arXiv:2606.22427v2 Announce Type: replace-cross
Abstract: We derive compact analytical formulae for the spectrum of nonlinear Compton scattering in a finite plane-wave pulse with a smooth temporal envelope. The strong-field QED probability is reduced to finite-pulse phase integrals, which are evaluated asymptotically for multicycle pulses with a broad class of smooth envelopes. We use the uniform approximation to remove the caustic divergences that appear at the nonlinear edges of broadened harmonics. Away from the caustics, it reduces to the standard saddle-point result. The behavior near the linear edge is further improved by an envelope-corrected saddle-point approximation. The approach retains the harmonic substructure in the spectral-angular region carrying the dominant part of the emitted radiation. The locally monochromatic approximation is recovered by averaging the finite-pulse interference. Within their asymptotic domain of applicability, the resulting formulae agree with direct numerical calculations and can be used to evaluate spectra from an electron beam.
Science Journals
arXiv:2603.05961v3 Announce Type: replace-cross
Abstract: Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure-volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this tutorial shows how to sample multiple Hugoniot curves in the pressure-volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine-Hugoniot equations to yield Hugoniot curves in the pressure-volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and made all code and data available at https://github.com/llnl/BALSCD.
arXiv:2607.12115v2 Announce Type: replace
Abstract: This paper presents a corpus-level analysis of generated behavior diagrams derived from Sony's R-CODE sample distribution for the ERS-111 AIBO. Rather than reading each script in isolation, the study compares named states across the corpus to identify the recurring control vocabulary that structures the sample set. The resulting aggregate shows that many superficially different routines are built from a compact embodied grammar centered on initialization, sensing, iterative action, synchronization, and recovery. It further shows that this vocabulary supports a graded scale of rising behavioral complexity, from capability activation and startup regularization to monitored locomotion, environmental decision loops, and fuller mode-based control. In addition to historical analysis, the paper argues that this form of state-based abstraction is useful as an intermediate representation for constructing new encapsulated behavior routines, especially on constrained native robotic systems where deterministic control, direct hardware access, and modular behavioral composition remain important.
arXiv:2607.12194v2 Announce Type: replace
Abstract: It was found that the differential equation of dynamo effect (i.e., generation of the electric fields and currents) in a uniformly-expanding plasma ball with strongly anisotropic conductivity possesses the unique mathematical property: namely, the spectrum of its eigenvalues is universal and independent of physical parameters of the medium. As a result, it becomes possible to introduce a special set of eigenfunctions - which we called the generalized spherical functions - that can be used to solve the dynamo problem in exactly the same way as ordinary spherical functions are used to solve the Laplace equation. The corresponding exact solutions should be especially valuable for treating the inverse dynamo-problem, i.e., determination of the plasma parameters from the experimentally measured electric fields and currents.
arXiv:2606.26910v3 Announce Type: replace-cross
Abstract: Photonic integrated circuits offer a scalable and robust route toward quantum information technologies by consolidating photon sources and linear optical networks onto compact, wafer-manufacturable chips. Although silicon photonics has enabled diverse discrete-variable quantum breakthroughs -- spanning multiphoton entanglement, quantum networking, and photonic qubit fusion for quantum computing -- scaling these platforms beyond proof-of-principle demonstrations remains severely constrained by a critical system-level bottleneck. Optical loss compounds rapidly across photon generation, routing, and state analysis, causing multiphoton generation probabilities to plummet exponentially as circuit depth and complexity grow. Here we overcome this rate-loss barrier by demonstrating a monolithic, ultralow-loss silicon nitride (Si$_3$N$_4$) integrated photonic platform engineered for high-performance discrete-variable quantum information processing. Our architecture seamlessly integrates narrowband photon-pair sources with low-loss qubit-fusion circuits and reconfigurable state-analysis interferometers. The on-chip sources prepare Einstein-Podolsky-Rosen (EPR) states with a fidelity of 0.9875(3) and exhibit near-unity photon indistinguishability, yielding a heralded Hong-Ou-Mandel interference visibility of 0.990(6). By executing on-chip fusion of two EPR states, we synthesize and characterize four-photon Greenberger-Horne-Zeilinger states with a record fidelity of 0.943(8) and a fourfold count rate of 27 Hz -- more than two orders of magnitude higher than previous silicon-photonic implementations. Combined with standard CMOS-compatible fabrication on 150-mm-diameter wafers, these results establish ultralow-loss Si$_3$N$_4$ integrated photonics as a definitive, manufacturable platform for deployable, large-scale quantum information processors.
