CVApr 27, 2023
DataComp: In search of the next generation of multimodal datasetsSamir Yitzhak Gadre, Gabriel Ilharco, Alex Fang et al. · allen-ai, stanford
Multimodal datasets are a critical component in recent breakthroughs such as Stable Diffusion and GPT-4, yet their design does not receive the same research attention as model architectures or training algorithms. To address this shortcoming in the ML ecosystem, we introduce DataComp, a testbed for dataset experiments centered around a new candidate pool of 12.8 billion image-text pairs from Common Crawl. Participants in our benchmark design new filtering techniques or curate new data sources and then evaluate their new dataset by running our standardized CLIP training code and testing the resulting model on 38 downstream test sets. Our benchmark consists of multiple compute scales spanning four orders of magnitude, which enables the study of scaling trends and makes the benchmark accessible to researchers with varying resources. Our baseline experiments show that the DataComp workflow leads to better training sets. In particular, our best baseline, DataComp-1B, enables training a CLIP ViT-L/14 from scratch to 79.2% zero-shot accuracy on ImageNet, outperforming OpenAI's CLIP ViT-L/14 by 3.7 percentage points while using the same training procedure and compute. We release DataComp and all accompanying code at www.datacomp.ai.
CVApr 14, 2023
Multimodal C4: An Open, Billion-scale Corpus of Images Interleaved with TextWanrong Zhu, Jack Hessel, Anas Awadalla et al. · allen-ai, cmu
In-context vision and language models like Flamingo support arbitrarily interleaved sequences of images and text as input. This format not only enables few-shot learning via interleaving independent supervised (image, text) examples, but also, more complex prompts involving interaction between images, e.g., "What do image A and image B have in common?" To support this interface, pretraining occurs over web corpora that similarly contain interleaved images+text. To date, however, large-scale data of this form have not been publicly available. We release Multimodal C4, an augmentation of the popular text-only C4 corpus with images interleaved. We use a linear assignment algorithm to place images into longer bodies of text using CLIP features, a process that we show outperforms alternatives. Multimodal C4 spans everyday topics like cooking, travel, technology, etc. A manual inspection of a random sample of documents shows that a vast majority (88%) of images are topically relevant, and that linear assignment frequently selects individual sentences specifically well-aligned with each image (80%). After filtering NSFW images, ads, etc., the resulting corpus consists of 101.2M documents with 571M images interleaved in 43B English tokens.
LGJun 16, 2023Code
Neural Priming for Sample-Efficient AdaptationMatthew Wallingford, Vivek Ramanujan, Alex Fang et al. · uw
We propose Neural Priming, a technique for adapting large pretrained models to distribution shifts and downstream tasks given few or no labeled examples. Presented with class names or unlabeled test samples, Neural Priming enables the model to recall and conditions its parameters on relevant data seen throughout pretraining, thereby priming it for the test distribution. Neural Priming can be performed at test time, even for pretraining datasets as large as LAION-2B. Performing lightweight updates on the recalled data significantly improves accuracy across a variety of distribution shift and transfer learning benchmarks. Concretely, in the zero-shot setting, we see a 2.45% improvement in accuracy on ImageNet and 3.81% accuracy improvement on average across standard transfer learning benchmarks. Further, using Neural Priming at inference to adapt to distribution shift, we see a 1.41% accuracy improvement on ImageNetV2. These results demonstrate the effectiveness of Neural Priming in addressing the challenge of limited labeled data and changing distributions. Code is available at github.com/RAIVNLab/neural-priming.
CVJan 10, 2023
Neural Radiance Field CodebooksMatthew Wallingford, Aditya Kusupati, Alex Fang et al. · uw
Compositional representations of the world are a promising step towards enabling high-level scene understanding and efficient transfer to downstream tasks. Learning such representations for complex scenes and tasks remains an open challenge. Towards this goal, we introduce Neural Radiance Field Codebooks (NRC), a scalable method for learning object-centric representations through novel view reconstruction. NRC learns to reconstruct scenes from novel views using a dictionary of object codes which are decoded through a volumetric renderer. This enables the discovery of reoccurring visual and geometric patterns across scenes which are transferable to downstream tasks. We show that NRC representations transfer well to object navigation in THOR, outperforming 2D and 3D representation learning methods by 3.1% success rate. We demonstrate that our approach is able to perform unsupervised segmentation for more complex synthetic (THOR) and real scenes (NYU Depth) better than prior methods (29% relative improvement). Finally, we show that NRC improves on the task of depth ordering by 5.5% accuracy in THOR.
