arXiv:2607.15267v1 Announce Type: new
Abstract: Poisoning pretraining data can introduce harmful behaviors to LMs that are difficult to detect and mitigate. Prior work on poisoning pretraining data has largely exploited established data sources such as Wikipedia, which do not represent the large scale and heterogeneity typical of pretraining corpora, and has ignored the interaction between poisoned data and data curation pipelines. We demonstrate that poisoning attacks on pretraining data are feasible beyond this limited setting through an existing web-scale content injection mechanism: public discussion interfaces. Additionally, to measure whether malicious content is included after web crawling and data curation, we introduce HalfLife, a novel analysis for estimating adversarial content inclusion in web-crawl based LM training data. We use HalfLife to explore the feasibility of poisoning pretraining corpora at web scale through open discussion interfaces. Our analysis demonstrates the importance of estimating whether poison injections are included in pretraining data, and establishes third-party webpage content as a possible vector for attacking language model pretraining.
Science Journals
arXiv:2607.15268v1 Announce Type: new
Abstract: Myocardial infarction (MI) remains a leading cause of mortality worldwide. Echocardiography (Echo) is a widely available modality for MI assessment, where regional wall motion abnormality is a key indicator. Prior learning based methods for myocardial motion analysis often use handcrafted descriptors or densely supervised estimation, but the need for extensive annotation limits applicability. Foundation models have recently improved vision-based Echo analysis; however, most methods operate on single views and segment-level localization remains unreliable under view-dependent ambiguity, especially in apical views. To address this, we propose MCF-Net, a novel motion-guided multi-view fusion framework that fuses myocardial motion cues with foundation model representations to localize infarction. Visual features are extracted using EchoPrime, a pretrained Echo foundation model shared across dual views. Cardiac motion is modeled with extremely sparse supervision: a single annotated template frame is transferred across videos to initialize point tracking, avoiding dense labels. Motion-derived segment-aware soft masks provide coarse spatial priors that selectively enhance features for challenging myocardial segments. A motion-conditioned fusion mechanism then integrates motion and vision across views, refining predictions without overriding strong appearance cues. On segment-level MI localization, MCF-Net achieves 72.4\% F1 and 84.9\% accuracy, outperforming state-of-the-art motion-only, vision-only, and fusion baselines.
arXiv:2607.14293v1 Announce Type: cross
Abstract: Ionizing radiation from cosmic rays and gammas can induce discontinuous jumps in the environmental charge of superconducting qubits (charge jumps), causing correlated errors that challenge fault-tolerant quantum computing while simultaneously providing a detection signature for quantum sensing applications. Current detection methods operate offline, introducing latency incompatible with in-the-loop qubit control. In this paper, an online detector of charge jumps for superconducting qubits, based on a dilated causal convolutional neural network (DCCNN) designed for in-the-loop deployment on the Quantum Instrumentation Control Kit (QICK) platform, is presented. The network is trained on synthetic Ramsey tomography scans generated from qubit templates measured at the Northwestern Experimental Underground Site (NEXUS) at Fermilab, and translated to FPGA firmware via hls4ml with ap_fixed$\langle 16,6 \rangle$ quantization, reaching a per-inference latency of $6.19 \mu$s on the Zynq UltraScale+ RFSoC ZCU216. At this operating point the DCCNN matches the detection efficiency of the established offline $\chi^2$ algorithm ($0.843 \pm 0.022$ vs. $0.866 \pm 0.020$ on $|\Delta q| \in [0.1, 0.5] e$ at matched false-positive rate), while requiring no per-qubit hyperparameter tuning. This shifts charge-jump detection from a post-hoc diagnostic to a control-loop primitive, enabling adaptive protocols that respond to radiation-induced events in situ, with applications to quantum-computing error mitigation and to the use of superconducting qubits as particle detectors.
