Search arXiv⌕ Search

SEARCH · Search arXiv

Results for “math.PR”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

1,329 records · Page 5Linked to original sources
arXiv2026

Correlated initialization of deep residual networks

We study the large-depth behavior of residual networks whose weights are correlated across layers at initialization. Our results confirm and extend a conjecture of Marion et al. [2025], according to which correlated initializations should interpolate continuously between the Brownian stochastic differential equation arising from independent initialization and the ordinary differential equation arising from perfectly correlated initialization. When the initialization is obtained from the application of a feature function to a stationary Gaussian sequence with regularly varying correlation, we prove that there exists a unique critical scaling such that the infinite-depth limit is the solution of a Young differential equation driven by a Hermite process. Hermite processes reduce to the fractional Brownian motion if the feature function generating the initialization has Hermite rank one, which is the case for the identity function, for example. We show that the critical scaling and asymptotic limit are uniquely determined by the decay of correlations together with the Hermite rank of the feature function. Consequently, the correlation structure and Hermite rank of the initialization represent meaningful hyperparameters in the asymptotic regime. By contrast, under finite-variance iid initialization, the asymptotic driver is universally Brownian up to normalization regardless of the choice of distribution. Our proofs rely on a collection of novel results establishing a robust stability theory for Young differential equations in Banach spaces.

math.PR↗
arXiv2026

Constant-Stepsize Stochastic Approximation: Finite-Time Convergence, Gaussian Approximation, and Tail Bounds

Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency, yet the distribution of the iterates is typically intractable. Classical asymptotics results give $X_k^{(α)} \approx X^{(α)} \approx x^\star+\sqrtαY$, where $X^{(α)}$ is the steady state and $Y$ is an appropriate Gaussian limit, by progressively taking the time $k\uparrow\infty$ and stepsize $α\downarrow0$. Such limit results, however, do not quantify finite-time, finite-stepsize errors. We develop an explicit pre-limit characterization for SA with i.i.d.\ and Markovian noise. We establish existence and uniqueness of the stationary law, a geometric Wasserstein convergence to stationarity, and almost-sure and $L^3$ convergence of the steady state to the root $x^\star$, identifying the scale $\sqrtα$ as first-order fluctuation. At this scale, we derive a higher-order quantitative Gaussian approximation with a Wasserstein error, using Stein's method and Poisson equation techniques. We further obtain non-uniform Berry--Esseen-type tail bounds, incorporating both steady-state approximation and finite-time convergence errors. We instantiate the theory for strongly convex smooth SGD, linear SA, and nonlinear contractive SA. Beyond strong convexity, for general convex SGD, we identify a Gibbs limiting law and prove a pre-limit Wasserstein approximation error under stability and Stein-equation hypothesis, which are validated numerically.

cs.LG↗
arXiv2026

On the Complexity of the Compatibility Problem for Succinctly Encoded Conditional Distributions

The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used to make predictions in the form of conditional probabilities. However, a pair of conditional distributions p(x|y) and p(y|x) may not be compatible with any joint distribution p(x,y). Given two such conditionals, determining if there exists a compatible joint is known as the compatibility problem. For discrete random variables, when the conditionals are encoded as probability tables, the compatibility problem has a known solution, which is computationally tractable. In this paper, we formalise and study a succinct version of the problem, encoding conditional distributions as arithmetic circuits. This is applicable to practical applications of probabilistic modelling in high-dimensional settings, including neural network models. We show that, for succinct circuit representations of conditionals, the compatibility problem is intractable. In the case that all probabilities are non-zero, the problem is co-NP-complete. In the case that probabilities can be zero, we give examples to demonstrate that several notions of compatibility can be distinguished, and we prove that multiple versions of the problem are PSPACE-complete. Furthermore, we show that, assuming the polynomial hierarchy does not collapse, there exist compatible succinct conditionals whose joint cannot be expressed succinctly. Implications of these results for probabilistic modelling and machine learning are discussed.

cs.LG↗
arXiv2026

Gaussian Approximation for Multivariate Martingale Sums from Uniformly Ergodic Markov Chains