CVMay 3, 2022
Data Determines Distributional Robustness in Contrastive Language Image Pre-training (CLIP)Alex Fang, Gabriel Ilharco, Mitchell Wortsman et al.
Contrastively trained language-image models such as CLIP, ALIGN, and BASIC have demonstrated unprecedented robustness to multiple challenging natural distribution shifts. Since these language-image models differ from previous training approaches in several ways, an important question is what causes the large robustness gains. We answer this question via a systematic experimental investigation. Concretely, we study five different possible causes for the robustness gains: (i) the training set size, (ii) the training distribution, (iii) language supervision at training time, (iv) language supervision at test time, and (v) the contrastive loss function. Our experiments show that the more diverse training distribution is the main cause for the robustness gains, with the other factors contributing little to no robustness. Beyond our experimental results, we also introduce ImageNet-Captions, a version of ImageNet with original text annotations from Flickr, to enable further controlled experiments of language-image training.
AISep 29, 2023
Data Filtering NetworksAlex Fang, Albin Madappally Jose, Amit Jain et al.
Large training sets have become a cornerstone of machine learning and are the foundation for recent advances in language modeling and multimodal learning. While data curation for pre-training is often still ad-hoc, one common paradigm is to first collect a massive pool of data from the Web and then filter this candidate pool down to an actual training set via various heuristics. In this work, we study the problem of learning a data filtering network (DFN) for this second step of filtering a large uncurated dataset. Our key finding is that the quality of a network for filtering is distinct from its performance on downstream tasks: for instance, a model that performs well on ImageNet can yield worse training sets than a model with low ImageNet accuracy that is trained on a small amount of high-quality data. Based on our insights, we construct new data filtering networks that induce state-of-the-art image-text datasets. Specifically, our best performing dataset DFN-5B enables us to train state-of-the-art CLIP models for their compute budgets: among other improvements on a variety of tasks, a ViT-H trained on our dataset achieves 84.4% zero-shot transfer accuracy on ImageNet, out-performing models trained on other datasets such as LAION-2B, DataComp-1B, or OpenAI's WIT. In order to facilitate further research in dataset design, we also release a new 2 billion example dataset DFN-2B and show that high performance data filtering networks can be trained from scratch using only publicly available data.
CVJan 11, 2023
Does progress on ImageNet transfer to real-world datasets?Alex Fang, Simon Kornblith, Ludwig Schmidt
Does progress on ImageNet transfer to real-world datasets? We investigate this question by evaluating ImageNet pre-trained models with varying accuracy (57% - 83%) on six practical image classification datasets. In particular, we study datasets collected with the goal of solving real-world tasks (e.g., classifying images from camera traps or satellites), as opposed to web-scraped benchmarks collected for comparing models. On multiple datasets, models with higher ImageNet accuracy do not consistently yield performance improvements. For certain tasks, interventions such as data augmentation improve performance even when architectures do not. We hope that future benchmarks will include more diverse datasets to encourage a more comprehensive approach to improving learning algorithms.
LGMar 17
The Finetuner's Fallacy: When to Pretrain with Your Finetuning DataChristina Baek, Ricardo Pio Monti, David Schwab et al.
