Synthetic data has the potential to improve the performance, training efficiency, and privacy of real training examples. Nevertheless, existing approaches for synthetic text generation are mostly heuristics and cannot generate human-readable text without compromising the privacy of real data or provide performance guarantees for training Large Language Models (LLMs). In this work, we propose the first theoretically rigorous approach for generating synthetic human-readable text that guarantees the convergence and performance of LLMs during fine-tuning on a target task. To do so, we leverage Alternating Direction Method of Multipliers (ADMM) that iteratively optimizes the embeddings of synthetic examples to match the gradient of the target training or validation data, and maps them to a sequence of text tokens with low perplexity. In doing so, the generated synthetic text can guarantee convergence of the model to a close neighborhood of the solution obtained by fine-tuning on real data. Experiments on various classification tasks confirm the effectiveness of our proposed approach.

Large Language Models (LLMs) suffer from hallucination problems, which hinder their reliability in sensitive applications. In the black-box setting, several self-consistency-based techniques have been proposed for hallucination detection. We empirically study these techniques and show that they achieve performance close to that of a supervised (still black-box) oracle, suggesting little room for improvement within this paradigm. To address this limitation, we explore cross-model consistency checking between the target model and an additional verifier LLM. With this extra information, we observe improved oracle performance compared to purely self-consistency-based methods. We then propose a budget-friendly, two-stage detection algorithm that calls the verifier model only for a subset of cases. It dynamically switches between self-consistency and cross-consistency based on an uncertainty interval of the self-consistency classifier. We provide a geometric interpretation of consistency-based hallucination detection methods through the lens of kernel mean embeddings, offering deeper theoretical insights. Extensive experiments show that this approach maintains high detection performance while significantly reducing computational cost.

Weak-to-Strong Generalization (W2SG), where a weak model supervises a stronger one, serves as an important analogy for understanding how humans might guide superhuman intelligence in the future. Promising empirical results revealed that a strong model can surpass its weak supervisor. While recent work has offered theoretical insights into this phenomenon, a clear understanding of the interactions between weak and strong models that drive W2SG remains elusive. We investigate W2SG through a theoretical lens and show that it can be characterized using kernels derived from the principal components of weak and strong models' internal representations. These kernels can be used to define a space that, at a high level, captures what the weak model is unable to learn but is learnable by the strong model. The projection of labels onto this space quantifies how much the strong model falls short of its full potential due to weak supervision. This characterization also provides insights into how certain errors in weak supervision can be corrected by the strong model, regardless of overfitting. Our theory has significant practical implications, providing a representation-based metric that predicts W2SG performance trends without requiring labels, as shown in experiments on molecular predictions with transformers and 5 NLP tasks involving 52 LLMs.

Vision-language models (VLMs) are highly effective but often underperform on specialized tasks; for example, Llava-1.5 struggles with chart and diagram understanding due to scarce task-specific training data. Existing training data, sourced from general-purpose datasets, fails to capture the nuanced details needed for these tasks. We introduce MM-Gen, a scalable method that generates task-specific, high-quality synthetic text for candidate images by leveraging stronger models. MM-Gen employs a three-stage targeted process: partitioning data into subgroups, generating targeted text based on task descriptions, and filtering out redundant and outlier data. Fine-tuning VLMs with data generated by MM-Gen leads to significant performance gains, including 29% on spatial reasoning and 15% on diagram understanding for Llava-1.5 (7B). Compared to human-curated caption data, MM-Gen achieves up to 1.6x better improvements for the original models, proving its effectiveness in enhancing task-specific VLM performance and bridging the gap between general-purpose datasets and specialized requirements. Code available at https://github.com/sjoshi804/MM-Gen.

Dataset distillation (DD) generates small synthetic datasets that can efficiently train deep networks with a limited amount of memory and compute. Despite the success of DD methods for supervised learning, DD for self-supervised pre-training of deep models has remained unaddressed. Pre-training on unlabeled data is crucial for efficiently generalizing to downstream tasks with limited labeled data. In this work, we propose the first effective DD method for SSL pre-training. First, we show, theoretically and empirically, that naive application of supervised DD methods to SSL fails, due to the high variance of the SSL gradient. Then, we address this issue by relying on insights from knowledge distillation (KD) literature. Specifically, we train a small student model to match the representations of a larger teacher model trained with SSL. Then, we generate a small synthetic dataset by matching the training trajectories of the student models. As the KD objective has considerably lower variance than SSL, our approach can generate synthetic datasets that can successfully pre-train high-quality encoders. Through extensive experiments, we show that our distilled sets lead to up to 13% higher accuracy than prior work, on a variety of downstream tasks, in the presence of limited labeled data.

