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Ethan Caballero

PhD - McGill University


Broken Neural Scaling Laws
Ethan Caballero
Kshitij Gupta
We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models&extra… (see more)polates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures&for each of various tasks within a large&diverse set of upstream&downstream tasks, in zero-shot, prompted,&finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems,"emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning,&reinforcement learning (single agent&multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models&extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent&the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws
Scaling Laws for the Few-Shot Adaptation of Pre-trained Image Classifiers
Gabriele Prato
Simon Guiroy
Ethan Caballero
Empirical science of neural scaling laws is a rapidly growing area of significant importance to the future of machine learning, particularly… (see more) in the light of recent breakthroughs achieved by large-scale pre-trained models such as GPT-3, CLIP and DALL-e. Accurately predicting the neural network performance with increasing resources such as data, compute and model size provides a more comprehensive evaluation of different approaches across multiple scales, as opposed to traditional point-wise comparisons of fixed-size models on fixed-size benchmarks, and, most importantly, allows for focus on the best-scaling, and thus most promising in the future, approaches. In this work, we consider a challenging problem of few-shot learning in image classification, especially when the target data distribution in the few-shot phase is different from the source, training, data distribution, in a sense that it includes new image classes not encountered during training. Our current main goal is to investigate how the amount of pre-training data affects the few-shot generalization performance of standard image classifiers. Our key observations are that (1) such performance improvements are well-approximated by power laws (linear log-log plots) as the training set size increases, (2) this applies to both cases of target data coming from either the same or from a different domain (i.e., new classes) as the training data, and (3) few-shot performance on new classes converges at a faster rate than the standard classification performance on previously seen classes. Our findings shed new light on the relationship between scale and generalization.
Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization
Kartik Ahuja
Ethan Caballero
Dinghuai Zhang
Jean-Christophe Gagnon-Audet
The invariance principle from causality is at the heart of notable approaches such as invariant risk minimization (IRM) that seek to address… (see more) out-of-distribution (OOD) generalization failures. Despite the promising theory, invariance principle-based approaches fail in common classification tasks, where invariant (causal) features capture all the information about the label. Are these failures due to the methods failing to capture the invariance? Or is the invariance principle itself insufficient? To answer these questions, we revisit the fundamental assumptions in linear regression tasks, where invariance-based approaches were shown to provably generalize OOD. In contrast to the linear regression tasks, we show that for linear classification tasks we need much stronger restrictions on the distribution shifts, or otherwise OOD generalization is impossible. Furthermore, even with appropriate restrictions on distribution shifts in place, we show that the invariance principle alone is insufficient. We prove that a form of the information bottleneck constraint along with invariance helps address key failures when invariant features capture all the information about the label and also retains the existing success when they do not. We propose an approach that incorporates both of these principles and demonstrate its effectiveness in several experiments.
In Search of Robust Measures of Generalization
Brady Neal
Nitarshan Rajkumar
Ethan Caballero
Linbo Wang
Daniel M. Roy
One of the principal scientific challenges in deep learning is explaining generalization, i.e., why the particular way the community now tra… (see more)ins networks to achieve small training error also leads to small error on held-out data from the same population. It is widely appreciated that some worst-case theories -- such as those based on the VC dimension of the class of predictors induced by modern neural network architectures -- are unable to explain empirical performance. A large volume of work aims to close this gap, primarily by developing bounds on generalization error, optimization error, and excess risk. When evaluated empirically, however, most of these bounds are numerically vacuous. Focusing on generalization bounds, this work addresses the question of how to evaluate such bounds empirically. Jiang et al. (2020) recently described a large-scale empirical study aimed at uncovering potential causal relationships between bounds/measures and generalization. Building on their study, we highlight where their proposed methods can obscure failures and successes of generalization measures in explaining generalization. We argue that generalization measures should instead be evaluated within the framework of distributional robustness.