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Fine-tune Language Models to Approximate Unbiased In-context Learning
To address this issue, we introduce a reweighted algorithm called RICL (Reweighted In-context Learning).
How to Protect Copyright Data in Optimization of Large Language Models?
Large language models (LLMs) and generative AI have played a transformative role in computer research and applications.
Spectral Clustering on Large Datasets: When Does it Work? Theory from Continuous Clustering and Density Cheeger-Buser
We provide theoretically-informed intuition about spectral clustering on large data sets drawn from probability densities, by proving when a continuous form of spectral clustering considered by past researchers (the unweighted spectral cut of a probability density) finds good clusters of the underlying density itself.
Metric Transforms and Low Rank Matrices via Representation Theory of the Real Hyperrectangle
This completes the theory of Manhattan to Manhattan metric transforms initiated by Assouad in 1980.
Algorithms and Hardness for Linear Algebra on Geometric Graphs
We investigate whether or not it is possible to solve the following problems in $n^{1+o(1)}$ time for a $\mathsf{K}$-graph $G_P$ when $d < n^{o(1)}$: $\bullet$ Multiply a given vector by the adjacency matrix or Laplacian matrix of $G_P$ $\bullet$ Find a spectral sparsifier of $G_P$ $\bullet$ Solve a Laplacian system in $G_P$'s Laplacian matrix For each of these problems, we consider all functions of the form $\mathsf{K}(u, v) = f(\|u-v\|_2^2)$ for a function $f:\mathbb{R} \rightarrow \mathbb{R}$.
Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities
In this paper, we show how sparse or isoperimetric cuts of a probability density function relate to Cheeger cuts of its principal eigenfunction, for appropriate definitions of `sparse cut' and `principal eigenfunction'.