arXiv:2607.15272v1 Announce Type: new
Abstract: Editing the figures in a research paper is a routine and time-consuming part of everyday research practice: authors relabel components, rearrange panels, and restyle visuals as they revise their manuscripts. Automating this editing workflow under a natural-language instruction, however, is challenging, because a scientific figure is a dense infographic in which heterogeneous visual elements such as schematics, plots, photos, captions, and arrows are composed under a tight visual grammar to advance a specific argument. To address this, we present SciDiagramEdit, a benchmark and skill-evolution framework that learns from natural paper revisions and operates on the figure's editable vector source, where users can inspect and co-edit individual primitives alongside the agent. Our benchmark mines before/after figure pairs from arXiv version histories, each grounded in the authors' own revision intent. To accommodate the diversity of editing instructions, we adopt agentic learning via skill evolution: an agentic proposer continually refines the agent's skill specification from execution traces over multiple epochs. The resulting skill progressively lifts edit accuracy on a held-out validation set, providing evidence that natural paper revisions are an effective training signal for instruction-driven figure editing.
arXiv:2607.15206v1 Announce Type: new
Abstract: The paper considers the effect of degenerate higher-order mode (HOM) interaction, which may lead to the formation of trapped modes with high shunt impedance. Methods for eliminating these modes are discussed.
arXiv:2607.15229v1 Announce Type: new
Abstract: We develop data-driven algorithms for maintaining $N$ independent identical machines under a \textit{block replacement policy}, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$. The goal is to learn the cost-minimizing interval $k^*$ from operational data when the lifetime distribution is unknown. At each decision epoch, the operator selects $k \in \{1, 2, \ldots, K\}$, observes the resulting failure history (a mixture of complete and right-censored lifetimes) and incurs a per-unit-time cost governed by the renewal function. We formulate this as a stochastic multi-armed bandit and propose Hoeffding- and Bernstein-based lower-confidence-bound algorithms achieving $O(K \log T)$ regret, matching the Lai--Robbins lower bound. Exploiting a nested observation property unique to block replacement, correlated variants attain $O((K-k^*)\log T)$ regret and require only $O(1)$ direct pulls of suboptimal arms $k < k^*$. A complementary Kaplan--Meier renewal algorithm estimates the lifetime distribution nonparametrically from censored data, achieving almost-sure policy consistency and empirically near-zero incremental regret at long horizons. We additionally analyze two average-cost MDPs: a time-elapsed formulation establishing that block replacement is optimal within its policy class for any lifetime distribution, and an age-vector formulation proving a monotone threshold structure under increasing failure rate distributions and providing a gold-standard cost benchmark. Numerical experiments confirm the theoretical ordering and reveal structural cost gaps between optimal block and age-dependent replacement.
arXiv:2607.15273v1 Announce Type: new
Abstract: MeanFlow generators achieve fast few-step sampling by predicting average velocities over time intervals, making them attractive for efficient generation. Reinforcement learning (RL) has become a powerful way to align diffusion and flow models with human preferences and task-specific objectives. In particular, DiffusionNFT offers an efficient forward-process RL framework that does not require reverse-process trajectories or likelihood estimation. However, applying such RL methods to MeanFlow remains underexplored. DiffusionNFT optimizes instantaneous velocities, whereas MeanFlow samples with average velocities. To bridge this gap, we introduce MeanFlowNFT. Inspired by the MeanFlow identity, which bridges average and instantaneous velocities, we construct an induced instantaneous-velocity predictor. We apply the DiffusionNFT objective to this predictor, making reward optimization well-defined for MeanFlow. Sampling remains based on the average velocity, preserving MeanFlow's fast few-step generation. We further prove that MeanFlowNFT inherits DiffusionNFT's strict policy-improvement guarantee. Experiments on image and video generation show that MeanFlowNFT consistently improves baselines. Moreover, it outperforms prior state-of-the-art RL-tuned few-step generators on most metrics ($6$ of $8$ on SD3.5-M), and can even surpass multi-step RL-tuned diffusion while using only a few sampling steps. For instance, on Wan 2.1, $4$-step MeanFlowNFT reaches a VBench score of $84.33$, surpassing $50$-step LongCat-Video RL ($82.57$).
