跳到正文
研踪PaperTrail

论文库

检索计算机领域论文，按研究方向、作者或关键词筛选。

部分采集异常
正在读取账号与研究记录…

全站更新概况

+0新增论文
+0其中 AI 相关
+2已有论文修订
+99新增 AI 导读

arXiv 最近完成扫描：2026-11-15 00:32 · 全站最近入库：2026-11-14 15:09各信源进度 →

统计口径与数据新鲜度

统计 2026-11-14 01:29 — 2026-11-15 01:29（北京时间） · 点击数字查看对应简报；AI 相关包含在新增论文内。

最近完成检查：2026-11-15 00:32最近发现新增版本：2026-11-14 15:09库内论文最新更新时间：2026-11-13 02:59

每分钟刷新已保存的数据。空检查不代表采集异常；新收录可能包含历史论文。AI 导读按新增版本计数。

23,348 已收录论文19,580 AI 相关6,729 有修订112 HF 社区发现

浏览论文库

研究日报 / 周报 →按信源浏览 →

时间范围跟随排序：版本更新、本站收录或首次发表。最新收录可能包含历史论文。部分信源异常，查看状态 →

找到 121 篇论文 · 按版本更新时间排序上轮扫描起点 2026-11-15 00:30（北京时间）
新论文 · v1arXiv:2610.39614

Emergence of the transformer architecture as the score of entropic laws of random measures

Giacomo Greco

原文摘要

We show that the transformer architecture emerges as the score of last-token laws in a natural statistical model of language, where sentences are empirical measures of tokens, a language is a law on $P(S^d)$, and our prior belief is that sentences carry no structure at all. By the maximum-entropy principle, we select the law closest to this prior in relative entropy among those reproducing an observed sentence-level statistic. We discuss the relevance of the statistic in the posterior interaction between tokens and we build a statistic, able to capture that interaction, with Luce's choice axiom truncated at the lowest relational order. This procedure gives the softmax choice rule, with the attention cross-moment as its mean parameter. The query--key matrix is then the Lagrange multiplier of a maximum-entropy problem inside each sentence, and the value matrix the multiplier of the constraint over the language, so that the two are untied. Under the optimal entropic law we then show that a transformer head appears in the score of the last-token law. For ordered sentences, causal masking follows from the masked reference choice rule, and with a next-token cross-moment the score equals one causally masked attention head. We also discuss multi-head attention, weight-tied unembedding, and a heuristic reading of residual blocks as projected Langevin steps.

cs.AI · math.PR · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v4arXiv:2411.19193

The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization

Pekka Malo, Lauri Viitasaari, Antti Suominen, Eeva Vilkkumaa, Olli Tahvonen

原文摘要

In many control problems, actions consume a resource budget, such as a wear allowance, and the probability of exhausting it within a given horizon must stay below a tolerance. A simple, widely used approach is to augment the state with the remaining budget, subtract an interior barrier from the utility and penalize exhaustion, so that policy-gradient methods can be applied unchanged. We clip the combined one-step reward from below at a level m to keep the returns of exploratory policies finite. The clip level is a price of failure risk, since the clipped value decomposes exactly into the utility before failure, the cost of the interior margin and m times a geometric failure risk. Consequently, an approximately optimal policy maximizes utility net of margin cost among policies with no greater risk. Its risk exceeds that of any comparison policy by at most order 1/m and can be certified from its value or from validation data. Our main result proves exponential convergence of the population policy-gradient flow for every parameter regularizer that is convex along generalized geodesics and sufficiently strong relative to the price. This extends the mean-field analysis from relative entropy to weight decay and to finite networks. Relative entropy adds parameter noise and a pull toward a prior, whereas weight decay provides only the pull. Action regularization bounds changes in failure risk by the relative entropy to a reference policy. The bounds are evaluated on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task.

cs.LG · cs.AI · math.OC · math.PR · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39535

Local Convergence of Triadic Closures of Sparse Random Graphs

Himasish Talukdar

原文摘要

Triadic closure is a natural mechanism for modeling the clustering phenomenon observed in many real-world networks. Given a possibly random undirected graph $H$, we consider pairs of non-adjacent vertices that have a common neighbor. Conditional on $H$, each such pair is joined by an edge independently and simultaneously, with a probability depending on the degrees of its endpoints and on the number of their common neighbors. The resulting graph is called a triadic closure of $H$. We study the effect of this operation on local convergence. More precisely, we prove that if a sequence of potentially random finite undirected graphs of $\left( H_n \right)_{n \in \mathbb{N}}$ converges locally in probability to a rooted graph $H^*$, then the corresponding sequence of triadic closures converges locally in probability to the same triadic closure of $H^*$. As a consequence, we obtain a general limit theorem for the clustering coefficients of triadic closures. In particular, we show that the triadic closures can have a strictly positive limiting clustering coefficients even when the limiting clustering coefficients of the parent graph sequence is zero. Finally, we apply our results to several classical sparse random graph models including Erdős-Rényi, configuration, preferential attachment models and compute the limiting clustering coefficients of their triadic closures.

