Daily Papers

Transformers have become the dominant model in deep learning, but the reason for their superior performance is poorly understood. Here, we hypothesize that the strong performance of Transformers stems from an architectural bias towards mesa-optimization, a learned process running within the forward pass of a model consisting of the following two steps: (i) the construction of an internal learning objective, and (ii) its corresponding solution found through optimization. To test this hypothesis, we reverse-engineer a series of autoregressive Transformers trained on simple sequence modeling tasks, uncovering underlying gradient-based mesa-optimization algorithms driving the generation of predictions. Moreover, we show that the learned forward-pass optimization algorithm can be immediately repurposed to solve supervised few-shot tasks, suggesting that mesa-optimization might underlie the in-context learning capabilities of large language models. Finally, we propose a novel self-attention layer, the mesa-layer, that explicitly and efficiently solves optimization problems specified in context. We find that this layer can lead to improved performance in synthetic and preliminary language modeling experiments, adding weight to our hypothesis that mesa-optimization is an important operation hidden within the weights of trained Transformers.

There has been an explosion of interest in designing high-performance Transformers. While Transformers have delivered significant performance improvements, training such networks is extremely memory intensive owing to storing all intermediate activations that are needed for gradient computation during backpropagation, especially for long sequences. To this end, we present Mesa, a memory-saving training framework for Transformers. Specifically, Mesa uses exact activations during forward pass while storing a low-precision version of activations to reduce memory consumption during training. The low-precision activations are then dequantized during back-propagation to compute gradients. Besides, to address the heterogeneous activation distributions in the multi-head self-attention layers, we propose a head-wise activation quantization strategy, which quantizes activations based on the statistics of each head to minimize the approximation error. To further boost training efficiency, we learn quantization parameters by running estimates. More importantly, by re-investing the saved memory in employing a larger batch size or scaling up model size, we may further improve the performance under constrained computational resources. Extensive experiments on ImageNet, CIFAR-100 and ADE20K demonstrate that Mesa can achieve flexible memory-savings (up to 50%) during training while achieving comparable or even better performance. Code is available at https://github.com/ziplab/Mesa.

Autoregressively trained transformers have brought a profound revolution to the world, especially with their in-context learning (ICL) ability to address downstream tasks. Recently, several studies suggest that transformers learn a mesa-optimizer during autoregressive (AR) pretraining to implement ICL. Namely, the forward pass of the trained transformer is equivalent to optimizing an inner objective function in-context. However, whether the practical non-convex training dynamics will converge to the ideal mesa-optimizer is still unclear. Towards filling this gap, we investigate the non-convex dynamics of a one-layer linear causal self-attention model autoregressively trained by gradient flow, where the sequences are generated by an AR process x_{t+1} = W x_t. First, under a certain condition of data distribution, we prove that an autoregressively trained transformer learns W by implementing one step of gradient descent to minimize an ordinary least squares (OLS) problem in-context. It then applies the learned W for next-token prediction, thereby verifying the mesa-optimization hypothesis. Next, under the same data conditions, we explore the capability limitations of the obtained mesa-optimizer. We show that a stronger assumption related to the moments of data is the sufficient and necessary condition that the learned mesa-optimizer recovers the distribution. Besides, we conduct exploratory analyses beyond the first data condition and prove that generally, the trained transformer will not perform vanilla gradient descent for the OLS problem. Finally, our simulation results verify the theoretical results.