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An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a single task or (ii) they are linear, very little is known about the closer-to-practice case of nonlinear NNs trained on multiple tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an r-dimensional subspace within the d k r-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of d. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all r ground-truth features.
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Learning Two-Layer Neural Networks with Symmetric Inputs
We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network y = Aσ(Wx) + ξ, where A,W are weight matrices, ξ represents noise, and the number of neurons in the hidden layer is no larger than the input or output, our algorithm is guaranteed to recover the parameters A,W of the ground-truth network. The only requirement on the input x is that it is symmetric, which still allows highly complicated and structured input. Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions.
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- Award ID(s):
- 1704656
- PAR ID:
- 10090510
- Date Published:
- Journal Name:
- International Conference on Learning Representations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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An increasingly popular machine learning paradigm is to pretrain a neural network (NN) on many tasks offline, then adapt it to downstream tasks, often by re-training only the last linear layer of the network. This approach yields strong downstream performance in a variety of contexts, demonstrating that multitask pretraining leads to effective feature learning. Although several recent theoretical studies have shown that shallow NNs learn meaningful features when either (i) they are trained on a single task or (ii) they are linear, very little is known about the closer-to-practice case of nonlinear NNs trained on multiple tasks. In this work, we present the first results proving that feature learning occurs during training with a nonlinear model on multiple tasks. Our key insight is that multi-task pretraining induces a pseudo-contrastive loss that favors representations that align points that typically have the same label across tasks. Using this observation, we show that when the tasks are binary classification tasks with labels depending on the projection of the data onto an 𝑟-dimensional subspace within the 𝑑 ≫𝑟-dimensional input space, a simple gradient-based multitask learning algorithm on a two-layer ReLU NN recovers this projection, allowing for generalization to downstream tasks with sample and neuron complexity independent of 𝑑. In contrast, we show that with high probability over the draw of a single task, training on this single task cannot guarantee to learn all 𝑟 ground-truth features.more » « less
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