arXiv:2607.16169v2 Announce Type: replace
Abstract: Muon is competitive with AdamW in large-scale pre-training, but its value for reinforcement-learning (RL) post-training remains unclear. We study vanilla Muon in sparse-reward agentic RL through matched single-seed comparisons with AdamW on ALFWorld using Qwen2.5-0.5B-Instruct. Under Group-in-Group Policy Optimization (GiGPO), applying Muon only to hidden weight matrices raises final-window validation success from 0.290 to 0.546 (+88%); high-rate AdamW controls retain no post-update success. The effect depends on the advantage estimator and learning rate. At 3e-5, Muon improves GRPO from 0.161 to 0.268, whereas GraphGPO's late-window gap narrows near saturation. At 1e-5, GraphGPO Muon reaches 0.901, raises normalized validation AUC from 0.399 to 0.556, and reaches 0.5 and 0.75 success 30 and 60 updates earlier, respectively. These exploratory results show that Muon can benefit agentic RL and motivate studying the policy optimizer, advantage estimator, and learning rate jointly.
arXiv:2604.13196v3 Announce Type: replace-cross
Abstract: We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic polynomials, all products and ratios of quantum factorials reduce to integer vector arithmetic. This ensures that cancellations between numerator and denominator are resolved exactly prior to any evaluation. This formulation yields the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object of the series, from which evaluation in any target field is realized as a ring homomorphism.
For quantum recoupling coefficients, we demonstrate that this framework achieves linear memory scaling in the compilation phase, eliminates intermediate expression swell in exact arithmetic, and substantially extends the range of reliable double-precision computation by reducing cancellation-induced error amplification. Beyond its computational advantages, the DCR provides a unified perspective on $q$-deformed amplitudes. Structural properties like admissibility at roots of unity, and the classical limit all emerge as intrinsic properties of a single underlying combinatorial object.
arXiv:2501.12842v5 Announce Type: replace-cross
Abstract: Symmetric private information retrieval is a cryptographic task allowing a user to query a database and obtain exactly one entry without revealing to the owner of the database which element was accessed. The task is a variant of general two-party protocols called one-sided secure function evaluation and is closely related to oblivious transfer. Under the name quantum private queries, quantum protocols have been proposed to solve this problem in a cheat-sensitive way: In such protocols, it is not impossible for dishonest participants to cheat, but they risk detection [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 100, 230502 (2008)]. We give an explicit attack against any cheat-sensitive symmetric private information retrieval protocol, showing that any protocol that is secure for the user cannot have non-trivial security guarantees for the owner of the database.
arXiv:2607.12428v2 Announce Type: replace
Abstract: The increasing adoption of autonomous coding agents accelerates software development but also introduces scoped security risks within high-impact file paths that can outpace traditional human review capacity. While prior research has primarily evaluated these systems in terms of functional correctness and productivity, this paper presents a large-scale empirical study using the AIDev dataset to systematically characterize security code smells in agent-generated pull requests (PRs). Through a combination of a validated LLM-as-a-judge framework and manual qualitative analysis, we identify and classify security misconfigurations across 16,112 file changes spanning 4,022 pull requests. Our results reveal that 38.9% of agent-generated PRs contain at least one security smell, with supply chain integrity issues accounting for 82.3% of all detected security smells. Furthermore, hard-coded credentials constitute 99.6% of all critical-severity security smells. Crucially, we find that human collaborators are responsible for introducing 67.6% of genuine leaked secrets within these agent-assisted workflows, while existing automated and human review processes fail to detect 81.1% of these credentials prior to integration. These findings highlight substantial security risks in agent-assisted software development workflows and suggest a potential reduction in developer vigilance. They also underscore the urgent need for context-aware security guardrails implemented directly at the point of human-AI collaboration.
arXiv:2510.03445v2 Announce Type: replace-cross
Abstract: Let $X$ be a set of $n$ points in the plane, not all on a line. According to the Gallai-Sylvester
theorem, $X$ always spans an \emph{ordinary line}, i.e., one that passes through precisely 2
elements of $X$. Given an integer $c\ge 2,$ a \emph{line} spanned by $X$ is called
\emph{$c$-ordinary} if it passes through at most $c$ points of $X$. A \emph{triangle} spanned by 3
noncollinear points of $X$ is called \emph{$c$-ordinary} if all 3 lines determined by its sides
are \emph{$c$-ordinary}. Motivated by a question of Erd\H os, Fulek \emph{et al.}~\cite{FMN+17}
proved that there exists an absolute constant $c > 2$ such that if $X$ cannot be covered by 2
lines, then it determines at least one $c$-ordinary triangle. Moreover, the number of such
triangles grows at least linearly in $n$. They raised the question whether the true growth rate of
this function is superlinear.
