Papers

Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals supported on fixed graphs, e.g., road-network traffic and sensor-network measurements. Many graph signals have nonuniform spectral energy, whereas isotropic corruption adds the same conditional noise variance to every graph-frequency mode. Driving all modes to near-zero terminal signal-to-noise ratio (SNR) requires strong corruption, which increases the noise range that must be covered under a fixed sampling budget. We introduce Graph Residual Conjugate Diffusion (GRCD), which replaces the shared clock of graph heat diffusion with a mode-dependent clock that gives every graph-Fourier mode the same conditional SNR. GRCD fits a zero-mean graph-spectral Gaussian reference on the training split and stops at a finite terminal SNR at which the propagated reference still carries the fitted spectral variances. The Gaussian component has an exact modewise propagator in the probability-flow ODE, so sampling advances it analytically and integrates only the learned residual score numerically. We evaluate GRCD on five settings (METR-LA traffic, Molene weather, and three stochastic block models) against seven comparators under a matched protocol: Graph-Aware Diffusion (GAD), EDM (graph backbone), two adaptations of Whitened Score Diffusion (WSD), and three preconditioning controls. At four function evaluations (NFEs), GRCD lowers averaged maximum mean discrepancy (aMMD) by 22 to 36 times over the best comparator on all five settings, reaching 0.054 on METR-LA, where it clears an aMMD 0.1 target with 87% less sampling wall-clock time than the cheapest comparator that reaches it. Fitting the terminal reference reduces aMMD by 2.7 to 7.3 times at finite terminal SNR, while the factors shrink to 1.00 to 1.01 near zero.

Distilling pretrained foundation models into an autoencoder bottleneck improves latent diffusability, enabling diffusion models to converge faster and reach higher sample quality. Standard distillation aligns the latent at each position to a co-located teacher feature, tying the latent layout to the teacher's. We show this constraint is unnecessary: aligning a single pooled image-level descriptor to the teacher's performs as well as or slightly better than dense position-wise distillation. We compare first-order and relational pooled objectives across latent shapes and teacher modalities. First-order matching extends naturally to 1D token-sequence latents and across modalities, where distilling a text encoder into an image autoencoder still improves diffusability; a relational objective based only on each image's nearest neighbours improves it as well. Code and blog post are available at https://github.com/AdrienRR/structure-agnostic-distillation and https://kyutai.org/blog/2026-09-28-structure-agnostic-distillation/.

We prove that, for every fixed nonempty graph $H$, induced-$H$-freeness is testable with $\varepsilon^{-O_H(1)}$ queries on outerplanar graphs with no maximum-degree bound in the $\textit{random-neighbor model}$, where each query at a vertex returns a uniformly random neighbor. Thus, the query complexity is polynomial in $1/\varepsilon$ and independent of the number $n$ of vertices. Previously, the best bound known for this problem was the $\operatorname{poly}(\log n)$-query guarantee that follows from the general outerplanar-graph tester of Babu, Khoury, and Newman (2016) in the stronger $\textit{adjacency-list model}$, which provides exact degree queries and indexed access to neighbors. Our tester has $\textit{two-sided error}$, which is necessary in general: induced-$P_3$-freeness has no one-sided constant-query tester in the random-neighbor model, even on outerplanar graphs of maximum degree two.

Motivated by questions arising in noncommutative Iwasawa theory, let $R$ be a (not necessarily commutative) ring, $T \in R$ a regular central element, and $M$ a pseudo-null $R$-module. We investigate necessary and sufficient conditions under which the quotient $M/TM$ is pseudo-null as an $R/TR$-module. We first give necessary and sufficient conditions in terms of associated prime ideals when $R$ is commutative. Then we apply this to the case when $R$ is a Krull domain and obtain a precise relationship between the characteristic ideals of $M/TM$ and the $T$-torsion submodule $M[T]$. We give necessary and sufficient conditions in terms of $\operatorname{Ext}$ groups when $R$ is a noncommutative ring and then compare them with the criterion when $R$ is commutative. Lastly, we give an application to noncommutative Iwasawa theory. Roughly speaking, if `big' dual fine Selmer group is pseudo-null, then `most' specialized dual fine Selmer group is pseudo-null.