Real-world model deployments demand strong performance on narrow domains where data is often scarce. Typically, practitioners finetune models to specialize them, but this risks overfitting to the domain and forgetting general knowledge. We study a simple strategy, specialized pretraining (SPT), where a small domain dataset, typically reserved for finetuning, is repeated starting from pretraining as a fraction of the total tokens. Across three specialized domains (ChemPile, MusicPile, and ProofPile), SPT improves domain performance and preserves general capabilities after finetuning compared to standard pretraining. In our experiments, SPT reduces the pretraining tokens needed to reach a given domain performance by up to 1.75x. These gains grow when the target domain is underrepresented in the pretraining corpus: on domains far from web text, a 1B SPT model outperforms a 3B standard pretrained model. Beyond these empirical gains, we derive overfitting scaling laws to guide practitioners in selecting the optimal domain-data repetition for a given pretraining compute budget. Our observations reveal the finetuner's fallacy: while finetuning may appear to be the cheapest path to domain adaptation, introducing specialized domain data during pretraining stretches its utility. SPT yields better specialized domain performance (via reduced overfitting across repeated exposures) and better general domain performance (via reduced forgetting during finetuning), ultimately achieving stronger results with fewer parameters and less total compute when amortized over inference. To get the most out of domain data, incorporate it as early in training as possible.
CLDec 9, 2025Code
Luxical: High-Speed Lexical-Dense Text EmbeddingsDatologyAI, Luke Merrick, Alex Fang et al.
Frontier language model quality increasingly hinges on our ability to organize web-scale text corpora for training. Today's dominant tools trade off speed and flexibility: lexical classifiers (e.g., FastText) are fast but limited to producing classification output scores, while the vector-valued outputs of transformer text embedding models flexibly support numerous workflows (e.g., clustering, classification, and retrieval) but are computationally expensive to produce. We introduce Luxical, a library for high-speed "lexical-dense" text embeddings that aims to recover the best properties of both approaches for web-scale text organization. Luxical combines sparse TF--IDF features, a small ReLU network, and a knowledge distillation training regimen to approximate large transformer embedding models at a fraction of their operational cost. In this technical report, we describe the Luxical architecture and training objective and evaluate a concrete Luxical model in two disparate applications: a targeted webcrawl document retrieval test and an end-to-end language model data curation task grounded in text classification. In these tasks we demonstrate speedups ranging from 3x to 100x over varying-sized neural baselines, and comparable to FastText model inference during the data curation task. On these evaluations, the tested Luxical model illustrates favorable compute/quality trade-offs for large-scale text organization, matching the quality of neural baselines. Luxical is available as open-source software at https://github.com/datologyai/luxical.
CLNov 6, 2025Code
Reusing Pre-Training Data at Test Time is a Compute MultiplierAlex Fang, Thomas Voice, Ruoming Pang et al.
Large language models learn from their vast pre-training corpora, gaining the ability to solve an ever increasing variety of tasks; yet although researchers work to improve these datasets, there is little effort to understand how efficient the pre-training apparatus is at extracting ideas and knowledge from the data. In this work, we use retrieval augmented generation along with test-time compute as a way to quantify how much dataset value was left behind by the process of pre-training, and how this changes across scale. We demonstrate that pre-training then retrieving from standard and largely open-sourced datasets results in significant accuracy gains in MMLU, Math-500, and SimpleQA, which persist through decontamination. For MMLU we observe that retrieval acts as a ~5x compute multiplier versus pre-training alone. We show that these results can be further improved by leveraging additional compute at test time to parse the retrieved context, demonstrating a 10 percentage point improvement on MMLU for the public LLaMA 3.1 8B model. Overall, our results suggest that today's pre-training methods do not make full use of the information in existing pre-training datasets, leaving significant room for progress.
CLMar 13, 2024Code
Language models scale reliably with over-training and on downstream tasksSamir Yitzhak Gadre, Georgios Smyrnis, Vaishaal Shankar et al. · allen-ai, cmu
Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are ultimately trained and evaluated. For instance, scaling is usually studied in the compute-optimal training regime (i.e., "Chinchilla optimal" regime). In contrast, models are often over-trained to reduce inference costs. Moreover, scaling laws mostly predict loss on next-token prediction, but models are usually compared on downstream task performance. To address both shortcomings, we create a testbed of 104 models with 0.011B to 6.9B parameters trained with various numbers of tokens on three data distributions. First, we fit scaling laws that extrapolate in both the amount of over-training and the number of model parameters. This enables us to predict the validation loss of a 1.4B parameter, 900B token run (i.e., 32$\times$ over-trained) and a 6.9B parameter, 138B token run (i.e., a compute-optimal run)$\unicode{x2014}$each from experiments that take 300$\times$ less compute. Second, we relate the perplexity of a language model to its downstream task performance by proposing a power law. We use this law to predict top-1 error averaged over downstream tasks for the two aforementioned models, using experiments that take 20$\times$ less compute. Our experiments are available at https://github.com/mlfoundations/scaling.