arXiv:2607.14122v1 Announce Type: cross
Abstract: We introduce the Generalized Neural Distributional Regression (GNDR) framework, which seamlessly embeds deep neural networks into the parameter space of classical probability distributions. To reconcile the inherent non-identifiability of deep architectures with maximum likelihood theory, we propose a two-step semi-parametric estimation procedure. By isolating the terminal prediction heads and treating the upstream network as a fixed, non-linear basis expansion, GNDR enables the extraction of analytical Fisher Information matrices. This facilitates rigorous uncertainty quantification, generating observation-specific confidence bands and tolerance intervals via the multivariate Delta method. We demonstrate the framework's versatility and superior distributional calibration across diverse data modalities, including overdispersed clinical counts, right-censored transcriptomic survival profiles under a mixture cure framework, and zero-truncated age distributions derived directly from unstructured facial images. The methodology is natively implemented in the open-source Python package \textit{thetaflow}.
arXiv:2607.15232v1 Announce Type: new
Abstract: A tokenizer fixed at the start of pre-training allocates vocabulary in proportion to the pre-training corpus, reflecting the deployment priorities at that time. When those priorities shift, languages added later are split into many more tokens per word, which can raise latency, compute, and energy consumption for users of those languages. Cloud models can afford a broad vocabulary because the embedding and LM-head matrices are a small fraction of their parameters. On a compact model those matrices are a material share of per-token decode bandwidth, so on-device models ship small vocabularies and accept fragmentation outside a fixed language set. We present tokenizer expansion, an in-place recipe for upgrading a pre-trained model's tokenizer when the model producer controls its design. We continue the existing tokenizer's BPE merges on a multilingual corpus, so most source tokens carry over unchanged as single tokens and every new token has an exact decomposition into source tokens. We copy the carried-over embedding rows unchanged and initialize new rows as the mean of their source sub-token embeddings. A two-stage adaptation, embedding-only training then full-model continued pre-training, recovers source-checkpoint quality. We apply the recipe to a continued pre-trained checkpoint of LFM2-8B-A1B, an 8B-parameter Mixture-of-Experts model, to help produce LFM2.5-8B-A1B with a 128K tokenizer. The expanded tokenizer encodes Hindi and Vietnamese in roughly $2.4\times$ and $2.6\times$ fewer tokens than the source (up to $4.0\times$ on Thai). Combining these reductions with the measured per-token cost of the larger vocabulary, we estimate a $2.2$-$3.7\times$ per-character decode speedup for these languages across our reference devices. We release the model weights and the expanded tokenizer, and report the negative findings that shaped the recipe.
arXiv:2607.15275v1 Announce Type: new
Abstract: Recent robot foundation models operate with single-step or short-history visuomotor context. We introduce Test-Time-Training Robot Policies (RoboTTT), a robot model and training recipe that scale visuomotor context to 8K timesteps, three orders of magnitude beyond state-of-the-art policies, without growing inference latency. At this context length, we unlock new robot capabilities: one-shot in-context imitation from human video demonstrations, on-the-fly policy improvement, robustness to perturbations, and stronger performance on multi-stage, long-horizon tasks. We also observe, for the first time, steady gains in closed-loop performance as pretraining context length scales. At its core, RoboTTT integrates Test-Time Training into robot foundation models such as Vision-Language-Action policies, yielding a sequence model whose recurrent state consists of fast weights, parameters updated by gradient descent during both training and inference, compressing histories into weight space and retrieving contextual information for long-context conditioning. To scale training context length, the recipe combines sequence action forcing with truncated backpropagation through time. On challenging real-robot manipulation tasks, RoboTTT improves overall performance by 87% over the single-step context baseline and fully completes a five-minute, ten-stage assembly task, which no baseline ever does. RoboTTT trained with 8K-timestep context outperforms the same model pretrained with 1K timesteps by 62%, suggesting context length as a new scaling axis for robot foundation models. Videos are available at https://research.nvidia.com/labs/gear/robottt/
arXiv:2607.15239v1 Announce Type: new
Abstract: Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.
