NeurIPS 2024 Papers

Large language models (LLMs) have shown impressive performance on downstream tasks by in-context learning (ICL), which heavily relies on the quality of demonstrations selected from a large set of annotated examples. Recent works claim that in-context learning is robust to noisy demonstrations in text classification. In this work, we show that, on text generation tasks, noisy annotations significantly hurt the performance of in-context learning. To circumvent the issue, we propose a simple and effective approach called Local Perplexity Ranking (LPR), which replaces the "noisy" candidates with their nearest neighbors that are more likely to be clean. Our method is motivated by analyzing the perplexity deviation caused by noisy labels and decomposing perplexity into inherent perplexity and matching perplexity. Our key idea behind LPR is thus to decouple the matching perplexity by performing the ranking among the neighbors in semantic space. Our approach can prevent the selected demonstrations from including mismatched input-label pairs while preserving the effectiveness of the original selection methods. Extensive experiments demonstrate the effectiveness of LPR, improving the EM score by up to 18.75 on common benchmarks with noisy annotations.

Machine learning based surrogate models offer researchers powerful tools for accelerating simulation-based workflows. However, as standard datasets in this space often cover small classes of physical behavior, it can be difficult to evaluate the efficacy of new approaches. To address this gap, we introduce the Well: a large-scale collection of datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. The Well draws from domain experts and numerical software developers to provide 15TB of data across 16 datasets covering diverse domains such as biological systems, fluid dynamics, acoustic scattering, as well as magneto-hydrodynamic simulations of extra-galactic fluids or supernova explosions. These datasets can be used individually or as part of a broader benchmark suite. To facilitate usage of the Well, we provide a unified PyTorch interface for training and evaluating models. We demonstrate the function of this library by introducing example baselines that highlight the new challenges posed by the complex dynamics of the Well. The code and data is available at https://github.com/PolymathicAI/the_well.

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights. We consider the asymptotic limit where the input dimension and the network width are proportionally large. Recent work [Cui et al., 2023] established that linear regression provides Bayes-optimal test error to learn such a function when the number of available samples is only linear in the dimension. That work stressed the open challenge of theoretically analyzing the optimal test error in the more interesting regime where the number of samples is quadratic in the dimension. In this paper, we solve this challenge for quadratic activations and derive a closed-form expression for the Bayes-optimal test error. We also provide an algorithm, that we call GAMP-RIE, which combines approximate message passing with rotationally invariant matrix denoising, and that asymptotically achieves the optimal performance. Technically, our result is enabled by establishing a link with recent works on optimal denoising of extensive-rank matrices and on the ellipsoid fitting problem. We further show empirically that, in the absence of noise, randomly-initialized gradient descent seems to sample the space of weights, leading to zero training loss, and averaging over initialization leads to a test error equal to the Bayes-optimal one.