DeepMind spinout raises $2.1 billion
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We study the problem of human gaze modeling, which aims to generate the gaze patterns a viewer produces while observing a visual stimulus. Gaze is primarily captured through two modalities: continuous eye-tracking trajectories, which describe fine-grained motion dynamics, and discrete scanpaths, which describe high-level fixation structure. Because gaze varies substantially across viewers and trials, we treat this variability as a defining property rather than noise and model gaze as a stochastic generative process. Existing generative gaze models supervise on only one of these two representations in isolation. We hypothesize that trajectories and scanpaths describe gaze at complementary scales and are jointly informative during training, and test this hypothesis through ST-DiffEye, a joint trajectory-scanpath diffusion framework that couples both modalities by concatenating them as an additional raw input channel, requiring no architectural overhead beyond an input and output channel expansion. We further introduce a principled evaluation framework based on the Continuous Ranked Probability Score (CRPS), which generalizes any existing sequence similarity metric into a proper scoring rule that jointly assesses the accuracy and diversity of generated gaze. Experiments on task-driven visual search, covering both target-present and target-absent scenarios, and on free-viewing benchmarks demonstrate state-of-the-art performance. These results, along with detailed ablations, confirm the benefit of joint modeling and the value of distribution-aware evaluation in capturing the intrinsic variability of human gaze. Project webpage: https://st-diffeye.github.io/
Self-supervised foundation models have shown strong promise in medical imaging. However, existing MRI foundation-model studies have primarily emphasized segmentation and dense prediction tasks, while systematic investigation of self-supervised foundation models for MRI-based disease detection remains limited. In this work, we investigate two major self-supervised pretraining paradigms for MRI-based disease detection: reconstruction-based learning via Masked Autoencoders (MAE) and predictive representation learning via Joint Embedding Predictive Architectures (JEPA). We study the role of auxiliary objectives by introducing a novel spectral-domain reconstruction loss for MAE to enhance sensitivity to fine-grained anatomical structure, and by integrating variance–covariance regularization (VCR) within our JEPA framework to encourage decorrelated latent representations. Our models are pretrained on heterogeneous single-contrast MRI volumes in a contrast-agnostic setting, without modality concatenation. Across five downstream disease detection tasks, our results highlight the importance of self-supervised objective design for medical foundation model pretraining, demonstrating that the downstream benefit of each objective is determined by its relevance to the task's structure. Specifically, spectral regularization yields the largest improvements when the downstream discriminative signal is characterized by strong high-frequency anatomical structures, while covariance regularization is most beneficial when discriminative information spans multiple decorrelated feature dimensions. MAE with spectral-domain supervision consistently achieves superior downstream performance for MRI-based disease detection. These findings suggest that self-supervised objectives in medical imaging encode specific biases, and their downstream benefit is fundamentally conditioned on the task's structure.
The rapid progress of image-guided video generation (I2V) has raised concerns about its potential misuse in misinformation and fraud, underscoring the urgent need for effective digital watermarking. While existing watermarking methods demonstrate robustness within a single modality, they fail to trace source images in I2V settings. To address this gap, we introduce the concept of Robust Diffusion Distance, which measures the temporal persistence of watermark signals in generated videos. Building on this, we propose I2VWM, a cross-modal watermarking framework designed to enhance watermark robustness across time. I2VWM leverages a video-simulation noise layer during training and employs an optical-flow-based alignment module during inference. Experiments on both open-source and commercial I2V models demonstrate that I2VWM significantly improves robustness while maintaining imperceptibility, establishing a new paradigm for cross-modal watermarking in the era of generative video. \href{https://github.com/MrCrims/I2VWM-Robust-Watermarking-for-Image-to-Video-Generation}{Code Released.}
arXiv:2606.12333v1 Announce Type: cross Abstract: Expectiles provide a class of asymmetric location functionals that incorporate the magnitude of deviations and admit a natural geometric interpretation. Building on their structural consistency with the convex stochastic order, this paper introduces a family of integrated expectile functionals for measuring risk, dispersion, and inequality. The proposed functionals admit analytical representations as integrals of expectiles across asymmetry levels. For a distinguished subclass of these constructions, a geometric representation is available: the resulting quantities can be expressed as weighted areas of star-shaped sets encoding the distributional asymmetry of a random variable. This approach yields a new class of expectile-based inequality indices, constituting a natural counterpart to classical Gini-type measures while preserving desirable monotonicity and consistency properties. Empirical counterparts are derived in closed form and admit explicit decompositions over finite samples. The framework extends naturally to multivariate settings through directional expectile constructions, leading to measures capable of capturing genuinely joint forms of multivariate dispersion and inequality.
