Influence functions provide a principled method to assess the contribution of individual training samples to a specific target. Yet, their high computational costs limit their applications on large-scale models and datasets. Existing methods proposed for influence function approximation have significantly reduced the computational overheads. However, they mostly suffer from inaccurate estimation due to the lack of strong convergence guarantees from the algorithm. The family of hyperpower methods are well-known for their rigorous convergence guarantees on matrix inverse approximation, while the matrix multiplication operation can involve intractable memory and computation costs on large-scale models. We propose HyperINF, an efficient and accurate influence function approximation method which leverages the hyperpower method, specifically Schulz's iterative algorithm. To deal with the computation-intensive matrix multiplication, we incorporate the generalized fisher information (GFIM) as a low-rank approximation of the Hessian matrix, which reduces the memory and computation overheads to constant costs independent of ranks on LoRA-tuned models. We first demonstrate the superior accuracy and stability of \method compared to other baselines through a synthetic convergence simulation for matrix inversion. We further validate the efficacy of \method through extensive real-world data attribution tasks, including mislabeled data detection and data selection for LLM and VLM fine-tuning. On LoRA-tuned models, HyperINF achieves superior downstream performance with minimal memory and computational overhead, while other baselines suffer from significant degradation. Our codebase is available at https://github.com/Blackzxy/HyperINF.

The composition of training data mixtures is critical for effectively training large language models (LLMs), as it directly impacts their performance on downstream tasks. Our goal is to identify an optimal data mixture to specialize an LLM for a specific task with access to only a few examples. Traditional approaches to this problem include ad-hoc reweighting methods, importance sampling, and gradient alignment techniques. This paper focuses on gradient alignment and introduces Dynamic Gradient Alignment (DGA), a scalable online gradient alignment algorithm. DGA dynamically estimates the pre-training data mixture on which the models' gradients align as well as possible with those of the model on the specific task. DGA is the first gradient alignment approach that incurs minimal overhead compared to standard pre-training and outputs a competitive model, eliminating the need for retraining the model. Experimentally, we demonstrate significant improvements over importance sampling in two key scenarios: (i) when the pre-training set is small and importance sampling overfits due to limited data; and (ii) when there is insufficient specialized data, trapping importance sampling on narrow pockets of data. Our findings underscore the effectiveness of gradient alignment methods in optimizing training data mixtures, particularly in data-constrained environments, and offer a practical solution for enhancing LLM performance on specific tasks with limited data availability.

Specialist language models (LMs) focus on a specific task or domain on which they often outperform generalist LMs of the same size. However, the specialist data needed to pretrain these models is only available in limited amount for most tasks. In this work, we build specialist models from large generalist training sets instead. We adjust the training distribution of the generalist data with guidance from the limited domain-specific data. We explore several approaches, with clustered importance sampling standing out. This method clusters the generalist dataset and samples from these clusters based on their frequencies in the smaller specialist dataset. It is scalable, suitable for pretraining and continued pretraining, it works well in multi-task settings. Our findings demonstrate improvements across different domains in terms of language modeling perplexity and accuracy on multiple-choice question tasks. We also present ablation studies that examine the impact of dataset sizes, clustering configurations, and model sizes. Generalist language models (LMs) can address a wide variety of tasks, but this generality comes at a cost (Brown et al., 2020). It necessitates a large training set representative of all prospective tasks, as well as a large model to fit such a comprehensive dataset.

Recent research on the grokking phenomenon has illuminated the intricacies of neural networks' training dynamics and their generalization behaviors. Grokking refers to a sharp rise of the network's generalization accuracy on the test set, which occurs long after an extended overfitting phase, during which the network perfectly fits the training set. While the existing research primarily focus on shallow networks such as 2-layer MLP and 1-layer Transformer, we explore grokking on deep networks (e.g. 12-layer MLP). We empirically replicate the phenomenon and find that deep neural networks can be more susceptible to grokking than its shallower counterparts. Meanwhile, we observe an intriguing multi-stage generalization phenomenon when increase the depth of the MLP model where the test accuracy exhibits a secondary surge, which is scarcely seen on shallow models. We further uncover compelling correspondences between the decreasing of feature ranks and the phase transition from overfitting to the generalization stage during grokking. Additionally, we find that the multi-stage generalization phenomenon often aligns with a double-descent pattern in feature ranks. These observations suggest that internal feature rank could serve as a more promising indicator of the model's generalization behavior compared to the weight-norm. We believe our work is the first one to dive into grokking in deep neural networks, and investigate the relationship of feature rank and generalization performance.

The coverage and composition of the pretraining data significantly impacts the generalization ability of Large Language Models (LLMs). Despite its importance, recent LLMs still rely on heuristics and trial and error to increase or reduce the influence of data-domains. We propose DOmain reweighting with Generalization Estimation (DoGE), which optimizes the probability of sampling from each domain (domain weights) in a principled way. Our approach is a two-stage process consisting of (i) training a proxy model to obtain domain weights using a bi-level optimization algorithm; (ii) training a larger base model by sampling training domains according to the learned domain weights. In our experiments, we extensively show how DoGE improves the generalization of the base model to any target data mixture. On the SlimPajama dataset, our base model gets better perplexity and few-shot reasoning accuracies across $6$ tasks compared to baseline methods. Moreover, aiming to generalize to out-of-domain target tasks, which is unseen in the pretraining corpus (OOD domain), DoGE can effectively identify inter-domain dependencies, and consistently achieves better test perplexity on the target domain.

Large language models (LLMs) can potentially democratize access to medical knowledge. While many efforts have been made to harness and improve LLMs' medical knowledge and reasoning capacities, the resulting models are either closed-source (e.g., PaLM, GPT-4) or limited in scale (<= 13B parameters), which restricts their abilities. In this work, we improve access to large-scale medical LLMs by releasing MEDITRON: a suite of open-source LLMs with 7B and 70B parameters adapted to the medical domain. MEDITRON builds on Llama-2 (through our adaptation of Nvidia's Megatron-LM distributed trainer), and extends pretraining on a comprehensively curated medical corpus, including selected PubMed articles, abstracts, and internationally-recognized medical guidelines. Evaluations using four major medical benchmarks show significant performance gains over several state-of-the-art baselines before and after task-specific finetuning. Overall, MEDITRON achieves a 6% absolute performance gain over the best public baseline in its parameter class and 3% over the strongest baseline we finetuned from Llama-2. Compared to closed-source LLMs, MEDITRON-70B outperforms GPT-3.5 and Med-PaLM and is within 5% of GPT-4 and 10% of Med-PaLM-2. We release our code for curating the medical pretraining corpus and the MEDITRON model weights to drive open-source development of more capable medical LLMs.

Automatic data selection and curriculum design for training large language models is challenging, with only a few existing methods showing improvements over standard training. Furthermore, current schemes focus on domain-level selection, overlooking the more fine-grained contributions of each individual training point. It is difficult to apply traditional datapoint selection methods on large language models: most online batch selection methods perform two-times forward or backward passes, which introduces considerable extra costs with large-scale models. To mitigate these obstacles, we propose irreducible curriculum as a curriculum learning algorithm for language model pretraining, which prioritizes samples with higher learnability. Specifically, to avoid prohibitive extra computation overhead, we simulate the sample loss along the main model's training trajectory using a small-scale proxy model. Our experiments on the RedPajama-1B dataset demonstrate a consistent improvement on validation perplexity across all 7 domains compared to random uniform baseline and the anti-curriculum strategy. Our method also reduces the sharpness of the network and illustrates a better 5-shot accuracy on MMLU benchmarks.