We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+η)p}$-moment condition with $η>0$, we establish the explicit bound $$ O\left( p^3 \|A\|_4^2 + pd^{1/4}\|A\|_2^{1/2}\|A\|_4^2 \right) $$ where $A\in\mathbb{R}^n$ collects the $L^{(2+η)p}$-sizes of the $n$ individual martingale increments. In the balanced-increment regime where the individual increments have comparable sizes of order $n^{-1/2}$, it yields the first optimal $O(n^{-1/2})$ Gaussian approximation rate for fixed $p$ and $d$. Consequently, we also obtain the first optimal $O(n^{-1/2})$ $W_p$ Gaussian approximation rate for multivariate additive functionals of uniformly ergodic Markov chains. Our analysis develops two techniques for addressing the interplay between higher-order Wasserstein distance and temporal dependence. First, building on the Ornstein--Uhlenbeck relative-score approach of Fang and Koike (2023), we formulate the bound in terms of antisymmetric Stein couplings while retaining the conditional tensor structure. Second, we develop a refresh-then-maximal coupling that combines an independent first-step resampling, which preserves the desired Stein identity, with a subsequent maximal coupling that provides effective control of the coupling increment. These tools may be useful more broadly for Gaussian approximation under temporal dependence.

math.PR↗
arXiv2026

Convergence rates for the RMSprop optimizer with full control of the hyperparameters

Popular adaptive stochastic gradient descent (SGD) methods to train artificial intelligence (AI) systems include the RMSprop, the Adam, and the AdamW optimizers, where the adaptivity parts in Adam and AdamW basically just coincide with RMSprop. Such adaptive methods involve several hyperparameters including the regularization parameter $ε$ (which ensures that one does not divide by 0 and is often chosen to be very close to zero such as $10^{-8}$ in PyTorch by default) and the second moment decay parameter $β$ (which is often chosen to be very close to $1$ such as 0.99 (RMSprop) and 0.999 (Adam and AdamW) in PyTorch by default). Despite the high relevance of such methods, it remains an open research problem to provide error estimates for such methods with the error constants being not exploding but uniformly bounded with the respect to the hyperparameters, even in the situation of convex stochastic optimization problems. It is the key contribution of this work to essentially solve this problem for RMSprop. Specifically, we bound the expectation of the stopped evaluation of the objective function at the RMSprop process from above by the sum of an initialization term that decays exponentially in the training time, a stochastic approximation remainder of order $γ_n$, and a memory error of order $( 1 - β)^2$ with the error constants being uniformly controlled over all admissible choices of the step sizes, the second moment decay parameter $β$ and the regularization parameter $ε\in[0,1]$ (also covering $ε=0$). Our non-asymptotic error estimates hold not just for all sufficiently large n but hold for every gradient step $n=1,2,3,...$ with all error constants being explicitly specified. The key innovative new feature in the proof of our analysis are suitable inverse moment bounds for the second moment process in RMSprop.

cs.LG↗
arXiv2026

High-Magnetization Sampling at Low Temperatures: Ising Models and Bayesian Sparse Linear Regression

Sparsity is a powerful structural resource in optimization and statistics. We develop frameworks for leveraging sparsity in sampling problems over the Hamming slice $\mathcal{X}_k^d:=\{\mathbf{x}\in\{\pm 1\}^d:|\{i:\mathbf{x}_i=1\}|=k\}$, in high-dimensional regimes where $k\ll d$ (i.e., where $\mathcal{X}_k^d$ is \emph{highly magnetized}). We use our frameworks to design improved samplers for canonical problems in the study of \emph{Ising models} and \emph{Bayesian sparse linear regression}. Our first main result considers the \emph{Sherrington--Kirkpatrick} (SK) model restricted to fixed-magnetization slices $\mathcal{X}_k^d$. We give a polynomial-time sampler for fixed-magnetization SK models at any inverse temperature $β>0$, under arbitrary external fields, provided that $k\le c_βd$ for an appropriate constant $c_β$. By combining this result with an annealing strategy for estimating normalizing constants, we obtain polynomial-time samplers for the SK model at arbitrarily low temperatures under a sufficiently strong external field of strength $h$. In the large-$β$ limit, our framework permits sampling at field strengths within constant factors of the \emph{Almeida--Thouless line} delineating the replica-symmetric and replica-symmetry-breaking regions ([dAT78]), improving polynomially over the field strength $h(β)$ required by the recent work of [BAR26]. Our second main result concerns the measurement complexity of polynomial-time Bayesian sparse linear regression. Recent work by [KSTZ25] shows how to sample from the canonical \emph{Gaussian spike-and-slab posterior} with expected sparsity $k$, at any signal-to-noise ratio, given $n\gtrsim k^3\log^3 d$ Gaussian measurements. We improve this requirement to $n\gtrsim k^{3/2}\log^2 d+k\log^3 d$, using a common sparsity-aware framework underlying both our results.