Background Intermittent preventive treatment in pregnancy with sulfadoxine-pyrimethamine (IPTp-SP) is a key preventive strategy. However, optimal uptake remains inconsistent despite high antenatal care (ANC) attendance. This study assessed factors associated with IPTp-SP uptake and explored the experiences of postpartum women in rural Ghana. Methods A mixed-method study was conducted among 1,155 postpartum women attending child welfare clinics in Jomoro, Prestea-Huni Valley and Ellembelle districts of the Western Region of Ghana. Quantitative data were collected using structured questionnaires and analysed using descriptive statistics and chi-square tests. Qualitative data from in-depth interviews and focus group discussions were analysed thematically to explore womens experiences and perceptions. Results Overall, 73.5% (812/1105) of respondents received at least three doses of SP during pregnancy, in line with WHO recommendations. The most common number of doses received was three doses (31.5%, 348/1105), followed by four doses (26.4%, 292/1105), while a smaller proportion (8.1%, 90/1105) received only one dose. Knowledge of malaria in pregnancy was generally high: 92.7% (1027/1155) of respondents correctly identified its mode of transmission, while 75.1% (830/1155) and 83.5% (923/1155) were aware of the effects of malaria on pregnancy and the foetus, respectively. Uptake was not significantly associated with socio-demographic characteristics, including age, education, occupation, marital status, gravidity, and parity (p > 0.05). However, number of ANC visits was significantly associated with uptake (p = 0.006). Although not statistically significant, lower uptake was observed among peri-urban residents and uninsured women. Qualitative findings indicated that while women recognized the benefits of IPTp-SP, side effects such as nausea, dizziness, and discomfort, as well as challenges with tablet formulation and dosing negatively influenced adherence. Conclusions IPTp-SP uptake was high and largely independent of socio-demographic factors but strongly influenced by ANC attendance. Addressing experiential barriers and strengthening patient-centered counselling during ANC may further improve uptake and adherence.
arXiv:2605.27864v4 Announce Type: replace Abstract: Large language models (LLMs) are increasingly applied in finance, yet most existing work emphasizes trading signals or financial NLP tasks centered on prediction. Institutional fundamental research, by contrast, requires human analysts or AI agents to gather evidence, identify business drivers, compare competing viewpoints, and generate investment memos. Its broader goal is not merely to predict outcomes, but to produce investment plans that are transparent, reusable, and verifiable, while contributing to the cumulative development of investment knowledge. We present FundaPod, a multi-persona agent platform for AI-assisted fundamental investment research. We argue that fundamental research is a human-centric decision-support task that is qualitatively distinct from trading-signal generation, and is therefore better served by an independence-preserving architecture. In FundaPod, AI agents with different personas, such as value investors or macro strategists, conduct research independently under a shared provenance contract. Their disagreements are then surfaced post hoc for adjudication by the human portfolio manager (PM) through a knowledge-graph memory system. This paper contributes five design principles for human-AI hybrid systems supporting fundamental research, grounded in design-science practice and theories of cognitive isolation and human-machine coordination. It also describes four architectural mechanisms: a persona distillation pipeline that turns public investor materials into deployable agents; a declarative skill registry that lets the planner derive typed task graphs; a grounded evidence model that links memo claims to verifiable sources; and a knowledge-graph "second brain" that connects tickers, memos, analysts, and themes. We demonstrate the architecture through a complete case study and a persona-based memo comparison.
