We develop a unified theoretical framework for data-free one-step sampling from unnormalized target distributions based on Wasserstein gradient flows. For a broad class of standard f-divergence objectives, we show that the induced velocity field admits the universal form $\mathbf{V}(x)=w(r(x))\,β(x)$, where $β(x)=\nabla \log (p(x)/q(x))$ is shared across objectives and $w$ is determined solely by the choice of divergence. This decomposition shows that standard f-divergence drifts share the same asymptotic target distribution $p$ and differ primarily in how they redistribute transient repair effort across under-covered regions. To formalize this distinction, we derive a one-step regional-response theory for a soft under-coverage functional and obtain a compression--elasticity identity that links divergence choice to the geometry of mass transport into under-covered regions. We further extend the framework beyond the f-divergence family to the Log-Variance (LV) divergence, analyze how the reference distribution alters the resulting drift structure, and motivate a practical LV-inspired surrogate for data-free training. Based on this theory, we instantiate the framework with a KDE-based implementation and describe a complementary normalizing-flow route, enabling one-step inference after training. Experiments on multimodal Gaussian-mixture benchmarks are consistent with the theoretical predictions and demonstrate effective one-step sampling on these targets.

PCWorld explains how using two SSDs in your PC can significantly boost performance by separating the operating system from applications and data across different drives. This setup prevents bandwidth competition during demanding tasks and offers better data protection through individual drive encryption capabilities.

Generative models are often conditioned on a small set of examples via cross-attention. Under the Gaussian optimal-transport path, we show that the exact velocity field induced by a finite support set is a Nadaraya--Watson kernel smoother whose bandwidth decreases with flow time, from broad averaging at early steps to nearest-neighbor at late steps. A single Gaussian-kernel attention head exactly computes this field, connecting cross-attention conditioning to classical kernel theory. The theory predicts three failure regimes: nearest-neighbor collapse of the kernel at high dimension, mismatch between the isotropic kernel and the data geometry, and insufficient support for nonparametric estimation. Experiments on Gaussian mixtures, spherical shells, and DINOv2 ImageNet features confirm that learned conditioning improves in precisely these regimes, and that IP-Adapter's cross-attention implements approximate NW smoothing in practice.

Training a language model on data scattered across bandwidth-limited nodes that cannot be centralized is a setting that arises in clinical networks, enterprise knowledge bases, and scientific consortia. We study the regime in which data must remain distributed across nodes, and ask what statistical guarantees are in principle achievable under explicit bandwidth budgets; we aim to characterize what is provably possible, not to demonstrate a deployment-ready system. Existing theory treats either training-time consistency or inference-time calibration in isolation, and none makes bandwidth a first-class statistical parameter. We analyze two protocols, Federated Probe-Logit Distillation (FPLD) for training and Federated Conformal RAG (FC-RAG) for inference, as the analytical vehicles for our results. Our first main result is an explicit high-probability KL-consistency rate for FPLD with simultaneous dependence on node count $K$, per-node sample size $n$, quantization budget $B$, probe-set size $m$, and vocabulary size $V$; bandwidth enters only through an exponentially vanishing quantization term. Our second main result is a distribution-free marginal-coverage bound for FC-RAG, whose novel retrieval-bandwidth slack $Δ_{\mathrm{RAG}} = f_{\max}\sqrt{K^{-2}\sum_i v(B_i)}$ makes per-node retrieval bandwidth a first-class statistical parameter, with arithmetic aggregation across $K$ nodes shrinking the slack as $K^{-1/2}$ in the per-node-uniform regime. A Pinsker-type corollary composes the two bounds into an end-to-end coverage guarantee. Synthetic experiments verify the predicted scaling along the bounds' parameters; small-scale experiments on a GPT-2 testbed illustrate that the qualitative bandwidth-accuracy tradeoff survives on a real language model. A deployment-scale empirical evaluation is out of scope.

