GenoBERT: A Language Model for Accurate Genotype Imputation

Genotype imputation enables dense variant coverage for genome-wide association and risk-prediction studies, yet conventional reference-panel methods remain limited by ancestry bias and reduced rare-variant accuracy. We present Genotype Bidirectional Encoder Representations from Transformers (GenoBERT), a transformer-based, reference-free framework that tokenizes phased genotypes and uses a self-attention mechanism to capture both short- and long-range linkage disequilibrium (LD) dependencies. Benchmarking on two independent datasets including the Louisiana Osteoporosis Study (LOS) and the 1000 Genomes Project (1KGP) across ancestry groups and multiple genotype missingness levels (5-50%) shows that GenoBERT achieves the highest overall accuracy compared to four baseline methods (Beagle5.4, SCDA, BiU-Net, and STICI). At practical sparsity levels (up to 25% missing), GenoBERT attains high overall imputation accuracy ($r^2 approx 0.98$) across datasets, and maintains robust performance ($r^2 > 0.90$) even at 50% missingness. Experimental results across different ancestries confirm consistent gains across datasets, with resilience to small sample sizes and weak LD. A 128-SNP (single-nucleotide polymorphism) context window (approximately 100 Kb) is validated through LD-decay analyses as sufficient to capture local correlation structures. By eliminating reference-panel dependence while preserving high accuracy, GenoBERT provides a scalable and robust solution for genotype imputation and a foundation for downstream genomic modeling.

Poincaré Inequality for Local Log-Polyak-Lojasiewicz Measures : Non-asymptotic Analysis in Low-temperature Regime

Potential functions in highly pertinent applications, such as deep learning in over-parameterized regime, are empirically observed to admit non-isolated minima. To understand the convergence behavior of stochastic dynamics in such landscapes, we propose to study the class of \logPLmeasure\ measures $\mu_\epsilon \propto \exp(-V/\epsilon)$, where the potential $V$ satisfies a local Polyak-{\L}ojasiewicz (P\L) inequality, and its set of local minima is provably \emph{connected}. Notably, potentials in this class can exhibit local maxima and we characterize its optimal set S to be a compact $\mathcal{C}^2$ \emph{embedding submanifold} of $\mathbb{R}^d$ without boundary. The \emph{non-contractibility} of S distinguishes our function class from the classical convex setting topologically. Moreover, the embedding structure induces a naturally defined Laplacian-Beltrami operator on S, and we show that its first non-trivial eigenvalue provides an \emph{$\epsilon$-independent} lower bound for the \Poincare\ constant in the \Poincare\ inequality of $\mu_\epsilon$. As a direct consequence, Langevin dynamics with such non-convex potential $V$ and diffusion coefficient $\epsilon$ converges to its equilibrium $\mu_\epsilon$ at a rate of $\tilde{\mathcal{O}}(1/\epsilon)$, provided $\epsilon$ is sufficiently small. Here $\tilde{\mathcal{O}}$ hides logarithmic terms.