arXiv:2605.20541v2 Announce Type: replace-cross Abstract: The expected signature uniquely determines the law of a random rough path under a moment-growth condition, yet finite-sample bounds for estimating its truncations from a single long dependent trajectory remain unavailable. We study a strictly stationary stochastic process equipped with a geometric rough-path lift, observed in non-overlapping blocks of equally-spaced samples, and prove a non-asymptotic mean-squared error (MSE) bound for the block-averaging estimator of its truncated expected signature. Under moment and stationarity assumptions together with a direct covariance-decay condition on block signatures – strictly weaker than $\alpha$-mixing and applicable to long-range-dependent processes – the error separates into a discretization term and a fluctuation term, with rates determined respectively by path regularity and dependence strength. A levelwise rough-factorial variance analysis keeps finite-truncation constants explicit and yields an optimal allocation rule under a fixed observation budget. We verify the assumptions for independent-coordinate fractional Ornstein–Uhlenbeck processes in three regimes: short-range (Hurst $1/41/2$. Monte Carlo experiments show empirical slopes steeper than the guaranteed upper-bound rates.
arXiv:2606.14791v1 Announce Type: cross Abstract: Self-supervised learning advances audio representation for multimedia analysis. However, prevailing data-centric approaches rely on massive real-world corpora, increasing training costs, curation burdens, and privacy barriers. To address this, we present AudioPG, a procedural synthesis framework eliminating real audio recordings during pre-training. AudioPG trains a Transformer-based masked autoencoder on waveforms generated on-the-fly from basic acoustic primitives and composition rules. The encoder transfers effectively to real audio benchmarks, achieving 90.60% accuracy on ESC-50, 0.546 mAP on FSD50K, 88.17% on UrbanSound8K, and 97.03% on Speech Commands V2. Notably, pre-training completes in under 20 minutes on a single GPU. Latent space analysis reveals physical factors, including fundamental frequency and relative intensity, emerge in orthogonal subspaces, making representations linearly decodable. These results establish procedural synthesis as an efficient, interpretable pre-training signal when large-scale corpora are unavailable. Our code is available at: https://github.com/Freyliu0516/audioPG.
arXiv:2603.22372v2 Announce Type: replace-cross Abstract: Recent advances in multimodal learning have motivated the integration of auxiliary modalities such as text or vision into time series (TS) forecasting. However, most existing methods provide limited gains, often improving performance only in specific datasets or relying on architecture-specific designs that limit generalization. In this paper, we show that multimodal models with naive fusion strategies (e.g., simple addition or concatenation) often underperform unimodal TS models, which we attribute to the uncontrolled integration of auxiliary modalities which may introduce irrelevant information. Motivated by this observation, we explore various constrained fusion methods designed to control such integration and find that they consistently outperform naive fusion methods. Furthermore, we propose Controlled Fusion Adapter (CFA), a simple plug-in method that enables controlled cross-modal interactions without modifying the TS backbone, integrating only relevant textual information aligned with TS dynamics. CFA employs low rank adapters to filter irrelevant textual information before fusing it into temporal representations. We conduct over 20K experiments across various datasets and TS/text models, demonstrating the effectiveness of the constrained fusion methods. Code is available at: https://github.com/seunghan96/cfa.
arXiv:2602.07294v4 Announce Type: replace-cross Abstract: With the increasing deployment of Large Language Models (LLMs) in the finance domain, LLMs are increasingly expected to parse complex regulatory disclosures. However, existing benchmarks often focus on isolated details, failing to reflect the complexity of professional analysis that requires synthesizing information across multiple documents, reporting periods, and corporate entities. Furthermore, these benchmarks do not disentangle whether errors arise from retrieval failures, generation inaccuracies, domain-specific reasoning mistakes, or misinterpretation of the query or context, making it difficult to precisely diagnose performance bottlenecks. To bridge these gaps, we introduce Fin-RATE, a benchmark built on U.S. Securities and Exchange Commission (SEC) filings and mirroring financial analyst workflows through three pathways: detail-oriented reasoning within individual disclosures, cross-entity comparison under shared topics, and longitudinal tracking of the same firm across reporting periods. We benchmark 17 leading LLMs, spanning open-source, closed-source, and finance-specialized models, under both ground-truth context and retrieval-augmented settings. Results show substantial performance degradation, with accuracy dropping by 18.60% and 14.35% as tasks shift from single-document reasoning to longitudinal and cross-entity analysis. This degradation is associated with increased comparison hallucinations, temporal and entity mismatches, and is further reflected in declines in reasoning quality and factual consistency–limitations that existing benchmarks have yet to formally categorize or quantify.
