How Well Can Transformers Emulate In-context Newton's Method?

• URL: http://arxiv.org/abs/2403.03183v1
• Date: Tue, 5 Mar 2024 18:20:10 GMT
• Title: How Well Can Transformers Emulate In-context Newton's Method?
• Authors: Angeliki Giannou, Liu Yang, Tianhao Wang, Dimitris Papailiopoulos, Jason D. Lee
• Abstract summary: We study whether Transformers can perform higher order optimization methods, beyond the case of linear regression. We demonstrate the ability of even linear attention-only Transformers in implementing a single step of Newton's iteration for matrix inversion with merely two layers.
• Score: 46.08521978754298
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transformer-based models have demonstrated remarkable in-context learning capabilities, prompting extensive research into its underlying mechanisms. Recent studies have suggested that Transformers can implement first-order optimization algorithms for in-context learning and even second order ones for the case of linear regression. In this work, we study whether Transformers can perform higher order optimization methods, beyond the case of linear regression. We establish that linear attention Transformers with ReLU layers can approximate second order optimization algorithms for the task of logistic regression and achieve $\epsilon$ error with only a logarithmic to the error more layers. As a by-product we demonstrate the ability of even linear attention-only Transformers in implementing a single step of Newton's iteration for matrix inversion with merely two layers. These results suggest the ability of the Transformer architecture to implement complex algorithms, beyond gradient descent.

Related papers

• Graph Transformers Dream of Electric Flow [72.06286909236827]
  We show that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems. We present explicit weight configurations for implementing each such graph algorithm, and we bound the errors of the constructed Transformers by the errors of the underlying algorithms.
  arXiv  Detail & Related papers  (2024-10-22T05:11:45Z)
• Can Looped Transformers Learn to Implement Multi-step Gradient Descent for In-context Learning? [69.4145579827826]
  We show a fast flow on the regression loss despite the gradient non-ity algorithms for our convergence landscape. This is the first theoretical analysis for multi-layer Transformer in this setting.
  arXiv  Detail & Related papers  (2024-10-10T18:29:05Z)
• Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis [63.66763657191476]
  We show that efficient numerical training and inference algorithms as low-rank computation have impressive performance for learning Transformer-based adaption. We analyze how magnitude-based models affect generalization while improving adaption. We conclude that proper magnitude-based has a slight on the testing performance.
  arXiv  Detail & Related papers  (2024-06-24T23:00:58Z)
• Linear Transformers are Versatile In-Context Learners [19.988368693379087]
  We prove that each layer of a linear transformer maintains a weight vector for an implicit linear regression problem. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm.
  arXiv  Detail & Related papers  (2024-02-21T23:45:57Z)
• Transformers Learn Higher-Order Optimization Methods for In-Context Learning: A Study with Linear Models [23.944430707096103]
  We show that Transformers learn to approximate higher-order optimization methods for in-context linear regression. For in-context linear regression, Transformers share a similar convergence rate as Iterative Newton's Method. We also show that Transformers can learn in-context on ill-conditioned data, a setting where Gradient Descent struggles but Iterative Newton succeeds.
  arXiv  Detail & Related papers  (2023-10-26T01:08:47Z)
• Linear attention is (maybe) all you need (to understand transformer optimization) [55.81555204646486]
  We make progress towards understanding the subtleties of training Transformers by studying a simple yet canonicalized shallow Transformer model. Most importantly, we observe that our proposed linearized models can reproduce several prominent aspects of Transformer training dynamics.
  arXiv  Detail & Related papers  (2023-10-02T10:48:42Z)
• Transformers learn to implement preconditioned gradient descent for in-context learning [41.74394657009037]
  Several recent works demonstrate that transformers can implement algorithms like gradient descent. We ask: Can transformers learn to implement such algorithms by training over random problem instances? For a transformer with $L$ attention layers, we prove certain critical points of the training objective implement $L$ iterations of preconditioned gradient descent.
  arXiv  Detail & Related papers  (2023-06-01T02:35:57Z)
• Transformers learn in-context by gradient descent [58.24152335931036]
  Training Transformers on auto-regressive objectives is closely related to gradient-based meta-learning formulations. We show how trained Transformers become mesa-optimizers i.e. learn models by gradient descent in their forward pass.
  arXiv  Detail & Related papers  (2022-12-15T09:21:21Z)

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.