The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative integration. Flow Maps bypass this bottleneck by compressing generative trajectories into single-step mappings, theoretically enabling the generation of full text sequences from noise in a single forward pass. However, standard formulations rely on Euclidean regression losses that are geometrically ill-suited for discrete data. In this work, we resolve this conflict with Discrete Flow Maps, a framework that reconciles trajectory compression with the geometry of the probability simplex. We recast standard flow map training for the discrete domain, aligning the training dynamics with the discrete nature of language. Empirically, this strict geometric alignment allows our method to surpass previous state-of-the-art results in discrete flow modeling.

Background: Single-cell RNA sequencing (scRNA-seq) enables gene expression profiling at cellular resolution but is inherently affected by sparsity caused by dropout events, where expressed genes are recorded as zeros due to technical limitations. These artifacts distort gene expression distributions and compromise downstream analyses. Numerous imputation methods have been proposed to recover latent transcriptional signals. These methods range from traditional statistical models to deep learning (DL)-based methods. However, their comparative performance remains unclear, as existing benchmarks evaluate only a limited subset of methods, datasets, and downstream analyses. Results: We present a comprehensive benchmark of 15 scRNA-seq imputation methods spanning 7 methodological categories, including traditional and DL-based methods. Methods are evaluated across 30 datasets from 10 experimental protocols on 6 downstream analyses. Results show that traditional methods, such as model-based, smoothing-based, and low-rank matrix-based methods, generally outperform DL-based methods, including diffusion-based, GAN-based, GNN-based, and autoencoder-based methods. In addition, strong performance in numerical gene expression recovery does not necessarily translate into improved biological interpretability in downstream analyses, including cell clustering, differential expression analysis, marker gene analysis, trajectory analysis, and cell type annotation. Furthermore, method performance varies substantially across datasets, protocols, and downstream analyses, with no single method consistently outperforming others. Conclusions: Our findings provide practical guidance for selecting imputation methods tailored to specific analytical objectives and underscore the importance of task-specific evaluation when assessing imputation performance in scRNA-seq data analysis.

We study offline-online reinforcement learning in linear mixture Markov decision processes (MDPs) under environment shift. In the offline phase, data are collected by an unknown behavior policy and may come from a mismatched environment, while in the online phase the learner interacts with the target environment. We propose an algorithm that adaptively leverages offline data. When the offline data are informative, either due to sufficient coverage or small environment shift, the algorithm provably improves over purely online learning. When the offline data are uninformative, it safely ignores them and matches the online-only performance. We establish regret upper bounds that explicitly characterize when offline data are beneficial, together with nearly matching lower bounds. Numerical experiments further corroborate our theoretical findings.

The Sauer-Shelah-Perles Lemma is a cornerstone of combinatorics and learning theory, bounding the size of a binary hypothesis class in terms of its Vapnik-Chervonenkis (VC) dimension. For classes of functions over a $k$-ary alphabet, namely the multiclass setting, the Natarajan dimension has long served as an analogue of VC dimension, yet the corresponding Sauer-type bounds are suboptimal for alphabet sizes $k>2$. In this work, we establish a sharp Sauer inequality for multiclass and list prediction. Our bound is expressed in terms of the Daniely--Shalev-Shwartz (DS) dimension, and more generally with its extension, the list-DS dimension -- the combinatorial parameters that characterize multiclass and list PAC learnability. Our bound is tight for every alphabet size $k$, list size $\ell$, and dimension value, replacing the exponential dependence on $\ell$ in the Natarajan-based bound by the optimal polynomial dependence, and improving the dependence on $k$ as well. Our proof uses the polynomial method. In contrast to the classical VC case, where several direct combinatorial proofs are known, we are not aware of any purely combinatorial proof in the DS setting. This motivates several directions for future research, which are discussed in the paper. As consequences, we obtain improved sample complexity upper bounds for list PAC learning and for uniform convergence of list predictors, sharpening the recent results of Charikar et al.~(STOC~2023), Hanneke et al.~(COLT~2024), and Brukhim et al.~(NeurIPS~2024).

