In the context of few-shot learning, it is currently believed that a fixed pre-trained (PT) model, along with fine-tuning the final layer during evaluation, outperforms standard meta-learning algorithms. We re-evaluate these claims under an in-depth empirical examination of an extensive set of formally diverse datasets and compare PT to Model Agnostic Meta-Learning (MAML). Unlike previous work, we emphasize a fair comparison by using: the same architecture, the same optimizer, and all models trained to convergence. Crucially, we use a more rigorous statistical tool -- the effect size (Cohen's d) -- to determine the practical significance of the difference between a model trained with PT vs. a MAML. We then use a previously proposed metric -- the diversity coefficient -- to compute the average formal diversity of a dataset. Using this analysis, we demonstrate the following: 1. when the formal diversity of a data set is low, PT beats MAML on average and 2. when the formal diversity is high, MAML beats PT on average. The caveat is that the magnitude of the average difference between a PT vs. MAML using the effect size is low (according to classical statistical thresholds) -- less than 0.2. Nevertheless, this observation is contrary to the currently held belief that a pre-trained model is always better than a meta-learning model. Our extensive experiments consider 21 few-shot learning benchmarks, including the large-scale few-shot learning dataset Meta-Data set. We also show no significant difference between a MAML model vs. a PT model with GPT-2 on Openwebtext. We, therefore, conclude that a pre-trained model does not always beat a meta-learned model and that the formal diversity of a dataset is a driving factor.
Current trends to pre-train capable Large Language Models (LLMs) mostly focus on scaling of model and dataset size. However, the quality of pre-training data is an important factor for training powerful LLMs, yet it is a nebulous concept that has not been fully characterized. Therefore, we use the recently proposed Task2Vec diversity coefficient to ground and understand formal aspects of data quality, to go beyond scale alone. Specifically, we measure the diversity coefficient of publicly available pre-training datasets to demonstrate that their formal diversity is high when compared to theoretical lower and upper bounds. In addition, to build confidence in the diversity coefficient, we conduct interpretability experiments and find that the coefficient aligns with intuitive properties of diversity, e.g., it increases as the number of latent concepts increases. We conclude the diversity coefficient is reliable, show it's high for publicly available LLM datasets, and conjecture it can be used to build useful diverse datasets for LLMs.
Recent work claims that large language models display emergent abilities, abilities not present in smaller-scale models that are present in larger-scale models. What makes emergent abilities intriguing is two-fold: their sharpness, transitioning seemingly instantaneously from not present to present, and their unpredictability, appearing at seemingly unforeseeable model scales. Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, one can choose a metric which leads to the inference of an emergent ability or another metric which does not. Thus, our alternative suggests that existing claims of emergent abilities are creations of the researcher's analyses, not fundamental changes in model behavior on specific tasks with scale. We present our explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities, (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show how similar metric decisions suggest apparent emergent abilities on vision tasks in diverse deep network architectures (convolutional, autoencoder, transformers). In all three analyses, we find strong supporting evidence that emergent abilities may not be a fundamental property of scaling AI models.
Recently, it has been observed that a transfer learning solution might be all we need to solve many few-shot learning benchmarks -- thus raising important questions about when and how meta-learning algorithms should be deployed. In this paper, we seek to clarify these questions by 1. proposing a novel metric -- the diversity coefficient -- to measure the diversity of tasks in a few-shot learning benchmark and 2. by comparing Model-Agnostic Meta-Learning (MAML) and transfer learning under fair conditions (same architecture, same optimizer, and all models trained to convergence). Using the diversity coefficient, we show that the popular MiniImageNet and CIFAR-FS few-shot learning benchmarks have low diversity. This novel insight contextualizes claims that transfer learning solutions are better than meta-learned solutions in the regime of low diversity under a fair comparison. Specifically, we empirically find that a low diversity coefficient correlates with a high similarity between transfer learning and MAML learned solutions in terms of accuracy at meta-test time and classification layer similarity (using feature based distance metrics like SVCCA, PWCCA, CKA, and OPD). To further support our claim, we find this meta-test accuracy holds even as the model size changes. Therefore, we conclude that in the low diversity regime, MAML and transfer learning have equivalent meta-test performance when both are compared fairly. We also hope our work inspires more thoughtful constructions and quantitative evaluations of meta-learning benchmarks in the future.
Recent work has suggested that a good embedding is all we need to solve many few-shot learning benchmarks. Furthermore, other work has strongly suggested that Model Agnostic Meta-Learning (MAML) also works via this same method - by learning a good embedding. These observations highlight our lack of understanding of what meta-learning algorithms are doing and when they work. In this work, we provide empirical results that shed some light on how meta-learned MAML representations function. In particular, we identify three interesting properties: 1) In contrast to previous work, we show that it is possible to define a family of synthetic benchmarks that result in a low degree of feature re-use - suggesting that current few-shot learning benchmarks might not have the properties needed for the success of meta-learning algorithms; 2) meta-overfitting occurs when the number of classes (or concepts) are finite, and this issue disappears once the task has an unbounded number of concepts (e.g., online learning); 3) more adaptation at meta-test time with MAML does not necessarily result in a significant representation change or even an improvement in meta-test performance - even when training on our proposed synthetic benchmarks. Finally, we suggest that to understand meta-learning algorithms better, we must go beyond tracking only absolute performance and, in addition, formally quantify the degree of meta-learning and track both metrics together. Reporting results in future work this way will help us identify the sources of meta-overfitting more accurately and help us design more flexible meta-learning algorithms that learn beyond fixed feature re-use. Finally, we conjecture the core challenge of re-thinking meta-learning is in the design of few-shot learning data sets and benchmarks - rather than in the algorithms, as suggested by previous work.