math.PR · cs.DM · math-ph · math.CO

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39378

Limit Theorems and Optimal Policies for Flock Flight through Poisson Forests

Lav R. Varshney

原文摘要

Inspired by birds flying through cluttered environments, Karaman and Frazzoli showed that high-speed flight through an ergodic random forest exhibits an ultimate speed limit: above a critical speed, almost surely no infinite collision-free trajectory exists for a single bird. This paper formulates a corresponding bulk-transport problem for many birds. We construct an explicit directed corridor network in a Poisson disk forest and impose a common temporal headway at its waypoints. The maximum current equals a minimum vertex-cut capacity and is achieved by repeated flight along vertex-disjoint paths. The same schedule maximizes completed traversals at every finite horizon, with constant forward speed and no internal waiting. For a forest belt of fixed depth, exact transverse superadditivity yields an almost-sure deterministic current-density limit. A uniform shape theorem for an asymmetric planar dual identifies the current when depth and width grow together. For diverging depth bounded by a constant times width, this current equals the width-first, depth-second limit and is independent of the positive aspect ratio. When diagonal corridors are available, bulk current is positive at sufficiently low obstacle intensity and zero at sufficiently high intensity. For stochastic demand, an upstream admission queue is stable at every rate below the finite-network capacity.

eess.SY · cs.RO · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.39239

Bregman projections and partition design for accelerating finite Markov chains

Michael C. H. Choi, Youjia Wang

原文摘要

We study Gibbs averaging of finite Markov chains with a prescribed stationary distribution $π$. Given a transition matrix $P$ and the Gibbs kernel $G$ induced by a state-space partition, we prove that $GPG$ is an information projection for every admissible Bregman generator $φ$, with divergences defined using transition probabilities relative to $π$. A Pythagorean identity characterizes this projection and recovers the relative entropy and weighted Frobenius cases. A dual characterization identifies $GPG$ as a kernel closest to stationarity among those with the same projection chain as $P$; for relative entropy, it maximizes the entropy rate. The identities also give monotonicity under partition coarsening. For every reversible ergodic baseline $P$, Gibbs averaging cannot increase the squared weighted Frobenius distance to stationarity at any positive integer time, and the inequality is strict unless $P=GPG$. The corresponding mixing time therefore cannot increase. To choose the partition, we identify the divergence of $G$ from stationarity as the exact worst-case divergence of $GPG$ over all $π$-stationary baselines $P$. This objective depends only on the block masses. We give an exact algorithm for concave block costs, including those arising from relative entropy and power generators $φ(u)=u^p$ with $1<p<2$, and a greedy approximation algorithm with a provable guarantee for $p>2$. For power generators $φ(u)=u^p$ with $p>1$, the objective is proportional to Tsallis entropy of order $2-p$: its minimization favors imbalanced block masses when $1<p<2$ and balanced block masses when $p>2$, while all $k$-block partitions have the same objective value when $p=2$. A numerical experiment compares the resulting projected chains with a local Metropolis sampler on a multi-modal $π$.

math.PR · cs.IT · math.OC · stat.CO

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38753

Metropolized backward sampling for conditional sequential Monte Carlo

Adrien Corenflos

原文摘要

Particle Gibbs samplers with backward sampling are widely used for sampling the smoothing distribution of state-space models, but, with few particles, the new trajectory often coincides with the current one at many time steps. A known but rarely used remedy replaces the random selection of the final particle by a Metropolis--Hastings move which avoids the current particle. We show that, with backward sampling, this remedy only helps at the last time steps, because its effect on the update rates decays geometrically with the distance to the final time. We propose instead Metropolized backward sampling, which makes such a move at every step of the backward pass, forcibly switching trajectories whenever possible. Additionally, we introduce a coupled version which prevents proposing the current trajectory, maximizing the chances of an actual switch versus the current trajectory and performing perfect sampling when the state-space model has no observations, a feature not shared by backward sampling. We prove that, at every time step, both methods dominate backward sampling as they update the state more often and have smaller lag-one autocorrelations than it does. Our methods are drop-in replacements for backward sampling, and can be used to improve any particle Gibbs sampler.

stat.CO · eess.SP · math.PR · stat.ME · stat.ML

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38525

Dimension-free exponential entropy quotients over $\mathbb{F}_2$

Josiah Park

原文摘要

Let $X$ be a random vector in $\mathbb{F}_2^m$, and let $X'$ be an independent copy. We prove that, for every $\varepsilon>0$, there is a subspace $G$ with $\dim G\le 2^{320(1+\varepsilon)/\varepsilon}H(X)$ such that $H(q_GX)\le(1+\varepsilon)(H(q_GX+q_GX')-H(q_GX))$. In particular, the quotient entropy is at most $(1+\varepsilon)(H(X+X')-H(X))$. The coefficient is independent of the ambient dimension, and its exponential order in $1/\varepsilon$ is necessary. The structural result is a logarithmic rigidity estimate for finite weighted families of laws with averaged subspace entropy sparsity. A common variational quotient controls both a family and its convolution family without decreasing the original family's normalized mean entropy defect. Posterior families preserve averaged sparsity, and a fresh-index argument combines a local-to-global estimate with the entropic Marton theorem to increase the defect ratio at a fixed multiplicative sparsity cost. We also obtain two-input almost-additivity and concentration of moderate-doubling sets on subspace cosets at the same exponential scale. The constants are not optimized.

