arXiv subjects

Vincent Lin

Publications and source records attributed to Vincent Lin.

3 recordsLinked to original sources

arXiv2025

Inference-Time Chain-of-Thought Pruning with Latent Informativeness Signals

Large language models (LLMs) improve reasoning accuracy when generating multiple candidate solutions at test time, but standard methods like Best-of-N (BoN) incur high computational cost by fully generating all branches. Self-Truncation Best-of-N (ST-BoN) mitigates this by truncating unpromising paths early, but its reliance on consistency-based heuristics is a limitation as it does not directly evaluate branch quality. We present KL-Adjusted Pruned Path Algorithm (KAPPA), an inference-time method that combines Kullback-Leibler divergence, confidence, and entropy into a principled scoring function to guide progressive pruning. By promoting diversity during exploration and selectively eliminating low-scoring branches, KAPPA maintains accuracy while substantially reducing memory and token usage. Experiments on GSM8K and MATH500 with DeepSeek-R1-Distill-Qwen-1.5B and Qwen2.5-7B-Instruct demonstrate that KAPPA stabilizes performance in smaller models and achieves up to ~60% reduction in peak memory and ~90% reduction in total token generation relative to BoN, with minimal impact on accuracy.

cs.LG↗

arXiv2023

Mosaic number and Tile number of Corner Connection Tiles

Lomonaco and Kauffman introduced knot mosaics in 2008 to model physical quantum states. These mosaics use a set of tiles to represent knots on $n x n$ grids. In 2023 Heap introduced a new set of tiles that can represent knots on a smaller board for small knots. Completing an exhaustive search of all knots or links, $K$, on different board sizes and types is the most common way to determine invariants for knots, such as the smallest board size needed to represent a knot, $m(K)$, and the least number of tiles needed to represent a knot, $t(K)$. In this paper, we propose a solution to an open question by providing a proof that all knots or links can be represented on corner connection mosaics using fewer tiles than traditional mosaics $t_c(K) < t(K)$, where $t_c(K)$ is the smallest number of corner connection tiles needed to represent knot \textit{K}. We also define bounds for corner connection mosaic size, $m_c(K)$, in terms of crossing number, $c(K)$, and simultaneously create a tool called the \textit{Corner Mosaic Complement} that we use to discover a relationship between traditional tiles and corner connection tiles. Finally, we construct an infinite family of links $L_n$ where the corner connection mosaic number $m_c(K)$ is known and provide a tool to analyze the efficiency of corner connection mosaic tiles.

math.GT↗

arXiv2015

The Proton Radius from Electron Scattering Data

[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. [Method] We make use of stepwise regression techniques using the $F$-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. [Results] Starting with the precision, low four-momentum transfer ($Q^2$) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Pad\'e ($N=M=1$) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E(Q^2) = ( 1 + Q^2/0.66\,\mathrm{GeV}^2)^{-2}$. [Conclusions] From this statistical analysis, we conclude that the electron scattering result and the muonic hydrogen result are consistent. It is the atomic hydrogen results that are the outliers.

nucl-ex↗