Unveiling Induction Heads: Provable Training Dynamics and Feature Learning in Transformers

• URL: http://arxiv.org/abs/2409.10559v1
• Date: Mon, 9 Sep 2024 18:10:26 GMT
• Title: Unveiling Induction Heads: Provable Training Dynamics and Feature Learning in Transformers
• Authors: Siyu Chen, Heejune Sheen, Tianhao Wang, Zhuoran Yang,
• Abstract summary: We study how a two-attention-layer transformer is trained to perform ICL on $n$-gram Markov chain data. We prove that the gradient flow with respect to a cross-entropy ICL loss converges to a limiting model.
• Score: 54.20763128054692
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In-context learning (ICL) is a cornerstone of large language model (LLM) functionality, yet its theoretical foundations remain elusive due to the complexity of transformer architectures. In particular, most existing work only theoretically explains how the attention mechanism facilitates ICL under certain data models. It remains unclear how the other building blocks of the transformer contribute to ICL. To address this question, we study how a two-attention-layer transformer is trained to perform ICL on $n$-gram Markov chain data, where each token in the Markov chain statistically depends on the previous $n$ tokens. We analyze a sophisticated transformer model featuring relative positional embedding, multi-head softmax attention, and a feed-forward layer with normalization. We prove that the gradient flow with respect to a cross-entropy ICL loss converges to a limiting model that performs a generalized version of the induction head mechanism with a learned feature, resulting from the congruous contribution of all the building blocks. In the limiting model, the first attention layer acts as a $\mathit{copier}$, copying past tokens within a given window to each position, and the feed-forward network with normalization acts as a $\mathit{selector}$ that generates a feature vector by only looking at informationally relevant parents from the window. Finally, the second attention layer is a $\mathit{classifier}$ that compares these features with the feature at the output position, and uses the resulting similarity scores to generate the desired output. Our theory is further validated by experiments.

Related papers

• Demystifying Singular Defects in Large Language Models [61.98878352956125]
  In large language models (LLMs), the underlying causes of high-norm tokens remain largely unexplored. We provide both theoretical insights and empirical validation across a range of recent models. We showcase two practical applications of these findings: the improvement of quantization schemes and the design of LLM signatures.
  arXiv  Detail & Related papers  (2025-02-10T20:09:16Z)
• Unified CNNs and transformers underlying learning mechanism reveals multi-head attention modus vivendi [0.0]
  Convolutional neural networks (CNNs) evaluate short-range correlations in input images which progress along the layers. vision transformer (ViT) architectures evaluate long-range correlations, using repeated transformer encoders composed of fully connected layers. This study demonstrates that CNNs and ViT architectures stem from a unified underlying learning mechanism.
  arXiv  Detail & Related papers  (2025-01-22T14:19:48Z)
• Token Statistics Transformer: Linear-Time Attention via Variational Rate Reduction [29.12836710966048]
  We propose a novel transformer attention operator whose computational complexity scales linearly with the number of tokens. Our results call into question the conventional wisdom that pairwise similarity style attention mechanisms are critical to the success of transformer architectures.
  arXiv  Detail & Related papers  (2024-12-23T18:59:21Z)
• Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers [14.59741397670484]
  We consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model. Experiments confirm our findings on both synthetic and real-world sequence classification tasks.
  arXiv  Detail & Related papers  (2024-05-24T20:34:18Z)
• Toward a Theory of Tokenization in LLMs [26.516041872337887]
  We study tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. We show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from $ktextth$-order Markov sources near optimally.
  arXiv  Detail & Related papers  (2024-04-12T09:01:14Z)
• How Do Transformers Learn In-Context Beyond Simple Functions? A Case Study on Learning with Representations [98.7450564309923]
  This paper takes initial steps on understanding in-context learning (ICL) in more complex scenarios, by studying learning with representations. We construct synthetic in-context learning problems with a compositional structure, where the label depends on the input through a possibly complex but fixed representation function. We show theoretically the existence of transformers that approximately implement such algorithms with mild depth and size.
  arXiv  Detail & Related papers  (2023-10-16T17:40:49Z)
• Transformers as Support Vector Machines [54.642793677472724]
  We establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem. We characterize the implicit bias of 1-layer transformers optimized with gradient descent. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.
  arXiv  Detail & Related papers  (2023-08-31T17:57:50Z)
• Combiner: Full Attention Transformer with Sparse Computation Cost [142.10203598824964]
  We propose Combiner, which provides full attention capability in each attention head while maintaining low computation complexity. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach.
  arXiv  Detail & Related papers  (2021-07-12T22:43:11Z)
• $O(n)$ Connections are Expressive Enough: Universal Approximability of Sparse Transformers [71.31712741938837]
  We show that sparse Transformers with only $O(n)$ connections per attention layer can approximate the same function class as the dense model with $n2$ connections. We also present experiments comparing different patterns/levels of sparsity on standard NLP tasks.
  arXiv  Detail & Related papers  (2020-06-08T18:30:12Z)

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.