cs.IT · math.CO · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2609.27836

Poincaré's Inequality on Sliding-Window Occupation Count Kernels and the Optimal Normalized Spectral-Gap Constant

Yanjin Xiang, Zhihua Zhang

原文摘要

Let $P$ be an irreducible reversible Markov kernel on an $m$-state space $Ω$, and denote its right spectral gap by $\Gap(P) =1-λ_2(P)$. For a stationary trajectory, let $K_t$ be the occupation-count vector of the length-$n$ window beginning at time $t$. The stationary pair $(K_0,K_1)$ defines a reversible projected count kernel $\widetilde P_n$. For each fixed $m\ge2$, define \[ c_m^\star= \inf_{\substack{|Ω|=m,\ P\ \mathrm{irreducible\ and\ reversible} n\ge2}} \frac{n\Gap(\widetilde P_n)}{\Gap(P)}. \] We prove \[ \frac1{1080m}\le c_m^\star\le q_{m-2}, \qquad q_0=\frac14,\quad q_{r+1}=q_r(1-q_r). \] We also show $q_{m-2}=(m+\log m+O(1))^{-1}$, which implies that $c_m^\star=Θ(m^{-1})$. Thus, the reciprocal optimal comparison coefficient $C_m^{\mathrm{opt}}=(c_m^\star)^{-1}$ is of the order $m$. In the two-state case, we determine the exact values $c_2^\star=1/4$ and $C_2^{\mathrm{opt}}=4$. %the exact constants for $m\ge3$ remain open. The lower bound also holds for $n=1$ and is uniform in $P$, including sparse and periodic kernels. The proof combines short-window decorrelation with an averaged anchor-excursion decomposition, a Green-kernel hitting estimate, and a stopped Carleson--Hardy inequality. A nested rare-state construction produces finite $m$-state witnesses whose normalized Rayleigh quotients approach $q_{m-2}$ through an ordered sequence of limits. For every fixed finite irreducible reversible aperiodic kernel on at least two states, $\Gap(\widetilde P_n)=Θ_P(n^{-1})$.

math.ST · math.PR · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.34682

Beyond Multiplicity Correction: Sharp Retrieval Thresholds for Attention with Correlated Distractors

Heehyun Park

原文摘要

Redundant context affects attention in two distinct ways: multiplicity adds normalization mass, while score variation within correlated groups can produce extreme individual scores. We separate these effects in a planted retrieval model with exponentially many Gaussian distractors organized into supplied clusters whose number and size both grow exponentially with dimension. The model is a two-level generalized random energy model, whose classical free energy yields exact retrieval thresholds. Gaussian interpolation further shows that increasing positive correlation at fixed token count lowers the distractor free energy, unlike adding duplicates. Our main result establishes a sharp limitation of count correction, which subtracts the log cluster size from pre-softmax scores: this correction removes multiplicity but retains within-cluster extremes. Even when the inverse temperature is chosen after observing all scores, count correction requires a signal at least $\sqrt{2α_1}$, where $α_1$ is the exponential growth rate of the number of clusters. By contrast, averaging scores before exponentiation suppresses token-level fluctuations and lowers the optimal signal threshold to $\sqrt{2ρα_1}$, where $ρ$ is the within-cluster correlation. This gap persists after adding exponentially many singleton distractors, so group size alone does not identify the target, and extends, under explicit cumulant regularity assumptions, to fixed finite hierarchies of independent-increment scores. Finite-sample, stability, and participation results complement the asymptotic analysis. A controlled retrieval experiment with frozen sentence embeddings illustrates both sides of the distinction: averaging helps when the relevant item is a singleton, but can discard useful evidence when a relevant group contains multiple matching items.

cs.LG · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38437

Capacity of the Hopfield-Hebbian dynamics with correlated patterns

Mihailo Stojnic

原文摘要

Allowing for small fraction of errors in retrieved stored binary patterns, Hopfield-Hebbian neural network (NN) associative memory dynamics [14] achieves linearly scaled capacity. The famous proportionality constant $α_c\approx 0.14$ is obtained in a large dimensional scenario as the ratio of the number of reliably stored patterns $m$ and the patterns' length $n$ under the assumption that uniformly randomly chosen binary patterns are \emph{independent} among themselves. While such an idealized scenario is now well understood, more practical scenarios with correlated/noisy datasets remaining challenging even for classical statistical mechanics replica approaches. We consider precisely such practical settings where each \emph{archetype} pattern is replaced with $M$ correlated \emph{examples} with parameter $r$ governing the quality of correlation. We develop a powerful Random Duality Theory (RDT) based framework to analyze correlated data and already on the first level of RDT lifting obtain capacity characterizations that remarkably well match behavior exhibited through simulated dynamics. Moreover, characterizations explicitly feature correlation parameters $M$ and $r$, which allows to precisely determine their effects on phase-transitioning behavior of the underlying dynamics. Our results are also a well-fitting complement to the existing literature. Namely, to circumvent challenging statistical mechanics analyses, an alternative combination of spectral and replica methods is considered in [4]. We confirm that [4]'s elegant spectral characterizations are excellent approximations in the low correlated regime. At the same time, we also close the gap in the regimes with higher correlation levels where spectral methods deviate from the practical dynamics performance.