arXiv:2607.15278v1 Announce Type: new
Abstract: Video models are evolving into vision foundation models, yet they still lack human-like multi-step reasoning. Streaming autoregressive diffusion models are efficient but limited in reasoning, while bidirectional diffusion enables global revision with high inference costs due to dense frame-level denoising. Both paradigms struggle to achieve logical consistency and low-latency streaming for complex reasoning tasks. We propose HDR (Hierarchical Denoising for Visual Reasoning), a unified framework that integrates hierarchical latents into causal video generation for multi-step reasoning. HDR organizes video latents into a tree-structured hierarchy, enabling coarse-to-fine reasoning before streaming output. Coarse denoising layers preserve uncertain hypotheses for global planning, while finer layers progressively refine them into concrete visual states. A sparse hierarchical attention pattern (SHAP) further reduces temporal attention costs. We introduce a level-stratified multi-step video reasoning benchmark with out-of-distribution cases, covering six tasks: maze navigation, Tower of Hanoi, one-line drawing, sliding puzzle, Sokoban, and water pouring. Compared with streaming autoregressive diffusion baselines, HDR improves success from 34.22 to 60.29 (76.2% relative gain) and increases average progress from 76.00 to 89.56, demonstrating more consistent reasoning trajectories. HDR maintains low-latency streaming at 0.70 seconds per latent, achieving 54.2 times faster inference than bidirectional diffusion. It also retains 82.9% of full-data performance with only 2% training data, compared with 52.0% for bidirectional diffusion. Real-world robot experiments further demonstrate HDR's potential for physical interaction and world modeling. Project demo: https://hierarchical-diffusion-reasoning.github.io/.
arXiv:2406.04737v2 Announce Type: cross
Abstract: The cellular network of magnetic Induction (MI) communication holds promise in long-distance underground environments. In the traditional MI communication, there is no fast-fading channel since the MI channel is treated as a quasi-static channel. However, for the vehicle (mobile) MI (VMI) communication, the unpredictable antenna vibration brings the remarkable fast-fading. As such fast-fading cannot be modeled by the central limit theorem, it differs radically from other wireless fast-fading channels. Unfortunately, few studies focus on this phenomenon. In this paper, using a novel space modeling based on the electromagnetic field theorem, we propose a 3-dimension model of the VMI antenna vibration. By proposing ``conjugate pseudo-piecewise functions'' and boundary $p(x)$ distribution, we derive the cumulative distribution function (CDF), probability density function (PDF) and the expectation of the VMI fast-fading channel. We also theoretically analyze the effects of the VMI fast-fading on the network throughput, including the VMI outage probability which can be ignored in the traditional MI channel study. We draw several intriguing conclusions different from those in wireless fast-fading studies. For instance, the fast-fading brings more uniformly distributed channel coefficients. Finally, we propose the power control algorithm using the non-cooperative game and multiagent Q-learning methods to optimize the throughput of the cellular VMI network. Simulations validate the derivation and the proposed algorithm.
arXiv:2607.14124v1 Announce Type: cross
Abstract: The increasing availability of large-scale educational datasets has expanded the use of quantitative methods for investigating school performance. However, institutional heterogeneity among schools and the structural complexity of educational data pose substantial challenges to traditional statistical modeling approaches. This study investigates the existence of school typologies based on structural, pedagogical, and demographic characteristics, and examines how these typologies relate to performance in the Brazilian Basic Education Assessment System (Saeb). Using data from the Brazilian School Census and Saeb, data preprocessing and normalization procedures are applied followed by hierarchical clustering to identify groups of schools with similar structural profiles. After the identification of these typologies, causal analysis techniques are employed to investigate potential causal relationships between school characteristics and educational outcomes. The results reveal the presence of distinct school profiles and statistically significant differences in average performance among them. The causal analysis provides insights into the structural and contextual factors that may influence educational performance, contributing to a better understanding of the mechanisms associated with school effectiveness.
arXiv:2607.14163v1 Announce Type: cross
Abstract: Most single-cell foundation models are adapted from language models, representing each cell as a sequence of gene tokens. This discards the relationships among genes and often the magnitude of their expression. We present scVision, a vision foundation model that instead renders each cell as a continuous image. Using optimal transport, it places genes at fixed positions on a single shared, pan-tissue layout so that co-expressed genes become spatial neighbours, turning a transcriptome into an image in which gene programs appear as local texture. We pretrain a vision transformer by masked image modelling on 72 million human cells and use the frozen encoder with no fine-tuning. In zero-shot evaluations on six independent, held-out studies, scVision is the most accurate cell-type annotator and recovers gene programs without supervision, ahead of existing foundation models and classical baselines; on multi-study integration it matches the strongest token-based model while conserving the most biological structure, without ever seeing a batch label. Permuting the gene layout with the network fixed sharply lowers accuracy, more than removing the vision transformer itself, showing that biologically meaningful position, not the network, carries the signal. By preserving expression magnitude and gene relationships, scVision reframes single-cell representation learning as a vision problem, connecting it to the mature methods of computer vision.
