Pre-training Small Base LMs with Fewer Tokens

We study the effectiveness of a simple approach to develop a small base language model (LM) starting from an existing large base LM: first inherit a few transformer blocks from the larger LM, and then train this smaller model on a very small subset (0.1\%) of the raw pretraining data of the larger model. We call our simple recipe Inheritune and first demonstrate it for building a small base LM with 1.5B parameters using 1B tokens (and a starting few layers of larger LM of 3B parameters); we do this using a single A6000 GPU for less than half a day. Across 9 diverse evaluation datasets as well as the MMLU benchmark, the resulting model compares favorably to publicly available base models of 1B-2B size, some of which have been trained using 50-1000 times more tokens. We investigate Inheritune in a slightly different setting where we train small LMs utilizing larger LMs and their full pre-training dataset. Here we show that smaller LMs trained utilizing some of the layers of GPT2-medium (355M) and GPT-2-large (770M) can effectively match the val loss of their bigger counterparts when trained from scratch for the same number of training steps on OpenWebText dataset with 9B tokens. We analyze our recipe with extensive experiments and demonstrate it efficacy on diverse settings. Our code is available at https://github.com/sanyalsunny111/LLM-Inheritune.

Time Weaver: A Conditional Time Series Generation Model

Imagine generating a city's electricity demand pattern based on weather, the presence of an electric vehicle, and location, which could be used for capacity planning during a winter freeze. Such real-world time series are often enriched with paired heterogeneous contextual metadata (weather, location, etc.). Current approaches to time series generation often ignore this paired metadata, and its heterogeneity poses several practical challenges in adapting existing conditional generation approaches from the image, audio, and video domains to the time series domain. To address this gap, we introduce Time Weaver, a novel diffusion-based model that leverages the heterogeneous metadata in the form of categorical, continuous, and even time-variant variables to significantly improve time series generation. Additionally, we show that naive extensions of standard evaluation metrics from the image to the time series domain are insufficient. These metrics do not penalize conditional generation approaches for their poor specificity in reproducing the metadata-specific features in the generated time series. Thus, we innovate a novel evaluation metric that accurately captures the specificity of conditional generation and the realism of the generated time series. We show that Time Weaver outperforms state-of-the-art benchmarks, such as Generative Adversarial Networks (GANs), by up to 27% in downstream classification tasks on real-world energy, medical, air quality, and traffic data sets.

In-Context Learning with Transformers: Softmax Attention Adapts to Function Lipschitzness

A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with making a prediction in that context. As such that learner must adapt to the context without additional training. We explore the role of softmax attention in an ICL setting where each context encodes a regression task. We show that an attention unit learns a window that it uses to implement a nearest-neighbors predictor adapted to the landscape of the pretraining tasks. Specifically, we show that this window widens with decreasing Lipschitzness and increasing label noise in the pretraining tasks. We also show that on low-rank, linear problems, the attention unit learns to project onto the appropriate subspace before inference. Further, we show that this adaptivity relies crucially on the softmax activation and thus cannot be replicated by the linear activation often studied in prior theoretical analyses.

Towards Quantifying the Preconditioning Effect of Adam

There is a notable dearth of results characterizing the preconditioning effect of Adam and showing how it may alleviate the curse of ill-conditioning -- an issue plaguing gradient descent (GD). In this work, we perform a detailed analysis of Adam's preconditioning effect for quadratic functions and quantify to what extent Adam can mitigate the dependence on the condition number of the Hessian. Our key finding is that Adam can suffer less from the condition number but at the expense of suffering a dimension-dependent quantity. Specifically, for a $d$-dimensional quadratic with a diagonal Hessian having condition number $\kappa$, we show that the effective condition number-like quantity controlling the iteration complexity of Adam without momentum is $\mathcal{O}(\min(d, \kappa))$. For a diagonally dominant Hessian, we obtain a bound of $\mathcal{O}(\min(d \sqrt{d \kappa}, \kappa))$ for the corresponding quantity. Thus, when $d < \mathcal{O}(\kappa^p)$ where $p = 1$ for a diagonal Hessian and $p = 1/3$ for a diagonally dominant Hessian, Adam can outperform GD (which has an $\mathcal{O}(\kappa)$ dependence). On the negative side, our results suggest that Adam can be worse than GD for a sufficiently non-diagonal Hessian even if $d \ll \mathcal{O}(\kappa^{1/3})$; we corroborate this with empirical evidence. Finally, we extend our analysis to functions satisfying per-coordinate Lipschitz smoothness and a modified version of the Polyak-\L ojasiewicz condition.

