Convexifying Transformers: Improving optimization and understanding of transformer networks

• URL: http://arxiv.org/abs/2211.11052v1
• Date: Sun, 20 Nov 2022 18:17:47 GMT
• Title: Convexifying Transformers: Improving optimization and understanding of transformer networks
• Authors: Tolga Ergen, Behnam Neyshabur, Harsh Mehta
• Abstract summary: We study the training problem of attention/transformer networks and introduce a novel convex analytic approach. We first introduce a convex alternative to the self-attention mechanism and reformulate the regularized training problem of transformer networks. As a byproduct of our convex analysis, we reveal an implicit regularization mechanism, which promotes sparsity across tokens.
• Score: 56.69983975369641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding the fundamental mechanism behind the success of transformer networks is still an open problem in the deep learning literature. Although their remarkable performance has been mostly attributed to the self-attention mechanism, the literature still lacks a solid analysis of these networks and interpretation of the functions learned by them. To this end, we study the training problem of attention/transformer networks and introduce a novel convex analytic approach to improve the understanding and optimization of these networks. Particularly, we first introduce a convex alternative to the self-attention mechanism and reformulate the regularized training problem of transformer networks with our alternative convex attention. Then, we cast the reformulation as a convex optimization problem that is interpretable and easier to optimize. Moreover, as a byproduct of our convex analysis, we reveal an implicit regularization mechanism, which promotes sparsity across tokens. Therefore, we not only improve the optimization of attention/transformer networks but also provide a solid theoretical understanding of the functions learned by them. We also demonstrate the effectiveness of our theory through several numerical experiments.

Related papers

• What Does It Mean to Be a Transformer? Insights from a Theoretical Hessian Analysis [8.008567379796666]
  The Transformer architecture has inarguably revolutionized deep learning. At its core, the attention block differs in form and functionality from most other architectural components in deep learning. The root causes behind these outward manifestations, and the precise mechanisms that govern them, remain poorly understood.
  arXiv  Detail & Related papers  (2024-10-14T18:15:02Z)
• Dynamical Mean-Field Theory of Self-Attention Neural Networks [0.0]
  Transformer-based models have demonstrated exceptional performance across diverse domains. Little is known about how they operate or what are their expected dynamics. We use methods for the study of asymmetric Hopfield networks in nonequilibrium regimes.
  arXiv  Detail & Related papers  (2024-06-11T13:29:34Z)
• CF-OPT: Counterfactual Explanations for Structured Prediction [47.36059095502583]
  optimization layers in deep neural networks have enjoyed a growing popularity in structured learning, improving the state of the art on a variety of applications. Yet, these pipelines lack interpretability since they are made of two opaque layers: a highly non-linear prediction model, such as a deep neural network, and an optimization layer, which is typically a complex black-box solver. Our goal is to improve the transparency of such methods by providing counterfactual explanations.
  arXiv  Detail & Related papers  (2024-05-28T15:48:27Z)
• On the Convergence of Encoder-only Shallow Transformers [62.639819460956176]
  We build the global convergence theory of encoder-only shallow Transformers under a realistic setting. Our results can pave the way for a better understanding of modern Transformers, particularly on training dynamics.
  arXiv  Detail & Related papers  (2023-11-02T20:03:05Z)
• Uncovering mesa-optimization algorithms in Transformers [61.06055590704677]
  Some autoregressive models can learn as an input sequence is processed, without undergoing any parameter changes, and without being explicitly trained to do so. We show that standard next-token prediction error minimization gives rise to a subsidiary learning algorithm that adjusts the model as new inputs are revealed. Our findings explain in-context learning as a product of autoregressive loss minimization and inform the design of new optimization-based Transformer layers.
  arXiv  Detail & Related papers  (2023-09-11T22:42:50Z)
• Centered Self-Attention Layers [89.21791761168032]
  The self-attention mechanism in transformers and the message-passing mechanism in graph neural networks are repeatedly applied. We show that this application inevitably leads to oversmoothing, i.e., to similar representations at the deeper layers. We present a correction term to the aggregating operator of these mechanisms.
  arXiv  Detail & Related papers  (2023-06-02T15:19:08Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Convergence Analysis and Implicit Regularization of Feedback Alignment for Deep Linear Networks [27.614609336582568]
  We theoretically analyze the Feedback Alignment (FA) algorithm, an efficient alternative to backpropagation for training neural networks. We provide convergence guarantees with rates for deep linear networks for both continuous and discrete dynamics.
  arXiv  Detail & Related papers  (2021-10-20T22:57:03Z)
• Attention that does not Explain Away [54.42960937271612]
  Models based on the Transformer architecture have achieved better accuracy than the ones based on competing architectures for a large set of tasks. A unique feature of the Transformer is its universal application of a self-attention mechanism, which allows for free information flow at arbitrary distances. We propose a doubly-normalized attention scheme that is simple to implement and provides theoretical guarantees for avoiding the "explaining away" effect.
  arXiv  Detail & Related papers  (2020-09-29T21:05:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.