arXiv:2607.14282v1 Announce Type: cross
Abstract: The performance of quantum annealing depends critically on how the available annealing time is distributed along the evolution. Although the Roland Cerf local adiabatic schedule is theoretically optimal, it requires complete knowledge of the instantaneous spectral gap, making it impractical for large optimization problems. We propose a computationally inexpensive surrogate schedule based on the worldline magnetization susceptibility measured during simulated quantum annealing. The susceptibility is obtained directly from equilibrium Monte Carlo sampling and identifies the critical region of the anneal without requiring spectral information. Using exact diagonalization of Sherrington Kirkpatrick spin glass instances as ground truth, we show that the resulting schedule consistently outperforms conventional linear annealing and, for a substantial fraction of instances, also surpasses the exact Roland Cerf schedule. We demonstrate that this unexpected behaviour originates from two finite time failure modes of exact local adiabatic scheduling a boundary gap trap, in which the minimum spectral gap occurs at the end of the anneal, and an oscillatory instability caused by excessively localized time allocation around an interior minimum gap. These results suggest that robust scheduling based on inexpensive equilibrium observables can outperform exact spectral gap based strategies under realistic finite time conditions. The complete methodology is implemented in the open source Qanneal framework.
arXiv:2607.14308v1 Announce Type: cross
Abstract: Nonlinear kinetic plasma simulation is high-dimensional and classically demanding, while quantum algorithms face different bottlenecks: embedding nonlinear dynamics into a linear computation, loading dense field-interaction data, and efficiently extracting information. We present an end-to-end quantum algorithm, with rigorous convergence guarantees, for a weakly nonlinear kinetic plasma model. The system describes a 3D electron-ion plasma with adiabatic electrons, kinetic ions, Debye screening, and Krook relaxation. After Fourier-Hermite truncation, the dynamics reduces to a high-dimensional quadratic ordinary differential equation. To tackle quantum bottlenecks we combine three key ingredients. First, we use a plasma free energy to identify a Lyapunov transform under which a Carleman linear embedding converges exponentially in the truncation order within a certified weakly nonlinear regime. Second, we develop a hierarchical block-encoding protocol for dense matrices, exploiting the spatial decay of the field to avoid polynomial overhead from sparse access encodings. Third, we introduce a subroutine for information extraction that exploits nonlinear components encoded in the full Carleman history state to improve the estimation of linear observables. We construct a quantum algorithm to estimate the spacetime-averaged kinetic energy using $\widetilde{O}\!\left( N_F N_H^{1/2} \operatorname{polylog}\!\left(\frac{T}{\epsilon}\right)\frac{1}{\epsilon}\right)$ gates and $\widetilde{O}\!\left(\log\!\left(N_F N_H^{1/2}T\right)\log\!\left(\frac{1}{\epsilon}\right)\right)$ qubits, where $N_F$ and $N_H$ are the Fourier and Hermite cutoffs. Relative to a Fourier-Hermite spectral solver, this yields exponential memory savings and superquadratic improvements in time. Together, these results establish a controlled nonlinear plasma benchmark for quantum simulation.