arXiv:2606.15678v1 Announce Type: cross Abstract: A feasibility and dynamics study of the Reservoir Attention Network (RAN), an architecture that injects a fixed, randomly-initialized reservoir into the mid-layer attention of a pretrained transformer to carry state across forward passes. Experiments span GPT-2 (124M, 355M) to Qwen2.5 (0.5B, 1.5B) on a single consumer GPU. The tasks are minimal probes chosen to isolate individual mechanisms; the broader always-alive agent vision is treated throughout as compute-limited future work, not a claim of this paper. The reservoir is left untrained (fixed random) by design: this isolates whether untrained recurrent dynamics alone suffice to carry usable cross-pass state, leaving trained recurrence as a complementary, more expensive direction.
Down syndrome, caused by trisomy 21, increases the risk of diverse co-occurring conditions. With more than 34,000 related publications indexed in PubMed as of early 2026, keeping pace with this expanding literature is challenging. While general-purpose large language models are widely used for information retrieval, they often rely on broad training data rather than specific evidence. Retrieval-augmented generation (RAG) improves rigor and reliability of responses by linking model outputs to source texts. In research, source texts are peer-reviewed articles. Standard implementations treat all manuscript sections equally, allowing background text to rank as highly as experimental results. To focus model outputs on experimentally supported responses, we developed the T21 Research Assistant, a section-aware RAG system that prioritizes Results sections to ground responses in primary experimental evidence. The system draws exclusively from 1,789 open-access Down syndrome publications from PubMed Central, including 327 NIH INCLUDE-funded studies, and uses a multistage pipeline for query validation, retrieval, reranking, synthesis, and citation verification. Built on NVIDIA Nemotron models, it generates structured, cited responses. Evaluation using expert-curated questions demonstrated strong performance, achieving a BERTScore F1 of 0.712 and recall of 0.758, comparable to or exceeding leading proprietary and open-source models. T21 Research Assistant is available at: https://bioinformatics.cuanschutz.edu/t21-res-assi/
Unsupervised object-centric learning (OCL) decomposes visual scenes into distinct entities. Slot attention is a popular approach that represents individual objects as latent vectors, called slots. Current methods obtain these slot representations solely from the last layer of a pre-trained vision transformer (ViT), ignoring valuable, semantically rich information encoded across the other layers. To better utilize this latent semantic information, we introduce MUFASA, a lightweight plug-and-play framework for slot-attention-based approaches to unsupervised object segmentation. Our model computes slot attention across multiple feature layers of the ViT encoder, fully leveraging their semantic richness. We propose a fusion strategy to aggregate slots obtained on multiple layers into a unified object-centric representation. Integrating MUFASA into existing OCL methods improves their segmentation results across multiple datasets, setting a new state of the art while simultaneously improving training convergence with only minor inference overhead.
Reproducible computational biology depends on statistical decisions that routine workflows often skip: verifying that a differential-expression test's assumptions hold across all genes, that a strategy-comparison ANOVA is robust to non-normality, or that a meta-analysis is not distorted by publication bias. Surveys consistently find that fewer than 20% of published biomedical studies report checking these assumptions, and existing statistical software leaves validation to the analyst as an optional step. We present StickForStats, an open-source web platform that reframes assumption validation as a default precondition for every analysis. Its Guardian system–a middleware pipeline of eight validators (normality, variance homogeneity, independence, outliers, sample size, modality, linearity, homoscedasticity)–checks assumptions before execution and, on critical violations, reroutes to an appropriate nonparametric alternative with a documented decision trail. At genome scale, applying Guardian to a 91-sample synovial-sarcoma RNA-seq study (GSE271517) cascaded 90.6% of 27,221 genes to a rank-based test and flipped the differential-expression verdict for 553 genes–479 rescued from an under-powered t-test and 74 outlier-driven false positives rejected–materially changing the gene list a biologist would act on. The same automatic validation generalizes across domains: a CRISPR editing-strategy comparison (ANOVA F = 1122, with Guardian recommending Kruskal-Wallis H = 36.6), an ordinal correlation (Pearson r = 0.476 corrected to Spearman {rho} = 0.479), and a sixteen-trial clinical meta-analysis revealing severe publication bias (Egger's t = -5.78, p < 0.001); a complementary module extends the same validators to published manuscripts, checking claims against CONSORT, STROBE, ICH-E9, and JARS-Quant reporting standards. By making assumption validation automatic and transparent, StickForStats targets a tractable, under-served contributor to irreproducibility. The platform is MIT-licensed, validated against SciPy and R, and freely available at https://github.com/visvikbharti/stickforstats_new.