Inferring the entropy production rate $\sigma$ from recorded trajectories is a key challenge in stochastic thermodynamics. In experiments, the forces governing the dynamics are usually unknown and often only some of the system's degrees of freedom can be observed. Building on a recently introduced method [I. Di Terlizzi, Phys. Rev. Lett. 135, 237101 (2025)], we develop and validate CYNAR (computation yields nonequilibrium analysis and reconstruction), a pipeline that estimates $\sigma$ from trajectories. It exploits a kinetic decomposition of $\sigma$ into a traffic term ${\cal T}$, inferred from the short-time curvature of correlation functions, and an inflow rate ${\cal G}$, computed from the steady-state score, i.e., the gradient of the log-density. We show that the same decomposition, evaluated on any subset of observed coordinates, always bounds $\sigma$ from below, for any diffusion tensor and without knowledge of the hidden degrees of freedom. We then compare CYNAR with a more standard approach that estimates $\sigma$ from steady-state probability currents, on four systems of increasing complexity. CYNAR proves to be more reliable, with no detectable bias close to equilibrium, weak dependence on spatial discretization, and marked robustness to measurement noise. It is also readily applicable to high-dimensional systems, where the traffic alone provides a lower bound close to $\sigma$, and remains informative under partial observation, including cases where the flux-based estimate vanishes identically. CYNAR is provided as an open-source Python package.

A measurement is presented of the triple-differential production cross section of Z/$\gamma^*$($\to$ $\mu\mu$)+jet events using proton-proton collision data recorded at a center-of-mass energy of 13 TeV by the CMS experiment at the CERN LHC. The data, collected in the years 2016$-$2018, correspond to an integrated luminosity of 138 fb$^{-1}$. The cross section is measured as a function of the transverse momentum of the muon pair, the boost in rapidity of the center-of-mass system of the muon pair and the leading jet with respect to the laboratory frame, and half of their absolute rapidity separation. This choice of observables ensures sensitivity to the scattering angle in the center-of-mass frame and the fractional momenta of the interacting partons. After unfolding for detector effects in all three dimensions simultaneously, the results are compared with predictions at next-to-next-to-leading order in perturbative quantum chromodynamics corrected for electroweak and nonperturbative effects. This measurement provides valuable information towards characterizing the partonic structure of the proton and determining the strong coupling.

Distributed manipulator systems manipulate objects through the coordinated motion of many actuators. However, an object must be supported by several actuators at once, so the centre-to-centre actuator spacing imposes a hard lower bound on manipulable object size. We remove this bound by coupling the end-effectors of an 8 x 8 array of three degrees-of-freedom delta robots with a stretchable fabric, turning 64 discrete contacts into a continuous surface capable of manipulating objects smaller than the actuator spacing. Viewing the array as a displacement field over that surface, we investigate local quasi-static and cyclic fields as manipulation primitives. These primitives can be applied globally across the array or locally confined around each tracked object to independently manipulate several objects in parallel. We then train a policy acting on low-order discrete cosine transform coefficients: at equal action dimension, commanding a nineteen-delta neighbourhood halves the placement error of commanding the whole array. The policy transfers to hardware without adaptation at 76% success. The platform manipulates objects from 15mm-90mm, a six-fold range spanning both sides of the actuator spacing, 43.3mm, on a single surface.

Audio deepfake detectors are typically evaluated on uncompressed audio, although real-world audio often undergoes low-bitrate coding. In this work, we investigate how audio coding affects deepfake detection across codecs, bitrates, and detectors, finding higher errors at lower rates. A mixed-pair protocol isolates codec-induced changes in bona fide and spoof audio, revealing asymmetric, codec-dependent failures: low-rate DAC and EnCodec mainly degrade bona fide detection, whereas X-Codec shows a stronger spoof-side limitation. Motivated by these, we propose a forensic-preserving neural audio codec (FP-NAC), which fine-tunes a pretrained codec using a detector-guided objective while preserving its native hard quantization path and bitrate. On ASVspoof 2019 LA, FP-NAC reduces EER by up to 49.8~pp compared with the original DAC at 0.5~kbps while maintaining comparable reconstruction quality. Although supervised by only one detector, FP-NAC improves performance across multiple detectors, highlighting forensic transparency as a codec design objective alongside perceptual quality. Our codes are available at https://github.com/kjungwoo03/FP-NAC.