We study nonparametric estimation of Schrödinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schrödinger bridge time-series (SBTS) drift formula, we analyze a direct Nadaraya--Watson plug-in estimator built from kernelized numerator and denominator terms. Unlike recent SB analyses based on entropic-OT potentials, Sinkhorn iterations, or iterative bridge solvers, our approach works directly at the drift level and isolates \emph{statistical error} from optimization, approximation, and discretization error. Under Hölder regularity, a marginal-density floor, and bounded support, we prove a uniform non-asymptotic bound for admissible bandwidth pairs, a pointwise CLT under genuine undersmoothing, and an adaptive bandwidth selector satisfying an oracle inequality. We also prove a pivot-local minimax lower bound which, through an explicit uniform pivot, yields a global minimax lower bound under transparent compatibility conditions; hence the adaptive selector is minimax-rate optimal up to logarithmic factors. Synthetic experiments provide theorem-targeted diagnostics for finite-sample scaling, Gaussian approximation, and adaptive behavior.

Double-machine-learning pipelines for the Average Dose-Response Function rely on kernel-weighted local-linear smoothers, which inherit unbounded functional influence: a single outlier within a kernel window biases the curve across the entire window. We introduce SHIFT (Self-calibrated Heavy-tail Inlier-Fit with Tempering), a robust DML estimator combining cross-fit nuisance orthogonalization with a kernel-local Welsch-loss second stage optimized by Graduated Non-Convexity, and -- the principal design choice -- a defensive OLS refit whose inlier cutoff is scaled by post-GNC residual MAD rather than the raw-outcome MAD. On a localized-contamination stress test at $p=0.25$ this design choice drops level-RMSE from 1.03 to 0.33 while leaving clean and uniformly-contaminated runs unchanged. Across 1,400 main-sweep fits, SHIFT has competitive worst-case shape recovery (RMSE $0.325$ at $p=0.25$, second to Huber-DML's $0.276$); among the three methods with worst-case RMSE below $0.35$, only SHIFT emits a non-uniform per-sample weight vector, recovering the ground-truth outlier mask at mean $F_1 \approx 0.96$ (range $0.945$--$0.968$) on Gaussian-jump DGPs. We pair the estimator with a six-technique Extreme Value Theory diagnostic suite (Hill, GPD-MLE/PWM, GEV, Mean Excess, parameter stability, causal tail coefficient) that lets a practitioner distinguish Frechet from Weibull regimes and choose between SHIFT and L1 alternatives on empirical grounds. Extensions to binary-treatment CATE (Huber pseudo-outcome X-Learner) and time-series ADRF (block-CV + rolling MAD) are included. A counter-intuitive ablation: linear nuisance models (Ridge, Lasso) outperform gradient-boosted nuisances for robust DML under uniform contamination, inverting the usual more-flexible-is-better heuristic.

Decision trees are regarded for high interpretability arising from their hierarchical partitioning structure built on simple decision rules. However, in practice, this is not realized because axis-aligned partitioning of realistic data results in deep trees, and because ensemble methods are used to mitigate overfitting. Even then, model complexity and performance remain sensitive to transformation of the input, and extensive expert crafting of features from the raw data is common. We propose the first system to alternate sparse feature learning with differentiable decision tree construction to produce small, interpretable trees with good performance. It benchmarks favorably against conventional tree-based models and demonstrates several notions of interpretability of a model and its predictions.

Modern deep learning applications require increasingly more compute to train state-of-the-art models. To address this demand, large corporations and institutions use dedicated High-Performance Computing clusters, whose construction and maintenance are both environmentally costly and well beyond the budget of most organizations. As a result, some research directions become the exclusive domain of a few large industrial and even fewer academic actors. To alleviate this disparity, smaller groups may pool their computational resources and run collaborative experiments that benefit all participants. This paradigm, known as grid-or volunteer computing, has seen successful applications in numerous scientific areas. However, using this approach for machine learning is difficult due to high latency, asymmetric bandwidth, and several challenges unique to volunteer computing. In this work, we carefully analyze these constraints and propose a novel algorithmic framework designed specifically for collaborative training. We demonstrate the effectiveness of our approach for SwAV and ALBERT pretraining in realistic conditions and achieve performance comparable to traditional setups at a fraction of the cost. Finally, we provide a detailed report of successful collaborative language model pretraining with 40 participants.