arXiv:2603.11242v2 Announce Type: replace-cross Abstract: Evaluating and interpreting latent representations, such as variational autoencoders (VAEs), remains a significant challenge for diverse data types, especially when ground-truth generative factors are unknown. To address this, we unify several state-of-the-art disentangled VAE approaches for latent space disentanglement into one framework – bfVAE. To assess the effectiveness of a disentangled VAE model and enhance latent space interpretability, we propose Feature Variance Heterogeneity via Latent Traversal (FVH-LT) and Dirty Block Sparse Regression in Latent Space (DBSR-LS). To ensure robust interpretability of learned latent space, we develop a greedy alignment strategy (GAS) that mitigates label switching and aligns latent dimensions across runs to set the foundation of result aggregation. We also introduce a convenient scalar latent space separation index (LSSI) based on the GAS-aligned outputs of FVH-LT and DBSR-LS to summarize the overall latent structural separation without knowledge of the ground-truth generative factors. We compare bfVAE to five VAE models and validate the effectiveness FVH-LT, DBSR-LS, and LSSI in on seven tabular and image datasets. Under our examined experimental settings, bfVAE provides a more flexible disentanglement framework achieves more favorable overall trade-off between disentanglement and reconstruction than the benchmark VAE models; FVH-LT and DBSR-LS reliably uncover semantically meaningful and domain-relevant latent structures and generally yield consistent results; and LSSI makes an effective quantitative summary of latent structural separation.
arXiv:2512.04801v2 Announce Type: replace Abstract: We propose a hybrid variational quantum algorithm that has variational parameters used by both the quantum circuit and the subsequent classical optimization. Similar to the Variational Quantum Eigensolver (VQE), this algorithm applies a parameterized unitary operator to the qubit register. We generate this operator using diabatic state preparation. The quantum measurement results then inform the classical optimization procedure used by the Cascaded Variational Quantum Eigensolver (CVQE). We demonstrate the algorithm on a system of interacting electrons and show how it can be used on long-term error-corrected as well as short-term intermediate-scale quantum computers. Our simulations performed on IBM Brisbane produced energies well within chemical accuracy.
arXiv:2606.15115v1 Announce Type: new Abstract: Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $IGD_offline$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.
Korean folk painting (minhwa) is built from a small vocabulary of auspicious symbols, a tiger for protection, a pair of birds for marital harmony, a peony for wealth, that recur across many of its painted genres. This suggests an obvious computational approach, identify which symbols appear in a painting and read the genre from the inventory. Working with a public corpus that pairs whole paintings, eight-field bilingual curatorial captions, and a separate set of expert object crops, we find that this approach does not work. A model given only a list of which symbols a painting contains predicts the genre far worse than a model that fuses the image with the curatorial text, and forcing the genre representation to be object-grounded actively hurts accuracy. The visual evidence on which the genre prediction rests is nonetheless localized and inspectable. A leakage-safe object evidence map projected from a part-level detector is spatially faithful to where curators isolated symbolic objects and to a patch-based surrogate's own gradient saliency. We name this configuration a faithful-but-insufficient dissociation. The part-level explanation is honest about what the part-level model sees, yet the genre target turns on how symbols are arranged rather than on which ones appear. The same lens separates a content label that survives transfer to held-out source institutions, genre, from a style label that does not, era, a prediction we confirm on two further labels in the corpus. We release the multimodal system, a worked-example reading of one painting's evidence map against its catalogue, and a set of evaluation cautions that recur in long-tailed heritage collections.