stat.ML · cond-mat.dis-nn · cs.IT · cs.LG · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38206

Averaged Annealed Markov Chains Achieve the Algorithmic Threshold for Tensor PCA, Part II: Langevin Dynamics

Aniket Das, Tselil Schramm

原文摘要

We consider the tensor principal components analysis (tensor PCA) problem on the sphere, in which we are asked to recover an unknown vector in $\mathcal{S}_N=\{x\in\mathbb{R}^N:\lVert x\rVert^2=N\}$ from a noisy observation of its $k$-th tensor power, for a fixed $k\ge3$. Tensor PCA exhibits a well-studied information-computation gap: global algorithms such as spectral methods and sum-of-squares work above an algorithmic threshold, below which we know matching lower bounds (against these and some other restricted models of computation). In contrast, local algorithms such as Markov chains were only known to succeed from a random initialization at a polynomially larger signal-to-noise ratio, and were believed to be inferior to global algorithms for tensor PCA. Continuing the program initiated in Part I [arXiv:2610.16705], we show that spherical Langevin dynamics, when supplemented with annealing and ergodic averaging, achieves polynomial-time strong recovery above the algorithmic threshold from a uniformly random initialization. Together with Part I, our results demonstrate that local Markov chains can succeed all the way down to the algorithmic threshold from an uninformative cold start.

cs.LG · cs.DS · math.PR · math.ST

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37866

Finite-Sample Optimal Conformal Prediction Sets under Covariate Shift

Zhongyang Li

原文摘要

We study conformal prediction under covariate shift with a known covariate density ratio, seeking prediction sets with minimum expected length under the target distribution. For every calibration sample size, we prove that the rule combining the inverse conditional-density score with randomized weighted conformal calibration minimizes this expected length among all rules valid over the full weighted-exchangeability class. We approximate the oracle using quantile and kernel histograms, including forest-weighted estimators, and select estimators and tuning parameters by resampling to estimate calibrated target length. On a bounded response domain, we bound excess length linearly in $L^1$ density error at fixed calibration size, without requiring a uniform positive lower bound on the true density. We also bound selection-pool and resampling errors. Under explicit growth conditions, the selected procedure approaches the same oracle while the calibration size remains fixed. Experiments on 36 known-density configurations and four public regression datasets compare coverage, prediction-set length, and runtime with existing methods. In targeted low-coverage and strong-shift comparisons, inverse-density selection yields shorter mean sets in most cases and lower mean runtime than the evaluated weighted baselines, with some differences in achieved coverage.

stat.ML · cs.LG · math.CO · math.PR · math.ST

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37630

Approximate Counting for Mixed $p$-Spin Glasses in Weak External Fields via Cluster Expansion

Qiang Wu

原文摘要

We give algorithms for approximating the partition function $Z_N$ of the Sherrington--Kirkpatrick (SK) model and finite mixed Ising $p$-spin models with $p\ge 3$. The algorithms apply at a fixed margin below the second-moment threshold $β_{\mathrm f}$ with homogeneous weak external fields $|h|\leqρ_0N^{-1/4}$, for fixed $ρ_0>0$. For any accuracy $\varepsilon\in(0,1)$ and failure parameter $δ\in(0,1)$, they approximate $\log Z_N$ to additive error $\varepsilon$. The number of exact operations is polynomial jointly in $N$, $\varepsilon^{-1}$, and $δ^{-1}$. The disorder variables have i.i.d symmetric distribution with unit variance. The failure probability is at most $δ$ plus an explicit disorder tail bound. This tail bound tends to zero under a finite fourth moment condition. Our approach builds on the cluster expansions of Aizenman--Lebowitz--Ruelle~\cite{ALR87} and Dey--Wu~\cites{DW23,DW26}. For higher-order mixtures, we retain hypergraphs using few vertices and evaluate their total weight deterministically through local spin averages and inclusion--exclusion. For SK, we impose cutoffs on the number of vertices of degree at least three and on the total number of edges. We estimate the retained sum using randomized color coding~\cite{AYZ95}. A lower tail control based on reverse hypercontractivity~\cite{MOS13} converts the mean-square approximation of the normalized partition function into logarithmic accuracy.