Avalanche-based detection of small perturbations is commonplace in precision measurement devices from Geiger counters to single-photon avalanche detectors. Here, we expand this principle to sensing of light waves below the quantum shot noise limit, demonstrating numerically how atomic clouds trapped in photonic cavities can exhibit non-perturbative sensitivity to changes in the cavity field when the cavity mode is tuned to a parity-prohibited transition. We find that, when pumped by a continuous-wave laser, the atomic cloud creates emissions which amplify the initially sub-shot-noise fluctuation by two orders of magnitude. Crucially, this amplification is broadly tunable with respect to frequency and independent of atomic energy structure. Even more strikingly, our amplification mechanism preserves the phase imparted on the atoms by the original ultra-weak light wave, marking a qualitative improvement over conventional protocols. Our finding has implications for both quantum state characterization and detection of weak classical signals.

Video super-resolution (VSR) is normally judged by PSNR and SSIM on clips that were downsampled bicubically, although in surveillance its purpose is to make faces and licence plates recognisable. We present FANVIDv2, a benchmark that scores VSR by what a recognition pipeline can do with its output. FANVIDv2 provides $320\times180$ low-resolution (LR) clips with high-resolution (HR) references for 48 public figures (with one HR gallery image each) and 375 licence-plate clips covering 360 distinct plate strings. LR clips are generated with a randomised compound degradation (blur, resize jitter, sensor noise, JPEG compression, final downsampling) rather than bicubic downsampling alone. Two metrics score recognition inside detections: FaceRecBox rewards a face only if it is localised and correctly identified, and TextRecBox scores plate transcriptions by normalised edit distance weighted by localisation quality. With a 2.3\,M-parameter VSR baseline (RCDM), FaceRecBox rises from 0.6864 to 0.7222, identity accuracy on matched faces from 84.35% to 86.93%, and TextRecBox from 0.3088 to 0.3667; a residual-map gated variant (RCDM-RMGF) reaches 0.3801 on plates. We describe the degradation model, the baseline architectures and the scorers in detail, and release annotations, metadata, download and degradation scripts and evaluation code.

Diffusion models are typically viewed as stochastic processes that transform noise into data. We take a complementary perspective: a diffusion model defines a family of deterministic dynamical systems indexed by noise scale. At each fixed scale $\sigma$, we treat the denoiser as a self-map and study its dynamics. For an exact denoiser, fixed points correspond to critical points of the smoothed data density, while attractors correspond to its modes; as $\sigma$ increases, sample-level modes merge into progressively coarser ones. This suggests a geometric view of memorization: examples that receive excess probability mass due to duplication or overfitting, as well as outliers, should remain distinguishable under stronger smoothing than ordinary examples. We quantify this persistence by the critical scale $\sigma_c$, the largest noise scale at which an example is retained by the fixed-scale dynamics. In conditional models, the same construction extends naturally to image–caption pairs. Experiments in controlled settings and on large-scale models show that $\sigma_c$ tracks memorization arising from duplication, overfitting, and outliers, and identifies both memorized and partially memorized examples in Stable Diffusion. Moreover, $\sigma_c$ yields interpretable measures of the image spatial distribution and caption dependence of memorization.

We study exclusive diffractive electroproduction of the $\rho^0$, $\phi$, $J/\psi$, and $\psi(2S)$ mesons in the color-dipole picture using two spin-orbit light-front wave functions, S-1 and S-2. S-1 follows from the Melosh–Wigner rotation in the light-front quark model (LFQM), while S-2 is the spin-improved form commonly used in holographic and boosted-Gaussian approaches. Both share the same radial wave function, with their parameters determined from the LFQM Hamiltonian. The color-glass-condensate dipole parameters are fixed from inclusive structure-function data, with no fit to diffractive data. We compare the predictions with measurements of cross sections, $R=\sigma_L/\sigma_T$, $t$ and $W$ dependences, and $\sigma_\phi/\sigma_\rho$. S-1 gives a better description of the light-meson observables, while S-2 provides a better description of the charmonium ratio $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ and the $J/\psi$ decay constant. We also present the charge, magnetic, and quadrupole form factors of the four mesons and compare them with available lattice-QCD results.