LGFeb 16
ÜberWeb: Insights from Multilingual Curation for a 20-Trillion-Token DatasetDatologyAI, Aldo Gael Carranza, Kaleigh Mentzer et al.
Multilinguality is a core capability for modern foundation models, yet training high-quality multilingual models remains challenging due to uneven data availability across languages. A further challenge is the performance interference that can arise from joint multilingual training, commonly referred to as the "curse of multilinguality". We study multilingual data curation across thirteen languages and find that many reported regressions are not inherent to multilingual scaling but instead stem from correctable deficiencies in data quality and composition rather than fundamental capacity limits. In controlled bilingual experiments, improving data quality for any single language benefits others: curating English improves non-English performance in 12 of 13 languages, while curating non-English yields reciprocal improvements in English. Bespoke per-language curation produces substantially larger within-language improvements. Extending these findings to large-scale general-purpose training mixtures, we show that curated multilingual allocations comprising under 8% of total tokens remain remarkably effective. We operationalize this approach within an effort that produced a 20T-token pretraining corpus derived entirely from public sources. Models with 3B and 8B parameters trained on a 1T-token random subset achieve competitive multilingual accuracy with 4-10x fewer training FLOPs than strong public baselines, establishing a new Pareto frontier in multilingual performance versus compute. Moreover, these benefits extend to frontier model scale: the 20T-token corpus served as part of the pretraining dataset for Trinity Large (400B/A13B), which exhibits strong multilingual performance relative to its training FLOPs. These results show that targeted, per-language data curation mitigates multilingual interference and enables compute-efficient multilingual scaling.
LGJan 5
DatBench: Discriminative, Faithful, and Efficient VLM EvaluationsDatologyAI, Siddharth Joshi, Haoli Yin et al.
Empirical evaluation serves as the primary compass guiding research progress in foundation models. Despite a large body of work focused on training frontier vision-language models (VLMs), approaches to their evaluation remain nascent. To guide their maturation, we propose three desiderata that evaluations should satisfy: (1) faithfulness to the modality and application, (2) discriminability between models of varying quality, and (3) efficiency in compute. Through this lens, we identify critical failure modes that violate faithfulness and discriminability, misrepresenting model capabilities: (i) multiple-choice formats reward guessing, poorly reflect downstream use cases, and saturate early as models improve; (ii) blindly solvable questions, which can be answered without images, constitute up to 70% of some evaluations; and (iii) mislabeled or ambiguous samples compromise up to 42% of examples in certain datasets. Regarding efficiency, the computational burden of evaluating frontier models has become prohibitive: by some accounts, nearly 20% of development compute is devoted to evaluation alone. Rather than discarding existing benchmarks, we curate them via transformation and filtering to maximize fidelity and discriminability. We find that converting multiple-choice questions to generative tasks reveals sharp capability drops of up to 35%. In addition, filtering blindly solvable and mislabeled samples improves discriminative power while simultaneously reducing computational cost. We release DatBench-Full, a cleaned evaluation suite of 33 datasets spanning nine VLM capabilities, and DatBench, a discriminative subset that achieves 13x average speedup (up to 50x) while closely matching the discriminative power of the original datasets. Our work outlines a path toward evaluation practices that are both rigorous and sustainable as VLMs continue to scale.
LGMay 12
20/20 Vision Language Models: A Prescription for Better VLMs through Data Curation AloneSiddharth Joshi, Haoli Yin, Rishabh Adiga et al.