cs.DS↗
arXiv2026

Beyond Worst-Case Coreset Bounds for $k$-Clustering via Determinantal Sampling

Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computational constraints demand compact yet faithful summaries. A standard approach is to construct an \textit{$ε$-coreset}: a small weighted subset that approximately preserves the clustering cost for every plausible choice of centers. For the \textit{$(k,z)$-clustering problem}, existing worst-case bounds on coreset size are essentially tight, ruling out substantially smaller coresets in general. However, such worst-case instances are often unrepresentative of real-world data. In this work, we show that significantly smaller coresets are possible under mild and natural assumptions on the underlying data distribution. We introduce a new correlated sampling framework, called \textit{determinantal sampling}, based on a novel application of determinantal point processes. Using this framework, we obtain an efficiently constructible $\varepsilon$-coreset for $(k,z)$-clustering in $\mathbb R^d$ whose dependence on $1/\varepsilon$ has exponent strictly smaller than $2$ when $d$ is fixed. This improves over the worst-case $\varepsilon^{-2}$ barrier under our beyond-worst-case assumptions. To the best of our knowledge, this is the first result that provably surpasses these lower bounds through beyond-worst-case assumptions. Finally, we validate our approach on synthetic and real-world benchmark datasets, where it consistently achieves smaller coresets than existing state-of-the-art methods, even without explicitly enforcing the assumptions used in the analysis.

stat.ML↗
arXiv2026

Diffuse Gaussian Truncation For Deterministic Approximate Counting

We give deterministic FPTASes for two dense counting problems on which the known deterministic algorithms, based on zero-free interpolation, run in quasipolynomial time. For fixed $0<γ<1/2$ and $0<θ\leq1$, the first approximates $\mathrm{haf}(A)$ for a symmetric matrix $A$ when its support graph $G$ has minimum degree at least $(1/2+γ)n$ and its nonzero entries lie in $[θ,1]$. It also approximates permanents under the analogous bipartite condition, including full-support matrices in $[θ,1]$. For fixed $β>0$ and $0<κ\leq1$, the second approximates the zero-field Ising partition function $Z(J)$ for zero-diagonal real symmetric matrices $J$ satisfying $\max_{i,j}|J_{ij}|\leqβ/n$ and $λ_{\max}(J)\leq1-κ$. No separate lower-eigenvalue condition is imposed. We further prove $\log\mathrm{haf}(A)=h_A(G)-n/2+O_{γ,θ}(1)$ and $Z(J)=2^n\det(I-J)^{-1/2}(1+O_{β,κ}(1/n))$. Here $h_A(G)$ is the maximum weighted fractional-matching entropy. For unweighted graphs, the first formula improves the Cuckler--Kahn error from $o(n)$ to $O_γ(1)$ on the fixed-margin class and extends it to weights in $[θ,1]$. Both algorithms use a common Gaussian truncation principle. Each problem becomes an integral of a product of a fixed entire function over Gaussian coordinates, with possibly indefinite moment matrix entries of order $1/n$. Cancelling the linear term and exactly resumming the quadratic term leaves a coordinate remainder vanishing to order at least three. Complex dilation handles small supports. For large supports, we bound the recombined tail by a large-deviation rate that beats the entropy of the subsets. The truncation error is at most $(CR/n)^{R/2}+e^{-cn}$. This faster-than-geometric decay permits $R\log(en/R)=O(\log n+\log(1/ε))$ and hence polynomial enumeration.

cs.DS↗
arXiv2026

Optimal mixing of the systematic scan dynamics via approximate tensorization of entropy