arXiv:2607.14328v1 Announce Type: cross
Abstract: In proton therapy planning, respiratory-gated non-contrast CT (NCCT) is commonly used for lesion segmentation; however, accurate delineation remains challenging due to low lesion-to-background contrast. Although learning-based methods have shown strong performance, they often struggle with non-contrast image segmentation. Inspired by clinical practice, where contrast-enhanced MRI is referenced to delineate lesions on NCCT, we propose ViPSAM, a visual prompting framework that leverages complementary cross-modality information. Built upon the Segment Anything Model (SAM), ViPSAM introduces a visual prompt encoder to extract guidance features from contrast-enhanced images and a visual-guided cross-attention module to integrate non-contrast and contrast-enhanced features, thereby enhancing lesion-relevant representations in low-contrast regions. The mask decoder is further adapted in a parameter-efficient manner to utilize visual prompts effectively. We evaluate the proposed method on liver lesion segmentation using NCCT acquired for proton therapy. Experimental results demonstrate that ViPSAM outperforms representative U-Net- and SAM-based methods, indicating that cross-modality visual prompting enables more robust and accurate segmentation in non-contrast images.
arXiv:2607.14361v1 Announce Type: cross
Abstract: We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$. These processes are central to continuous-time stochastic control, reinforcement learning, and mathematical finance. Although Wiener-chaos expansions offer strong theoretical tools, traditional computational methods are hindered by the need for large chaos dictionaries and high-order iterated integrals. To overcome these obstacles, we introduce NeuralChaos -- a neural operator architecture that produces elements of $\mathcal{H}^2_T(\mathbb{R}^{d})$ using only finitely many evaluations of the driving Brownian motion, while preserving predictability and square-integrability. We prove that NeuralChaos is dense in $\mathcal{H}^2_T(\mathbb{R}^{d})$ and achieves the best $N$-term chaoslet approximation rates for compressible and Malliavin--Sobolev regular processes. Moreover, compressibility is shown to be typical for processes from $\mathcal{H}^2_T(\mathbb{R}^{d})$ under non-degenerate sub-Gaussian sampling. In contrast, we show that finite-dimensional Markovian neural SDE models constitute a meagre and Gaussian-null subset in $\mathcal{H}^2_T(\mathbb{R}^{d})$, regardless of discretization, whereas compressible processes are generic. Numerical experiments on a stochastic optimal control problem and dynamic hedging highlight the practical effectiveness of our approach. Our results enable more efficient and expressive modelling in stochastic analysis and mathematical finance.
arXiv:2607.14384v1 Announce Type: cross
Abstract: A central question in quantum information theory is the circuit complexity of states arising from standard many-body models. We study this question for quantum $p$-spin glasses, random Hamiltonians whose interactions act on $p$-tuples of qubits through Pauli strings. Anschuetz, Gamarnik, and Kiani (arXiv:2404.07231) showed that the optimum energy is separated from the best energy achievable by product states. This leaves open whether shallow circuits can close the gap, since even depth-one circuits can generate entanglement.
We show that the entanglement needed to close the product-state gap cannot be generated at shallow depth. When the average interaction degree grows with $n$, we prove that, for all sufficiently large fixed $p$, any circuit preparing an $n$-qubit state whose normalized energy is within a fixed positive constant of the optimum must have depth $\Omega_p(\log n)$. In the bounded-average-degree regime, we prove a fixed-depth obstruction: for every fixed $D$, a sufficiently large degree prefactor rules out depth-$D$ preparation of near-ground states. Both results hold uniformly over circuits with an arbitrary number of ancilla qubits.
Our results give an obstruction in the spirit of the No Low-Energy Trivial States problem of Freedman and Hastings (arXiv:1301.1363), but for random quantum spin glasses rather than code-based Hamiltonians such as those of Anshu, Breuckmann, and Nirkhe (arXiv:2206.13228), whose ground states admit polynomial-size preparation circuits. This setting opens a probabilistic route to NLTS-like questions: we recast state-preparation lower bounds for random quantum Hamiltonians as uniform control of Gaussian processes indexed by shallow circuits.
arXiv:2607.14409v1 Announce Type: cross
Abstract: Given only the probability distribution of an aggregate counting variable, what independent latent counting processes are compatible with the observation? Equivalently, when does a probability-generating function admit a factorization into normalized polynomials with nonnegative coefficients? We develop a mathematical theory of such positive factorizations.
We introduce the positive factorization poset, whose elements are all positive factorizations ordered by refinement, and define the factorization entropy, measuring the maximal latent Shannon entropy compatible with the observed distribution. We prove a sharp entropy inequality, characterize the equality case by injectivity of the latent addition map, show that entropy optimization may be restricted to maximal atomizations, and exhibit examples where distinct maximal atomizations have different entropy.