Data curation has shifted the quality-compute frontier for language-model and contrastive image-text pretraining, but its role for vision-language models (VLMs) is far less established. We ask how far data curation alone can take VLM performance, holding architecture, training recipe, and compute fixed and varying only the training data. Our pipeline, applied to the MAmmoTH-VL single-image subset, lifts performance by +11.7pp on average across 20 public VLM benchmarks (spanning grounding, VQA, OCR/documents, captioning, spatial/3D, counting, charts, math, brand-ID, and multi-image reasoning) and by +11.3pp on average across all nine capability axes of DatBench, our high-fidelity VLM eval suite. At 2B, our curated model surpasses InternVL3.5-2B by 9.9pp at ~17x less training compute and closes the gap to Qwen3-VL-2B to within 1.8pp at ~87x less compute, from pretraining alone. Beyond accuracy, curation delivers four further properties: (1) Reliability: per-capability std across training seeds drops by ~67% and the lift survives a 4k-to-16k context-length sweep; (2) OOD generalization: the 9-eval OOD average rises by +7.2pp, and multi-image BLINK rises by +3.09pp despite single-image-only training, with Visual Correspondence gaining +11.8pp; (3) Behavioral gains beyond benchmarks: across ~1,100 open-ended queries the curated 2B is more honest and more specific than the matched-compute baseline, and more concise and less refusal-prone than a frontier 2B reference; (4) Pareto-dominance on inference cost: at every scale (1B, 2B, 4B) the curated model raises accuracy while lowering response FLOPs vs. the matched-compute baseline, and the curated 4B matches near-frontier accuracy at 3.3x lower response FLOPs than Qwen3-VL-4B. Data curation is a high-leverage tool for building better VLMs, reaching near-frontier accuracy at up to ~150x less training compute.
ROMay 19, 2024
URDFormer: A Pipeline for Constructing Articulated Simulation Environments from Real-World ImagesZoey Chen, Aaron Walsman, Marius Memmel et al.
Constructing simulation scenes that are both visually and physically realistic is a problem of practical interest in domains ranging from robotics to computer vision. This problem has become even more relevant as researchers wielding large data-hungry learning methods seek new sources of training data for physical decision-making systems. However, building simulation models is often still done by hand. A graphic designer and a simulation engineer work with predefined assets to construct rich scenes with realistic dynamic and kinematic properties. While this may scale to small numbers of scenes, to achieve the generalization properties that are required for data-driven robotic control, we require a pipeline that is able to synthesize large numbers of realistic scenes, complete with 'natural' kinematic and dynamic structures. To attack this problem, we develop models for inferring structure and generating simulation scenes from natural images, allowing for scalable scene generation from web-scale datasets. To train these image-to-simulation models, we show how controllable text-to-image generative models can be used in generating paired training data that allows for modeling of the inverse problem, mapping from realistic images back to complete scene models. We show how this paradigm allows us to build large datasets of scenes in simulation with semantic and physical realism. We present an integrated end-to-end pipeline that generates simulation scenes complete with articulated kinematic and dynamic structures from real-world images and use these for training robotic control policies. We then robustly deploy in the real world for tasks like articulated object manipulation. In doing so, our work provides both a pipeline for large-scale generation of simulation environments and an integrated system for training robust robotic control policies in the resulting environments.
LGAug 14, 2025
BeyondWeb: Lessons from Scaling Synthetic Data for Trillion-scale PretrainingDatologyAI, Pratyush Maini, Vineeth Dorna et al.
Recent advances in large language model (LLM) pretraining have shown that simply scaling data quantity eventually leads to diminishing returns, hitting a data wall. In response, the use of synthetic data for pretraining has emerged as a promising paradigm for pushing the frontier of performance. Despite this, the factors affecting synthetic data quality remain poorly understood. In this work, we introduce BeyondWeb, a synthetic data generation framework that produces high-quality synthetic data for pretraining. BeyondWeb significantly extends the capabilities of traditional web-scale datasets, outperforming state-of-the-art synthetic pretraining datasets such as Cosmopedia and Nemotron-CC's high-quality synthetic subset (Nemotron-Synth) by up to 5.1 percentage points (pp) and 2.6pp, respectively, when averaged across a suite of 14 benchmark evaluations. It delivers up to 7.7x faster training than open web data and 2.7x faster than Nemotron-Synth. Remarkably, a 3B model trained for 180B tokens on BeyondWeb outperforms an 8B model trained for the same token budget on Cosmopedia. We also present several insights from BeyondWeb on synthetic data for pretraining: what drives its benefits, which data to rephrase and how, and the impact of model size and family on data quality. Overall, our work shows that there's no silver bullet for generating high-quality synthetic pretraining data. The best outcomes require jointly optimizing many factors, a challenging task that requires rigorous science and practical expertise. Naive approaches can yield modest improvements, potentially at great cost, while well-executed methods can yield transformative improvements, as exemplified by BeyondWeb.