Understanding the Training Speedup from Sampling with Approximate Losses

It is well known that selecting samples with large losses/gradients can significantly reduce the number of training steps. However, the selection overhead is often too high to yield any meaningful gains in terms of overall training time. In this work, we focus on the greedy approach of selecting samples with large \textit{approximate losses} instead of exact losses in order to reduce the selection overhead. For smooth convex losses, we show that such a greedy strategy can converge to a constant factor of the minimum value of the average loss in fewer iterations than the standard approach of random selection. We also theoretically quantify the effect of the approximation level. We then develop SIFT which uses early exiting to obtain approximate losses with an intermediate layer's representations for sample selection. We evaluate SIFT on the task of training a 110M parameter 12-layer BERT base model and show significant gains (in terms of training hours and number of backpropagation steps) without any optimized implementation over vanilla training. For e.g., to reach 64% validation accuracy, SIFT with exit at the first layer takes ~43 hours compared to ~57 hours of vanilla training.

Contrastive Approach to Prior Free Positive Unlabeled Learning

Positive Unlabeled (PU) learning refers to the task of learning a binary classifier given a few labeled positive samples, and a set of unlabeled samples (which could be positive or negative). In this paper, we propose a novel PU learning framework, that starts by learning a feature space through pretext-invariant representation learning and then applies pseudo-labeling to the unlabeled examples, leveraging the concentration property of the embeddings. Overall, our proposed approach handily outperforms state-of-the-art PU learning methods across several standard PU benchmark datasets, while not requiring a-priori knowledge or estimate of class prior. Remarkably, our method remains effective even when labeled data is scant, where most PU learning algorithms falter. We also provide simple theoretical analysis motivating our proposed algorithms and establish generalization guarantee for our approach.

Pretrained deep models outperform GBDTs in Learning-To-Rank under label scarcity

While deep learning (DL) models are state-of-the-art in text and image domains, they have not yet consistently outperformed Gradient Boosted Decision Trees (GBDTs) on tabular Learning-To-Rank (LTR) problems. Most of the recent performance gains attained by DL models in text and image tasks have used unsupervised pretraining, which exploits orders of magnitude more unlabeled data than labeled data. To the best of our knowledge, unsupervised pretraining has not been applied to the LTR problem, which often produces vast amounts of unlabeled data. In this work, we study whether unsupervised pretraining can improve LTR performance over GBDTs and other non-pretrained models. Using simple design choices--including SimCLR-Rank, our ranking-specific modification of SimCLR (an unsupervised pretraining method for images)--we produce pretrained deep learning models that soundly outperform GBDTs (and other non-pretrained models) in the case where labeled data is vastly outnumbered by unlabeled data. We also show that pretrained models also often achieve significantly better robustness than non-pretrained models (GBDTs or DL models) in ranking outlier data.

Logarithmic Bayes Regret Bounds

We derive the first finite-time logarithmic regret bounds for Bayesian bandits. For Gaussian bandits, we obtain a $O(c_h \log^2 n)$ bound, where $c_h$ is a prior-dependent constant. This matches the asymptotic lower bound of Lai (1987). Our proofs mark a technical departure from prior works, and are simple and general. To show generality, we apply our technique to linear bandits. Our bounds shed light on the value of the prior in the Bayesian setting, both in the objective and as a side information given to the learner. They significantly improve the $\tilde{O}(\sqrt{n})$ bounds, that despite the existing lower bounds, have become standard in the literature.

Understanding the Effectiveness of Early Weight Averaging for Training Large Language Models

Training LLMs is expensive, and recent evidence indicates training all the way to convergence is inefficient. In this paper, we investigate the ability of a simple idea, checkpoint averaging along the trajectory of a training run to improve the quality of models before they have converged. This approach incurs no extra cost during training or inference. Specifically, we analyze the training trajectories of Pythia LLMs with 1 to 12 billion parameters and demonstrate that, particularly during the early to mid stages of training, this idea accelerates convergence and improves both test and zero-shot generalization. Loss spikes are a well recognized problem in LLM training; in our analysis we encountered two instances of this in the underlying trajectories, and both instances were mitigated by our averaging. For a 6.9B parameter LLM, for example, our early weight averaging recipe can save upto 4200 hours of GPU time, which corresponds to significant savings in cloud compute costs.

Understanding Self-Distillation in the Presence of Label Noise

Self-distillation (SD) is the process of first training a \enquote{teacher} model and then using its predictions to train a \enquote{student} model with the \textit{same} architecture. Specifically, the student's objective function is $\big(\xi*\ell(\text{teacher's predictions}, \text{ student's predictions}) + (1-\xi)*\ell(\text{given labels}, \text{ student's predictions})\big)$, where $\ell$ is some loss function and $\xi$ is some parameter $\in [0,1]$. Empirically, SD has been observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with \textit{noisy labels}. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of $\xi$ that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that $\xi > 1$ works better than $\xi \leq 1$ even with the cross-entropy loss for several classification datasets when 50\% or 30\% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher in terms of accuracy. To our knowledge, this is the first result of its kind for the cross-entropy loss.