We prove that if $X$ cannot be covered by 2 lines, and no line passes through more than $n-t(n)$
points of $X$, for some function $t(n)\rightarrow\infty,$ then the number of $17$-ordinary
triangles spanned by $X$ is at least constant times $n \cdot t(n)$, i.e., superlinear in $n$. We also
show that the assumption $t(n)\rightarrow\infty$ is necessary. If we further assume that no line
passes through more than $n/2-t(n)$ points of $X$, then the number of $17$-ordinary triangles
grows superquadratically in $n$. This statement does not hold if $t(n)$ is bounded. We close this
paper with some algorithmic results. In particular, we provide a $O(n^{2.372})$ time algorithm for
counting all $c$-ordinary triangles in an $n$-element point set, for any $c<n$.
arXiv:2607.12759v2 Announce Type: replace
Abstract: A charge simulation method is applied to approximate the multi-phase Mullins--Sekerka flow in $\mathbb R^{2}$ and in a half-plane bounded by a Neumann wall. In the underlying mathematical model, interfaces driven by their curvature are coupled through a harmonic chemical-potential field. We use a charge simulation method, a variant of the method of fundamental solutions: each chemical potential is represented by fundamental solutions centered at charge points off the curve, so no bulk mesh is required. It treats curve networks separating several phases at triple junctions, including phases that occupy more than one region; on the half-plane boundary, the no-flux condition is imposed exactly by image charges, and mobile contacts stay orthogonal to the wall. The discretization is structure-preserving in the sense that every bounded phase area is conserved to machine precision at the velocity level by a null-space projection of the discrete area constraints. The proposed scheme is assessed through a convergence test against an exact three-concentric-circle solution.
arXiv:2604.01028v2 Announce Type: replace-cross
Abstract: The coronal magnetic field plays a fundamental role in governing coronal activities, driving space-weather events, and shaping the heliosphere. Due to a lack of direct observations, extrapolation models such as the Potential Field Source Surface (PFSS) model become the primary method to obtain the three-dimensional magnetic field distribution in the corona. However, the PFSS model cannot solve the long-standing open-flux problem, in which the extrapolated open magnetic flux is significantly lower than that inferred from in-situ measurements. To address this issue, we develop a Non-Spherical Potential Field (NSPF) model. The model introduces a Non-Spherical Source Surface (NSSS) defined as an isosurface of the total magnetic field. The NSSS naturally forms concave structures beneath external current sheets, enabling the model to generate substantially more open magnetic flux while yielding a physically plausible distribution of open field regions. As a result, the NSPF model successfully reproduces complex coronal magnetic topologies, interplanetary magnetic field properties, and solar wind source mappings. Our refined coronal magnetic model provides a useful framework for future research on solar and heliospheric magnetic coupling.
arXiv:2607.14707v2 Announce Type: replace
Abstract: Large language models routinely produce fluent answers to single-shot prompts, yet deploying them as reliable components of a domain decision system is substantially harder. Closing this gap is the work of harness engineering: the deliberate composition of deterministic scaffolding (symbolic filters, retrieval, schema-typed I/O, LLM-as-judge loops, HITL gates, persistent state, audit trails) around an LLM core. We present a case study in academic supervision, a domain combining high-stakes recommendation, longitudinal accountability, and structured operational workflows.