Position information is essential for language modeling. In softmax transformers, Rotary Position Embeddings (RoPE) encode positions through fixed-angle rotations, while in linear transformers, order is handled via input-dependent (selective) gating that decays past key-value associations. Selectivity has generally been shown to improve language-related tasks. Inspired by this, we introduce Selective RoPE, an input-dependent rotary embedding mechanism, that generalizes RoPE, and enables rotation in arbitrary angles for both linear and softmax transformers. We show that softmax attention already performs a hidden form of these rotations on query-key pairs, uncovering an implicit positional structure. We further show that in state-space models and gated linear transformers, the real part manages forgetting while the imaginary part encodes positions through rotations. We validate our method by equipping gated transformers with Selective RoPE, demonstrating that its input-dependent rotations improve performance in language modeling and on difficult sequence tasks like copying, state tracking, and retrieval.
arXiv:2606.18535v1 Announce Type: cross Abstract: Multi-cause observational studies contain information about unmeasured confounding through the dependence structure among causes. However, literal imputation of the unobserved confounder is often more complex than learning a lower-dimensional substitute score that preserves the shared assignment variation needed for stable causal adjustment. The deconfounder (Wang and Blei, 2019) and related substitute confounder methods exploit this idea, but flexible assignment models can fit the joint distribution of the causes while producing scores that over-encode the treatment vector, collapse overlap, or capture single-cause variation. We develop a Bayesian factor assignment framework for learning sparse substitute confounders that retain coarse multi-cause dependence with shrinkage priors. The theory is stated at the level of posterior concentration, factor score contraction, and overlap-preserving assignment geometry and therefore does not rely on a particular shrinkage prior. Under these conditions, the proposed regression-adjusted estimators are consistent for mean potential outcomes when the corresponding latent variable identification assumptions hold. Shrinkage priors provide a natural tool for latent structural learning: they favour low-dimensional factors supported by multiple causes, discourage effectively single-cause factors, and induce an ordering of the latent factors through progressive shrinkage. Synthetic experiments illustrate the roles of signal strength, outcome validity, and geometry-aware regularization. In an Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline analysis, sparse substitute scores recover much of the adjustment obtained by directly conditioning on invasive cerebrospinal-fluid biomarkers, while collapse diagnostics identify when fitted factors reduce to individual observed measurements.
arXiv:2403.13927v3 Announce Type: replace Abstract: Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that in the task of estimating observable expectation values any noise truncates most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise do not exhibit barren plateaus for cost functions composed of local observables. However, by using the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. Taken together, our results establish that, unless we carefully engineer quantum circuits to take advantage of the noise, noisy quantum circuits are unlikely to offer an advantage over shallow ones for algorithms that output observable expectation value estimates, such as many variational quantum machine learning proposals.
Existing global efforts to reduce harms caused by smoking have targeted tobacco smoking, but vapes containing nicotine are also harmful. Existing global efforts to reduce harms caused by smoking have targeted tobacco smoking, but vapes containing nicotine are also harmful.
arXiv:2606.14170v1 Announce Type: new Abstract: In this work, by construct an asymptotic coupling by reflection, we first explore the uniform-in-time estimate on probability distance for two measure-valued processes induced by a McKean-Vlasov SDE with common noise and an interacting particle system, where the drift terms are dissipative merely in the long distance. As direct applications of this estimate, we establish the uniform-in-time error estimates for the numerical solutions derived via backward/tamed/adaptive Euler-Maruyama methods. Moreover, as another direct application, the uniform-in-time conditional propagation of chaos is quantified.
arXiv:2511.19716v2 Announce Type: replace-cross Abstract: Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise. We analyze preconditioned SGD in the geometry induced by a symmetric positive definite matrix $\mathbf{M}$, deriving bounds in which both the convergence rate and the stochastic noise floor are governed by $\mathbf{M}$-dependent quantities: the rate through an effective condition number in the $\mathbf{M}$-metric, and the floor through the product of that condition number and the preconditioned noise level. For nonconvex objectives, we establish a preconditioner-dependent basin-stability guarantee: when smoothness and basin size are measured in the $\mathbf{M}$-norm, the probability that the iterates remain in a well-behaved local region admits an explicit lower bound. This perspective is particularly relevant in Scientific Machine Learning (SciML), where achieving small training loss under stochastic updates is closely tied to physical fidelity, numerical stability, and constraint satisfaction. The framework applies to both diagonal/adaptive and curvature-aware preconditioners and yields a simple design principle: choose $\mathbf{M}$ to improve local conditioning while attenuating noise. Experiments on a quadratic diagnostic and three SciML benchmarks validate the predicted rate-floor behavior.