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Global Optimization with A Power-Transformed Objective and Gaussian Smoothing

arXiv.org Artificial Intelligence

We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-$N$ transformation to the not-necessarily differentiable objective function $f$ and get $f_N$, and (2) optimize the Gaussian-smoothed $f_N$ with stochastic approximations. Under mild conditions on $f$, for any $\delta>0$, we prove that with a sufficiently large power $N_\delta$, this method converges to a solution in the $\delta$-neighborhood of $f$'s global optimum point. The convergence rate is $O(d^2\sigma^4\varepsilon^{-2})$, which is faster than both the standard and single-loop homotopy methods if $\sigma$ is pre-selected to be in $(0,1)$. In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.


Evaluation data contamination in LLMs: how do we measure it and (when) does it matter?

arXiv.org Artificial Intelligence

Hampering the interpretation of benchmark scores, evaluation data contamination has become a growing concern in the evaluation of LLMs, and an active area of research studies its effects. While evaluation data contamination is easily understood intuitively, it is surprisingly difficult to define precisely which samples should be considered contaminated and, consequently, how it impacts benchmark scores. We propose that these questions should be addressed together and that contamination metrics can be assessed based on whether models benefit from the examples they mark contaminated. We propose a novel analysis method called ConTAM, and show with a large scale survey of existing and novel n-gram based contamination metrics across 13 benchmarks and 7 models from 2 different families that ConTAM can be used to better understand evaluation data contamination and its effects. We find that contamination may have a much larger effect than reported in recent LLM releases and benefits models differently at different scales. We also find that considering only the longest contaminated substring provides a better signal than considering a union of all contaminated substrings, and that doing model and benchmark specific threshold analysis greatly increases the specificity of the results. Lastly, we investigate the impact of hyperparameter choices, finding that, among other things, both using larger values of n and disregarding matches that are infrequent in the pre-training data lead to many false negatives. With ConTAM, we provide a method to empirically ground evaluation data contamination metrics in downstream effects. With our exploration, we shed light on how evaluation data contamination can impact LLMs and provide insight into the considerations important when doing contamination analysis. We end our paper by discussing these in more detail and providing concrete suggestions for future work.


Embedding Pose Graph, Enabling 3D Foundation Model Capabilities with a Compact Representation

arXiv.org Artificial Intelligence

This paper presents the Embedding Pose Graph (EPG), an innovative method that combines the strengths of foundation models with a simple 3D representation suitable for robotics applications. Addressing the need for efficient spatial understanding in robotics, EPG provides a compact yet powerful approach by attaching foundation model features to the nodes of a pose graph. Unlike traditional methods that rely on bulky data formats like voxel grids or point clouds, EPG is lightweight and scalable. It facilitates a range of robotic tasks, including open-vocabulary querying, disambiguation, image-based querying, language-directed navigation, and re-localization in 3D environments. We showcase the effectiveness of EPG in handling these tasks, demonstrating its capacity to improve how robots interact with and navigate through complex spaces. Through both qualitative and quantitative assessments, we illustrate EPG's strong performance and its ability to outperform existing methods in re-localization. Our work introduces a crucial step forward in enabling robots to efficiently understand and operate within large-scale 3D spaces.