Learning Mixtures of Experts with EM

Mixtures of Experts (MoE) are Machine Learning models that involve partitioning the input space, with a separate "expert" model trained on each partition. Recently, MoE have become popular as components in today's large language models as a means to reduce training and inference costs. There, the partitioning function and the experts are both learnt jointly via gradient descent on the log-likelihood. In this paper we focus on studying the efficiency of the Expectation Maximization (EM) algorithm for the training of MoE models. We first rigorously analyze EM for the cases of linear or logistic experts, where we show that EM is equivalent to Mirror Descent with unit step size and a Kullback-Leibler Divergence regularizer. This perspective allows us to derive new convergence results and identify conditions for local linear convergence based on the signal-to-noise ratio (SNR). Experiments on synthetic and (small-scale) real-world data show that EM outperforms the gradient descent algorithm both in terms of convergence rate and the achieved accuracy.

RARe: Retrieval Augmented Retrieval with In-Context Examples

We investigate whether in-context examples, widely used in decoder-only language models (LLMs), can improve embedding model performance in retrieval tasks. Unlike in LLMs, naively prepending in-context examples (query-document pairs) to the target query at inference time does not work out of the box. We introduce a simple approach to enable retrievers to use in-context examples. Our approach, RARe, finetunes a pre-trained model with in-context examples whose query is semantically similar to the target query. This can be applied to adapt various base architectures (i.e., decoder-only language models, retriever models) and consistently achieves performance gains of up to +2.72% nDCG across various open-domain retrieval datasets (BeIR, RAR-b). In particular, we find RARe exhibits stronger out-of-domain generalization compared to models using queries without in-context examples, similar to what is seen for in-context learning in LLMs. We further provide analysis on the design choices of in-context example augmentation and lay the foundation for future work in this space.

Geometric Median (GM) Matching for Robust Data Pruning

Data pruning, the combinatorial task of selecting a small and informative subset from a large dataset, is crucial for mitigating the enormous computational costs associated with training data-hungry modern deep learning models at scale. Since large-scale data collections are invariably noisy, developing data pruning strategies that remain robust even in the presence of corruption is critical in practice. Unfortunately, the existing heuristics for (robust) data pruning lack theoretical coherence and rely on heroic assumptions, that are, often unattainable, by the very nature of the problem setting. Moreover, these strategies often yield sub-optimal neural scaling laws even compared to random sampling, especially in scenarios involving strong corruption and aggressive pruning rates -- making provably robust data pruning an open challenge. In response, in this work, we propose Geometric Median ($\gm$) Matching -- a herding~\citep{welling2009herding} style greedy algorithm -- that yields a $k$-subset such that the mean of the subset approximates the geometric median of the (potentially) noisy dataset. Theoretically, we show that $\gm$ Matching enjoys an improved $\gO(1/k)$ scaling over $\gO(1/\sqrt{k})$ scaling of uniform sampling; while achieving the optimal breakdown point of 1/2 even under arbitrary corruption. Extensive experiments across popular deep learning benchmarks indicate that $\gm$ Matching consistently outperforms prior state-of-the-art; the gains become more profound at high rates of corruption and aggressive pruning rates; making $\gm$ Matching a strong baseline for future research in robust data pruning.

DataComp-LM: In search of the next generation of training sets for language models

We introduce DataComp for Language Models (DCLM), a testbed for controlled dataset experiments with the goal of improving language models. As part of DCLM, we provide a standardized corpus of 240T tokens extracted from Common Crawl, effective pretraining recipes based on the OpenLM framework, and a broad suite of 53 downstream evaluations. Participants in the DCLM benchmark can experiment with data curation strategies such as deduplication, filtering, and data mixing at model scales ranging from 412M to 7B parameters. As a baseline for DCLM, we conduct extensive experiments and find that model-based filtering is key to assembling a high-quality training set. The resulting dataset, DCLM-Baseline enables training a 7B parameter language model from scratch to 64% 5-shot accuracy on MMLU with 2.6T training tokens. Compared to MAP-Neo, the previous state-of-the-art in open-data language models, DCLM-Baseline represents a 6.6 percentage point improvement on MMLU while being trained with 40% less compute. Our baseline model is also comparable to Mistral-7B-v0.3 and Llama 3 8B on MMLU (63% & 66%), and performs similarly on an average of 53 natural language understanding tasks while being trained with 6.6x less compute than Llama 3 8B. Our results highlight the importance of dataset design for training language models and offer a starting point for further research on data curation.

Retraining with Predicted Hard Labels Provably Increases Model Accuracy

The performance of a model trained with \textit{noisy labels} is often improved by simply \textit{retraining} the model with its own predicted \textit{hard} labels (i.e., $1$/$0$ labels). Yet, a detailed theoretical characterization of this phenomenon is lacking. In this paper, we theoretically analyze retraining in a linearly separable setting with randomly corrupted labels given to us and prove that retraining can improve the population accuracy obtained by initially training with the given (noisy) labels. To the best of our knowledge, this is the first such theoretical result. Retraining finds application in improving training with label differential privacy (DP) which involves training with noisy labels. We empirically show that retraining selectively on the samples for which the predicted label matches the given label significantly improves label DP training at \textit{no extra privacy cost}; we call this \textit{consensus-based retraining}. For e.g., when training ResNet-18 on CIFAR-100 with $\epsilon=3$ label DP, we obtain $6.4\%$ improvement in accuracy with consensus-based retraining.

Adaptive and Optimal Second-order Optimistic Methods for Minimax Optimization

We propose adaptive, line search-free second-order methods with optimal rate of convergence for solving convex-concave min-max problems. By means of an adaptive step size, our algorithms feature a simple update rule that requires solving only one linear system per iteration, eliminating the need for line search or backtracking mechanisms. Specifically, we base our algorithms on the optimistic method and appropriately combine it with second-order information. Moreover, distinct from common adaptive schemes, we define the step size recursively as a function of the gradient norm and the prediction error in the optimistic update. We first analyze a variant where the step size requires knowledge of the Lipschitz constant of the Hessian. Under the additional assumption of Lipschitz continuous gradients, we further design a parameter-free version by tracking the Hessian Lipschitz constant locally and ensuring the iterates remain bounded. We also evaluate the practical performance of our algorithm by comparing it to existing second-order algorithms for minimax optimization.

SVFT: Parameter-Efficient Fine-Tuning with Singular Vectors

Popular parameter-efficient fine-tuning (PEFT) methods, such as LoRA and its variants, freeze pre-trained model weights \(W\) and inject learnable matrices \(\Delta W\). These \(\Delta W\) matrices are structured for efficient parameterization, often using techniques like low-rank approximations or scaling vectors. However, these methods typically show a performance gap compared to full fine-tuning. Although recent PEFT methods have narrowed this gap, they do so at the cost of additional learnable parameters. We propose SVFT, a simple approach that fundamentally differs from existing methods: the structure imposed on \(\Delta W\) depends on the specific weight matrix \(W\). Specifically, SVFT updates \(W\) as a sparse combination of outer products of its singular vectors, training only the coefficients (scales) of these sparse combinations. This approach allows fine-grained control over expressivity through the number of coefficients. Extensive experiments on language and vision benchmarks show that SVFT recovers up to 96% of full fine-tuning performance while training only 0.006 to 0.25% of parameters, outperforming existing methods that only recover up to 85% performance using 0.03 to 0.8% of the trainable parameter budget.

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.