math.PR · cs.DS

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37521

Approaching Optimal Scaling of Queue Size for an Input-Queued Switch

Taha Ameen, Weina Wang

原文摘要

We study the scaling of the expected total queue length in an $n\times n$ input-queued switch. It has been conjectured that the optimal scaling is $O(n/(1-ρ))$, up to logarithmic factors, where $ρ$ is the system load. This conjecture has been established in the traditional heavy-traffic regime and in certain sub-regimes of the large-system regime. But it remains unresolved over a wide range of load scalings in the large-system regime. In this paper, we develop a family of scheduling policies parameterized by a positive integer $k\ge 2$. We show that under uniform traffic, our policy achieves an expected total queue length of $O\bigl({n\log\max\{n,1/(1-ρ)\}}\big/{(1-ρ)^{2^k/(2^k-1)}}\bigr)$, as long as $ρ\to 1$ in the large-system regime. As $k$ increases, the exponent $2^k/(2^k-1)$ approaches $1$, bringing our bound arbitrarily close to the conjectured scaling. The expected amortized scheduling cost of the policy is $O(n^3 k)$ per time slot. Our policy is of a batching type, with a novel recursive design that allows an arbitrary number of batching levels. This design principle may also be useful for other scheduling problems in which combinatorial constraints restrict which jobs can be served simultaneously.

cs.PF · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37388

Para-Gaussian Approximations of Random Deep Neural Networks

Mihai Nica, Janosch Ortmann

原文摘要

It is known that randomly initialized neural networks have Gaussian behaviour in the $n\to \infty$ limit. Unfortunately, this approximation can be poor for finite $n$ and gets worse as one goes deeper into the network. In this work, we develop a more accurate approximation that is \emph{slightly} non-Gaussian, which we call the para-Gaussian distribution and is constructed from the Hermite polynomials. We show how this para-Gaussian approximation can lead to a practical recursive method to approximate the deeper layers of the network. Finally, we apply this theory to linear neural networks (where things can be solved exactly) and to ReLU neural networks (where things can be approximated).

cs.LG · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:1909.12353

Interactive Particle Systems on Hypergraphs, Drift Analysis and the WalkSAT algorithm

Gabriel Istrate, Cosmin Bonchis, Mircea Marin

原文摘要

We analyze the expected running time of WalkSAT, a well-known local search procedure for satisfiability solving, on satisfiable instances of the k-XOR SAT problem. We obtain estimates of this expected running time by reducing the problem to a setting amenable to classical techniques from drift analysis. A crucial ingredient of this reduction is the definition of (new, explosive) hypergraph versions of interacting particle systems, notably of coalescing and annihilating random walks as well as the voter model. The use of these tools allows to show that the expected running time of WalkSAT depends on structural parameter (we call odd Cheeger drift) of the dual of the formula hypergraph.

cs.DS · cs.DM · math.CO · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37729

Pooled Testing under Congestion: Operational Scaling Laws for Pool-Size Selection

Ioannis Dimitriou, Johan van Leeuwaarden

原文摘要

Classical pooled-testing rules choose pool sizes to reduce the number of tests. In practice, however, samples arrive over time, pools take time to form, testing capacity is finite, and positive pools create bursts of follow-up work. These operational features can make the test-efficient pool size far from the delay-efficient one. We formulate pooled testing with stochastic arrivals and finite testing capacity as a queueing system, and derive exact performance representations and asymptotic scaling laws for fixed-batch Dorfman testing and a dynamic two-threshold policy. The analysis reveals three distinct design regimes. When test usage is the main concern, the classical Dorfman rule is recovered and the optimal pool size scales with the inverse square root of prevalence. When delay accumulated while the laboratory is busy testing another batch matters, positive pools create service-time variability that grows more rapidly with pool size than the mean retesting burden, and the optimal scale shifts to the inverse cube root of prevalence. When waiting to assemble a pool is itself costly, the optimal fixed pool size remains bounded even as prevalence becomes very small. Under severe capacity scarcity, congestion remains relevant at the classical Dorfman scale: the square-root law survives, but with a capacity-dependent constant. Dynamic pooling separates two operational decisions that fixed pool sizes conflate. A lower threshold determines when routine testing should begin, while an upper threshold limits pooling when backlog is high. The lower threshold follows the cube-root scale, whereas the upper threshold primarily acts as congestion control. The results show how prevalence, capacity, and delay jointly determine pooling decisions and explain why operationally optimal pools can be much smaller than those suggested by test-efficiency calculations alone.

cs.IT · math.OC · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37015

RePAIR: Inverting Backdoor Attacks in Semantic Segmentation

Arnold Brosch, Kira Maag

原文摘要

Despite significant advances in computer vision, semantic segmentation models remain vulnerable to backdoor attacks, posing a security risk. These attacks redirect pixels of a chosen victim class to an attacker-specified target class when a trigger is present, while preserving clean predictions. Existing defenses are largely derived from image classification, while dedicated segmentation defenses remain scarce and typically require retraining or model modification. We introduce RePAIR, a post-hoc, label-free, attack-unaware defense based on the observation that backdoor-induced shifts can be stronger in the classifier head than in internal representations, leaving recoverable victim-class semantics. RePAIR infers the victim-target relation from an unlabeled, potentially contaminated image pool, constructs a safety-approved semantic reference, and localizes suspicious pixels by comparing head predictions with internal semantic evidence. It then applies feature-space and output corrections toward the inferred victim semantics, while conservative localization and output constraints limit changes to benign predictions. We model the attack as adversarial probability transport and repair as its approximate reversal, deriving bounds and sufficient conditions for localization, residual attack success, clean-side changes, defense-induced target predictions, and attack-unaware pair identification. Experiments across segmentation architectures and attack settings show that RePAIR substantially reduces attack success while largely preserving clean performance.