We compare a baseline Academic Supervision Assistant (ASA), a GPT-5 chatbot with no scaffolding, against a multi-module system, Academic Supervision System (ASuS) that wraps the much smaller GPT-4o-mini in a LangGraph harness with symbolic semantic retrieval, schema-validated outputs, LLM-as-judge with bounded retry, HITL gates, deterministic weighted risk scoring with LLM narration, and a per-node SQLite audit trail. The evaluation rubric is retargeted at six harness-mechanism dimensions (grounding, explainability, consistency, process integrity, cognitive load, constraint adherence). A blind ten-rater hybrid evaluation, supplemented by a 2 x 2 model-harness ablation, finds that ASuS, despite using a much smaller base model, outscores ASA on every dimension. Across ten raters the pooled mean for ASuS is 4.08 versus 1.23 for ASA, and 8 of 10 raters reject the null at alpha = 0.05 on a paired Wilcoxon test; full numbers are in Sections 6.4 and 6.7. The ablation confirms that the structural contributions of the harness are largely model-invariant. We extract seven recurring harness-engineering patterns and argue that where reliability, traceability, and institutional consistency matter more than open-ended fluency, harness engineering challenges the prevailing 'bigger model is better' intuition.
arXiv:2604.02263v2 Announce Type: replace-cross
Abstract: We demonstrate that wave amplification enables even weak nonlinearities to reshape linear wave-packet transport in nonreciprocal systems. We study the dynamics of bulk Gaussian wave-packets in the Hatano--Nelson model with on-site cubic nonlinearity. We show that the interplay between nonlinearity and amplification generates growing frequency shifts that drive the wave-packet through three successive dynamical regimes: an early nonlinear-skin regime with coherent propagation, an intermediate wave-mixing regime driven by eigenmode resonances, and a self-trapping regime in which part of the packet localizes while the remainder ballistically spreads along the system favored direction. The crossover time scales are set by the width and averaged spacing of the eigenfrequency spectrum. Crucially, within the nonlinear-skin regime, we derive analytical predictions for the wave-packet dynamics and show that nonlinearity couples amplification, dispersion, and nonreciprocity, thereby modifying the magnitude of the wave-packet acceleration and introducing an explicit time dependence into its evolution. Focusing nonlinearities suppress the acceleration and cause it to decrease in time, whereas defocusing nonlinearities enhance it and cause it to increase. We further show that nonlinear interactions typically break down the wave-packet before the non-Hermitian jump can occur. Our results provide a route toward accurate control of waves in nonreciprocal metamaterials.
arXiv:2607.14952v2 Announce Type: replace
Abstract: A widening gap separates million-token inference from RL post-training, which remains at 256K tokens or below. The gap matters for AI agents, whose observations, tool outputs, documents, and decisions accumulate over long trajectories. Unlike inference, GRPO scores and backpropagates through multiple responses conditioned on one history, making attention and long-lived backward state a primary GPU-memory barrier.
We present LongStraw, an objective- and architecture-aware system for million-token RL post-training under a fixed GPU budget. Resident state retains only model-native prompt state needed by later tokens, not the full graph. Response replay restores that state, scores graph-free old/reference branches, rebuilds one policy response under autograd, backpropagates, and pops to the prompt boundary. Distributed, model-native execution assigns state and gradients to context and expert owners. State is shared within a group and recaptured or reused under a measured refresh policy after an update.
For Qwen3.6-27B, LongStraw combines compact GDN state, CP8-sharded KV pages, exact attention composition, and reverse block replay. For GLM-5.2, it combines CPU-resident MLA/DSA state, IndexShare-aware selection, and native top-8 MoE replay over CP32/EP32. On eight H20 GPUs, Qwen completes exact-attention response-only GRPO at 2,097,152 positions for G=2 and G=8; a 4,456,448-position prefix supports eight G=8 cycles (64 replays) at 83.894 GB per rank. On 32 H20 GPUs, GLM completes deterministic 2M execution and two 78-layer backward passes; archived external integrations provide preliminary validation of the real vLLM-DAPO-Tinker/Megatron loop. Practical training context is set by resident-state lifetime, replay, and distributed ownership rather than attention kernels alone. The measured objective is response-only execution, not full-sequence gradient equivalence.
arXiv:2604.18531v2 Announce Type: replace-cross
Abstract: AtomTwin$.$jl is an open-source Julia package for developing and simulating quantum protocols, hardware configurations and building digital twins for neutral-atom quantum processors and related atomic quantum devices. AtomTwin operates between mathematical models and physical devices; modeling atoms, optical tweezers, laser fields, atomic motion, interactions, and noise processes natively from physical geometry and parameters, without requiring users to define Hamiltonians manually. The package provides hardware-level instruction sequences, high-performance solvers for coupled quantum and classical dynamics, and a ready-to-use model for ytterbium-171 atoms in an extensible framework designed to accommodate a greater variety of atomic species and hardware components in the future. This paper describes the software architecture, performance benchmarks against existing toolboxes, and a demonstrated end-to-end application: preparation of a logical Bell state in the $[[4,2,2]]$ error-detecting code with four $^{171}$Yb atoms in moveable tweezers.
