Scaling Laws for the Value of Individual Data Points in Machine Learning

Recent works have shown that machine learning models improve at a predictable rate with the total amount of training data, leading to scaling laws that describe the relationship between error and dataset size. These scaling laws can help design a model's training dataset, but they typically take an aggregate view of the data by only considering the dataset's size. We introduce a new perspective by investigating scaling behavior for the value of individual data points: we find that a data point's contribution to model's performance shrinks predictably with the size of the dataset in a log-linear manner. Interestingly, there is significant variability in the scaling exponent among different data points, indicating that certain points are more valuable in small datasets while others are relatively more useful as a part of large datasets. We provide learning theory to support our scaling law, and we observe empirically that it holds across diverse model classes. We further propose a maximum likelihood estimator and an amortized estimator to efficiently learn the individualized scaling behaviors from a small number of noisy observations per data point. Using our estimators, we provide insights into factors that influence the scaling behavior of different data points. Finally, we demonstrate applications of the individualized scaling laws to data valuation and data subset selection. Overall, our work represents a first step towards understanding and utilizing scaling properties for the value of individual data points.

Mapping the Increasing Use of LLMs in Scientific Papers

Scientific publishing lays the foundation of science by disseminating research findings, fostering collaboration, encouraging reproducibility, and ensuring that scientific knowledge is accessible, verifiable, and built upon over time. Recently, there has been immense speculation about how many people are using large language models (LLMs) like ChatGPT in their academic writing, and to what extent this tool might have an effect on global scientific practices. However, we lack a precise measure of the proportion of academic writing substantially modified or produced by LLMs. To address this gap, we conduct the first systematic, large-scale analysis across 950,965 papers published between January 2020 and February 2024 on the arXiv, bioRxiv, and Nature portfolio journals, using a population-level statistical framework to measure the prevalence of LLM-modified content over time. Our statistical estimation operates on the corpus level and is more robust than inference on individual instances. Our findings reveal a steady increase in LLM usage, with the largest and fastest growth observed in Computer Science papers (up to 17.5%). In comparison, Mathematics papers and the Nature portfolio showed the least LLM modification (up to 6.3%). Moreover, at an aggregate level, our analysis reveals that higher levels of LLM-modification are associated with papers whose first authors post preprints more frequently, papers in more crowded research areas, and papers of shorter lengths. Our findings suggests that LLMs are being broadly used in scientific writings.

Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects

Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper partial identification bounds; however, unless the covariates are discrete with relatively small support, this approach typically requires consistent estimation of the conditional distributions of the potential outcomes given the covariates. Thus, existing approaches may fail under model misspecification or if consistency assumptions are violated. In this study, we propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands, based on duality theory for optimal transport problems. In randomized experiments, our approach can wrap around any estimates of the conditional distributions and provide uniformly valid inference, even if the initial estimates are arbitrarily inaccurate. Also, our approach is doubly robust in observational studies. Notably, this property allows analysts to use the multiplier bootstrap to select covariates and models without sacrificing validity even if the true model is not included. Furthermore, if the conditional distributions are estimated at semiparametric rates, our approach matches the performance of an oracle with perfect knowledge of the outcome model. Finally, we propose an efficient computational framework, enabling implementation on many practical problems in causal inference.

Understanding Multimodal Contrastive Learning and Incorporating Unpaired Data

Language-supervised vision models have recently attracted great attention in computer vision. A common approach to build such models is to use contrastive learning on paired data across the two modalities, as exemplified by Contrastive Language-Image Pre-Training (CLIP). In this paper, under linear representation settings, (i) we initiate the investigation of a general class of nonlinear loss functions for multimodal contrastive learning (MMCL) including CLIP loss and show its connection to singular value decomposition (SVD). Namely, we show that each step of loss minimization by gradient descent can be seen as performing SVD on a contrastive cross-covariance matrix. Based on this insight, (ii) we analyze the performance of MMCL. We quantitatively show that the feature learning ability of MMCL can be better than that of unimodal contrastive learning applied to each modality even under the presence of wrongly matched pairs. This characterizes the robustness of MMCL to noisy data. Furthermore, when we have access to additional unpaired data, (iii) we propose a new MMCL loss that incorporates additional unpaired datasets. We show that the algorithm can detect the ground-truth pairs and improve performance by fully exploiting unpaired datasets. The performance of the proposed algorithm was verified by numerical experiments.

Importance Tempering: Group Robustness for Overparameterized Models

Although overparameterized models have shown their success on many machine learning tasks, the accuracy could drop on the testing distribution that is different from the training one. This accuracy drop still limits applying machine learning in the wild. At the same time, importance weighting, a traditional technique to handle distribution shifts, has been demonstrated to have less or even no effect on overparameterized models both empirically and theoretically. In this paper, we propose importance tempering to improve the decision boundary and achieve consistently better results for overparameterized models. Theoretically, we justify that the selection of group temperature can be different under label shift and spurious correlation setting. At the same time, we also prove that properly selected temperatures can extricate the minority collapse for imbalanced classification. Empirically, we achieve state-of-the-art results on worst group classification tasks using importance tempering.

An Unconstrained Layer-Peeled Perspective on Neural Collapse

Neural collapse is a highly symmetric geometric pattern of neural networks that emerges during the terminal phase of training, with profound implications on the generalization performance and robustness of the trained networks. To understand how the last-layer features and classifiers exhibit this recently discovered implicit bias, in this paper, we introduce a surrogate model called the unconstrained layer-peeled model (ULPM). We prove that gradient flow on this model converges to critical points of a minimum-norm separation problem exhibiting neural collapse in its global minimizer. Moreover, we show that the ULPM with the cross-entropy loss has a benign global landscape for its loss function, which allows us to prove that all the critical points are strict saddle points except the global minimizers that exhibit the neural collapse phenomenon. Empirically, we show that our results also hold during the training of neural networks in real-world tasks when explicit regularization or weight decay is not used.

The Power of Contrast for Feature Learning: A Theoretical Analysis

Contrastive learning has achieved state-of-the-art performance in various self-supervised learning tasks and even outperforms its supervised counterpart. Despite its empirical success, theoretical understanding of why contrastive learning works is still limited. In this paper, (i) we provably show that contrastive learning outperforms autoencoder, a classical unsupervised learning method, for both feature recovery and downstream tasks; (ii) we also illustrate the role of labeled data in supervised contrastive learning. This provides theoretical support for recent findings that contrastive learning with labels improves the performance of learned representations in the in-domain downstream task, but it can harm the performance in transfer learning. We verify our theory with numerical experiments.