cs.CV · cs.CR · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37721

Local-to-Global Theorems Based on Cones with Applications to Graph Coloring

Anqi Li, Shayan Oveis Gharan

原文摘要

Local-to-Global theorems are a cornerstone of many of recent developments in theoretical computer science from coding theory and PCPs all the way to analyzing mixing time of Markov chains. Building on trickledown theorems on simplicial complexes, several techniques have been established to obtain tighter local-to-global theorems to analyze the spectral gap of the Glauber dynamics, namely matrix trickledown, ${\mathcal C}$-Lorentzian polynomials and more recently Bochner type inequalities. In this paper, we adopt non-local local-to-global/Bochner type inequalities on "cones", corresponding to the local neighborhood of a given vertex, to show that the Glauber dynamics mixes in polynomial time to sample proper colorings of maximum degree $Δ$ graphs as long as $q\geq 1.7408Δ$.

math.PR · cs.DM · cs.DS · math.CO

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36744

When do token systems stabilize? Compatibility constraints and community structure

Flore Sentenac, Mingwei Yang, Sophie H. Yu

原文摘要

Token systems support repeated service exchange without monetary transfers, but their viability depends on the stability of token balances. We study token systems with compatibility constraints among agents. A requester is randomly sampled in each period, and only a few randomly sampled agents are available to provide service. We establish a necessary and sufficient condition for stability and show that the minimum-token rule, which selects the available provider with the lowest token balance, achieves the optimal stability region. We then apply this stability criterion to a random token system generated from stochastic block models with uniformly sampled requesters. We tightly characterize the stability regime by identifying two obstructions to stability: insufficient service opportunities for a group of communities or for an individual agent.

cs.GT · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36470

Underdamped Anchored Langevin Dynamics

Qi Feng, Hoang M. Nguyen, Lingjiong Zhu

原文摘要

Classical Langevin Monte Carlo algorithms, such as the unadjusted Langevin algorithm (ULA), are based on discretization schemes of the overdamped Langevin dynamics and are widely used for sampling in machine learning because they scale to high dimensions and large datasets. However, they require differentiable log-densities, and are less efficient for sampling heavy-tailed distributions. Although various approaches have been proposed in the literature for sampling non-differentiable and heavy-tailed targets, all of them are developed in the overdamped setting only. We propose a novel momentum-based underdamped anchored Langevin dynamics (UALD), and underdamped anchored Langevin Monte Carlo (UALMC) algorithm based on a discretization scheme of UALD. Our paper is the first to provide a kinetic (momentum-based) Langevin algorithm for non-differentiable and heavy-tailed targets that is free of asymptotic bias. The method replaces the original potential with a smooth reference potential and modifies the underdamped Langevin dynamics via multiplicative scaling in the drift term. We establish non-asymptotic guarantees in the 2-Wasserstein distance to the target distribution and show that the resulting iteration complexity has better dependence on dimension and accuracy level compared to overdamped-based anchored Langevin algorithms. We provide numerical experiments to illustrate the theory and practical performance of our proposed approach.

cs.LG · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.02487

Computational and Statistical Guarantees of the c-Rectified flow

Leda Wang, Zhehao Xu, Qiang Liu, Harrison H. Zhou

原文摘要

Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying c-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussian case study, the iteration converges to the optimal coupling if and only if the source and target covariance matrices commute. More generally, for a Gaussian to log-concave coupling, the ordinary rectified flow can reach a fixed point after one step from independent initialization. In contrast, under suitable regularity and uniform-integrability assumptions, iterative c-rectified flow always converges to the optimal transport coupling. We further establish quantitative one-step contraction and exponential convergence guarantees under projection-stability assumptions for both quadratic and strongly convex displacement costs. Finally, under a Hölder ball assumption, we develop new minimax-optimal score estimation rates and show that, when combined with iterative c-rectified flow, they yield a rate-optimal estimator of the optimal transport for the dimension \(d \ge 3\) and a nearly parametric rate for \(d=1,2\).

stat.ML · cs.LG · math.OC · math.PR · math.ST

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2509.00924

When is Fine-Tuning Scalable? Certified Recovery from Noisy Data and Linear-Cost Fine-Tuning on Structured Task Shifts