Fine-tuning is a widely used strategy for adapting pre-trained models to new tasks, yet its methodology and theoretical properties in high-dimensional nonparametric settings with variable selection have not yet been developed. This paper introduces the fine-tuning factor augmented neural Lasso (FAN-Lasso), a transfer learning framework for high-dimensional nonparametric regression with variable selection that simultaneously handles covariate and posterior shifts. We use a low-rank factor structure to manage high-dimensional dependent covariates and propose a novel residual fine-tuning decomposition in which the target function is expressed as a transformation of a frozen source function and other variables to achieve transfer learning and nonparametric variable selection. This augmented feature from the source predictor allows for the transfer of knowledge to the target domain and reduces model complexity there. We derive minimax-optimal excess risk bounds for the fine-tuning FAN-Lasso, characterizing the precise conditions, in terms of relative sample sizes and function complexities, under which fine-tuning yields statistical acceleration over single-task learning. The proposed framework also provides a theoretical perspective on parameter-efficient fine-tuning methods. Extensive numerical experiments across diverse covariate- and posterior-shift scenarios demonstrate that the fine-tuning FAN-Lasso consistently outperforms standard baselines and achieves near-oracle performance even under severe target sample size constraints, empirically validating the derived rates.

We decompose the Kullback--Leibler generalization error (GE) -- the expected KL divergence from the data distribution to the trained model -- of unsupervised learning into three non-negative components: model error, data bias, and variance. The decomposition is exact for any e-flat model class and follows from two identities of information geometry: the generalized Pythagorean theorem and a dual e-mixture variance identity. As an analytically tractable demonstration, we apply the framework to $ε$-PCA, a regularized principal component analysis in which the empirical covariance is truncated at rank $N_K$ and discarded directions are pinned at a fixed noise floor $ε$. Although rank-constrained $ε$-PCA is not itself e-flat, it admits a technical reformulation with the same total GE on isotropic Gaussian data, under which each component of the decomposition takes closed form. The optimal rank emerges as the cutoff $λ_{\mathrm{cut}}^{*} = ε$ -- the model retains exactly those empirical eigenvalues exceeding the noise floor -- with the cutoff reflecting a marginal-rate balance between model-error gain and data-bias cost. A boundary comparison further yields a three-regime phase diagram -- retain-all, interior, and collapse -- separated by the lower Marchenko--Pastur edge and an analytically computable collapse threshold $ε_{*}(α)$, where $α$ is the dimension-to-sample-size ratio. All claims are verified numerically.

Large language models (LLMs) can generate survey responses at low cost, but their reliability varies substantially across questions and is unknown before data collection. Deploying LLMs in surveys still requires costly human responses for verification and correction. How should a limited human-labeling budget be allocated across questions in real time? We propose an adaptive allocation algorithm that learns which questions are hardest for the LLM while simultaneously collecting human responses. Each human label serves a dual role: it improves the estimate for that question and reveals how well the LLM predicts human responses on it. The algorithm directs more budget to questions where the LLM is least reliable, without requiring any prior knowledge of question-level LLM accuracy. We prove that the allocation gap relative to the best possible allocation vanishes as the budget grows, and validate the approach on both synthetic data and a real survey dataset with 68 questions and over 2000 respondents. On real survey data, the standard practice of allocating human labels uniformly across questions wastes 10--12% of the budget relative to the optimal; our algorithm reduces this waste to 2--6%, and the advantage grows as questions become more heterogeneous in LLM prediction quality. The algorithm achieves the same estimation quality as traditional uniform sampling with fewer human samples, requires no pilot study, and is backed by formal performance guarantees validated on real survey data. More broadly, the framework applies whenever scarce human oversight must be allocated across tasks where LLM reliability is unknown.

Maybe the tiny hunter should've been named after Metallica? More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. We can call this newly discovered spider another brick--or web--in the wall. Scientists in Colombia named the new species in honor of English rock band Pink Floyd and the arachnid's preferred habitat--walls.

More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Hurricane Edouard as seen from the International Space Station in 2014. Breakthroughs, discoveries, and DIY tips sent six days a week. More signs indicate the 2026 Atlantic hurricane season could ultimately be a welcome reprieve from more recent devastating storms . As La Niña transitions into a stronger El Niño climate pattern later this summer, the United States may experience a below-average number of hurricanes.

From recipe changes to aging taste buds, here's why those peanut butter cups don't hit like they used to. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. There's a reason you might remember Hershey's chocolate differently. Breakthroughs, discoveries, and DIY tips sent six days a week. Brad Reese, grandson of Reese's Peanut Butter Cups inventor H.B. Reese, caused a stir this year with his claims that The Hershey Company had changed his grandfather's recipes beyond recognition .