We study the mixing time of the systematic scan dynamics for high-dimensional discrete distributions. This Markov chain updates coordinates sequentially according to a fixed predetermined order, in contrast to the Glauber dynamics that updates coordinates selected uniformly at random. The systematic scan is often favored in practice because it exhibits strong empirical performance, but its theoretical analysis remains far less developed than that of Glauber dynamics. We take a step toward addressing this imbalance by showing that two standard functional notions of weak dependence between the coordinates of the distribution provide strong convergence guarantees for the systematic scan dynamics. First, we show that approximate tensorization of entropy implies optimal $O(\log n)$ mixing time for every scan order under standard marginal, connectivity, and bounded interaction degree assumptions about the distribution. Second, we show that approximate tensorization of variance yields a constant-factor contraction of the variance functional per scan, which in turn implies an optimal $O(1)$ relaxation time for the natural additive and multiplicative reversibilizations of the systematic scan dynamics. Compared with our entropy result, the variance bound improves the dependence on the maximum interaction degree from exponential to quadratic and requires weaker assumptions on the distribution. As concrete applications of our results, we establish optimal $O(\log n)$ mixing of the systematic scan dynamics for bounded-degree antiferromagnetic two-spin systems in the tree-uniqueness region and for the ferromagnetic $q$-state Potts model on square boxes in $\mathbb{Z}^2$ throughout its subcritical regime.

math.PR↗
arXiv2026

From Truncation to Commitment: Persistent Context in Uniform Discrete Diffusion

Uniform-state discrete diffusion models update all tokens in parallel while keeping every position revisable. Even when the commonly used top-$p$ rule leaves only one candidate at a position, that choice affects only the current reverse step and can be revised at the next sampling step. We ask what changes when selected hypotheses instead become persistent context for later predictions. We therefore propose committed reveal sampling (CRS), a training-free sampler that stores selected argmax tokens and inserts them into subsequent model inputs. Our analysis gives a rationale for selecting later and for keeping selected tokens visible. Under the exact forward process, the Bayes error of selecting a clean token cannot increase as noise decreases, while in a simple latent-mode model, keeping the selected token visible helps later parallel predictions agree on the same sequence-level choice. Empirically, paired experiments on Duo-distilled then separate this persistent effect from single-step top-$p$ restriction and scalar temperature scaling. Under the same finalization rule, CRS without top-$p$ truncation reaches lower generative perplexity (GenPPL) than fixed $p=0.95$ and $p=0.9$ baselines across budgets of 8--64 function evaluations (NFE). At 64 NFE, the comparison at matched unigram entropy also gives lower GenPPL for CRS, yielding a more favorable GenPPL--entropy tradeoff. Base Duo shows the same direction in a descriptive comparison, while other diversity and continuation metrics can rank these operating points differently. These results identify support restriction and persistent context as distinct controls of that tradeoff.

cs.LG↗
arXiv2026

The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy

How deep does a graph neural network need to be on a sparse graph? We study its purest statistical form: node classification on the sparse contextual stochastic block model (CSBM) with average degree $Δ=O(1)$, whose local weak limit is a broadcast-labelled Poisson Galton-Watson tree. Prior work derived a message-passing classifier $h_\ell$ that aggregates from each vertex at distance $k\le\ell$ the attenuated evidence $2\operatorname{artanh}(γ^k t(X_v))$, with $γ$ the edge signal and $t$ a bounded likelihood-ratio transform of the feature. We prove that the value of depth is governed by a single number, the Kesten-Stigum ratio $κ=γ^2Δ$. Below the threshold ($κ<1$), the error sequence is Cauchy at a geometric rate, $|\mathcal{E}(\ell)-\mathcal{E}(\ell')|\le Cκ^{(\ell+1)/3}$ for all $\ell'>\ell$, so all layers beyond depth $O(\log(1/ε))$ change the error by less than $ε$; conversely, under mild regularity each sufficiently deep layer still flips the decision with probability at least $cκ^{\ell/2}$, the empirically sharp exponent. Above the threshold ($κ>1$), depth is geometrically productive: $\mathcal{E}(\ell)$ is driven to a branching-process floor of order at most $1/(κ-1)$ at any geometric rate $κ^{-s\ell}$, $s<1$ (this bound has content only for $κ>17$). No local classifier of any depth beats the universal floor $e^{-Δ}Φ(-ζ)$ set by isolated roots ($ζ$ the feature signal-to-noise ratio), while the first layer provably helps by an explicit total-variation amount. Simulations with an exact belief-propagation baseline on the same trees show that the pairwise rule's error curve is mildly non-monotone in $\ell$, so an optimal finite depth exists (an exact instance is certified in the appendix), while BP saturates strictly faster, at an effective per-layer ratio below $κ$ that we identify.