Anastasis Kratsios, Tin Sum Cheng, Bum Jun Kim, Daniel Roy

原文摘要

Transformers often transfer across related tasks with little fine-tuning; we study this question in noisy nonparametric regression for continuous maps $f,g:[0,1]^d\to\mathbb{R}^D$, representing the source and shifted tasks, using a single-query, single-head transformer $\mathcal{T}(\cdot)=V\operatorname{Softmax}(-α(\cdot,K))$ with $\ell^{\infty}$-based alignment scores $α$. Rather than assume that gradient-based training reaches an empirical risk minimizer, we give a model-specific two-stage procedure \textbf{certifying} source-task recovery and out-of-distribution (OOD) adaptation. With high probability, the resulting attention head recovers $f$ to arbitrary accuracy $\varepsilon>0$ in every fixed $L^p([0,1]^d)$ norm, $1\le p<\infty$, from noisy observations. For Lipschitz targets, its rate is minimax-optimal up to logarithmic factors without assuming oracle access to an asymptotic ERM. If $D=1$ and $f$ is Pfaffian than the values matrix factors into $AC$ with $A$ scaling at-most linearly $\mathcal{O}(\varepsilon^{-1})$ in the reciprocal approximation error $\varepsilon>0$. Importantly, our training procedure encodes all our identified (potentially) shared geometric structure from $f$ only into the values matrix factor $C$ and the keys matrix $K$ allowing for rapid access, and all $f$-specific structure only into $A$. Our main result concerns the OOD phase; where we identify geometric structures, which if shared by the source $f$ and OOD $g$ task; then only only the values matrix factor $A$ needs to be fine-tuned to guarantee an $L^p$-recovery of $g$. Critically, fine-tuning only $A$ is a convex problem which involving an \textit{at-most linear} number of parameters $\mathcal{O}(\varepsilon^{-1})$; dramatically cutting down on the worst-case scaling of $\mathcal{O}(\varepsilon^{-\mathbf{d}})$ unavoidable in the source-training phase.

stat.ML · cs.LG · cs.NE · math.NA · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2604.08095

The estimates for Boolean surface area of polynomial threshold functions

Fan Chang, Joseph Slote, Chun-Kai Tseng, Alexander Volberg, Haonan Zhang

原文摘要

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and isoperimetric properties of the class, especially bounds on average sensitivity, one of the central themes in the study of PTFs since the Gotsman--Linial conjecture recently solved by OpenAI, \cite{GLsol}. In this work we study PTFs through the lens of the Boolean surface area (or Talagrand boundary) \[ \mathbf{BSA}[f]=\mathbb{E}|\nabla f|=\mathbb{E}\sqrt{s_{f}(x)}, \] a natural measure of vertex-boundary complexity on the discrete cube. Our main result is that every degree-$d$ PTF has polylogarithmic Boolean surface area: \[ \mathbf{BSA}[f]\le C_d(\log(en))^{C_d}. \] The proof is based on the PTF Restriction Lemma of Kabanets, Kane, and Lu \cite{KKL2017} and proceeds through a tail bound for the pointwise sensitivity. In particular, it controls all subcritical fractional moments of the sensitivity. We also record a random block partition principle for Boolean surface area and an alternative recursive argument following Kane's work \cite{DK} on average sensitivity, which independently yields the second bound \[ \mathbf{BSA}[f]\le \exp(C(d)\sqrt{\log n}). \] This bound was obtained in \cite{FSVZ} without clarifying the magnitude of $C(d)$, which we do below. For lower moments $\bE |\nabla f|^η \le C(d, η)$ there is no dependence on $n$ for $0<η<1$.

cs.CC · math.AP · math.CA · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v3arXiv:2605.08424

Generalized Wasserstein Flow Matching: Nested Couplings for Point Cloud Generation

Moritz Piening, Richard Duong, Gabriele Steidl

原文摘要

We formulate flow matching on probability measures over probability measures. Directly from the Wasserstein-on-Wasserstein (WoW) continuity equation, we show that admissible nested outer and inner couplings induce a valid metameasure flow and non-local velocity field. Validity requires neither optimal plans nor a smooth manifold. Practically, this opens up the design space of multisample flow matching: exact Wasserstein plans are distinguished by energy and straightness, while sliced and lazy linear plans yield scalable alternatives. Point-cloud experiments, including controlled Bures-Wasserstein and Euclidean minibatch baselines, demonstrate the resulting geometry-cost trade-off.

cs.LG · math.OC · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.34750

Linear Hashing Is Poissonesque

Vinayak M. Kumar

原文摘要

The Poisson approximation theorem states that when $m$ balls are tossed uniformly and randomly into $n$ bins, the distribution of the bin loads can sometimes be approximated by $n$ independent Poisson random variables of mean $m/n$. We show that when the balls are tossed via a random $\mathbb{F}_2$-linear map, the load distribution is still governed by this Poisson distribution, albeit in a (necessarily) weaker manner. This allows us to show that a random linear map behaves like a fully random map in the following ways: 1. $\textbf{Expected loads.}$ We show that the expected value of the $r$th largest bin is governed by the $r$th largest value among $n$ independent Poisson random variables of mean $m/n$. Specializing to the canonical setting of $m=n$ and $r=1$, our bounds show that the expected maximum load when $n$ balls are hashed into $n$ bins by a random $\mathbb{F}_2$-linear map is no more than the corresponding expectation for a fully random map $\textit{plus}$ $\frac{3}2 + o(1)$. Specializing to $m\gg n\log n$, we show that the expected max load is $(1+o(1))m/n$ in this regime. 2. $\textbf{Concentration.}$ When $m\gg n\log (1/ρ)$ balls are tossed into $n$ bins randomly, we expect with $0.99$ probability that $\textit{every}$ density-$ρ$ subset of bins will contain a $(1\pm o(1) )ρ$-fraction of the balls. We show that this remains the case if the $m$ balls are tossed using a random linear map, and our bound matches the $o(1)$-factor produced by the fully random case. This gives a stronger version of the Leftover Hash Lemma for linear maps. An implication of this is that all bins have load $m/n \pm O(\sqrt{(m/n)\log n})$ with probability $0.99$. We obtain these results by showing that the average of a log-potential on the bin loads is upper bounded by the cumulant generating function of a Poisson random variable of mean $m/n$.