arXiv:2111.05554v5 Announce Type: replace-cross
Abstract: Recent advancements in strong single-photon optomechanical coupling also demand a deeper understanding of environmental interactions in this regime.In this regime the standard Lindblad master equation, which is derived in the eigenbasis of the bare optical and mechanical modes, misassigns the dephasing rate. We therefore use the Dressed-State Master Equation (DSME), which is formulated in the eigenbasis of the strongly coupled photon-phonon Hamiltonian, the dressed states of the system. This work investigates the impact of squeezed vacuum and thermal reservoirs on the decoherence of cavity photon Fock states in the strong coupling regime. We demonstrate that decoherence can be effectively controlled by tuning reservoir parameters, with the control mediated through a cavity dephasing term that becomes significant at high temperatures. The findings presented provide critical insights into reservoir engineering for precise control of quantum decoherence, advancing the understanding of strongly coupled optomechanical systems in engineered environments.
arXiv:2505.00462v2 Announce Type: replace-cross
Abstract: We develop CorStitch, a video-stitching software that automates the process of stitching underwater videos for coral reef monitoring and assessment. It offers a free, flexible, and user-friendly alternative to existing stitching software that may be difficult to access. CorStitch utilizes a Fourier-based image registration algorithm to stitch the central horizontal strips of successive frames of down-looking belt and dive transect videos, generating georeferenced and marked mosaics. Tests show that CorStitch can produce high-quality mosaics that are comparable to those generated by existing stitching software, with the added advantage of being open-source and accessible to users with varying levels of technical expertise. CorStitch has the potential to supplement the coral reef monitoring efforts of local communities, government agencies, and non-governmental organizations.
arXiv:2510.08093v2 Announce Type: replace-cross
Abstract: The present note studies \emph{surjective rational endomorphisms} $f: \mathbb{P}^2 \dashrightarrow \mathbb{P}^2$ with \emph{cubic} terms and the indeterminacy locus $I_f \ne \emptyset$. We develop an experimental approach, based on some Python programming and Machine Learning, towards the classification of such maps; a couple of new explicit $f$ is constructed in this way. We also prove (via pure projective geometry) that a general non-regular cubic endomorphism $f$ of $\mathbb{P}^2$ is surjective if and only if the set $I_f$ has cardinality at least $3$.
arXiv:2505.13518v3 Announce Type: replace-cross
Abstract: Imbalanced datasets, where one class significantly outnumbers others, remain a persistent challenge in machine learning, often biasing predictions toward the majority class and degrading classifier performance. This paper provides a comprehensive, systematic review of data balancing methods, extending beyond foundational oversampling techniques such as the Synthetic Minority Oversampling Technique (SMOTE) and its variants (e.g., Borderline SMOTE, K-Means SMOTE, and Safe-Level SMOTE) to encompass advanced adaptive methods (MWMOTE, AMDO), deep generative models (generative adversarial networks, variational autoencoders, and diffusion models), undersampling techniques (NearMiss, Tomek Links), combination/hybrid methods (SMOTE-ENN, SMOTE-Tomek, and SMOTE+OCSVM), ensemble strategies (SMOTEBoost, RUSBoost, Balanced Random Forest, and One-Sided Selection), and specialized approaches for multi-label and clustered data. Beyond descriptive categorization, this review critically examines each method's underlying assumptions, operational mechanisms, and suitability for diverse data characteristics, including high dimensionality, mixed feature types, class overlap, and noise. Key findings demonstrate that no single method universally outperforms others; optimal selection depends critically on dataset characteristics, classifier choice, and evaluation metrics. The paper concludes by identifying emerging research directions, including self-supervised learning for imbalance, diffusion-based generative oversampling, distribution-preserving resampling, knowledge distillation for imbalanced deployment, and the adaptation of foundation models to skewed distributions, offering practical guidelines for practitioners and a roadmap for future methodological development.
arXiv:2604.00930v2 Announce Type: replace-cross
Abstract: The phase transition in the Vicsek model is widely believed to be associated with spontaneous symmetry breaking of the two-dimensional rotational symmetry $\mathrm{O} (2)$.