Federated learning faces severe communication bottlenecks when clients upload high-dimensional model updates. Existing methods often compress these updates uniformly across all layers. This uniform approach ignores the heterogeneous value of different parameter blocks and wastes limited bandwidth on insensitive layers. To address this issue, we propose Layer-wise Budgeted Adaptive Transmission (LBAT). LBAT reframes federated communication under extreme uplink budgets as a resource allocation problem. Our framework dynamically estimates the transmission value of different layers utilising local training signals. It then employs an exact byte dynamic programming allocator to determine optimal rank and bit configurations under strict budgets. We validate LBAT on highly heterogeneous federated tabular prediction and data generation tasks. Extensive experiments demonstrate that LBAT consistently outperforms uniform rank, uniform quantisation, and fixed compression baselines across various extreme budget regimes. Furthermore, it achieves significantly better communication and utility tradeoffs while preserving essential distributional fidelity.

Multi-agent collaboration lets large language models (LLMs) improve question answering through deliberation and feedback. Yet shared discussion couples correction with exposure to the same mistakes, which can erode the diversity needed for voting. Self-consistency offers sampling diversity without feedback, while single-pair Actor-Critic collaboration refines only one candidate. We introduce SEPAL, which assigns three private Actor-Critic teams to direct reasoning, evidence grounding, and verification. Role-specific training gives the teams different reasoning objectives beyond sampling variation. Each Critic guides revisions within its own team, preventing feedback from carrying errors across candidates. Once revision ends, majority voting combines only the final answers, keeping the reasoning histories separate until the decision. Across five open-weight backbones and five question-answering benchmarks, SEPAL improves mean accuracy by 1.81 percentage points over a matched single Actor-Critic pair, with improvements across all five backbones. Code is available at https://github.com/zhansan114514/SEPAL.

Ribosome profiling (Ribo-seq) measures ribosome distributions along mRNAs, but observed occupancy profiles also contain experiment-specific distortions and stochastic variability. Consequently, models that accurately predict measured profiles may reproduce technical effects rather than recover the underlying biology. We ask whether jointly modeling datasets collected under different experimental conditions can reveal shared, sequence-dependent patterns of ribosome occupancy. We introduce RiboUnmix, a probabilistic multi-dataset framework in which each expected measured profile is represented as a shared sequence-dependent signal modulated by a dataset-specific multiplicative factor. A negative-binomial observation model captures variability across replicates. We evaluate RiboUnmix on a controlled synthetic benchmark combining programmed translation kinetics, ribosome traffic, stochastic count sampling, and sequence-dependent experimental distortions. Because the underlying kinetics and distortions are known, recovery of the shared profile and dataset-specific effects can be assessed separately. Both inferred components correlate strongly with their targets, demonstrating that RiboUnmix can disentangle shared kinetic patterns from experimental effects. Across four organism-specific real-data benchmarks, RiboUnmix outperforms sequence-to-profile baselines in predicting measured profiles. Models trained independently on subsets of 114 HEK-derived datasets recover concordant shared profiles for held-out transcripts, and experiments varying the number and composition of training datasets show that the learned representation remains stable. RiboUnmix thus converts variation across experiments into evidence for reproducible sequence-dependent patterns of ribosome occupancy, supporting biological hypothesis generation from diverse Ribo-seq datasets.

This paper constructs explicit closed-form Green's functions for the Helmholtz equation on annular and spherical-shell domains with two independent Robin impedances on the inner and outer boundaries. Graf's and the hyperspherical addition theorems reduce each angular mode to an explicit $2\times2$ linear system, and the resonance spectrum is governed by a characteristic determinant bilinear in the two impedances. This bilinearity has a direct inverse-problem consequence: two resonant frequencies of one non-radial angular mode generate at most two candidate impedance pairs via an explicit quadratic equation, a third resonance selects the physical pair, and an exact reflection-symmetry obstruction identifies where the radial spherical mode cannot recover the impedances. Spectrally, we prove the branches positive, simple and strictly increasing in both impedances; derive first-order asymptotics at the four corners of the impedance plane, with coefficients given by boundary masses and normal derivatives of the limiting eigenfunctions, and an explicit mixed second-order coefficient at the Dirichlet–Dirichlet corner, which for the radial mode evaluates in closed form to $2\pi/(R_2-R_1)^3$; establish a low-frequency resonance-free band, with a second-order threshold expansion explicit in dimension three and a rational approximation accurate over the whole impedance range; and prove the universal high-frequency spacing law with a shell-curvature correction. Jacobian-based sensitivity and conditioning criteria are included. The kernels and spectra are computable to machine precision, all asymptotic regimes are confirmed numerically, and the kernels provide reference solutions for finite-element and boundary-element validation.