cs.DS · cs.CC · cs.IT · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.06283

The Tamed Subgradient Unadjusted Langevin Algorithm beyond Convexity

Iosif Lytras, Nikolaos Makras, Sotirios Sabanis

原文摘要

We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex. We introduce the Subgradient Tamed Unadjusted Langevin Algorithm (SG-TULA), a discretisation of the Langevin diffusion that operates directly on subgradients, without relying on computationally demanding smoothing procedures. To handle the superlinear regime, taming techniques are employed to produce a stable, explicit scheme. We derive non-asymptotic convergence bounds in Wasserstein-2 distance, with all constants tracked explicitly in terms of dimension and inverse temperature, improving upon the currently known rates for subgradient-based Langevin algorithms. We further provide excess risk estimates for the associated optimisation problem. We verify the assumptions, with explicit constants, for the regularized pretraining potential of a LLM in the GPT-2 lineage and the boosted coordinate-wise variant of SG-TULA pretrains the former competitively against finetuned AdamW and Muon, for which no comparable non-asymptotic guarantees are presently available.

cs.LG · math.OC · math.PR · stat.ML

查看论文
arXiv ↗PDF ↗
版本更新 · v4arXiv:2503.09762

Optimal regret for dynamic matching with static priorities

Süleyman Kerimov, Pengyu Qian, Mingwei Yang, Sophie H. Yu

原文摘要

We study centralized two-way dynamic matching markets in which agents arrive stochastically over time and wait in queues associated with their types. We focus on static priority policies that assign each agent type a fixed ranking over its neighbors and make online matching decisions using only queue availability. We propose the General Priority ($\mathbf{GP}$) policy, which builds on the Tree Priority ($\mathbf{TP}$) policy introduced in [KAG25]. Under the general position gap condition, $\mathbf{GP}$ selects matches using a nondegenerate optimal basic solution of the fluid relaxation. It prioritizes children over parents within trees and consistently gives clockwise neighbors priority over counterclockwise neighbors on each cycle. We establish the optimal all-time regret scaling $O(ε^{-1})$ for $\mathbf{GP}$ on general two-way matching networks, where the general position gap $ε$ measures the fluid relaxation's distance from degeneracy. In particular, this resolves the conjecture by [KAG25] on the optimal $ε$-dependence for $\mathbf{TP}$.

cs.DS · math.OC · math.PR

查看论文
arXiv ↗PDF ↗
新论文 · v1arXiv:2610.34433

Non-Ergodic Markovian Mirror Descent with Unbounded Noise

Yunus Alp Biyikoglu, R. Srikant

原文摘要

We analyze stochastic mirror descent for minimizing a convex objective expressed as an expectation under the stationary distribution of a Markov chain, using noisy subgradient observations along a single sample path. Through Poisson's equation, we decompose the Markovian noise and control its contribution under regularity and moment conditions that allow the stochastic subgradients and the Poisson solution to be unbounded across the state space. We establish an $O(T^{-1/2})$ bound on the expected suboptimality gap of the weighted-average iterate for an appropriately chosen step size. The analysis does not require aperiodicity or convergence of the chain's marginal distributions to stationarity. For irreducible finite-state chains, we verify the required conditions on the Poisson solution and derive explicit bounds that quantify the effect of periodicity. For irreducible countable-state chains, we verify the required regularity and moment conditions under a geometric Lyapunov drift condition and suitable growth bounds on the stochastic subgradients.

math.OC · cs.LG · math.PR

查看论文
arXiv ↗PDF ↗
版本更新 · v2arXiv:2208.05314Google Research

Convergence of denoising diffusion models under the manifold hypothesis

Valentin De Bortoli

原文摘要

Denoising diffusion models are a recent class of generative models exhibiting state-of-the-art performance in image and audio synthesis. Such models approximate the time-reversal of a forward noising process from a target distribution to a reference density, which is usually Gaussian. Despite their strong empirical results, the theoretical analysis of such models remains limited. In particular, all current approaches crucially assume that the target density admits a density w.r.t. the Lebesgue measure. This does not cover settings where the target distribution is supported on a lower-dimensional manifold or is given by some empirical distribution. In this paper, we bridge this gap by providing the first convergence results for diffusion models in this more general setting. In particular, we provide quantitative bounds on the Wasserstein distance of order one between the target data distribution and the generative distribution of the diffusion model.

stat.ML · cs.LG · math.PR

查看论文
arXiv ↗PDF ↗