In this paper, we revisit the original Vicsek model introduced by Vicsek \textit{et al.} [Phys.~Rev.~Lett.~75,~1226~(1995)] and demonstrate that the original angle-based update rule is not invariant under global phase shifts at the level of angular increments when it is implemented using the principal-value arctangent, as in the original definition.
As a consequence, we numerically demonstrate that the phase transition reported in the original paper vanishes when the global phase is adaptively chosen.
arXiv:2604.15031v2 Announce Type: replace-cross
Abstract: We develop a hypergraph container method for the Boolean Satisfiability Problem (SAT) via the newly developed container results [Campos and Samotij (2026)]. This provides an explicit connection between the extent of spread of clauses and the efficiency of container-based algorithms. Informally, the more evenly the clauses are distributed, the stronger the shrinking effect of the containers, which leads to faster algorithms for SAT.
To quantify the extent of spread, we use a weighted point of view, in which a clause of size $s$ receives weight $p^s$ for some $0<p\le 1$.In this way, we introduce the notion of $(\lambda,p)_k$-structure for SAT formulas, where $\lambda$ is the spread parameter and $k$ is the maximum size of clauses. By the almost-independence property of containers, we prove that for formulas with $(\lambda,p)_k$-structures, one can distinguish between ``unsatisfiable formulas'' and ``formulas satisfying at least a $(1-\delta)$-fraction of clauses'' in sub-exponential time. This shows that sufficiently spread formulas are not worst-case instances for Gap-ETH. Moreover, we show that the speedup is directly controlled by the spread parameter $\lambda$, yielding faster exact algorithms for SAT formulas containing a $(\lambda,p)_k$-structure. This result extends previous work [Zamir (STOC 2023)] to the non-uniform case.
arXiv:2606.25824v2 Announce Type: replace-cross
Abstract: A method for testing the hypothesis of an ultrametric organization of the energy landscape of RNA secondary structures is proposed, based on the analysis of the kinetics of transitions between basins of attraction. The method is based on a kinetic metric constructed from the spectral decomposition of the symmetrized Kramers transition rate matrix and the Mahalanobis distance, and it is not an ultrametric by construction. A computational scheme has been developed that includes automatic filtering of noise eigenmodes and a procedure for analyzing disconnected structure graphs. The performance of the method is demonstrated on a sample of reference and random RNAs.
arXiv:2605.04344v2 Announce Type: replace-cross
Abstract: This paper develops a statistical theory of extrapolation for large language models, by reinterpreting them through pre-post-additive noise models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we introduce a perturbation-based procedure that first transforms the prefix into a semantic neighbour and then conditions on this perturbed variant for next-token prediction. This yields a hierarchical model with a pre-post-additive noise structure. Within this framework, we develop a rigorous theory of extrapolability, namely, the capacity of a model class to make reliable predictions for token sequences that lie outside the empirical support of the training corpus, by establishing five properties of the proposed procedure: adaptivity, contractivity, robustness, extrapolability, and double robustness. We evaluate the finite sample performance of the proposed procedure using both synthetic and real world language data. Results show that the proposed method consistently improves out-of-support prediction while maintaining competitive in-support performance, demonstrating that perturbation offers a practical route to language modelling.
arXiv:2605.25811v2 Announce Type: replace-cross
Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure. Standard isotropic smoothing ignores this geometry, leading to unfavorable scaling and unstable local inference. We propose semiparametrically debiased, diffusion-guided estimators for smoothed counterfactual densities and their scores. These estimators combine causal nuisance adjustment with geometry-adaptive localization driven by a learned diffusion score, yielding second-order nuisance remainders while aligning smoothing with local outcome geometry. We derive asymptotic expansions, integrated risk bounds, and simultaneous inference for smoothed densities and Stein functionals, with extensions to ambient density and score targets under additional approximation conditions. The variance term in the risk bounds is governed by the concentration of the smoothing operator: suitable geometric conditions yield intrinsic rather than ambient scaling, while an explicit drift term quantifies the cost of estimating the geometry. CelebA-based semi-synthetic experiments show faster error decay and improved stability for geometry-adaptive one-step methods, illustrating their applicability to high-dimensional embeddings.