A technical condition arising in the analysis of atomistic models for dislocations is studied. Key estimates for the far-field strain behaviour proved in Ehrlacher, Ortner, Shapeev (2016) rely on a summation-by-parts argument for linearised forces, under conditions of sufficient decay and of vanishing net force in an infinite system. In particular, the latter condition is required for an application of this theory to the standard far-field dislocation predictor, but the vanishing of the associated force sum has not been fully justified. Here, the missing verification of this condition is provided and its role in determining the far-field decay of the corrector is clarified. It is moreover shown that for more general physically compatible predictors, the linearised force sum need not vanish, leading to slower decay and potentially divergent finite-domain approximations.

Problems developed for a mathematics circle conducted throughout the school year in a primary school class, involving all pupils without any selection, thus working with a heterogeneous group of children.

Cross-lingual transfer describes how knowledge in a source language benefits a target language. Measuring it quantitatively requires broad multilingual pre-training, as prior work has done with cross-lingual transfer matrices. We ask whether transfer is predictable from freely available typological features, and whether the prominence of high-resource source languages reflects typology or data quality and quantity. We show that typological databases contain cheap and dense signals about cross-lingual transfer. Our typology-only random forest on a 24-language prior-work transfer matrix scores leave-one-language-out $\rho{=}0.705$ and $R^2{=}0.49$, against $\rho{=}0.62$ for a tuned non-typological control, an increment that a paired bootstrap cannot separate at this scale. When both languages of a held-out pair are unseen, performance degrades to $\rho{\approx}0.41$, so the model interpolates a ground-truth matrix more reliably than it predicts new languages. The signal survives leave-one-script-out and leave-one-family-out protocols, so script and family confounding do not explain the effect. By decomposing the transfer into a typology term and a resource-and-script bias term, we find the best-source ranking sensitive to this bias. Typological features never observe this bias, which makes them a zero-compute screening tool that replaces hundreds of training runs with a model fit. Our code is available \href{https://github.com/dharmsen/typo-x-ling-transfer}{here}.

Tabular learning uses structured data to predict target outcomes. Traditionally, this process has relied on labeled data. However, large language models (LLMs) can be used to elicit domain priors based on the task description and feature semantics, thereby enabling predictions without labeled data. We propose Marginal Response Surface Elicitation (MARS), a method that transforms feature-level LLM priors into a reusable, zero-shot tabular classifier. To construct this classifier, MARS selects representative values for each feature from unlabeled data and prompts the LLM to provide corresponding class support scores and feature weights. It then aggregates multiple responses using the median to construct feature response functions, and makes predictions through their weighted sum without further LLM queries. Across eight tabular benchmark tasks, MARS achieves the highest average AUC and AP, outperforming direct prompting by 1.97 and 6.21 percentage points respectively, while substantially reducing end-to-end costs. Evaluations with LLMs of different sizes further demonstrate its predictive advantage over direct prompting.

The Dirac equation in stationary curved spacetime implies that describing two-flavor neutrino oscillations requires treating the invariant mass and conserved energy of each propagating state distinctly, as gravity affects energy differently than mass. By re-analysing the publicly released KamLAND dataset, we show that modeling flavor states of massless neutrinos as two-level quantum states with energy-dependent level splitting, analogous to modified Jaynes-Cummings models, results in a higher-likelihood fit to the observed data than the standard massive-neutrino paradigm.

A central question in deploying teams of mobile robots for persistent monitoring is how task performance scales with fleet size, and whether this scaling holds once sensing drives downstream action rather than mere observation. We study this question for a team of drones performing traffic-jam detection and prediction in a simulated road network, whose reports drive an adaptive traffic-signal controller in closed loop. We build a multi-agent simulation, with vehicles following Nagel-Schreckenberg cellular-automaton dynamics and drones patrolling junctions via a round-robin policy, and sweep fleet size, traffic level, and network size to evaluate detection rate, detection delay, and prediction rate. We show how performance plateaus for fleet size approximating the number of junctions being monitored, and offer a general fleet-provisioning rule for persistent-monitoring deployments. More significantly, adapting the signal on a predicted jam, rather than a detected one, roughly doubles the resulting reduction in jam duration, showing that the value of onboard prediction in a sensing-to-action pipeline can exceed the value of adding more robots. Prediction accuracy, not sensing coverage, is now the binding constraint on further improvement, pointing to onboard inference, not fleet size, as the more promising direction for future work.