math.ST↗
arXiv2026

Spawn Freely, Act Sparingly: Progressive Risk Vesting for Recursive LLM-Agent Trees

Recursive LLM agents can broaden their search by spawning specialists. Some branches later request tools that send data or deploy code. When should a branch receive authority to act? We distinguish sandbox spawning, in which external controls prevent the specified harm, from capability activation, in which a selected branch crosses an irreversible-action boundary. Progressive Risk Vesting (PRV) holds a trajectory-level risk budget in escrow and debits it as branches are activated. We prove an anytime harm bound for adaptively generated trees. Branch outcomes may be dependent, but each local certificate needs to remain valid conditional on the full pre-activation history, including the information used to select the request. When activation gates, branch charges, and compute constraints are held fixed, delayed vesting preserves every policy available under irrevocable spawn charging. Marginal risk estimates can still fail after branch selection. In a stylized branching model, trajectory harm changes as the authority reproduction number $\mathcal{R}_A$ crosses one. As local risk $p$ approaches zero, trajectory harm is proportional to $p$ below criticality, proportional to $\sqrt{p}$ at criticality, and retains a positive floor above it. A finite-type occupancy model yields risk and compute shadow prices. For nested fanout modes with decreasing marginal value per unit risk, these prices produce a threshold rule. Branching calculations and a split-sample experiment illustrate the results. These synthetic studies do not estimate safety in deployed agents. The analysis suggests a design rule: search broadly in the sandbox and grant recursive authority sparingly, with an explicit risk charge.

cs.AI↗
arXiv2026

Quantitative Target Convergence and Uniform-in-Time Propagation of Chaos for Langevin-Regularized SVGD

We establish quantitative convergence to the target and uniform-in-time propagation of chaos for Langevin-regularized Stein variational gradient descent. The Stein interaction need not be small relative to the confining Langevin drift and does not generally yield a contractive particle coupling. At the mean-field level, the Stein and Langevin components dissipate the same relative entropy in the kernel-induced Stein and $2$-Wasserstein geometries, producing the squared kernel Stein discrepancy and relative Fisher information. Under a log-Sobolev inequality for the target, this yields exponential last-iterate convergence. We also derive a finite-particle entropy identity relative to the product target, giving exponential-in-time convergence of the empirical measure up to polynomial sampling errors. For propagation of chaos, we develop two complementary finite-time approaches. A synchronous coupling, combined with exponential moment estimates for the nonlinear mean-field diffusion, yields explicit single-exponential bounds in Wasserstein distance and kernel Stein discrepancy (KSD). Moving-product entropy gives joint-law relative entropy control relative to the evolving mean-field product law and, through entropy superadditivity and concentration, fixed-marginal relative entropy and total variation bounds and empirical KSD estimates. Under an additional $T_2$ inequality for the initial law, it also yields Wasserstein bounds. Combining these finite-time estimates with target convergence at a logarithmic cutoff time gives polynomial uniform-in-time propagation of chaos rates in expectation for empirical KSD and $W_2^2$, and for fixed-marginal total variation and $W_2^2$. All bounds control the last iterate in physical time. We also compare the two finite-time mechanisms and identify regimes in which each gives the sharper polynomial exponent.

stat.ML↗
arXiv2026

Signed random Fourier features for fast density estimation with indefinite kernels