Can we modify the training data distribution to encourage the underlying optimization method toward finding solutions with superior generalization performance on in-distribution data? In this work, we approach this question for the first time by comparing the inductive bias of gradient descent (GD) with that of sharpness-aware minimization (SAM). By studying a two-layer CNN, we prove that SAM learns easy and difficult features more uniformly, particularly in early epochs. That is, SAM is less susceptible to simplicity bias compared to GD. Based on this observation, we propose USEFUL, an algorithm that clusters examples based on the network output early in training and upsamples examples with no easy features to alleviate the pitfalls of the simplicity bias. We show empirically that modifying the training data distribution in this way effectively improves the generalization performance on the original data distribution when training with (S)GD by mimicking the training dynamics of SAM. Notably, we demonstrate that our method can be combined with SAM and existing data augmentation strategies to achieve, to the best of our knowledge, state-of-the-art performance for training ResNet18 on CIFAR10, STL10, CINIC10, Tiny-ImageNet; ResNet34 on CIFAR100; and VGG19 and DenseNet121 on CIFAR10.

Contrastive Language-Image Pre-training (CLIP) on large-scale image-caption datasets learns representations that can achieve remarkable zero-shot generalization. However, such models require a massive amount of pre-training data. Improving the quality of the pre-training data has been shown to be much more effective in improving CLIP's performance than increasing its volume. Nevertheless, finding small subsets of training data that provably generalize the best has remained an open question. In this work, we propose the first theoretically rigorous data selection method for CLIP. We show that subsets that closely preserve the cross-covariance of the images and captions of the full data provably achieve a superior generalization performance. Our extensive experiments on ConceptualCaptions3M and ConceptualCaptions12M demonstrate that subsets found by \method\ achieve over 2.7x and 1.4x the accuracy of the next best baseline on ImageNet and its shifted versions. Moreover, we show that our subsets obtain 1.5x the average accuracy across 11 downstream datasets, of the next best baseline. The code is available at: https://github.com/BigML-CS-UCLA/clipcov-data-efficient-clip.

An effective technique for obtaining high-quality representations is adding a projection head on top of the encoder during training, then discarding it and using the pre-projection representations. Despite its proven practical effectiveness, the reason behind the success of this technique is poorly understood. The pre-projection representations are not directly optimized by the loss function, raising the question: what makes them better? In this work, we provide a rigorous theoretical answer to this question. We start by examining linear models trained with self-supervised contrastive loss. We reveal that the implicit bias of training algorithms leads to layer-wise progressive feature weighting, where features become increasingly unequal as we go deeper into the layers. Consequently, lower layers tend to have more normalized and less specialized representations. We theoretically characterize scenarios where such representations are more beneficial, highlighting the intricate interplay between data augmentation and input features. Additionally, we demonstrate that introducing non-linearity into the network allows lower layers to learn features that are completely absent in higher layers. Finally, we show how this mechanism improves the robustness in supervised contrastive learning and supervised learning. We empirically validate our results through various experiments on CIFAR-10/100, UrbanCars and shifted versions of ImageNet. We also introduce a potential alternative to projection head, which offers a more interpretable and controllable design.

Recently, multimodal contrastive learning (MMCL) approaches, such as CLIP, have achieved a remarkable success in learning representations that are robust against distribution shift and generalize to new domains. Despite the empirical success, the mechanism behind learning such generalizable representations is not understood. In this work, we rigorously analyze this problem and uncover two mechanisms behind MMCL's robustness: \emph{intra-class contrasting}, which allows the model to learn features with a high variance, and \emph{inter-class feature sharing}, where annotated details in one class help learning other classes better. Both mechanisms prevent spurious features that are over-represented in the training data to overshadow the generalizable core features. This yields superior zero-shot classification accuracy under distribution shift. Furthermore, we theoretically demonstrate the benefits of using rich captions on robustness and explore the effect of annotating different types of details in the captions. We validate our theoretical findings through experiments, including a well-designed synthetic experiment and an experiment involving training CLIP models on MSCOCO/Conceptual Captions and evaluating them on shifted ImageNets.

Despite the effectiveness of data selection for large language models (LLMs) during pretraining and instruction fine-tuning phases, improving data efficiency in supervised fine-tuning (SFT) for specialized domains poses significant challenges due to the complexity of fine-tuning data. To bridge this gap, we introduce an effective and scalable data selection method for SFT, SmallToLarge (S2L), which leverages training trajectories from small models to guide the data selection for larger models. We demonstrate through extensive experiments that S2L significantly improves data efficiency in SFT for mathematical problem-solving, reducing the training data to just 11% of the original MathInstruct dataset (Yue et al., 2023) to match full dataset performance while outperforming state-of-the-art data selection algorithms by an average of 4.7% across 6 in- and out-domain evaluation datasets. Remarkably, selecting only 50K data for SFT, S2L achieves a 32.7% accuracy on the most challenging MATH (Hendrycks et al., 2021) benchmark, improving Phi-2 (Li et al., 2023b) by 16.6%. In clinical text summarization on the MIMIC-III dataset (Johnson et al., 2016), S2L again outperforms training on the full dataset using only 50% of the data. Notably, S2L can perform data selection using a reference model 40x smaller than the target model, proportionally reducing the cost of data selection.