We determine the exact number, up to rotations, of nonconstant positive $C^2$ solutions to the planar isotropic $L_p$ dual Minkowski problem for every $(p, q) \in \mathbb{R}^2$. We obtain a new parametrization of the associated period integral, characterize the regions where the period is strictly increasing or strictly decreasing, and prove that in the remaining nonmonotone region it has a unique nondegenerate maximum. As a consequence, we have a complete classification.

Given a target dataset, such as faces with eyeglasses, and a background dataset, such as faces without, contrastive analysis separates salient factors specific to the target from common content shared by both. We aim for salient representations that capture target-specific detail in each image, such as the shape, color, and position of the glasses, so that they reveal subtypes without subtype labels and guide the generation of new examples of a discovered subtype, even one with no name or text description. We introduce SAGE, which learns both factors directly in the high-dimensional spatial latent of a frozen representation autoencoder and conditions a diffusion transformer on the learned salient representation of a reference image. On Digits-ImageNet and FFHQ eyeglasses, SAGE combines high-fidelity reconstruction (rFID below $2$) with unsupervised subtype discovery, recovering the digits better than baselines (probe accuracy $0.950$ vs.\ at most $0.281$) and revealing eyewear types, finer sunglasses styles, and mislabeled images; salient-conditioned generation raises Digits-ImageNet subtype accuracy over the unfactorized latent ($90.5\%$ vs.\ $27.7\%$) and diversity on both datasets. On retinal OCT, SAGE's salient space separates three diseases using only normal/disease labels.

Common policy improvement methods, including TRPO, PPO, and GRPO, estimate policy improvement under the behavioral policy's state-visitation distribution rather than the improved policy's own. The substitution makes the objective estimable from the behavioral policy's rollouts but adds a bias growing with policy divergence, hence the trust region or clip, and hence no reuse of a batch far off-policy. We show that under history-injective dynamics, where each state is reached by exactly one history, the dropped state-visitation ratio equals the product of per-step policy ratios along the sampled prefix, on every trajectory and not only in expectation. The ratio is therefore restored exactly, from log-probabilities PPO already computes. Autoregressive generation and canonical-order constructive optimization are both history-injective. The exact correction pays importance-sampling variance that grows with the horizon, so we generalize it to a one-parameter family with PPO ($\alpha{=}0$) and the full correction ($\alpha{=}1$) as endpoints: a single bias–variance knob. A gradient-level analysis of the unclipped surrogate identifies two channels the correction acts through and three conditions under which it carries signal; an enumerable testbed confirms the conditions' predictions. On hard credit-assignment scheduling tasks, a short corrected warmup with aggressive early sample reuse learns faster than PPO and than the same reuse uncorrected; the marginal gain grows with task difficulty ($+0.02$ to $+0.09$ learning-curve AUC), and the early win over PPO tracks the prefix bias that reuse incurs. A correction held throughout, or applied where clipping already contains the reuse bias, is null to harmful.

We study a support-collapse version of graph pebbling on paths. A configuration is stackable if a sequence of legal pebbling moves can produce a nonzero configuration supported on a single vertex. On the path P_n, we choose a configuration uniformly from all weak compositions of total n times mu_n, where mu_n is a positive integer. We prove a two-sided fixed-offset transition for the logarithmic density. The transition is centred at sqrt(log_2 n) - (1/2) log_2 log_2 n + log_2(3e). For every fixed epsilon greater than zero, the stackability probability tends to zero when log_2 mu_n is eventually at most the centre minus epsilon, and tends to one when it is eventually at least the centre plus epsilon. No assertion is made at zero offset. The proof uses an exact recursive stackability score on trees, a one-dimensional path-message recurrence, binary-partition asymptotics for rare dyadic deficit excursions, a constant-cost regeneration argument, and an exact deep-message necessity theorem. Conditioning independent geometric occupancies on their sum returns the uniform fixed-total model. The finite deterministic necessity theorem and its exact fixed-total corollary are formalised in Lean and registered with Palomar; the full probabilistic asymptotic theorem is not part of that registration.