Kernel density estimation (KDE) is one of the most fundamental statistical estimators of density functions. Its direct implementation on a dataset of $N$ points incurs an $\mathcal{O}(N^{2})$ computational cost, which is prohibitive for large-scale datasets. Kernel approximation techniques can be applied to bring the computational cost down to $\mathcal{O}(N)$. The random Fourier features (RFF) technique, based on sampling from the spectral density of the kernel function, has become popular to speed up kernel estimators for machine learning applications. Unfortunately, it is restricted to positive definite kernels, while the majority of kernel functions popular in KDE, such as the parabolic kernel, do not satisfy this property. To overcome this limitation, this article introduces the signed random Fourier features (SRFF) technique. It is a generalization of RFF compatible with indefinite kernels whose inverse Fourier transform is absolutely integrable. The motivation for introducing this method is to speed up KDE in the case of multivariate compact kernels, which are generally not positive definite. We detail how to implement SRFF for both product kernels and isotropic kernels. For the class of Kuttner-Golubov kernels $K(\boldsymbol{x}_{i},\boldsymbol{x}_{j})=(1-\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert ^α)^β\mathbf{1}_{\{\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \leq1\}}$ where $\boldsymbol{x}_{i}\in\mathbb{R}^{d}$, $\boldsymbol{x}_{j}\in\mathbb{R}^{d}$, $α>0$, $β>0$, which includes the triangular, parabolic, biweight, triweight, and other kernel functions of interest for KDE as particular examples, we provide an explicit acceptance-rejection algorithm to sample from its signed spectral density. Our numerical tests on a dataset of one million points confirm the computational efficiency and accuracy of SRFF for large-scale KDE.

stat.CO↗
arXiv2026

Sharp Normalized Covariance Bounds and Constant-Stretch Correlated Sampling on the Hypersimplex

We establish the normalized covariance bound conjectured by Anari et al. (2026, Conjecture 3) for fixed-rank external-field measures. Let $d\ge2$ and $m\in[d-1]$. For $w\in(0,+\infty)^d$, let $\mathsf S$ be an $m$-subset of $[d]$ with rank-$m$ external-field law $\mathbb P(\mathsf S=S)=\frac{\prod_{i\in S}w_i}{e_m(w)},S\subseteq[d],|S|=m,$ where $e_m(w):=\sum_{T\subseteq[d], |T|=m}\prod_{\ell\in T}w_\ell$ is the $m$th elementary symmetric polynomial in $w_1,\dots,w_d$. Let $X:=(X_1,\dots,X_d)^\top$ be its indicator vector, i.e., $X_i=\mathbb I\{i\in\mathsf S\},i\in\{1,\dots,d\}.$ Let $Σ:=\mathrm{Cov}(X)$, put $v_i:=Σ_{ii}$ for each $i\in[d]$, and define $v:=(v_1,\dots,v_d)^\top,D:=\mathrm{diag}(v),V:=\sum_{i=1}^dv_i.$ We prove $Σ\succeq D-\frac{vv^\top}{V}.$ This improves the coefficient $1/2$ in the first version of our work (Cesari and Colomboni, 2026, Corollary 1.3) to the optimal universal value $1$. As a first corollary, we improve the coefficient in the pseudoinverse bound of Bacchiocchi et al. (2026, Lemma 2) from $2$ to the optimal value $1$. Specializing this bound to coordinate differences gives an alternative proof of our effective-resistance theorem from the first version of our work (Cesari and Colomboni, 2026, Theorem 1.1). The framework of Anari et al. (2026, Theorem 1 and Corollary 2) also yields unconditional correlated-sampling guarantees with stretch $6$ on the hypersimplex and $12$ on its at-most variant. Unconditional constant-stretch guarantees were first established in the first version of our work (Cesari and Colomboni, 2026, Corollaries 1.4 and 1.5), with constants $16$ and $32$, which we improve here to $6$ and $12$. These improved constants strengthen the positive resolution, established in the first version of our work, of the constant-stretch question posed by Naor et al. (2026, Theorem 2 and Section 5).

math.PR↗
arXiv2026

Security in the Age of AI Teammates: An Empirical Study of Agentic Pull Requests on GitHub