We further establish support-based obstructions to positive factorization, characterize the real-rooted and Hurwitz-stable sectors, prove a local stability theorem for coprime factorizations, determine exactly the factorable regions in degrees two and three, obtain an exact quartic Hurwitz volume, and investigate the geometry of the factorable region inside the probability simplex through exact calculations and Monte Carlo experiments. These results identify the positive factorization poset as a natural algebraic object associated with probability-generating functions and provide a framework for studying latent independent structure in aggregate counting statistics.
arXiv:2607.15271v1 Announce Type: new
Abstract: Online novel view synthesis from multi-view streaming videos faces a fundamental trade-off: maintaining a persistent, long-horizon memory to reconstruct temporarily occluded regions while operating under strict real-time constraints. While Test-Time Training (TTT) offers a powerful memory mechanism, standard models mandate gradient-based memory updates at every frame to adapt to the changing motion in dynamic scenes. The computational cost of heavy memory updates precludes real-time application and can lead to instability over long contexts. Given that memory updates are more demanding than memory application and video content is largely redundant, we propose to decouple the frequencies of these two processes. Our approach performs periodic memory updates while applying the memory on a per-frame basis, using cross-view attention to manage deformations between the prior memory state and the current frame. To lock in the historical context, we introduce two critical mechanisms: an auxiliary Memory Loss that forces persistent internalization of the scene, and a Memory Caching strategy that regularizes active weights against catastrophic drift. Our method demonstrates real-time, state-of-the-art performance on scenes with dynamic human motion as well as minute-scale online memorization.
arXiv:2607.14451v1 Announce Type: cross
Abstract: Biomolecular condensates are continually remodeled by biochemical reactions that can exhibit non-Markovian, history-dependent dynamics. We develop a theory of active phase separation with non-Markovian reactions and show that delayed reaction feedback destabilizes stationary droplets: when the memory time becomes comparable to the reaction turnover time, condensates deform and spontaneously acquire a polar, self-propelled state. In multidroplet systems, persistent memory wakes mediate alignment, producing polar flocks and, at higher concentrations, traveling labyrinths. These results establish reaction memory as a control parameter of active phase separation, linking condensate remodeling, autonomous motility, and collective organization, and suggest a possible route to flocking-like behavior within cells.
arXiv:2607.14469v1 Announce Type: cross
Abstract: Maximal quantum leakage (MQL) is a worst-case information leakage measure that quantifies an adversary's inference advantage gained from accessing quantum encoding of classical data with arbitrary measurements. While MQL admits an exact characterization for a given ensemble of quantum states, its robustness to implementation imperfections has not been systematically studied. In this paper, we analyze the sensitivity of maximal quantum leakage under perturbations of the quantum encoding. We establish a continuity bound in terms of the trace distance between ideal and perturbed quantum states, and show, via an example, that this bound is attainable. We further derive fidelity-based and relative-entropy-based sufficient conditions for bounding the variation of maximal quantum leakage, and illustrate numerically that these conditions can be loose.
arXiv:2607.14527v1 Announce Type: cross
Abstract: Stein variational gradient descent (SVGD) transports interacting particles toward a target distribution through deterministic kernelized dynamics. Singular Riesz kernels are attractive because they can provide quantitative population-level convergence, but at the finite-particle level the corresponding Stein energy has infinite self-interaction. We study periodic Riesz SVGD with self-interaction removed and prove a many-particle, long-time sampling theorem. Throughout the range in which the singular Stein energy is locally integrable, under a uniform bound on the initial relative entropy per particle, the time-averaged empirical-measure law converges weakly to the point mass \(\delta_\pi\) at the target as the particle number and any diverging averaging horizon tend to infinity. We also show that the empirical-measure laws induced by invariant particle laws of finite relative entropy converge weakly to \(\delta_\pi\), without a uniform entropy bound. Below the logarithmic singularity threshold, we obtain an explicit algebraic finite-particle error bound. These results extend the joint-entropy approach for smooth-kernel SVGD to singular interactions.