With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks.

Large language models have an exceptional capability to incorporate new information in a contextual manner.

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While the latest LLMs are astonishingly fluent when interacting with humans, they suffer from the misinformation problem by unintentionally generating factually false statements. This can lead to harmful consequences, especially when produced within sensitive contexts, such as healthcare.

Given a single observation from a Gaussian distribution with unknown mean $θ$, we design computationally efficient procedures that can approximately generate an observation from a different target distribution $Q_θ$ uniformly for all $θ$ in a parameter set. We leverage our technique to establish reduction-based computational lower bounds for several canonical high-dimensional statistical models under widely-believed conjectures in average-case complexity. In particular, we cover cases in which: 1. $Q_θ$ is a general location model with non-Gaussian distribution, including both light-tailed examples (e.g., generalized normal distributions) and heavy-tailed ones (e.g., Student's $t$-distributions). As a consequence, we show that computational lower bounds proved for spiked tensor PCA with Gaussian noise are universal, in that they extend to other non-Gaussian noise distributions within our class. 2. $Q_θ$ is a normal distribution with mean $f(θ)$ for a general, smooth, and nonlinear link function $f:\mathbb{R} \rightarrow \mathbb{R}$. Using this reduction, we construct a reduction from symmetric mixtures of linear regressions to generalized linear models with link function $f$, and establish computational lower bounds for solving the $k$-sparse generalized linear model when $f$ is an even function. This result constitutes the first reduction-based confirmation of a $k$-to-$k^2$ statistical-to-computational gap in $k$-sparse phase retrieval, resolving a conjecture posed by Cai et al. (2016). As a second application, we construct a reduction from the sparse rank-1 submatrix model to the planted submatrix model, establishing a pointwise correspondence between the phase diagrams of the two models that faithfully preserves regions of computational hardness and tractability.