It has been recently observed that a transfer learning solution might be all we needed to solve many few-shot learning benchmarks. This raises important questions about when and how meta-learning algorithms should be deployed. In this paper, we make a first step in clarifying these questions by first formulating a computable metric for a few-shot learning benchmark that we hypothesize is predictive of whether meta-learning solutions will succeed or not. We name this metric the diversity coefficient of a few-shot learning benchmark. Using the diversity coefficient, we show that the MiniImagenet benchmark has zero diversity - according to twenty-four different ways to compute the diversity. We proceed to show that when making a fair comparison between MAML learned solutions to transfer learning, both have identical meta-test accuracy. This suggests that transfer learning fails to outperform MAML - contrary to what previous work suggests. Together, these two facts provide the first test of whether diversity correlates with meta-learning success and therefore show that a diversity coefficient of zero correlates with a high similarity between transfer learning and MAML learned solutions - especially at meta-test time. We therefore conjecture meta-learned solutions have the same meta-test performance as transfer learning when the diversity coefficient is zero.
We review recent observations on the dynamical systems induced by gradient descent (GD) methods used for training deep networks and summarize properties of the solutions they converge to. Recent results illuminate the absence of overfitting in the special case of linear networks for binary classification. They prove that minimization of loss functions such as the logistic, the cross-entropy and the exponential loss yields asymptotic convergence to the maximum margin solution for linearly separable datasets, independently of the initial conditions. Here we discuss the case of nonlinear DNNs near zero minima of the empirical loss, under exponential-type and square losses, for several variations of the basic GD algorithm, including a new NMGD version that converges to the minimum norm fixed points. Our main results are: 1) GD algorithms with weight normalization constraint achieve generalization; 2) the fundamental reason for the effectiveness of existing weight and batch normalization techniques is that they are approximate implementations of maximizing the margin under unit norm constraint; 3) even without explicit unit norm constraints, generalization can still be obtained for not-too-deep networks because standard GD is intrinsically consistent with the dynamics of normalized weights. In addition, the balance of the weights across different layers, if present at initialization, is maintained by the gradient flow. In the perspective of these theoretical results, we discuss experimental evidence around the apparent absence of overfitting, that is the observation that the expected classification error does not get worse when increasing the number of parameters. Our explanation focuses on the implicit normalization enforced by algorithms such as batch normalization. In particular, the control of the norm of the weights is related to Halpern iterations for minimum norm solutions.
Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors? Better understanding of this question of generalization may improve practical applications of deep networks. In this paper we show that with cross-entropy loss it is surprisingly simple to induce significantly different generalization performances for two networks that have the same architecture, the same meta parameters and the same training error: one can either pretrain the networks with different levels of "corrupted" data or simply initialize the networks with weights of different Gaussian standard deviations. A corollary of recent theoretical results on overfitting shows that these effects are due to an intrinsic problem of measuring test performance with a cross-entropy/exponential-type loss, which can be decomposed into two components both minimized by SGD -- one of which is not related to expected classification performance. However, if we factor out this component of the loss, a linear relationship emerges between training and test losses. Under this transformation, classical generalization bounds are surprisingly tight: the empirical/training loss is very close to the expected/test loss. Furthermore, the empirical relation between classification error and normalized cross-entropy loss seem to be approximately monotonic
A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient descent. This is surprising because of the large capacity demonstrated by DNNs to fit randomly labeled data and the absence of explicit regularization. Recent results by Srebro et al. provide a satisfying solution of the puzzle for linear networks used in binary classification. They prove that minimization of loss functions such as the logistic, the cross-entropy and the exp-loss yields asymptotic, "slow" convergence to the maximum margin solution for linearly separable datasets, independently of the initial conditions. Here we prove a similar result for nonlinear multilayer DNNs near zero minima of the empirical loss. The result holds for exponential-type losses but not for the square loss. In particular, we prove that the weight matrix at each layer of a deep network converges to a minimum norm solution up to a scale factor (in the separable case). Our analysis of the dynamical system corresponding to gradient descent of a multilayer network suggests a simple criterion for ranking the generalization performance of different zero minimizers of the empirical loss.
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics associated to gradient descent minimization of nonlinear networks is topologically equivalent, near the asymptotically stable minima of the empirical error, to linear gradient system in a quadratic potential with a degenerate (for square loss) or almost degenerate (for logistic or crossentropy loss) Hessian. The proposition depends on the qualitative theory of dynamical systems and is supported by numerical results. Our main propositions extend to deep nonlinear networks two properties of gradient descent for linear networks, that have been recently established (1) to be key to their generalization properties: 1. Gradient descent enforces a form of implicit regularization controlled by the number of iterations, and asymptotically converges to the minimum norm solution for appropriate initial conditions of gradient descent. This implies that there is usually an optimum early stopping that avoids overfitting of the loss. This property, valid for the square loss and many other loss functions, is relevant especially for regression. 2. For classification, the asymptotic convergence to the minimum norm solution implies convergence to the maximum margin solution which guarantees good classification error for "low noise" datasets. This property holds for loss functions such as the logistic and cross-entropy loss independently of the initial conditions. The robustness to overparametrization has suggestive implications for the robustness of the architecture of deep convolutional networks with respect to the curse of dimensionality.