation, we forecast the lower bound $\log_{10}p \gtrsim 3$ for a GW250114-like event observed with Cosmic Explorer or Einstein Telescope. Our results disfavour rapid gap reopening, shedding light on how the swift memory burden effect can be probed with current and next-generation detectors.

gr-qc↗

arXiv2025

GW231123 Mass Gap Event and the Primordial Black Hole Scenario

We investigate the possibility that the recently reported GW231123 event, with component masses $M_1=137^{+22}_{-17}\,M_\odot$, $M_2=103^{+20}_{-52}\,M_\odot$ and a local merger rate $R_{\mathrm{local}}=0.08^{+0.19}_{-0.07}\,\mathrm{Gpc^{-3}\,yr^{-1}}$, originates from primordial black holes (PBHs) formed during an early matter-dominated era. We compute the PBH mass function, abundance, spin distribution and the merger rate density and find a set of choices for the parameters to reproduce the key properties of GW231123. While PBHs formed in such a scenario can acquire large spins through sustained tidal torques, the spin distribution remains uncertain and additional accretion might lead to extreme spin values inferred in GW231123. We also show that the resulting PBH abundance, $f_{\mathrm{pbh}}=1.64^{+5.00}_{-1.59}\times10^{-1}$, lies close to the exclusion bounds from CMB accretion limits and other probes, highlighting a potential tension with current constraints. Finally, we estimate the scalar-induced gravitational waves (SIGWs) that are inevitably generated during PBH formation. PBHs that interpret GW231123 are accompanied by negligible SIGWs in the nano-hertz band, indicating no conflict with current pulsar timing arrays data.

astro-ph.CO↗

arXiv2025

Whispers from the Early Universe: The Ringdown of Primordial Black Holes

We investigate the stochastic gravitational wave background (SGWB) generated by the ringdown phase of primordial black holes (PBHs) formed in the early universe. As the ringdown signal is independent of the PBH formation mechanism, the resulting SGWB offers a model-independent probe of PBHs. We numerically compute the ringdown waveform and derive the corresponding SGWB. We show that such a signal could be detected by future pulsar timing arrays (PTAs) for PBHs heavier than the solar mass. Additionally, we evaluate the SGWB from binary PBH mergers and demonstrate that it lies within the sensitivity bands of next-generation ground-based interferometers such as Cosmic Explorer and Einstein Telescope, suggesting a multi-band observational strategy for probing the PBH dark matter scenario.

astro-ph.CO↗

arXiv2025

On the Gauge Invariance of Secondary Gravitational Waves

Second-order tensor perturbations induced by primordial fluctuations play a crucial role in probing small-scale physics, but gauge dependence of their energy density has remained a fundamental challenge in cosmological perturbation theory. We address this issue by introducing a boundary condition-based filtering method that extracts physical radiation through the Sommerfeld criterion. We demonstrate that after filtering non-physical modes, the energy density of secondary gravitational waves becomes gauge-invariant and exhibits physically consistent behavior in the sub-horizon limit. This approach provides a unified framework for both adiabatic and isocurvature perturbations, enhancing theoretical predictions and observational signatures of early universe physics.

astro-ph.CO↗

arXiv2025

Gauge Dependence of Gravitational Waves Induced by Primordial Isocurvature Fluctuations

Primordial isocurvature perturbations, which can arise from various sources in the early Universe, have the potential to leave observable imprints on the gravitational-wave background and provide insights into the nature of primordial fluctuations. In this study, we investigate the gauge dependence of induced gravitational waves (IGWs) sourced by these isocurvature perturbations during radiation dominated era and the kination period in the early universe. We analyze the energy density spectra of IGWs in three different gauges: synchronous, Newtonian, and uniform curvature gauges. To facilitate this analysis, we derive analytical solutions for the perturbations that contribute to the IGW spectra and a general gauge transformation from Newtonian gauge to an arbitrary gauge. Our results reveal significant differences in the energy spectra across these gauges. We find that the energy density of IGWs during radiation domination increases with conformal time as $η^8$ and $η^4$ for synchronous and uniform curvature gauges, respectively, while it converges in the Newtonian gauge. These findings highlight the importance of gauge choice in calculating IGWs and have implications for the interpretation of future observations of the gravitational-wave background.

gr-qc↗

arXiv2025

Gravitational Waves Induced by Scalar Perturbations with a Broken Power-law Peak

We give an analytical approximation for the energy spectrum of the scalar-induced gravitational waves (SIGWs) generated by a broken power-law power spectrum, and find that both the asymptotic power-law tails and the intermediate peak contribute distinct features to the SIGW spectrum. Moreover, the broken power-law power spectrum has abundant near-peak features and our results can be used as a near-peak approximation that covers a wide range of models. Our analytical approximation is useful in the rapid generation of the SIGW energy spectrum, which is beneficial for gravitational wave data analysis.

gr-qc↗