Test-time scaling improves language model reasoning by spending additional compute at inference. However, both classes of existing methods often fail to continue improving over long timescales. Parallel methods repeatedly sample independent answers from the model, scaling poorly on problems the model is unlikely to solve in a single attempt. In contrast, sequential methods build on previous answers to access new ideas, yet so far have not been shown to reach answers beyond those found by parallel scaling. First, we show that sequential scaling often stops improving because it becomes prematurely trapped in an attractor: a set of answers that prevents exploration of different answers once entered. Across 27 combinations of scaling methods, models, and benchmarks, we find that 53.8% of sequential scaling trajectories enter an attractor within four iterations. Second, we show that a simple model-mixing intervention helps escape attractors. This reduces the attractor hit rate by 21.2 percentage points on average, expands solution coverage beyond a compute-matched parallel baseline, and improves accuracy of recursive self-aggregation by at least 2.2 percentage points. Our results motivate refocusing long-horizon test-time scaling from parallel methods to sequential methods that improve previous answers.

Modern cloud computing infrastructure relies heavily on virtualization to provide workload isolation and resource efficiency. While containers have become the dominant deployment primitive due to their fast orchestration compared to traditional virtual machines, they still introduce non-trivial overhead. WebAssembly (Wasm) has emerged as an alternative isolation technology, offering a lightweight execution model. Because of compatibility limitations, WebAssembly has mainly been applied to Function-as-a-Service (FaaS) and Edge Computing scenarios, where it has attracted growing research interest. However, recent advances in the WebAssembly ecosystem have significantly matured the technology, raising the question of whether it can serve as a viable replacement for containers in cloud-native workloads. In this paper, we present Kirin, an orchestrator for cloud-native WebAssembly services. It supports core orchestration responsibilities, including resource scheduling, lifecycle management, scaling, and request routing. We evaluate Kirin against container-based deployments for several service workloads and demonstrate promising results, particularly in service lifecycle management. Simultaneously, we confirm known limitations in CPU-intensive workloads. However, for typical service workloads, Kirin demonstrates competitive performance, suggesting that WebAssembly is a viable candidate for broader adoption as a cloud-native deployment technology.

Pretrained tabular generators can reproduce training records even when aggregate utility remains high. When retraining is unavailable or too costly, sampling and release are the remaining intervention points. We present PEG-Tab (Post-Training Energy Guidance for Tabular Synthesis), a post-training repair and release-control framework for frozen tabular generators. For each generated row, a generator-native operator creates two alternatives. A shared calibrated score compares the three candidates, favours lower-risk records, and applies a final release check. We instantiate this interface for GReaT, CTGAN, TVAE, and TabDDPM without updating their parameters. Across five datasets and four generator families, PEG-Tab reduces mean Near Copy from $0.078$ to $0.027$ and lowers aggregate Exact Copy to zero. Relative to a $3\times$ post hoc filter, it retains higher utility in 12 of 16 transfer settings and Pareto-dominates the filter in eight. Gains are concentrated in copy and proximity-related risks.

Differential privacy (DP) in machine learning is typically achieved by adding noise to model parameters (private learning) or to model outputs (private prediction). Recent work uses formal methods, namely abstract interpretation, to provide tighter privacy guarantees, but only for private prediction in classification settings. In this work, we investigate the use of formal methods as a general tool for tighter privacy analysis. First, we generalize the abstract gradient training (AGT) framework to private prediction in continuous, unbounded regression. Second, by reducing learning in parameterized models to a regression problem over the parameter space, we introduce Abstract Gradient Sampling (AGS), an algorithm that enables reachability-based analysis to provide guarantees for private learning. In both private prediction and private learning, we provide tightened privacy accounting for the AGT framework and a theoretical analysis demonstrating when our smooth sensitivity upper-bounds yield favourable privacy-utility trade-off. In practice, we validate that our regression bounds are tighter than global-sensitivity baselines on regression benchmarks, and, notably, yield the first finite privacy guarantees in settings where global prediction sensitivity is a priori unbounded. We also find that under matched conditions, our private learning algorithm can outperform standard private learners.