Theoretical efforts to prove advantages of Transformers in comparison with classical architectures such as feedforward and recurrent neural networks have mostly focused on representational power. In this work, we take an alternative perspective and prove that even with infinite compute, feedforward and recurrent networks may suffer from larger sample complexity compared to Transformers, as the latter can adapt to a form of dynamic sparsity. Specifically, we consider a sequence-tosequence data generating model on sequences of length N, where the output at each position only depends on q N relevant tokens, and the positions of these tokens are described in the input prompt. We prove that a single-layer Transformer can learn this model if and only if its number of attention heads is at least q, in which case it achieves a sample complexity almost independent of N, while recurrent networks require NΩ(1) samples on the same problem. If we simplify this model, recurrent networks may achieve a complexity almost independent of N, while feedforward networks still require N samples. Our proposed sparse retrieval model illustrates a natural hierarchy in sample complexity across these architectures.

Neural Information Processing Systems http://nips.cc/

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in deep learning. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations.Experimental results on MNIST, FashionMNIST, CIFAR10, CIFAR100, and STL-10 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biological plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning.Our work presents a promising direction for biologically inspired and plausible learning algorithms, offering insights into the mechanisms of learning and adaptation in neural networks.

The sufficiency result can be extendedtodeepernetworks;weshowthatan L-layernetworkwith W parameters in the hidden layers can memorizeN data points ifW = Ω(N).

Model sizes range from 1B to 70B.