CLJul 16, 2025
Language Models Improve When Pretraining Data Matches Target TasksDavid Mizrahi, Anders Boesen Lindbo Larsen, Jesse Allardice et al.
Every data selection method inherently has a target. In practice, these targets often emerge implicitly through benchmark-driven iteration: researchers develop selection strategies, train models, measure benchmark performance, then refine accordingly. This raises a natural question: what happens when we make this optimization explicit? To explore this, we propose benchmark-targeted ranking (BETR), a simple method that selects pretraining documents based on similarity to benchmark training examples. BETR embeds benchmark examples and a sample of pretraining documents in a shared space, scores this sample by similarity to benchmarks, then trains a lightweight classifier to predict these scores for the full corpus. We compare data selection methods by training over 500 models spanning $10^{19}$ to $10^{22}$ FLOPs and fitting scaling laws to them. From this, we find that simply aligning pretraining data to evaluation benchmarks using BETR achieves a 2.1x compute multiplier over DCLM-Baseline (4.7x over unfiltered data) and improves performance on 9 out of 10 tasks across all scales. BETR also generalizes well: when targeting a diverse set of benchmarks disjoint from our evaluation suite, it still matches or outperforms baselines. Our scaling analysis further reveals a clear trend: larger models require less aggressive filtering. Overall, our findings show that directly matching pretraining data to target tasks precisely shapes model capabilities and highlight that optimal selection strategies must adapt to model scale.
CLMar 10, 2025
Datasets, Documents, and Repetitions: The Practicalities of Unequal Data QualityAlex Fang, Hadi Pouransari, Matt Jordan et al.
Data filtering has become a powerful tool for improving model performance while reducing computational cost. However, as large language model compute budgets continue to grow, the limited data volume provided by heavily filtered and deduplicated datasets will become a practical constraint. In efforts to better understand how to proceed, we study model performance at various compute budgets and across multiple pre-training datasets created through data filtering and deduplication. We find that, given appropriate modifications to the training recipe, repeating existing aggressively filtered datasets for up to ten epochs can outperform training on the ten times larger superset for a single epoch across multiple compute budget orders of magnitude. While this finding relies on repeating the dataset for many epochs, we also investigate repeats within these datasets at the document level. We find that not all documents within a dataset are equal, and we can create better datasets relative to a token budget by explicitly manipulating the counts of individual documents. We conclude by arguing that even as large language models scale, data filtering remains an important direction of research.
LGJun 17, 2024
DataComp-LM: In search of the next generation of training sets for language modelsJeffrey Li, Alex Fang, Georgios Smyrnis et al.
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.
LGMar 4, 2020
Neural Kernels Without TangentsVaishaal Shankar, Alex Fang, Wenshuo Guo et al.
We investigate the connections between neural networks and simple building blocks in kernel space. In particular, using well established feature space tools such as direct sum, averaging, and moment lifting, we present an algebra for creating "compositional" kernels from bags of features. We show that these operations correspond to many of the building blocks of "neural tangent kernels (NTK)". Experimentally, we show that there is a correlation in test error between neural network architectures and the associated kernels. We construct a simple neural network architecture using only 3x3 convolutions, 2x2 average pooling, ReLU, and optimized with SGD and MSE loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel achieves 90% accuracy. We also use our constructions to investigate the relative performance of neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we find that compositional kernels outperform NTKs and neural networks outperform both kernel methods.