Autonomous coding agents are increasingly deployed as AI teammates in modern software engineering, independently authoring pull requests (PRs) that modify production code at scale. This study aims to systematically characterize how autonomous coding agents contribute to software security in practice, how these security-related contributions are reviewed and accepted, and which observable signals are associated with PR rejection. We conduct a large-scale empirical analysis of agent-authored PRs using the AIDev dataset, comprising of over 33,000 curated PRs from popular GitHub repositories. Security-relevant PRs are identified using a keyword filtering strategy, followed by manual validation, resulting in 1,293 confirmed security-related agentic-PRs. We then analyze prevalence, acceptance outcomes, and review latency across autonomous agents, programming ecosystems, and types of code changes. Moreover, we apply qualitative open coding to identify recurring security-related actions and underlying intents, and examine review metadata to identify early signals associated with PR rejection. Security-related Agentic-PRs constitute a meaningful share of agent activity (approximately 4\%). Rather than focusing solely on narrow vulnerability fixes, agents most frequently perform supportive security hardening activities, including testing, documentation, configuration, and improved error handling. Compared to non-security PRs, security-related Agentic-PRs exhibit lower merge rates and longer review latency, reflecting heightened human scrutiny, with variation across agents and programming ecosystems. PR rejection is more strongly associated with PR complexity and verbosity than with explicit security topics.

cs.CR↗
arXiv2026

Fine-Tuning Large Language Models to Classify Pull Request-Issue Alignments: Going Beyond Prompting

Context: Accurate alignment between pull requests (PRs) and corresponding issues is crucial for efficient software development and maintaining code quality, as misalignments can reduce traceability, hinder defect localization, and decrease maintainability. Objective: This study aims to improve automated PR-issue alignment classification by leveraging fine-tuned large language models (LLMs) across multiple alignment categories, and conducts interpretability analysis to investigate the effects of PR-issue fields on the predictions of fine-tuned LLMs. Method: Our methodology consists of dataset preparation, LLM fine-tuning, and interpretability analysis. We first extended an existing dataset and applied data augmentation to address class imbalance. GPT-4o was then fine-tuned via instruction tuning, and open-source LLMs including CodeLlama-7B, CodeQwen1.5-7B, StableCode-3B, CodeGemma-7B, and Deepseek-Coder-6.7B were fine-tuned using classification-specific heads. Interpretability analysis using Shapley Additive Explanations (SHAP) was conducted to examine the influence of PR-issue fields on predictions for the best-performing open-source LLM. Results: Fine-tuned LLMs outperformed baseline models, achieving average improvements of 6.15% in accuracy and F1-micro, 14.69% in F1-macro, and 6.15% in recall. CodeLlama-7B emerged as the best-performing fine-tuned LLM overall, while interpretability analysis revealed that code diffs together with issue body and PR body contents exert the greatest influence on predictions. Conclusions: Fine-tuning substantially enhances PR-issue alignment classification, improving both accuracy and efficiency. Interpretability analysis provides actionable insights into the dataset features driving alignment decisions, deepening understanding of how LLMs reason over software artifacts.

cs.SE↗
arXiv2026

MTD-Playground: An Attacker-Aware Evaluation Framework for Network Moving Target Defense

Moving Target Defense (MTD) has emerged as a proactive network cyber defense paradigm that increases attacker uncertainty through dynamic network reconfiguration techniques such as Software-Defined Networking (SDN)-enabled path randomization. However, existing evaluations remain fragmented due to inconsistent attacker assumptions, attack scenarios, and evaluation metrics, limiting reproducibility and deployment-oriented comparison. In this paper, we present MTD-Playground, an attacker-aware evaluation framework for benchmarking SDN-enabled path-randomization (PR) MTD techniques under realistic enterprise-style multi-stage attack scenarios. Beyond isolated security and performance metrics, MTD-Playground introduces a composite evaluation methodology for analyzing deployment effectiveness, mutation-interval trade-offs, and defender-attacker operational balance. Using periodic path randomization as a representative PR-MTD strategy, our evaluation shows that aggressive mutation intervals reduce attack success rates to 4-20% while increasing attack completion time to 160-311s across evaluated attack scenarios. At the same time, PR-MTD improves throughput by up to 30.9% and reduces internal-path latency without service interruption. Composite analysis further shows that shorter mutation intervals consistently achieve the highest deployment effectiveness and positive defender advantage. These results demonstrate that SDN-based PR-MTD can substantially disrupt multi-stage attack progression while remaining practically deployable in enterprise environments.

cs.CR↗